| Title: | Test of Periodicity using Response Surface Regression |
|---|---|
| Description: | Tests periodicity in short time series using response surface regression. |
| Authors: | M. S. Islam |
| Maintainer: | M. S. Islam <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 3.1.1 |
| Built: | 2024-10-31 20:37:58 UTC |
| Source: | CRAN |
It tests periodicity for any series using response surface regression (RSR). Whole response surface is integrated in the package. Therefore, one can easily get the pvalue for testing periodicity for any series length. However, the main focus of this algorithm is for short series. Plot for response surface regression for different quantile values can also be obtained.
| Package: pRSR Type: Package Title: Test of Periodicity using Response Surface Regression Version: 3.1.1 Date: 2016-05-12 Author: M. S. Islam Maintainer: M. S. Islam <[email protected]> Depends: R (>= 2.15.1) Description: Tests periodicity in short time series using response surface regression. Moreover, some useful graphs can be produced. License: GPL (>= 2) LazyLoad: yes |
M. S. Islam Maintainer: M. S. Islam <[email protected]>
Islam, M.S. (2008). Peridocity, Change Detection and Prediction in Microarrays. Ph.D. Thesis, The University of Western Ontario.
MacKinnon, J. G. (2002). Computing numerical distribution functions in econometrics. In proceedings of High Performance Computing Systems and Applications, edited by Pollard, A., Mewhort, D. J. and Weaver, D. F. Springer US. Vol. 451, 455-471.
# #Testing periodicity z<-SimulateHReg(20, f=2.5/20, 1, 2) pvalrsr(z) # finding p-value using RSR # For comparing with Fisher's g test # library(GeneCycle) # fisher.g.test(z) # Fisher's g test # Plot for 75%, 90% and 95% quantiles. plotrsr(n=10:50, q=c(75,90,95))# #Testing periodicity z<-SimulateHReg(20, f=2.5/20, 1, 2) pvalrsr(z) # finding p-value using RSR # For comparing with Fisher's g test # library(GeneCycle) # fisher.g.test(z) # Fisher's g test # Plot for 75%, 90% and 95% quantiles. plotrsr(n=10:50, q=c(75,90,95))
Estimates A, B and f in the harmonic regression, y(t)=mu+A*cos(2*pi*f*t)+B*sin(2*pi*f*t)+e(t) using LS.
FitHReg(y, t = 1:length(y), nf=150)FitHReg(y, t = 1:length(y), nf=150)
y |
series |
t |
time points |
nf |
nf, number of frequencies to enumerate |
Program is interfaced to C for efficient computation.
Object of class "HReg" produced. This is a list with components: 'coefficients', 'residuals', 'Rsq', 'fstatistic', 'sigma', 'freq', 'LRStat' corresponding to the 3 regression coefficients, residuals, R-squared, F-statistic, residual sd, optimal frequency and LR-test statistic for null hypothesis white noise.
Islam, M.S. (2008). Peridocity, Change Detection and Prediction in Microarrays. Ph.D. Thesis, The University of Western Ontario.
z<-SimulateHReg(10, f=2.5/10, 1, 2) FitHReg(z)z<-SimulateHReg(10, f=2.5/10, 1, 2) FitHReg(z)
The loglikelihood ratio test statistic is computed for testing for periodicity
GetFitHReg(y, t, nf=150)GetFitHReg(y, t, nf=150)
y |
vector containing the series |
t |
vector of corresponding time points |
nf |
nf, number of frequencies to enumerate |
This function interfaces with C code for fast evaluation.
LR statistic and estimated frequency
Islam, M.S. (2008). Peridocity, Change Detection and Prediction in Microarrays. Ph.D. Thesis, The University of Western Ontario.
#Simple Examples z<-SimulateHReg(10, f=2.5/10, 1, 2) GetFitHReg(z) t<-seq(2,20,2) GetFitHReg(y=z, t=t) GetFitHReg(z, nf=25)#Simple Examples z<-SimulateHReg(10, f=2.5/10, 1, 2) GetFitHReg(z) t<-seq(2,20,2) GetFitHReg(y=z, t=t) GetFitHReg(z, nf=25)
It produces a single plot of response surface regression for different quantile values.
plotrsr(n = 20:50, q = c(90, 95),...)plotrsr(n = 20:50, q = c(90, 95),...)
n |
Sequence of series size for the plot |
q |
Vector or single quantile value |
... |
Further arguments for function lines() |
Plot of RSR
M. S. Islam
MacKinnon, J. G. (2002). Computing numerical distribution functions in econometrics. In proceedings of High Performance Computing Systems and Applications, edited by Pollard, A., Mewhort, D. J. and Weaver, D. F. Springer US. Vol. 451, 455-471.
# Plot for 75%, 90% and 95% quantiles. plotrsr(n=10:50, q=c(75,90,95)) # Plot for 80%, 90%, 95% and 99% quantiles. # We use color red and dashed line plotrsr(n=10:50, q=c(80,90,95, 99), col=2, lty=3)# Plot for 75%, 90% and 95% quantiles. plotrsr(n=10:50, q=c(75,90,95)) # Plot for 80%, 90%, 95% and 99% quantiles. # We use color red and dashed line plotrsr(n=10:50, q=c(80,90,95, 99), col=2, lty=3)
It finds pvalue for tesing periodicity for any series using RSR.
pvalrsr(x, t=1:length(x), nf=150, Numpq = 11)pvalrsr(x, t=1:length(x), nf=150, Numpq = 11)
x |
series to be tested for periodicity |
t |
vector of corresponding time points |
nf |
number of frequencies to enumerate |
Numpq |
Numebr of indices for interpolation in RSR |
A full RSR is integral part of the package. This was done using likelihood ratio statistic for simulated series from white noise process. For more information about the procedure, please see the first reference.
pvalue
M. S. Islam
Islam, M.S. (2008). Peridocity, Change Detection and Prediction in Microarrays. Ph.D. Thesis, The University of Western Ontario.
MacKinnon, J. G. (2001). Computing numerical distribution functions in econometrics. In proceedings of High Performance Computing Systems and Applications, edited by Pollard, A., Mewhort, D. J. and Weaver, D. F. Springer US. Vol. 451, 455-471.
# Non-Fourier frequency z<-SimulateHReg(20, f=2.5/20, 1, 2) pvalrsr(z) # finding p-value using RSR # For comparing with Fisher's g test # library(GeneCycle) # fisher.g.test(z) # Fisher's g test # Fourier frequency y<-SimulateHReg(20, f=2/20, 1, 2) pvalrsr(y) # finding p-value using RSR # For comparing with Fisher's g test # library(GeneCycle) # fisher.g.test(z) # Fisher's g test# Non-Fourier frequency z<-SimulateHReg(20, f=2.5/20, 1, 2) pvalrsr(z) # finding p-value using RSR # For comparing with Fisher's g test # library(GeneCycle) # fisher.g.test(z) # Fisher's g test # Fourier frequency y<-SimulateHReg(20, f=2/20, 1, 2) pvalrsr(y) # finding p-value using RSR # For comparing with Fisher's g test # library(GeneCycle) # fisher.g.test(z) # Fisher's g test
An AR(1) series with mean zero and variance 1 and with autocorrelation paramater phi is simulated.
SimulateAR1(n, phi)SimulateAR1(n, phi)
n |
length of series |
phi |
autocorrelation parameter |
The model equation is:
z[t] = phi*z[t-1]+a[t],
where z[1] is N(0,1) and a[t] are NID(0, siga),
.
autocorrelated time series of length n
e<-SimulateAR1(10^4, phi=0.8) mean(e) sd(e) acf(e, lag.max=5, plot=FALSE)e<-SimulateAR1(10^4, phi=0.8) mean(e) sd(e) acf(e, lag.max=5, plot=FALSE)
Simulates a harmonic regression. Possible error distributions are normal, t(5), t(5,6), AR1.
SimulateHReg(n, f, A, B, simPlot = FALSE, Dist = "n", phi = 0.3)SimulateHReg(n, f, A, B, simPlot = FALSE, Dist = "n", phi = 0.3)
n |
length of series |
f |
frequency |
A |
cosine amplitude |
B |
sine amplitude |
simPlot |
plot simulated series |
Dist |
one of "n" for normal, "t" for t(5), "s" skewed t(5,6), "a" autocorrelated AR1 with parameter phi |
phi |
only used if AR1 error distribution is selected |
This will simulate harmonic hegression
vector of length n, simulated harmonic series
z<-SimulateHReg(10, f=2.5/10, 1, 2) FitHReg(z)z<-SimulateHReg(10, f=2.5/10, 1, 2) FitHReg(z)
Utility function that contains all objects for RSR
data(TPout)data(TPout)
The format is: List of 4 $ qhatM : num [1:341, 1:195] 3.6 3.68 3.73 3.78 3.81 ... $ probs : num [1:341] 1e-04 2e-04 3e-04 4e-04 5e-04 6e-04 7e-04 8e-04 9e-04 1e-03 ... $ n : num [1:33] 6 8 10 12 14 16 18 20 22 24 ... $ MeanVar:List of 1 ..$ :'data.frame': 33 obs. of 682 variables: .. ..$ Qt0.01 : num [1:33] 3.46 3.49 3.53 3.63 3.72 ... .. ..$ Var0.01 : num [1:33] 0.00866 0.01268 0.01014 0.01387 0.01532 ... .. ..$ Qt0.02 : num [1:33] 3.52 3.55 3.6 3.7 3.8 ... .. ..$ Var0.02 : num [1:33] 0.00753 0.00985 0.0067 0.01003 0.01245 ... .. ..$ Qt0.03 : num [1:33] 3.57 3.6 3.65 3.75 3.86 ... .. ..$ Var0.03 : num [1:33] 0.00654 0.00816 0.00577 0.00838 0.00953 ... .. ..$ Qt0.04 : num [1:33] 3.6 3.64 3.7 3.79 3.91 ... .. ..$ Var0.04 : num [1:33] 0.00606 0.00664 0.0058 0.00671 0.0068 ... .. ..$ Qt0.05 : num [1:33] 3.63 3.67 3.73 3.83 3.95 ... .. ..$ Var0.05 : num [1:33] 0.00521 0.00618 0.00455 0.00546 0.00602 ... .. ..$ Qt0.06 : num [1:33] 3.66 3.7 3.76 3.86 3.98 ... .. ..$ Var0.06 : num [1:33] 0.00488 0.00522 0.00435 0.00507 0.00572 ... .. ..$ Qt0.07 : num [1:33] 3.69 3.72 3.78 3.89 4.01 ... .. ..$ Var0.07 : num [1:33] 0.00426 0.00464 0.0041 0.00464 0.00512 ... .. ..$ Qt0.08 : num [1:33] 3.71 3.75 3.81 3.92 4.03 ... .. ..$ Var0.08 : num [1:33] 0.00374 0.00408 0.00395 0.00407 0.00477 ... .. ..$ Qt0.09 : num [1:33] 3.74 3.77 3.83 3.94 4.05 ... .. ..$ Var0.09 : num [1:33] 0.00362 0.00377 0.00384 0.00389 0.00462 ... .. ..$ Qt0.1 : num [1:33] 3.75 3.79 3.85 3.96 4.07 ... .. ..$ Var0.1 : num [1:33] 0.00345 0.00324 0.00364 0.00357 0.00441 ... .. ..$ Qt0.11 : num [1:33] 3.77 3.8 3.87 3.98 4.09 ... .. ..$ Var0.11 : num [1:33] 0.00334 0.00335 0.00344 0.00343 0.00457 ... .. ..$ Qt0.12 : num [1:33] 3.79 3.82 3.89 4 4.11 ... .. ..$ Var0.12 : num [1:33] 0.00308 0.00327 0.00314 0.00316 0.00436 ... .. ..$ Qt0.13 : num [1:33] 3.81 3.84 3.9 4.01 4.13 ... .. ..$ Var0.13 : num [1:33] 0.0029 0.00305 0.00305 0.00318 0.00426 ... .. ..$ Qt0.14 : num [1:33] 3.82 3.85 3.92 4.03 4.14 ... .. ..$ Var0.14 : num [1:33] 0.00285 0.00298 0.00286 0.00308 0.00407 ... .. ..$ Qt0.15 : num [1:33] 3.83 3.87 3.93 4.04 4.16 ... .. ..$ Var0.15 : num [1:33] 0.00284 0.00299 0.00289 0.00301 0.00375 ... .. ..$ Qt0.16 : num [1:33] 3.85 3.88 3.95 4.06 4.17 ... .. ..$ Var0.16 : num [1:33] 0.00286 0.00301 0.00271 0.00299 0.00358 ... .. ..$ Qt0.17 : num [1:33] 3.86 3.89 3.96 4.07 4.18 ... .. ..$ Var0.17 : num [1:33] 0.0028 0.00288 0.00254 0.00304 0.00341 ... .. ..$ Qt0.18 : num [1:33] 3.87 3.9 3.97 4.08 4.2 ... .. ..$ Var0.18 : num [1:33] 0.00271 0.00292 0.00251 0.00289 0.00328 ... .. ..$ Qt0.19 : num [1:33] 3.89 3.92 3.99 4.09 4.21 ... .. ..$ Var0.19 : num [1:33] 0.00267 0.00282 0.00244 0.00281 0.00327 ... .. ..$ Qt0.2 : num [1:33] 3.9 3.93 4 4.1 4.22 ... .. ..$ Var0.2 : num [1:33] 0.00258 0.00272 0.00234 0.00283 0.00311 ... .. ..$ Qt0.21 : num [1:33] 3.91 3.94 4.01 4.11 4.24 ... .. ..$ Var0.21 : num [1:33] 0.00255 0.00248 0.00234 0.00273 0.003 ... .. ..$ Qt0.22 : num [1:33] 3.92 3.95 4.02 4.13 4.25 ... .. ..$ Var0.22 : num [1:33] 0.00242 0.0024 0.00228 0.00254 0.00297 ... .. ..$ Qt0.23 : num [1:33] 3.93 3.96 4.03 4.14 4.26 ... .. ..$ Var0.23 : num [1:33] 0.00239 0.00223 0.00219 0.00249 0.00298 ... .. ..$ Qt0.24 : num [1:33] 3.94 3.97 4.04 4.15 4.27 ... .. ..$ Var0.24 : num [1:33] 0.00238 0.00214 0.00214 0.00237 0.00283 ... .. ..$ Qt0.25 : num [1:33] 3.95 3.98 4.05 4.16 4.28 ... .. ..$ Var0.25 : num [1:33] 0.00239 0.00212 0.00213 0.00233 0.00272 ... .. ..$ Qt0.26 : num [1:33] 3.96 3.99 4.06 4.17 4.28 ... .. ..$ Var0.26 : num [1:33] 0.00241 0.00209 0.00211 0.00227 0.00272 ... .. ..$ Qt0.27 : num [1:33] 3.97 3.99 4.07 4.18 4.29 ... .. ..$ Var0.27 : num [1:33] 0.00233 0.00212 0.00211 0.00211 0.00269 ... .. ..$ Qt0.28 : num [1:33] 3.98 4 4.08 4.19 4.3 ... .. ..$ Var0.28 : num [1:33] 0.0023 0.00209 0.00202 0.00214 0.00262 ... .. ..$ Qt0.29 : num [1:33] 3.99 4.01 4.08 4.2 4.31 ... .. ..$ Var0.29 : num [1:33] 0.00223 0.00205 0.00196 0.00208 0.00254 ... .. ..$ Qt0.3 : num [1:33] 4 4.02 4.09 4.2 4.32 ... .. ..$ Var0.3 : num [1:33] 0.00218 0.00195 0.00198 0.00203 0.00245 ... .. ..$ Qt0.31 : num [1:33] 4.01 4.03 4.1 4.21 4.33 ... .. ..$ Var0.31 : num [1:33] 0.00225 0.00192 0.00194 0.00196 0.00235 ... .. ..$ Qt0.32 : num [1:33] 4.02 4.04 4.11 4.22 4.34 ... .. ..$ Var0.32 : num [1:33] 0.00221 0.00195 0.00192 0.00193 0.00235 ... .. ..$ Qt0.33 : num [1:33] 4.03 4.04 4.12 4.23 4.34 ... .. ..$ Var0.33 : num [1:33] 0.00222 0.00193 0.00192 0.00192 0.00233 ... .. ..$ Qt0.34 : num [1:33] 4.03 4.05 4.13 4.24 4.35 ... .. ..$ Var0.34 : num [1:33] 0.00221 0.00195 0.00191 0.00177 0.00223 ... .. ..$ Qt0.35 : num [1:33] 4.04 4.06 4.13 4.24 4.36 ... .. ..$ Var0.35 : num [1:33] 0.00221 0.00198 0.00196 0.00179 0.00216 ... .. ..$ Qt0.36 : num [1:33] 4.05 4.07 4.14 4.25 4.37 ... .. ..$ Var0.36 : num [1:33] 0.00214 0.00198 0.00195 0.00183 0.00218 ... .. ..$ Qt0.37 : num [1:33] 4.06 4.07 4.15 4.26 4.37 ... .. ..$ Var0.37 : num [1:33] 0.0021 0.00201 0.00195 0.00174 0.00212 ... .. ..$ Qt0.38 : num [1:33] 4.07 4.08 4.16 4.27 4.38 ... .. ..$ Var0.38 : num [1:33] 0.00207 0.00203 0.00196 0.0017 0.00209 ... .. ..$ Qt0.39 : num [1:33] 4.07 4.09 4.16 4.27 4.39 ... .. ..$ Var0.39 : num [1:33] 0.00198 0.00194 0.00194 0.00169 0.00207 ... .. ..$ Qt0.4 : num [1:33] 4.08 4.09 4.17 4.28 4.39 ... .. ..$ Var0.4 : num [1:33] 0.00198 0.00191 0.00191 0.00169 0.00207 ... .. ..$ Qt0.41 : num [1:33] 4.09 4.1 4.18 4.29 4.4 ... .. ..$ Var0.41 : num [1:33] 0.00198 0.00187 0.00187 0.00161 0.00199 ... .. ..$ Qt0.42 : num [1:33] 4.09 4.11 4.18 4.29 4.41 ... .. ..$ Var0.42 : num [1:33] 0.00196 0.00185 0.00183 0.00162 0.00199 ... .. ..$ Qt0.43 : num [1:33] 4.1 4.11 4.19 4.3 4.41 ... .. ..$ Var0.43 : num [1:33] 0.00197 0.0018 0.00183 0.00159 0.00192 ... .. ..$ Qt0.44 : num [1:33] 4.11 4.12 4.2 4.31 4.42 ... .. ..$ Var0.44 : num [1:33] 0.002 0.00181 0.00181 0.00159 0.00193 ... .. ..$ Qt0.45 : num [1:33] 4.12 4.12 4.2 4.31 4.43 ... .. ..$ Var0.45 : num [1:33] 0.00195 0.00183 0.00186 0.00163 0.00185 ... .. ..$ Qt0.46 : num [1:33] 4.12 4.13 4.21 4.32 4.43 ... .. ..$ Var0.46 : num [1:33] 0.00192 0.00185 0.0018 0.00156 0.00182 ... .. ..$ Qt0.47 : num [1:33] 4.13 4.14 4.22 4.33 4.44 ... .. ..$ Var0.47 : num [1:33] 0.0019 0.00184 0.00182 0.00155 0.0018 ... .. ..$ Qt0.48 : num [1:33] 4.13 4.14 4.22 4.33 4.45 ... .. ..$ Var0.48 : num [1:33] 0.00186 0.00188 0.00187 0.00157 0.00176 ... .. ..$ Qt0.49 : num [1:33] 4.14 4.15 4.23 4.34 4.45 ... .. ..$ Var0.49 : num [1:33] 0.00186 0.00184 0.00182 0.00151 0.0017 ... .. ..$ Qt0.5 : num [1:33] 4.15 4.15 4.23 4.34 4.46 ... .. .. [list output truncated]
MacKinnon, J. G. (2002). Computing numerical distribution functions in econometrics. In proceedings of High Performance Computing Systems and Applications, edited by Pollard, A., Mewhort, D. J. and Weaver, D. F. Springer US. Vol. 451, 455-47