| Title: | Irregularly Observed Autoregressive Models |
|---|---|
| Description: | Data sets, functions and scripts with examples to implement autoregressive models for irregularly observed time series. The models available in this package are the irregular autoregressive model (Eyheramendy et al.(2018) <doi:10.1093/mnras/sty2487>), the complex irregular autoregressive model (Elorrieta et al.(2019) <doi:10.1051/0004-6361/201935560>) and the bivariate irregular autoregressive model (Elorrieta et al.(2021) <doi:10.1093/mnras/stab1216>). |
| Authors: | Elorrieta Felipe [aut, cre], Ojeda Cesar [aut], Eyheramendy Susana [aut], Palma Wilfredo [aut] |
| Maintainer: | Elorrieta Felipe <[email protected]> |
| License: | GPL-2 |
| Version: | 1.2.0 |
| Built: | 2024-11-18 06:53:31 UTC |
| Source: | CRAN |
Time series of the AGN MCG-6-30-15 measured in the K-band between 2006 August and 2011 July with the ANDICAM camera mounted on the 1.3 m telescope at Cerro Tololo Inter-American Observatory (CTIO)
agnagn
A data frame with 237 observations on the following 3 variables:
heliocentric Julian Day - 2450000
Flux $(10^(-15) ergs/s/cm^2 /A)$
measurement error standard deviations.
Lira P, Arévalo P, Uttley P, McHardy IMM, Videla L (2015). “Long-term monitoring of the archetype Seyfert galaxy MCG-6-30-15: X-ray, optical and near-IR variability of the corona, disc and torus.” Monthly Notices of the Royal Astronomical Society, 454(1), 368-379. ISSN 0035-8711, doi:10.1093/mnras/stv1945.
data(agn) plot(agn$t,agn$m,type="l",ylab="",xlab="")data(agn) plot(agn$t,agn$m,type="l",ylab="",xlab="")
Fit a BIAR model to a bivariate irregularly observed time series.
BIARfit(phiValues, y1, y2, t, yerr1, yerr2, zeroMean = TRUE)BIARfit(phiValues, y1, y2, t, yerr1, yerr2, zeroMean = TRUE)
phiValues |
An array with the parameters of the BIAR model. The elements of the array are, in order, the autocorrelation and the cross correlation parameter of the BIAR model. |
y1 |
Array with the observations of the first time series of the BIAR process. |
y2 |
Array with the observations of the second time series of the BIAR process. |
t |
Array with the irregular observational times. |
yerr1 |
Array with the measurements error standard deviations of the first time series of the BIAR process. |
yerr2 |
Array with the measurements error standard deviations of the second time series of the BIAR process. |
zeroMean |
logical; if TRUE, the array y has zero mean; if FALSE, y has a mean different from zero. |
A list with the following components:
rho Estimated value of the contemporary correlation coefficient.
innov.var Estimated value of the innovation variance.
fitted Fitted values of the BIAR model.
fitted.state Fitted state values of the BIAR model.
Lambda Lambda value estimated by the BIAR model at the last time point.
Theta Theta array estimated by the BIAR model at the last time point.
Sighat Covariance matrix estimated by the BIAR model at the last time point.
Qt Covariance matrix of the state equation estimated by the BIAR model at the last time point.
Elorrieta F, Eyheramendy S, Palma W, Ojeda C (2021). “A novel bivariate autoregressive model for predicting and forecasting irregularly observed time series.” Monthly Notices of the Royal Astronomical Society, 505(1), 1105-1116. ISSN 0035-8711, doi:10.1093/mnras/stab1216, https://academic.oup.com/mnras/article-pdf/505/1/1105/38391762/stab1216.pdf.
gentime, BIARsample, BIARphikalman, BIARkalman
n=80 set.seed(6714) st<-gentime(n) x=BIARsample(n=n,phiR=0.9,phiI=0.3,st=st,rho=0.9) y=x$y y1=y/apply(y,1,sd) yerr1=rep(0,n) yerr2=rep(0,n) biar=BIARkalman(y1=y1[1,],y2=y1[2,],t=st,delta1 = yerr1,delta2=yerr2) biar predbiar=BIARfit(phiValues=c(biar$phiR,biar$phiI),y1=y1[1,],y2=y1[2,],t=st,yerr1 = rep(0,length(y[1,])),yerr2=rep(0,length(y[1,]))) rho=predbiar$rho print(rho) yhat=predbiar$fittedn=80 set.seed(6714) st<-gentime(n) x=BIARsample(n=n,phiR=0.9,phiI=0.3,st=st,rho=0.9) y=x$y y1=y/apply(y,1,sd) yerr1=rep(0,n) yerr2=rep(0,n) biar=BIARkalman(y1=y1[1,],y2=y1[2,],t=st,delta1 = yerr1,delta2=yerr2) biar predbiar=BIARfit(phiValues=c(biar$phiR,biar$phiI),y1=y1[1,],y2=y1[2,],t=st,yerr1 = rep(0,length(y[1,])),yerr2=rep(0,length(y[1,]))) rho=predbiar$rho print(rho) yhat=predbiar$fitted
Forecast from models fitted by BIARkalman
BIARforecast(phiR, phiI, y1, y2, t, tAhead)BIARforecast(phiR, phiI, y1, y2, t, tAhead)
phiR |
Autocorrelation coefficient of BIAR model. |
phiI |
Cross-correlation coefficient of BIAR model. |
y1 |
Array with the observations of the first time series of the BIAR process. |
y2 |
Array with the observations of the second time series of the BIAR process. |
t |
Array with the observational times. |
tAhead |
The time ahead for which the forecast is required. |
A list with the following components:
fitted Fitted values by the BIAR model.
forecast Point forecast in the time ahead required.
Lambda Lambda value estimated by the BIAR model at the last time point.
Sighat Covariance matrix estimated by the BIAR model at the last time point.
Elorrieta F, Eyheramendy S, Palma W, Ojeda C (2021). “A novel bivariate autoregressive model for predicting and forecasting irregularly observed time series.” Monthly Notices of the Royal Astronomical Society, 505(1), 1105-1116. ISSN 0035-8711, doi:10.1093/mnras/stab1216, https://academic.oup.com/mnras/article-pdf/505/1/1105/38391762/stab1216.pdf.
BIARsample, BIARkalman, BIARfit
#Simulated Data n=100 set.seed(6714) st<-gentime(n) x=BIARsample(n=n,phiR=0.9,phiI=0.3,st=st) biar=iAR::BIARkalman(y1=x$y[1,],y2=x$y[2,],t=st) forBIAR<-BIARforecast(phiR=biar$phiR,phiI=biar$phiI,y1=x$y[1,],y2=x$y[2,],t=st,tAhead=c(1.3))#Simulated Data n=100 set.seed(6714) st<-gentime(n) x=BIARsample(n=n,phiR=0.9,phiI=0.3,st=st) biar=iAR::BIARkalman(y1=x$y[1,],y2=x$y[2,],t=st) forBIAR<-BIARforecast(phiR=biar$phiR,phiI=biar$phiI,y1=x$y[1,],y2=x$y[2,],t=st,tAhead=c(1.3))
Interpolation of missing values from models fitted by BIARkalman
BIARinterpolation( x, y1, y2, t, delta1 = 0, delta2 = 0, yini1 = 0, yini2 = 0, zero.mean = TRUE, niter = 10, seed = 1234, nsmooth = 1 )BIARinterpolation( x, y1, y2, t, delta1 = 0, delta2 = 0, yini1 = 0, yini2 = 0, zero.mean = TRUE, niter = 10, seed = 1234, nsmooth = 1 )
x |
An array with the parameters of the BIAR model. The elements of the array are, in order, the real (phiR) and the imaginary (phiI) part of the coefficient of BIAR model. |
y1 |
Array with the observations of the first time series of the BIAR process. |
y2 |
Array with the observations of the second time series of the BIAR process. |
t |
Array with the irregular observational times. |
delta1 |
Array with the measurements error standard deviations of the first time series of the BIAR process. |
delta2 |
Array with the measurements error standard deviations of the second time series of the BIAR process. |
yini1 |
a single value, initial value of the estimation of the missing value of the first time series of the BIAR process. |
yini2 |
a single value, initial value of the estimation of the missing value of the second time series of the BIAR process. |
zero.mean |
logical; if TRUE, the array y has zero mean; if FALSE, y has a mean different from zero. |
niter |
Number of iterations in which the function nlminb will be repeated. |
seed |
a single value, interpreted as the seed of the random process. |
nsmooth |
a single value; If 1, only one time series of the BIAR process has a missing value. If 2, both time series of the BIAR process have a missing value. |
A list with the following components:
fitted Estimation of the missing values of the BIAR process.
ll Value of the negative log likelihood evaluated in the fitted missing values.
Elorrieta F, Eyheramendy S, Palma W, Ojeda C (2021). “A novel bivariate autoregressive model for predicting and forecasting irregularly observed time series.” Monthly Notices of the Royal Astronomical Society, 505(1), 1105-1116. ISSN 0035-8711, doi:10.1093/mnras/stab1216, https://academic.oup.com/mnras/article-pdf/505/1/1105/38391762/stab1216.pdf.
gentime, BIARsample, BIARphikalman
set.seed(6713) n=100 st<-gentime(n) x=BIARsample(n=n,phiR=0.9,phiI=0.3,st=st,rho=0.9) y=x$y y1=y/apply(y,1,sd) yerr1=rep(0,n) yerr2=rep(0,n) biar=BIARkalman(y1=y1[1,],y2=y1[2,],t=st,delta1 = yerr1,delta2=yerr2) biar napos=10 y0=y1 y1[1,napos]=NA xest=c(biar$phiR,biar$phiI) yest=BIARinterpolation(xest,y1=y1[1,],y2=y1[2,],t=st,delta1=yerr1, delta2=yerr2,nsmooth=1) yest$fitted mse=(y0[1,napos]-yest$fitted)^2 print(mse) par(mfrow=c(2,1)) plot(st,x$y[1,],type='l',xlim=c(st[napos-5],st[napos+5])) points(st,x$y[1,],pch=20) points(st[napos],yest$fitted*apply(y,1,sd)[1],col="red",pch=20) plot(st,x$y[2,],type='l',xlim=c(st[napos-5],st[napos+5])) points(st,x$y[2,],pch=20)set.seed(6713) n=100 st<-gentime(n) x=BIARsample(n=n,phiR=0.9,phiI=0.3,st=st,rho=0.9) y=x$y y1=y/apply(y,1,sd) yerr1=rep(0,n) yerr2=rep(0,n) biar=BIARkalman(y1=y1[1,],y2=y1[2,],t=st,delta1 = yerr1,delta2=yerr2) biar napos=10 y0=y1 y1[1,napos]=NA xest=c(biar$phiR,biar$phiI) yest=BIARinterpolation(xest,y1=y1[1,],y2=y1[2,],t=st,delta1=yerr1, delta2=yerr2,nsmooth=1) yest$fitted mse=(y0[1,napos]-yest$fitted)^2 print(mse) par(mfrow=c(2,1)) plot(st,x$y[1,],type='l',xlim=c(st[napos-5],st[napos+5])) points(st,x$y[1,],pch=20) points(st[napos],yest$fitted*apply(y,1,sd)[1],col="red",pch=20) plot(st,x$y[2,],type='l',xlim=c(st[napos-5],st[napos+5])) points(st,x$y[2,],pch=20)
Maximum Likelihood Estimation of the BIAR model parameters phiR and phiI. The estimation procedure uses the Kalman Filter to find the maximum of the likelihood.
BIARkalman( y1, y2, t, delta1 = 0, delta2 = 0, zero.mean = "TRUE", niter = 10, seed = 1234 )BIARkalman( y1, y2, t, delta1 = 0, delta2 = 0, zero.mean = "TRUE", niter = 10, seed = 1234 )
y1 |
Array with the observations of the first time series of the BIAR process. |
y2 |
Array with the observations of the second time series of the BIAR process. |
t |
Array with the irregular observational times. |
delta1 |
Array with the measurements error standard deviations of the first time series of the BIAR process. |
delta2 |
Array with the measurements error standard deviations of the second time series of the BIAR process. |
zero.mean |
logical; if true, the array y has zero mean; if false, y has a mean different from zero. |
niter |
Number of iterations in which the function nlminb will be repeated. |
seed |
a single value, interpreted as the seed of the random process. |
A list with the following components:
phiR MLE of the autocorrelation coefficient of BIAR model (phiR).
phiI MLE of the cross-correlation coefficient of the BIAR model (phiI).
ll Value of the negative log likelihood evaluated in phiR and phiI.
Elorrieta F, Eyheramendy S, Palma W, Ojeda C (2021). “A novel bivariate autoregressive model for predicting and forecasting irregularly observed time series.” Monthly Notices of the Royal Astronomical Society, 505(1), 1105-1116. ISSN 0035-8711, doi:10.1093/mnras/stab1216, https://academic.oup.com/mnras/article-pdf/505/1/1105/38391762/stab1216.pdf.
gentime, BIARsample, BIARphikalman
n=80 set.seed(6714) st<-gentime(n) x=BIARsample(n=n,phiR=0.9,phiI=0,st=st,rho=0) y=x$y y1=y/apply(y,1,sd) biar=BIARkalman(y1=y1[1,],y2=y1[2,],t=st,delta1 = rep(0,length(y[1,])), delta2=rep(0,length(y[1,]))) biarn=80 set.seed(6714) st<-gentime(n) x=BIARsample(n=n,phiR=0.9,phiI=0,st=st,rho=0) y=x$y y1=y/apply(y,1,sd) biar=BIARkalman(y1=y1[1,],y2=y1[2,],t=st,delta1 = rep(0,length(y[1,])), delta2=rep(0,length(y[1,]))) biar
This function return the negative log likelihood of the BIAR process given specific values of phiR and phiI
BIARphikalman(yest, phiValues, y1, y2, t, yerr1, yerr2, zeroMean = TRUE)BIARphikalman(yest, phiValues, y1, y2, t, yerr1, yerr2, zeroMean = TRUE)
yest |
An array with the estimate of a missing value in one or both time series of the bivariate process. This function recognizes a missing value with a NA. If the bivariate time series does not have a missing value, this value does not affect the computation of the likelihood. |
phiValues |
An array with the parameters of the BIAR model. The elements of the array are, in order, the real (phiR) and the imaginary (phiI) part of the coefficient of BIAR model. |
y1 |
Array with the observations of the first time series of the BIAR process. |
y2 |
Array with the observations of the second time series of the BIAR process. |
t |
Array with the irregular observational times. |
yerr1 |
Array with the measurements error standard deviations of the first time series of the BIAR process. |
yerr2 |
Array with the measurements error standard deviations of the second time series of the BIAR process. |
zeroMean |
logical; if TRUE, the array y has zero mean; if FALSE, y has a mean different from zero. |
Value of the negative log likelihood evaluated in phiR and phiI.
Elorrieta F, Eyheramendy S, Palma W, Ojeda C (2021). “A novel bivariate autoregressive model for predicting and forecasting irregularly observed time series.” Monthly Notices of the Royal Astronomical Society, 505(1), 1105-1116. ISSN 0035-8711, doi:10.1093/mnras/stab1216, https://academic.oup.com/mnras/article-pdf/505/1/1105/38391762/stab1216.pdf.
n=300 set.seed(6714) st<-gentime(n) x=BIARsample(n=n,phiR=0.9,phiI=0.3,st=st) y=x$y y1=y[1,] y2=y[2,] yerr1=rep(0,n) yerr2=rep(0,n) BIARphikalman(phiValues=c(0.8,0.2),y1=y1,y2=y2,t=st,yerr1=yerr1,yerr2=yerr2,yest=c(0,0))n=300 set.seed(6714) st<-gentime(n) x=BIARsample(n=n,phiR=0.9,phiI=0.3,st=st) y=x$y y1=y[1,] y2=y[2,] yerr1=rep(0,n) yerr2=rep(0,n) BIARphikalman(phiValues=c(0.8,0.2),y1=y1,y2=y2,t=st,yerr1=yerr1,yerr2=yerr2,yest=c(0,0))
Simulates a BIAR Time Series Model
BIARsample(n, st, phiR, phiI, delta1 = 0, delta2 = 0, rho = 0)BIARsample(n, st, phiR, phiI, delta1 = 0, delta2 = 0, rho = 0)
n |
Length of the output bivariate time series. A strictly positive integer. |
st |
Array with observational times. |
phiR |
Autocorrelation coefficient of BIAR model. A value between -1 and 1. |
phiI |
Crosscorrelation coefficient of BIAR model. A value between -1 and 1. |
delta1 |
Array with the measurements error standard deviations of the first time series of the bivariate process. |
delta2 |
Array with the measurements error standard deviations of the second time series of the bivariate process. |
rho |
Contemporary correlation coefficient of BIAR model. A value between -1 and 1. |
The chosen phiR and phiI values must satisfy the condition $|phiR + i phiI| < 1$.
A list with the following components:
y Matrix with the simulated BIAR process.
t Array with observation times.
Sigma Covariance matrix of the process.
Elorrieta F, Eyheramendy S, Palma W, Ojeda C (2021). “A novel bivariate autoregressive model for predicting and forecasting irregularly observed time series.” Monthly Notices of the Royal Astronomical Society, 505(1), 1105-1116. ISSN 0035-8711, doi:10.1093/mnras/stab1216, https://academic.oup.com/mnras/article-pdf/505/1/1105/38391762/stab1216.pdf.
n=300 set.seed(6714) st<-gentime(n) x=BIARsample(n=n,phiR=0.9,phiI=0.3,st=st) plot(st,x$y[1,],type='l') plot(st,x$y[2,],type='l') x=BIARsample(n=n,phiR=-0.9,phiI=-0.3,st=st) plot(st,x$y[1,],type='l') plot(st,x$y[2,],type='l')n=300 set.seed(6714) st<-gentime(n) x=BIARsample(n=n,phiR=0.9,phiI=0.3,st=st) plot(st,x$y[1,],type='l') plot(st,x$y[2,],type='l') x=BIARsample(n=n,phiR=-0.9,phiI=-0.3,st=st) plot(st,x$y[1,],type='l') plot(st,x$y[2,],type='l')
Fit a CIAR model to an irregularly observed time series.
CIARfit(phiValues, y, t, standardized = TRUE, c = 1)CIARfit(phiValues, y, t, standardized = TRUE, c = 1)
phiValues |
An array with the parameters of the CIAR model. The elements of the array are, in order, the real and the imaginary part of the phi parameter of the CIAR model. |
y |
Array with the time series observations. |
t |
Array with the irregular observational times. |
standardized |
logical; if TRUE, the array y is standardized; if FALSE, y contains the raw time series |
c |
Nuisance parameter corresponding to the variance of the imaginary part. |
A list with the following components:
yhat Fitted values of the observable part of CIAR model.
xhat Fitted values of both observable part and imaginary part of CIAR model.
Lambda Lambda value estimated by the CIAR model at the last time point.
Theta Theta array estimated by the CIAR model at the last time point.
Sighat Covariance matrix estimated by the CIAR model at the last time point.
Qt Covariance matrix of the state equation estimated by the CIAR model at the last time point.
Elorrieta, F, Eyheramendy, S, Palma, W (2019). “Discrete-time autoregressive model for unequally spaced time-series observations.” A&A, 627, A120. doi:10.1051/0004-6361/201935560.
gentime, CIARsample, CIARphikalman,CIARkalman
n=100 set.seed(6714) st<-gentime(n) x=CIARsample(n=n,phiR=0.9,phiI=0,st=st,c=1) y=x$y y1=y/sd(y) ciar=CIARkalman(y=y1,t=st) ciar yhat=CIARfit(phiValues=c(ciar$phiR,ciar$phiI),y=y1,t=st)n=100 set.seed(6714) st<-gentime(n) x=CIARsample(n=n,phiR=0.9,phiI=0,st=st,c=1) y=x$y y1=y/sd(y) ciar=CIARkalman(y=y1,t=st) ciar yhat=CIARfit(phiValues=c(ciar$phiR,ciar$phiI),y=y1,t=st)
Forecast from models fitted by CIARkalman
CIARforecast(phiR, phiI, y1, st, tAhead)CIARforecast(phiR, phiI, y1, st, tAhead)
phiR |
Real part of the phi coefficient of CIAR model. |
phiI |
Imaginary part of the phi coefficient of CIAR model. |
y1 |
Array with the time series observations. |
st |
Array with the observational times. |
tAhead |
The time ahead for which the forecast is required. |
A list with the following components:
fitted Fitted values by the CIAR model.
forecast Point forecast in the time ahead required.
Lambda Lambda value estimated by the CIAR model at the last time point.
Sighat Covariance matrix estimated by the CIAR model at the last time point.
Elorrieta, F, Eyheramendy, S, Palma, W (2019). “Discrete-time autoregressive model for unequally spaced time-series observations.” A&A, 627, A120. doi:10.1051/0004-6361/201935560.
CIARsample, CIARkalman, CIARfit
#Simulated Data n=100 set.seed(6714) st<-gentime(n) x=CIARsample(n=n,phiR=0.9,phiI=0,st=st,c=1) y=x$y y1=y/sd(y) n=length(y1) p=trunc(n*0.99) ytr=y1[1:p] yte=y1[(p+1):n] str=st[1:p] ste=st[(p+1):n] tahead=ste-str[p] ciar=CIARkalman(y=ytr,t=str) forCIAR<-CIARforecast(ciar$phiR,ciar$phiI,ytr,str,tAhead=tahead)#Simulated Data n=100 set.seed(6714) st<-gentime(n) x=CIARsample(n=n,phiR=0.9,phiI=0,st=st,c=1) y=x$y y1=y/sd(y) n=length(y1) p=trunc(n*0.99) ytr=y1[1:p] yte=y1[(p+1):n] str=st[1:p] ste=st[(p+1):n] tahead=ste-str[p] ciar=CIARkalman(y=ytr,t=str) forCIAR<-CIARforecast(ciar$phiR,ciar$phiI,ytr,str,tAhead=tahead)
Interpolation of missing values from models fitted by CIARkalman
CIARinterpolation( x, y, t, delta = 0, yini = 0, zero.mean = TRUE, standardized = TRUE, c = 1, seed = 1234 )CIARinterpolation( x, y, t, delta = 0, yini = 0, zero.mean = TRUE, standardized = TRUE, c = 1, seed = 1234 )
x |
An array with the parameters of the CIAR model. The elements of the array are, in order, the real (phiR) and the imaginary (phiI) part of the coefficient of CIAR model. |
y |
Array with the time series observations. |
t |
Array with the irregular observational times. |
delta |
Array with the measurements error standard deviations. |
yini |
a single value, initial value for the estimation of the missing value of the time series. |
zero.mean |
logical; if TRUE, the array y has zero mean; if FALSE, y has a mean different from zero. |
standardized |
logical; if TRUE, the array y is standardized; if FALSE, y contains the raw time series. |
c |
Nuisance parameter corresponding to the variance of the imaginary part. |
seed |
a single value, interpreted as the seed of the random process. |
A list with the following components:
fitted Estimation of a missing value of the CIAR process.
ll Value of the negative log likelihood evaluated in the fitted missing values.
Elorrieta, F, Eyheramendy, S, Palma, W (2019). “Discrete-time autoregressive model for unequally spaced time-series observations.” A&A, 627, A120. doi:10.1051/0004-6361/201935560.
gentime, CIARsample, CIARkalman
n=100 set.seed(6714) st<-gentime(n) x=CIARsample(n=n,phiR=0.9,phiI=0,st=st,c=1) y=x$y y1=y/sd(y) ciar=CIARkalman(y=y1,t=st) ciar napos=10 y0=y1 y1[napos]=NA xest=c(ciar$phiR,ciar$phiI) yest=CIARinterpolation(xest,y=y1,t=st) yest$fitted mse=(y0[napos]-yest$fitted)^2 print(mse) plot(st,y,type='l',xlim=c(st[napos-5],st[napos+5])) points(st,y,pch=20) points(st[napos],yest$fitted*sd(y),col="red",pch=20)n=100 set.seed(6714) st<-gentime(n) x=CIARsample(n=n,phiR=0.9,phiI=0,st=st,c=1) y=x$y y1=y/sd(y) ciar=CIARkalman(y=y1,t=st) ciar napos=10 y0=y1 y1[napos]=NA xest=c(ciar$phiR,ciar$phiI) yest=CIARinterpolation(xest,y=y1,t=st) yest$fitted mse=(y0[napos]-yest$fitted)^2 print(mse) plot(st,y,type='l',xlim=c(st[napos-5],st[napos+5])) points(st,y,pch=20) points(st[napos],yest$fitted*sd(y),col="red",pch=20)
Maximum Likelihood Estimation of the CIAR model parameters phiR and phiI. The estimation procedure uses the Kalman Filter to find the maximum of the likelihood.
CIARkalman( y, t, delta = 0, zero.mean = TRUE, standardized = TRUE, c = 1, niter = 10, seed = 1234 )CIARkalman( y, t, delta = 0, zero.mean = TRUE, standardized = TRUE, c = 1, niter = 10, seed = 1234 )
y |
Array with the time series observations. |
t |
Array with the irregular observational times. |
delta |
Array with the measurements error standard deviations. |
zero.mean |
logical; if TRUE, the array y has zero mean; if FALSE, y has a mean different from zero. |
standardized |
logical; if TRUE, the array y is standardized; if FALSE, y contains the raw time series. |
c |
Nuisance parameter corresponding to the variance of the imaginary part. |
niter |
Number of iterations in which the function nlminb will be repeated. |
seed |
a single value, interpreted as the seed of the random process. |
A list with the following components:
phiR MLE of the Real part of the coefficient of CIAR model (phiR).
phiI MLE of the Imaginary part of the coefficient of the CIAR model (phiI).
ll Value of the negative log likelihood evaluated in phiR and phiI.
Elorrieta, F, Eyheramendy, S, Palma, W (2019). “Discrete-time autoregressive model for unequally spaced time-series observations.” A&A, 627, A120. doi:10.1051/0004-6361/201935560.
gentime, CIARsample, CIARphikalman
n=100 set.seed(6714) st<-gentime(n) x=CIARsample(n=n,phiR=0.9,phiI=0,st=st,c=1) y=x$y y1=y/sd(y) ciar=CIARkalman(y=y1,t=st) ciar Mod(complex(real=ciar$phiR,imaginary=ciar$phiI))n=100 set.seed(6714) st<-gentime(n) x=CIARsample(n=n,phiR=0.9,phiI=0,st=st,c=1) y=x$y y1=y/sd(y) ciar=CIARkalman(y=y1,t=st) ciar Mod(complex(real=ciar$phiR,imaginary=ciar$phiI))
This function return the negative log likelihood of the CIAR process given specific values of phiR and phiI
CIARphikalman(yest, x, y, t, yerr, zeroMean = TRUE, standardized = TRUE, c = 1)CIARphikalman(yest, x, y, t, yerr, zeroMean = TRUE, standardized = TRUE, c = 1)
yest |
The estimate of a missing value in the time series. This function recognizes a missing value with a NA. If the time series does not have a missing value, this value does not affect the computation of the likelihood. |
x |
An array with the parameters of the CIAR model. The elements of the array are, in order, the real (phiR) and the imaginary (phiI) part of the coefficient of CIAR model. |
y |
Array with the time series observations. |
t |
Array with the irregular observational times. |
yerr |
Array with the measurements error standard deviations. |
zeroMean |
logical; if TRUE, the array y has zero mean; if FALSE, y has a mean different from zero. |
standardized |
logical; if TRUE, the array y is standardized; if FALSE, y contains the raw time series. |
c |
Nuisance parameter corresponding to the variance of the imaginary part. |
Value of the negative log likelihood evaluated in phiR and phiI.
Elorrieta, F, Eyheramendy, S, Palma, W (2019). “Discrete-time autoregressive model for unequally spaced time-series observations.” A&A, 627, A120. doi:10.1051/0004-6361/201935560.
n=300 set.seed(6714) st<-gentime(n) x=CIARsample(n=n,phiR=0.9,phiI=0,st=st,c=1) y=x$y yerr=rep(0,n) CIARphikalman(x=c(0.8,0),y=y,t=st,yerr=yerr,yest=0)n=300 set.seed(6714) st<-gentime(n) x=CIARsample(n=n,phiR=0.9,phiI=0,st=st,c=1) y=x$y yerr=rep(0,n) CIARphikalman(x=c(0.8,0),y=y,t=st,yerr=yerr,yest=0)
Simulates a CIAR Time Series Model
CIARsample(n, phiR, phiI, st, rho = 0L, c = 1L)CIARsample(n, phiR, phiI, st, rho = 0L, c = 1L)
n |
Length of the output time series. A strictly positive integer. |
phiR |
Real part of the coefficient of CIAR model. A value between -1 and 1. |
phiI |
Imaginary part of the coefficient of CIAR model. A value between -1 and 1. |
st |
Array with observational times. |
rho |
Correlation between the real and the imaginary part of the process. A value between -1 and 1. |
c |
Nuisance parameter corresponding to the variance of the imaginary part. |
The chosen phiR and phiI values must satisfy the condition $|phiR + i phiI| < 1$.
A list with the following components:
yArray with the simulated real part of the CIAR process.
t Array with observation times.
Sigma Covariance matrix of the process.
Elorrieta, F, Eyheramendy, S, Palma, W (2019). “Discrete-time autoregressive model for unequally spaced time-series observations.” A&A, 627, A120. doi:10.1051/0004-6361/201935560.
n=300 set.seed(6714) st<-gentime(n) x=CIARsample(n=n,phiR=0.9,phiI=0,st=st,c=1) plot(st,x$y,type='l') x=CIARsample(n=n,phiR=-0.9,phiI=0,st=st,c=1) plot(st,x$y,type='l')n=300 set.seed(6714) st<-gentime(n) x=CIARsample(n=n,phiR=0.9,phiI=0,st=st,c=1) plot(st,x$y,type='l') x=CIARsample(n=n,phiR=-0.9,phiI=0,st=st,c=1) plot(st,x$y,type='l')
Time series of a classical cepheid variable star obtained from HIPPARCOS.
clcepclcep
A data frame with 109 observations on the following 3 variables:
heliocentric Julian Day
magnitude
measurement error of the magnitude (in mag).
The frequency computed by GLS for this light curve is 0.060033386. Catalogs and designations of this star: HD 1989: HD 305996 TYCHO-2 2000:TYC 8958-2333-1 USNO-A2.0:USNO-A2 0225-10347916 HIP: HIP-54101
data(clcep) f1=0.060033386 foldlc(clcep,f1)data(clcep) f1=0.060033386 foldlc(clcep,f1)
Time series of a cataclysmic variable/nova object observed in the g-band of the ZTF survey and processed by the ALeRCE broker.ZTF Object code: ZTF18aayzpbr
cvnovagcvnovag
A data frame with 67 observations on the following 3 variables:
heliocentric Julian Day - 2400000
magnitude
measurement error standard deviations.
Förster F, Cabrera-Vives G, Castillo-Navarrete E, Estévez PA, Sánchez-Sáez P, Arredondo J, Bauer FE, Carrasco-Davis R, Catelan M, Elorrieta F, Eyheramendy S, Huijse P, Pignata G, Reyes E, Reyes I, Rodríguez-Mancini D, Ruz-Mieres D, Valenzuela C, Álvarez-Maldonado I, Astorga N, Borissova J, Clocchiatti A, Cicco DD, Donoso-Oliva C, Hernández-García L, Graham MJ, Jordán A, Kurtev R, Mahabal A, Maureira JC, Muñoz-Arancibia A, Molina-Ferreiro R, Moya A, Palma W, Pérez-Carrasco M, Protopapas P, Romero M, Sabatini-Gacitua L, Sánchez A, Martín JS, Sepúlveda-Cobo C, Vera E, Vergara JR (2021). “The Automatic Learning for the Rapid Classification of Events (ALeRCE) Alert Broker.” The Astronomical Journal, 161(5), 242. doi:10.3847/1538-3881/abe9bc.
data(cvnovag) plot(cvnovag$t,cvnovag$m,type="l",ylab="",xlab="",col="green")data(cvnovag) plot(cvnovag$t,cvnovag$m,type="l",ylab="",xlab="",col="green")
Time series of a cataclysmic variable/nova object observed in the r-band of the ZTF survey and processed by the ALeRCE broker.ZTF Object code: ZTF18aayzpbr
cvnovarcvnovar
A data frame with 65 observations on the following 3 variables:
heliocentric Julian Day - 2400000
magnitude
measurement error standard deviations.
Förster F, Cabrera-Vives G, Castillo-Navarrete E, Estévez PA, Sánchez-Sáez P, Arredondo J, Bauer FE, Carrasco-Davis R, Catelan M, Elorrieta F, Eyheramendy S, Huijse P, Pignata G, Reyes E, Reyes I, Rodríguez-Mancini D, Ruz-Mieres D, Valenzuela C, Álvarez-Maldonado I, Astorga N, Borissova J, Clocchiatti A, Cicco DD, Donoso-Oliva C, Hernández-García L, Graham MJ, Jordán A, Kurtev R, Mahabal A, Maureira JC, Muñoz-Arancibia A, Molina-Ferreiro R, Moya A, Palma W, Pérez-Carrasco M, Protopapas P, Romero M, Sabatini-Gacitua L, Sánchez A, Martín JS, Sepúlveda-Cobo C, Vera E, Vergara JR (2021). “The Automatic Learning for the Rapid Classification of Events (ALeRCE) Alert Broker.” The Astronomical Journal, 161(5), 242. doi:10.3847/1538-3881/abe9bc.
data(cvnovar) plot(cvnovar$t,cvnovar$m,type="l",ylab="",xlab="",col="red")data(cvnovar) plot(cvnovar$t,cvnovar$m,type="l",ylab="",xlab="",col="red")
Time series of a double mode cepheid variable star obtained from OGLE.
dmcepdmcep
A data frame with 191 observations on the following 3 variables:
heliocentric Julian Day
magnitude
measurement error of the magnitude (in mag).
The dominant frequency computed by GLS for this light curve is 0.7410152. The second frequency computed by GLS for this light curve is 0.5433353. OGLE-ID:175210
data(dmcep) f1=0.7410152 foldlc(dmcep,f1) fit=harmonicfit(dmcep,f1) f2=0.5433353 foldlc(cbind(dmcep$t,fit$res,dmcep$merr),f2)data(dmcep) f1=0.7410152 foldlc(dmcep,f1) fit=harmonicfit(dmcep,f1) f2=0.5433353 foldlc(cbind(dmcep$t,fit$res,dmcep$merr),f2)
Time series of a Delta Scuti variable star obtained from HIPPARCOS.
dscutdscut
A data frame with 116 observations on the following 3 variables:
heliocentric Julian Day
magnitude
measurement error of the magnitude (in mag).
The frequency computed by GLS for this light curve is 14.88558646. Catalogs and designations of this star: HD 1989: HD 199757 TYCHO-2 2000: TYC 7973-401-1 USNO-A2.0: USNO-A2 0450-39390397 HIP: HIP 103684
data(dscut) f1=14.88558646 foldlc(dscut,f1)data(dscut) f1=14.88558646 foldlc(dscut,f1)
Time series of a Beta Lyrae variable star obtained from OGLE.
ebeb
A data frame with 470 observations on the following 3 variables:
heliocentric Julian Day
magnitude
measurement error of the magnitude (in mag).
The frequency computed by GLS for this light curve is 1.510571586. Catalogs and designations of this star:OGLE051951.22-694002.7
data(eb) f1=1.510571586 foldlc(eb,f1)data(eb) f1=1.510571586 foldlc(eb,f1)
This function plots a time series folded on its period.
foldlc(file, f1, plot = TRUE)foldlc(file, f1, plot = TRUE)
file |
Matrix with the light curve observations. The first column must have the irregular times, the second column must have the brightness magnitudes and the third column must have the measurement errors. |
f1 |
Frequency (1/Period) of the light curve. |
plot |
logical; if TRUE, the function returns the plot of folded time series. |
A matrix whose first column has the folded (phased) observational times.
data(clcep) f1=0.060033386 foldlc(clcep,f1)data(clcep) f1=0.060033386 foldlc(clcep,f1)
Forecast with any of the models available in the iAR package
Forecast_iARModels( phi, y, st, tAhead, model = "iAR", mu = NULL, phiI = NULL, nu = NULL, level = 95 )Forecast_iARModels( phi, y, st, tAhead, model = "iAR", mu = NULL, phiI = NULL, nu = NULL, level = 95 )
phi |
Autocorrelation coefficient estimated by the method specified. |
y |
Array with the time series observations. |
st |
Array with the observational times. |
tAhead |
The time ahead for which the forecast is required. |
model |
model to be used for the forecast. The default is to use the iAR model. Other models available are "iAR-T", "iAR-Gamma", "CiAR" and "BiAR". |
mu |
Level parameter of the IAR-Gamma process. A positive value. |
phiI |
Imaginary parameter of CIAR model or Cross-correlation parameter of BIAR model. |
nu |
degrees of freedom parameter of iAR-T model. |
level |
significance level for the confidence interval. The default value is 95. |
A dataframe with the following columns:
tAhead The time ahead used for the forecast.
forecast Point forecast in the time ahead required.
stderror Standard error of the forecast.
lowerCI Lower limit of the confidence interval.
upperCI Upper limit of the confidence interval.
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
gentime, IARforecast, IARgforecast, IARforecast, BIARforecast
st <- gentime(n=200,lambda1=15,lambda2=2) y <- IARsample(phi=0.9,n=200,st=st) model<-IARloglik(y=y$series,st=st) phi=model$phi forIAR<-IARforecast(phi=phi,y$series,st=st,tAhead=c(1.3),standardized=FALSE,zero.mean=FALSE) forIAR forIAR<-Forecast_iARModels(phi=phi,y=y$series,st=st,tAhead=c(1.3,2.6)) forIARst <- gentime(n=200,lambda1=15,lambda2=2) y <- IARsample(phi=0.9,n=200,st=st) model<-IARloglik(y=y$series,st=st) phi=model$phi forIAR<-IARforecast(phi=phi,y$series,st=st,tAhead=c(1.3),standardized=FALSE,zero.mean=FALSE) forIAR forIAR<-Forecast_iARModels(phi=phi,y=y$series,st=st,tAhead=c(1.3,2.6)) forIAR
Function to generate irregularly spaced times from a mixture of exponential distributions.
gentime( n, distribution = "expmixture", lambda1 = 130, lambda2 = 6.5, p1 = 0.15, p2 = 0.85, a = 0, b = 1 )gentime( n, distribution = "expmixture", lambda1 = 130, lambda2 = 6.5, p1 = 0.15, p2 = 0.85, a = 0, b = 1 )
n |
A positive integer. Length of observation times. |
distribution |
Distribution of the observation times that will be generated. Default value is "expmixture" for a mixture of exponential distributions. Alternative distributions are "uniform", "exponential" and "gamma". |
lambda1 |
Mean (1/rate) of the exponential distribution or the first exponential distribution in a mixture of exponential distributions. |
lambda2 |
Mean (1/rate) of the second exponential distribution in a mixture of exponential distributions. |
p1 |
Weight of the first exponential distribution in a mixture of exponential distributions. |
p2 |
Weight of the second exponential distribution in a mixture of exponential distributions. |
a |
Shape parameter of a gamma distribution or lower limit of the uniform distribution. |
b |
Scale parameter of a gamma distribution or upper limit of the uniform distribution. |
Array with irregularly spaced observations times
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
st<-gentime(n=100) st<-gentime(n=100,distribution="uniform") st<-gentime(n=100,distribution="gamma",a=1,b=1) st<-gentime(n=100,distribution="exponential",lambda1=1)st<-gentime(n=100) st<-gentime(n=100,distribution="uniform") st<-gentime(n=100,distribution="gamma",a=1,b=1) st<-gentime(n=100,distribution="exponential",lambda1=1)
This function fit an k-harmonic function to time series data.
harmonicfit( file, f1, nham = 4, weights = NULL, print = FALSE, remove_trend = TRUE )harmonicfit( file, f1, nham = 4, weights = NULL, print = FALSE, remove_trend = TRUE )
file |
A matrix with two columns. The first column corresponds to the observations times, and the second column corresponds to the measures. |
f1 |
Frequency (1/Period) of the time series |
nham |
Number of harmonic components in the model |
weights |
An array with the weights of each observation |
print |
logical; if true, the summary of the harmonic fitted model will be printed. The default value is false. |
remove_trend |
logical; if true, the linear trend of time series will be removed before the the harmonic model is fitted. |
A list with the following components:
res Residuals to the harmonic fit of the time series.
t Observations times.
R2 Adjusted R-Squared.
MSE Mean Squared Error.
coef Summary of the coefficients estimated by the harmonic model.
data(clcep) f1=0.060033386 results=harmonicfit(file=clcep[,1:2],f1=f1) results$R2 results$MSE results=harmonicfit(file=clcep[,1:2],f1=f1,nham=3) results$R2 results$MSE results=harmonicfit(file=clcep[,1:2],f1=f1,weights=clcep[,3]) results$R2 results$MSEdata(clcep) f1=0.060033386 results=harmonicfit(file=clcep[,1:2],f1=f1) results$R2 results$MSE results=harmonicfit(file=clcep[,1:2],f1=f1,nham=3) results$R2 results$MSE results=harmonicfit(file=clcep[,1:2],f1=f1,weights=clcep[,3]) results$R2 results$MSE
Description: Data sets, functions and scripts with examples to implement autoregressive models for irregularly observed time series. The models available in this package are the irregular autoregressive model (Eyheramendy et al.(2018) <doi:10.1093/mnras/sty2487>), the complex irregular autoregressive model (Elorrieta et al.(2019) <doi:10.1051/0004-6361/201935560>) and the bivariate irregular autoregressive model (Elorrieta et al.(2021) <doi:10.1093/mnras/stab1216>)
The foo functions ...
The foo functions ...
heloo
Fit an IAR model to an irregularly observed time series.
IARfit(phi, y, st, standardized = TRUE, zero.mean = TRUE)IARfit(phi, y, st, standardized = TRUE, zero.mean = TRUE)
phi |
Estimated phi parameter by the iAR model. |
y |
Array with the time series observations. |
st |
Array with the irregular observational times. |
standardized |
logical; if TRUE, the array y is standardized; if FALSE, y contains the raw time series |
zero.mean |
logical; if TRUE, the array y has zero mean; if FALSE, y has a mean different from zero. |
Fitted values of the iAR model
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
gentime, IARsample, IARloglik, IARkalman
set.seed(6714) st<-gentime(n=100) y<-IARsample(phi=0.99,st=st,n=100) y<-y$series phi=IARloglik(y=y,st=st)$phi fit=IARfit(phi=phi,y=y,st=st)set.seed(6714) st<-gentime(n=100) y<-IARsample(phi=0.99,st=st,n=100) y<-y$series phi=IARloglik(y=y,st=st)$phi fit=IARfit(phi=phi,y=y,st=st)
Forecast from models fitted by IARloglik
IARforecast(phi, y, st, standardized = TRUE, zero.mean = TRUE, tAhead)IARforecast(phi, y, st, standardized = TRUE, zero.mean = TRUE, tAhead)
phi |
Estimated phi parameter by the iAR model. |
y |
Array with the time series observations. |
st |
Array with the irregular observational times. |
standardized |
logical; if TRUE, the array y is standardized; if FALSE, y contains the raw time series |
zero.mean |
logical; if TRUE, the array y has zero mean; if FALSE, y has a mean different from zero. |
tAhead |
The time ahead for forecast is required. |
Forecasted value from the iAR model
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
gentime, IARsample, IARloglik, IARkalman, IARfit
set.seed(6714) st<-gentime(n=100) y<-IARsample(phi=0.99,st=st,n=100) y<-y$series n=length(y) p=trunc(n*0.99) ytr=y[1:p] yte=y[(p+1):n] str=st[1:p] ste=st[(p+1):n] tahead=ste-str[p] phi=IARloglik(y=ytr,st=str)$phi forIAR=IARforecast(phi=phi,y=ytr,st=str,tAhead=tahead)set.seed(6714) st<-gentime(n=100) y<-IARsample(phi=0.99,st=st,n=100) y<-y$series n=length(y) p=trunc(n*0.99) ytr=y[1:p] yte=y[(p+1):n] str=st[1:p] ste=st[(p+1):n] tahead=ste-str[p] phi=IARloglik(y=ytr,st=str)$phi forIAR=IARforecast(phi=phi,y=ytr,st=str,tAhead=tahead)
Maximum Likelihood Estimation of the IAR-Gamma model.
IARgamma(y, st)IARgamma(y, st)
y |
Array with the time series observations |
st |
Array with the irregular observational times |
A list with the following components:
phi MLE of the phi parameter of the IAR-Gamma model.
mu MLE of the mu parameter of the IAR-Gamma model.
sigma MLE of the sigma parameter of the IAR-Gamma model.
ll Value of the negative log likelihood evaluated in phi, mu and sigma.
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
gentime, IARgsample, IARphigamma
n=300 set.seed(6714) st<-gentime(n) y<-IARgsample(phi=0.9,st=st,n=n,sigma2=1,mu=1) model<-IARgamma(y$y, st=st) phi=model$phi muest=model$mu sigmaest=model$sigman=300 set.seed(6714) st<-gentime(n) y<-IARgsample(phi=0.9,st=st,n=n,sigma2=1,mu=1) model<-IARgamma(y$y, st=st) phi=model$phi muest=model$mu sigmaest=model$sigma
Fit an IAR-Gamma model to an irregularly observed time series.
IARgfit(phi, mu, y, st)IARgfit(phi, mu, y, st)
phi |
Estimated phi parameter by the iAR-Gamma model. |
mu |
Estimated mu parameter by the iAR-Gamma model. |
y |
Array with the time series observations. |
st |
Array with the irregular observational times. |
Fitted values of the iAR-Gamma model
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
n=300 set.seed(6714) st<-gentime(n) y<-IARgsample(phi=0.9,st=st,n=n,sigma2=1,mu=1) model<-IARgamma(y$y, st=st) phi=model$phi muest=model$mu sigmaest=model$sigma fit=IARgfit(phi=phi,mu=muest,y=y$y,st=st)n=300 set.seed(6714) st<-gentime(n) y<-IARgsample(phi=0.9,st=st,n=n,sigma2=1,mu=1) model<-IARgamma(y$y, st=st) phi=model$phi muest=model$mu sigmaest=model$sigma fit=IARgfit(phi=phi,mu=muest,y=y$y,st=st)
Forecast from models fitted by IARgamma
IARgforecast(phi, mu, y, st, tAhead)IARgforecast(phi, mu, y, st, tAhead)
phi |
Estimated phi parameter by the iAR-Gamma model. |
mu |
Estimated mu parameter by the iAR-Gamma model. |
y |
Array with the time series observations. |
st |
Array with the irregular observational times. |
tAhead |
The time ahead for forecast is required. |
Forecasted value from the iAR-Gamma model
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
gentime, IARgsample, IARgamma, IARgfit
n=100 set.seed(6714) st<-gentime(n) y<-IARgsample(phi=0.9,st=st,n=n,sigma2=1,mu=1) y<-y$y n=length(y) p=trunc(n*0.99) ytr=y[1:p] yte=y[(p+1):n] str=st[1:p] ste=st[(p+1):n] tahead=ste-str[p] model<-IARgamma(ytr, st=str) phi=model$phi muest=model$mu sigmaest=model$sigma fit=IARgforecast(phi=phi,mu=muest,y=ytr,st=str,tAhead=tahead)n=100 set.seed(6714) st<-gentime(n) y<-IARgsample(phi=0.9,st=st,n=n,sigma2=1,mu=1) y<-y$y n=length(y) p=trunc(n*0.99) ytr=y[1:p] yte=y[(p+1):n] str=st[1:p] ste=st[(p+1):n] tahead=ste-str[p] model<-IARgamma(ytr, st=str) phi=model$phi muest=model$mu sigmaest=model$sigma fit=IARgforecast(phi=phi,mu=muest,y=ytr,st=str,tAhead=tahead)
Interpolation of missing values from models fitted by IARgamma
IARginterpolation(x, y, st, yini = 1)IARginterpolation(x, y, st, yini = 1)
x |
A given array with the parameters of the IAR-Gamma model. The first element of the array corresponding to the phi parameter, the second to the level parameter mu, and the last one to the scale parameter sigma. |
y |
Array with the time series observations. |
st |
Array with the irregular observational times. |
yini |
a single value, initial value for the estimation of the missing value of the time series. |
A list with the following components:
fitted Estimation of a missing value of the IAR-Gamma process.
ll Value of the negative log likelihood evaluated in the fitted missing values.
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
set.seed(6714) n<-100 st<-gentime(n) y<-IARgsample(phi=0.9,st=st,n=n,sigma2=1,mu=1) model<-IARgamma(y$y, st=st) y<-y$y napos=10 y0=y y[napos]=NA xest=c(model$phi,model$mu,model$sigma) yest=IARginterpolation(x=xest,y=y,st=st) yest$fitted mse=(y0[napos]-yest$fitted)^2 print(mse) plot(st,y,type='l',xlim=c(st[napos-5],st[napos+5])) points(st,y,pch=20) points(st[napos],yest$fitted,col="red",pch=20)set.seed(6714) n<-100 st<-gentime(n) y<-IARgsample(phi=0.9,st=st,n=n,sigma2=1,mu=1) model<-IARgamma(y$y, st=st) y<-y$y napos=10 y0=y y[napos]=NA xest=c(model$phi,model$mu,model$sigma) yest=IARginterpolation(x=xest,y=y,st=st) yest$fitted mse=(y0[napos]-yest$fitted)^2 print(mse) plot(st,y,type='l',xlim=c(st[napos-5],st[napos+5])) points(st,y,pch=20) points(st[napos],yest$fitted,col="red",pch=20)
Simulates an IAR-Gamma Time Series Model.
IARgsample(phi, st, n = 100L, sigma2 = 1L, mu = 1L)IARgsample(phi, st, n = 100L, sigma2 = 1L, mu = 1L)
phi |
A coefficient of IAR-Gamma model. A value between 0 and 1. |
st |
Array with observational times. |
n |
Length of the output time series. A strictly positive integer. |
sigma2 |
Scale parameter of the IAR-Gamma process. A positive value. |
mu |
Level parameter of the IAR-Gamma process. A positive value. |
A list with the following components:
y Array with simulated IAR-Gamma process.
st Array with observation times.
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
n=100 set.seed(6714) st<-gentime(n) y<-IARgsample(phi=0.9,st=st,n=n,sigma2=1,mu=1) plot(st,y$y,type='l') hist(y$y,breaks=20)n=100 set.seed(6714) st<-gentime(n) y<-IARgsample(phi=0.9,st=st,n=n,sigma2=1,mu=1) plot(st,y$y,type='l') hist(y$y,breaks=20)
Interpolation of missing values from models fitted by IARkalman
IARinterpolation( x, y, st, delta = 0, yini = 0, zero.mean = TRUE, standardized = TRUE )IARinterpolation( x, y, st, delta = 0, yini = 0, zero.mean = TRUE, standardized = TRUE )
x |
A given phi coefficient of the IAR model. |
y |
Array with the time series observations. |
st |
Array with the irregular observational times. |
delta |
Array with the measurements error standard deviations. |
yini |
a single value, initial value for the estimation of the missing value of the time series. |
zero.mean |
logical; if TRUE, the array y has zero mean; if FALSE, y has a mean different from zero. |
standardized |
logical; if TRUE, the array y is standardized; if FALSE, y contains the raw time series. |
A list with the following components:
fitted Estimation of a missing value of the IAR process.
ll Value of the negative log likelihood evaluated in the fitted missing values.
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
set.seed(6714) st<-gentime(n=100) y<-IARsample(phi=0.99,st=st,n=100) y<-y$series phi=IARkalman(y=y,st=st)$phi print(phi) napos=10 y0=y y[napos]=NA xest=phi yest=IARinterpolation(xest,y=y,st=st) yest$fitted mse=(y0[napos]-yest$fitted)^2 print(mse) plot(st,y,type='l',xlim=c(st[napos-5],st[napos+5])) points(st,y,pch=20) points(st[napos],yest$fitted,col="red",pch=20)set.seed(6714) st<-gentime(n=100) y<-IARsample(phi=0.99,st=st,n=100) y<-y$series phi=IARkalman(y=y,st=st)$phi print(phi) napos=10 y0=y y[napos]=NA xest=phi yest=IARinterpolation(xest,y=y,st=st) yest$fitted mse=(y0[napos]-yest$fitted)^2 print(mse) plot(st,y,type='l',xlim=c(st[napos-5],st[napos+5])) points(st,y,pch=20) points(st[napos],yest$fitted,col="red",pch=20)
Maximum Likelihood Estimation of the IAR model parameter phi. The estimation procedure uses the Kalman Filter to find the maximum of the likelihood.
IARkalman(y, st, delta = 0, zero.mean = TRUE, standardized = TRUE)IARkalman(y, st, delta = 0, zero.mean = TRUE, standardized = TRUE)
y |
Array with the time series observations. |
st |
Array with the irregular observational times. |
delta |
Array with the measurements error standard deviations. |
zero.mean |
logical; if TRUE, the array y has zero mean; if FALSE, y has a mean different from zero. |
standardized |
logical; if TRUE, the array y is standardized; if FALSE, y contains the raw time series. |
A list with the following components:
phi MLE of the phi parameter of the IAR model.
ll Value of the negative log likelihood evaluated in phi.
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
gentime, IARsample, arima,IARphikalman
set.seed(6714) st<-gentime(n=100) y<-IARsample(phi=0.99,st=st,n=100) y<-y$series phi=IARkalman(y=y,st=st)$phi print(phi)set.seed(6714) st<-gentime(n=100) y<-IARsample(phi=0.99,st=st,n=100) y<-y$series phi=IARkalman(y=y,st=st)$phi print(phi)
Maximum Likelihood Estimation of the IAR Model.
IARloglik(y, st, delta = 0, zero.mean = TRUE, standardized = TRUE)IARloglik(y, st, delta = 0, zero.mean = TRUE, standardized = TRUE)
y |
Array with the time series observations. |
st |
Array with the irregular observational times. |
delta |
Array with the measurements error standard deviations. |
zero.mean |
logical; if TRUE, the array y has zero mean; if FALSE, y has a mean different from zero. |
standardized |
logical; if TRUE, the array y is standardized; if FALSE, y contains the raw time series. |
A list with the following components:
phi MLE of the phi parameter of the IAR model.
ll Value of the negative log likelihood evaluated in phi.
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
gentime, IARsample, arima, IARphiloglik
#Generating IAR sample set.seed(6714) st<-gentime(n=100) y<-IARsample(phi=0.99,st=st,n=100) y<-y$series #Compute Phi phi=IARloglik(y=y,st=st)$phi print(phi) #Compute the standard deviation of innovations n=length(y) d=c(0,diff(st)) phi1=phi**d yhat=phi1*as.vector(c(0,y[1:(n-1)])) plot(st,y,type='l') lines(st,yhat,col='red') sigma=var(y) nu=c(sigma,sigma*(1-phi1**(2))[-1]) tau<-nu/sigma sigmahat<-mean(c((y-yhat)**2/tau)) nuhat<-sigmahat*(1-phi1**(2)) nuhat2<-sqrt(nuhat) #Equally spaced models require(arfima) fit2<-arfima(y,order=c(1,0,0)) fit<-arima(y,order=c(1,0,0),include.mean=FALSE) syarf<-tacvfARFIMA(phi=fit2$modes[[1]]$phi,dfrac=fit2$modes[[1]]$dfrac, sigma2=fit2$modes[[1]]$sigma,maxlag=20)[1] syar<-fit$sigma/(1-fit$coef[1]**2) print(sigmahat) print(syar) print(syarf) carf<-fit2$modes[[1]]$sigma/syarf car<-(1-fit$coef[1]**2) ciar<-(1-phi1**(2)) #Compute the standard deviation of innovations (regular case) sigma=var(y) nuhat3=sqrt(sigma*ciar) searf<-sqrt(sigma*carf) sear<-sqrt(sigma*car) #Plot the standard deviation of innovations plot(st[-1], nuhat3[-1], t="n", axes=FALSE,xlab='Time',ylab='Standard Deviation of Innovations') axis(1) axis(2) segments(x0=st[-1], y0=nuhat3[-1], y1=0, col=8) points(st, nuhat3, pch=20, col=1, bg=1) abline(h=sd(y),col='red',lwd=2) abline(h=sear,col='blue',lwd=2) abline(h=searf,col='green',lwd=2) abline(h=mean(nuhat3[-1]),col='black',lwd=2)#Generating IAR sample set.seed(6714) st<-gentime(n=100) y<-IARsample(phi=0.99,st=st,n=100) y<-y$series #Compute Phi phi=IARloglik(y=y,st=st)$phi print(phi) #Compute the standard deviation of innovations n=length(y) d=c(0,diff(st)) phi1=phi**d yhat=phi1*as.vector(c(0,y[1:(n-1)])) plot(st,y,type='l') lines(st,yhat,col='red') sigma=var(y) nu=c(sigma,sigma*(1-phi1**(2))[-1]) tau<-nu/sigma sigmahat<-mean(c((y-yhat)**2/tau)) nuhat<-sigmahat*(1-phi1**(2)) nuhat2<-sqrt(nuhat) #Equally spaced models require(arfima) fit2<-arfima(y,order=c(1,0,0)) fit<-arima(y,order=c(1,0,0),include.mean=FALSE) syarf<-tacvfARFIMA(phi=fit2$modes[[1]]$phi,dfrac=fit2$modes[[1]]$dfrac, sigma2=fit2$modes[[1]]$sigma,maxlag=20)[1] syar<-fit$sigma/(1-fit$coef[1]**2) print(sigmahat) print(syar) print(syarf) carf<-fit2$modes[[1]]$sigma/syarf car<-(1-fit$coef[1]**2) ciar<-(1-phi1**(2)) #Compute the standard deviation of innovations (regular case) sigma=var(y) nuhat3=sqrt(sigma*ciar) searf<-sqrt(sigma*carf) sear<-sqrt(sigma*car) #Plot the standard deviation of innovations plot(st[-1], nuhat3[-1], t="n", axes=FALSE,xlab='Time',ylab='Standard Deviation of Innovations') axis(1) axis(2) segments(x0=st[-1], y0=nuhat3[-1], y1=0, col=8) points(st, nuhat3, pch=20, col=1, bg=1) abline(h=sd(y),col='red',lwd=2) abline(h=sear,col='blue',lwd=2) abline(h=searf,col='green',lwd=2) abline(h=mean(nuhat3[-1]),col='black',lwd=2)
This function perform a test for the significance of the autocorrelation estimated by the iAR package models. This test is based in to take N disordered samples of the original data.
IARPermutation( y, st, merr = 0, iter = 100, phi, model = "iAR", plot = TRUE, xlim = c(-1, 0), nu = 3 )IARPermutation( y, st, merr = 0, iter = 100, phi, model = "iAR", plot = TRUE, xlim = c(-1, 0), nu = 3 )
y |
Array with the time series observations. |
st |
Array with the irregular observational times. |
merr |
Array with the variance of the measurement errors. |
iter |
Number of disordered samples of the original data (N). |
phi |
autocorrelation estimated by one of the iAR package models. |
model |
model used to estimate the autocorrelation parameter ("iAR", "iAR-Gamma", "iAR-T", "CiAR" or "BiAR"). |
plot |
logical; if true, the function return a density plot of the distribution of the bad fitted examples; if false, this function does not return a plot. |
xlim |
The x-axis limits (x1, x2) of the plot. Only works if plot='TRUE'. See |
nu |
degrees of freedom parameter of the iAR-T model. |
The null hypothesis of the test is: The autocorrelation coefficient estimated for the time series belongs to the distribution of the coefficients estimated on the disordered data, which are assumed to be uncorrelated. Therefore, if the hypothesis is accepted, it can be concluded that the observations of the time series are uncorrelated.The statistic of the test is log(phi) which was contrasted with a normal distribution with parameters corresponding to the log of the mean and the variance of the phi computed for the N samples of the disordered data. This test differs for IARTest in that to perform this test it is not necessary to know the period of the time series.
A list with the following components:
phi MLE of the autocorrelation parameter of the model.
bad MLEs of the autocorrelation parameters of the models that has been fitted to the disordered samples.
norm Mean and variance of the normal distribution of the disordered data.
z0 Statistic of the test (log(abs(phi))).
pvalue P-value computed for the test.
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
Planets,IARloglik, IARTest, CIARkalman
data(Planets) t<-Planets[,1] res<-Planets[,2] y=res/sqrt(var(res)) res3=IARloglik(y,t,standardized=TRUE)[1] res3$phi set.seed(6713) require(ggplot2) test<-IARPermutation(y=y,st=t,phi=res3$phi,model="iAR",plot=TRUE,xlim=c(-9.6,-9.45))data(Planets) t<-Planets[,1] res<-Planets[,2] y=res/sqrt(var(res)) res3=IARloglik(y,t,standardized=TRUE)[1] res3$phi set.seed(6713) require(ggplot2) test<-IARPermutation(y=y,st=t,phi=res3$phi,model="iAR",plot=TRUE,xlim=c(-9.6,-9.45))
This function return the negative log likelihood of the IAR-Gamma given specific values of phi, mu and sigma.
IARphigamma(yest, x_input, y, st)IARphigamma(yest, x_input, y, st)
yest |
The estimate of a missing value in the time series. This function recognizes a missing value with a NA. If the time series does not have a missing value, this value does not affect the computation of the likelihood. |
x_input |
An array with the parameters of the IAR-Gamma model. The first element of the array corresponding to the phi parameter, the second to the level parameter mu, and the last one to the scale parameter sigma. |
y |
Array with the time series observations. |
st |
Array with the irregular observational times. |
Value of the negative log likelihood evaluated in phi, mu and sigma.
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
n=100 set.seed(6714) st<-gentime(n) y<-IARgsample(phi=0.9,st=st,n=n,sigma2=1,mu=1) IARphigamma(x_input=c(0.9,1,1),y=y$y,st=st,yest=0)n=100 set.seed(6714) st<-gentime(n) y<-IARgsample(phi=0.9,st=st,n=n,sigma2=1,mu=1) IARphigamma(x_input=c(0.9,1,1),y=y$y,st=st,yest=0)
This function return the negative log likelihood of the IAR process given a specific value of phi.
IARphikalman(yest, x, y, yerr, st, zeroMean = TRUE, standardized = TRUE)IARphikalman(yest, x, y, yerr, st, zeroMean = TRUE, standardized = TRUE)
yest |
The estimate of a missing value in the time series. This function recognizes a missing value with a NA. If the time series does not have a missing value, this value does not affect the computation of the likelihood. |
x |
A given phi coefficient of the IAR model. |
y |
Array with the time series observations. |
yerr |
Array with the measurements error standard deviations. |
st |
Array with the irregular observational times. |
zeroMean |
logical; if TRUE, the array y has zero mean; if FALSE, y has a mean different from zero. |
standardized |
logical; if TRUE, the array y is standardized; if FALSE, y contains the raw time series. |
Value of the negative log likelihood evaluated in phi.
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
set.seed(6714) st<-gentime(n=100) y<-IARsample(phi=0.99,st=st,n=100) y<-y$series yerr=rep(0,100) IARphikalman(x=0.8,y=y,yerr=yerr,st=st,yest=0)set.seed(6714) st<-gentime(n=100) y<-IARsample(phi=0.99,st=st,n=100) y<-y$series yerr=rep(0,100) IARphikalman(x=0.8,y=y,yerr=yerr,st=st,yest=0)
This function return the negative log likelihood of the IAR Model for a specific value of phi.
IARphiloglik(x, y, st, delta_input, zeroMean = TRUE, standardized = TRUE)IARphiloglik(x, y, st, delta_input, zeroMean = TRUE, standardized = TRUE)
x |
A given phi coefficient of the IAR model. |
y |
Array with the time series observations. |
st |
Array with the irregular observational times. |
delta_input |
Array with the measurements error standard deviations. |
zeroMean |
logical; if TRUE, the array y has zero mean; if FALSE, y has a mean different from zero. |
standardized |
logical; if TRUE, the array y was standardized; if FALSE, y contains the raw data |
Value of the negative log likelihood evaluated in phi.
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
set.seed(6714) st<-gentime(n=100) y<-IARsample(phi=0.99,st=st,n=100) y<-y$series IARphiloglik(x=0.8,y=y,st=st,delta_input=c(0))set.seed(6714) st<-gentime(n=100) y<-IARsample(phi=0.99,st=st,n=100) y<-y$series IARphiloglik(x=0.8,y=y,st=st,delta_input=c(0))
This function return the negative log likelihood of the IAR-T given specific values of phi and sigma.
IARphit(yest, x, y, st, nu = 3)IARphit(yest, x, y, st, nu = 3)
yest |
The estimate of a missing value in the time series. This function recognizes a missing value with a NA. If the time series does not have a missing value, this value does not affect the computation of the likelihood. |
x |
An array with the parameters of the IAR-T model. The first element of the array corresponding to the phi parameter and the second element to the scale parameter sigma |
y |
Array with the time series observations |
st |
Array with the irregular observational times |
nu |
degrees of freedom |
Value of the negative log likelihood evaluated in phi,sigma and nu.
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
n=300 set.seed(6714) st<-gentime(n) y<-IARtsample(n,0.9,st,sigma2=1,nu=3) IARphit(x=c(0.9,1),y=y$y,st=st,yest=0)n=300 set.seed(6714) st<-gentime(n) y<-IARtsample(n,0.9,st,sigma2=1,nu=3) IARphit(x=c(0.9,1),y=y$y,st=st,yest=0)
Simulates an IAR Time Series Model.
IARsample(phi, st, n = 100L)IARsample(phi, st, n = 100L)
phi |
A coefficient of IAR model. A value between 0 and 1 |
st |
Array with observational times. |
n |
Length of the output time series. A strictly positive integer. |
A list with the following components:
times Array with observation times.
series Array with simulated IAR data.
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
set.seed(6714) st<-gentime(n=100) y<-IARsample(phi=0.99,st=st, n=100) y<-y$series plot(st,y,type='l')set.seed(6714) st<-gentime(n=100) y<-IARsample(phi=0.99,st=st, n=100) y<-y$series plot(st,y,type='l')
Maximum Likelihood Estimation of the IAR-T model.
IARt(y, st, nu = 3)IARt(y, st, nu = 3)
y |
Array with the time series observations |
st |
Array with the irregular observational times |
nu |
degrees of freedom |
A list with the following components:
phi MLE of the phi parameter of the IAR-T model.
sigma MLE of the sigma parameter of the IAR-T model.
ll Value of the negative log likelihood evaluated in phi and sigma.
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
n=300 set.seed(6714) st<-gentime(n) y<-IARtsample(n,0.9,st,sigma2=1,nu=3) model<-IARt(y$y, st=st) phi=model$phi sigmaest=model$sigman=300 set.seed(6714) st<-gentime(n) y<-IARtsample(n,0.9,st,sigma2=1,nu=3) model<-IARt(y$y, st=st) phi=model$phi sigmaest=model$sigma
This function perform a test for the significance of the autocorrelation estimated by the iAR package models. This test is based on the residuals of the periodical time series fitted with an harmonic model using an incorrect period.
IARTest( y, st, merr = 0, f, phi, model = "iAR", plot = TRUE, xlim = c(-1, 0), nu = 3 )IARTest( y, st, merr = 0, f, phi, model = "iAR", plot = TRUE, xlim = c(-1, 0), nu = 3 )
y |
Array with the time series observations. |
st |
Array with the irregular observational times. |
merr |
Array with the variance of the measurement errors. |
f |
Frequency (1/Period) of the raw time series. |
phi |
autocorrelation estimated by one of the iAR package models. |
model |
model used to estimate the autocorrelation parameter ("iAR", "iAR-Gamma", "iAR-T", "CiAR" or "BiAR"). |
plot |
logical; if true, the function return a density plot of the distribution of the bad fitted examples; if false, this function does not return a plot. |
xlim |
The x-axis limits (x1, x2) of the plot. Only works if plot='TRUE'. See |
nu |
degrees of freedom parameter of the iAR-T model. |
The null hypothesis of the test is: The autocorrelation estimated in the time series belongs to the distribution of the coefficients estimated for the residuals of the data fitted using wrong periods. Therefore, if the hypothesis is rejected, it can be concluded that the residuals of the harmonic model do not remain a time dependency structure.The statistic of the test is log(phi) which was contrasted with a normal distribution with parameters corresponding to the log of the mean and the variance of the phi computed for the residuals of the bad fitted light curves.
A list with the following components:
phi MLE of the autocorrelation parameter of the IAR/CIAR model.
bad A matrix with two columns. The first column contains the incorrect frequencies used to fit each harmonic model. The second column has the MLEs of the autocorrelation parameters of the IAR/CIAR model that has been fitted to the residuals of the harmonic model fitted using the frequencies of the first column.
norm Mean and variance of the normal distribution of the bad fitted examples.
z0 Statistic of the test (log(abs(phi))).
pvalue P-value computed for the test.
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
clcep, harmonicfit, IARloglik, CIARkalman,IARPermutation
data(clcep) f1=0.060033386 results=harmonicfit(file=clcep,f1=f1) y=results$res/sqrt(var(results$res)) st=results$t res3=IARloglik(y,st,standardized=TRUE)[1] res3$phi require(ggplot2) test<-IARTest(y=clcep[,2],st=clcep[,1],f=f1,phi=res3$phi,model="iAR",plot=TRUE,xlim=c(-10,0.5)) testdata(clcep) f1=0.060033386 results=harmonicfit(file=clcep,f1=f1) y=results$res/sqrt(var(results$res)) st=results$t res3=IARloglik(y,st,standardized=TRUE)[1] res3$phi require(ggplot2) test<-IARTest(y=clcep[,2],st=clcep[,1],f=f1,phi=res3$phi,model="iAR",plot=TRUE,xlim=c(-10,0.5)) test
Interpolation of missing values from models fitted by IARt
IARtinterpolation(x, y, st, nu = 3, yini = 0)IARtinterpolation(x, y, st, nu = 3, yini = 0)
x |
A given array with the parameters of the IAR-T model. The first element of the array corresponding to the phi parameter and the second element to the scale parameter sigma |
y |
Array with the time series observations. |
st |
Array with the irregular observational times. |
nu |
degrees of freedom |
yini |
a single value, initial value for the estimation of the missing value of the time series. |
A list with the following components:
fitted Estimation of a missing value of the IAR-T process.
ll Value of the negative log likelihood evaluated in the fitted missing values.
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
set.seed(6714) n<-100 st<-gentime(n) y<-IARtsample(n,0.9,st,sigma2=1,nu=3) model<-IARt(y$y, st=st) napos=10 y0=y$y y=y$y y[napos]=NA xest=c(model$phi,model$sigma) yest=IARtinterpolation(x=xest,y=y,st=st) yest$fitted mse=(y0[napos]-yest$fitted)^2 print(mse) plot(st,y,type='l',xlim=c(st[napos-5],st[napos+5])) points(st,y,pch=20) points(st[napos],yest$fitted,col="red",pch=20)set.seed(6714) n<-100 st<-gentime(n) y<-IARtsample(n,0.9,st,sigma2=1,nu=3) model<-IARt(y$y, st=st) napos=10 y0=y$y y=y$y y[napos]=NA xest=c(model$phi,model$sigma) yest=IARtinterpolation(x=xest,y=y,st=st) yest$fitted mse=(y0[napos]-yest$fitted)^2 print(mse) plot(st,y,type='l',xlim=c(st[napos-5],st[napos+5])) points(st,y,pch=20) points(st[napos],yest$fitted,col="red",pch=20)
Simulates an IAR-T Time Series Model.
IARtsample(n, phi, st, sigma2 = 1, nu = 3)IARtsample(n, phi, st, sigma2 = 1, nu = 3)
n |
Length of the output time series. A strictly positive integer. |
phi |
A coefficient of IAR-T model. A value between 0 and 1. |
st |
Array with observational times. |
sigma2 |
Scale parameter of the IAR-T process. A positive value. |
nu |
degrees of freedom. |
A list with the following components:
y Array with simulated IAR-t process.
st Array with observation times.
Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.
n=300 set.seed(6714) st<-gentime(n) y<-IARtsample(n,0.9,st,sigma2=1,nu=3) plot(st,y$y,type='l') hist(y$y,breaks=20)n=300 set.seed(6714) st<-gentime(n) y<-IARtsample(n,0.9,st,sigma2=1,nu=3) plot(st,y$y,type='l') hist(y$y,breaks=20)
Pairing the observational times of two irregularly observed time series
pairingits(lc1, lc2, tol = 0.1)pairingits(lc1, lc2, tol = 0.1)
lc1 |
data frame with three columns corresponding to the first irregularly observed time series. The columns must be ordered as follow: First the observational times, second the measures of each time, and third the measurement errors. |
lc2 |
data frame with three columns corresponding to the second irregularly observed time series. The columns must be ordered as follow: First the observational times, second the measures of each time, and third the measurement errors. |
tol |
tolerance parameter. Minimum time gap to consider that two observations have measured at different times. |
A list with the following components:
n Number of observations paired by their observational times.
parData Frame with the paired datasets.
Elorrieta F, Eyheramendy S, Palma W, Ojeda C (2021). “A novel bivariate autoregressive model for predicting and forecasting irregularly observed time series.” Monthly Notices of the Royal Astronomical Society, 505(1), 1105-1116. ISSN 0035-8711, doi:10.1093/mnras/stab1216, https://academic.oup.com/mnras/article-pdf/505/1/1105/38391762/stab1216.pdf.
data(cvnovag) data(cvnovar) pargr=pairingits(cvnovag,cvnovar,tol=0.1)data(cvnovag) data(cvnovar) pargr=pairingits(cvnovag,cvnovar,tol=0.1)
Time series corresponding to the residuals of the parametric model fitted by Jordan et al (2013) for a transit of an extrasolar planet.
PlanetsPlanets
A data frame with 91 observations on the following 2 variables:
Time from mid-transit (hours).
Residuals of the parametric model fitted by Jordan et al (2013).
Jordán A, Espinoza N, Rabus M, Eyheramendy S, Sing D~K, Désert J, Bakos G~Á, Fortney J~J, López-Morales M, Maxted P~F~L, Triaud A~H~M~J, Szentgyorgyi A (2013). “A Ground-based Optical Transmission Spectrum of WASP-6b.” The Astrophysical Journal, 778, 184. doi:10.1088/0004-637X/778/2/184, 1310.6048.
data(Planets) plot(Planets[,1],Planets[,2],xlab='Time from mid-transit (hours)',ylab='Noise',pch=20)data(Planets) plot(Planets[,1],Planets[,2],xlab='Time from mid-transit (hours)',ylab='Noise',pch=20)