| Title: | Student's t Regression Models |
|---|---|
| Description: | It contains functions to estimate multivariate Student's t dynamic and static regression models for given degrees of freedom and lag length. Users can also specify the trends and dummies of any kind in matrix form. Poudyal, N., and Spanos, A. (2022) <doi:10.3390/econometrics10020017>. Spanos, A. (1994) <http://www.jstor.org/stable/3532870>. |
| Authors: | Niraj Poudyal [aut, cre] |
| Maintainer: | Niraj Poudyal <[email protected]> |
| License: | GPL-2 |
| Version: | 1.1 |
| Built: | 2024-12-09 06:49:30 UTC |
| Source: | CRAN |
Maximum likelihood estimation of Student's t autoregression model is the purpose of this function. It can be used to estimate the linear autoregressive function (conditional mean) and the quadratic autoskedastic function (conditional variance). Users can specify the model with deterministic variables such as trends and dummies in matrix form.
StAR(Data,Trend=1,lag=1,v=1,maxiter=1000,meth="BFGS",hes="FALSE",init="na")StAR(Data,Trend=1,lag=1,v=1,maxiter=1000,meth="BFGS",hes="FALSE",init="na")
Data |
A data vector with one column. Cannot be empty. |
Trend |
A matrix with columns representing deterministic variables like trends and dummies. If 1 (default), model with only constant intercept is estimated. If 0, the model is estimated without an intercept term. |
lag |
A positive integer (default value is 1) as lag length. |
v |
A scalar (default value is 1) greater than or equal to 1. Degrees of freedom parameter. |
maxiter |
Maximum number of iteration. Must be an integer bigger than 10. |
meth |
One of the optimization method from |
hes |
Logical (default value is FALSE). If TRUE produces estimated hessian matrix and the standard errors of estimates. |
init |
If na (default), initial values for optimization are generated from a uniform distribution. A vector of initial values can also be used (not recommended). The length of the init vector must be equal to the number of parameters of the joint distribution. |
For the functional form of the autoregressive function and the autoskedastic function, see Spanos (1994) and Poudyal (2012).
beta |
coefficients of the autoregressive function including the coefficients of trends in matrix form with standard errors and p-values. If some of the standard errors are
NA's, the |
var.coef |
coefficients of the autoregressive function, standard errors and p-values if |
like |
maximum log likelihood value. |
sigma |
contemporary variance covariance matrix. |
cvar |
|
trend |
estimated trend in the variables. |
res |
non-standardized residuals |
fitted |
fitted values of the autoregressive function. |
init |
estimates of the joint distribution parameters. It can be used as new initial value |
hes |
estimated hessian matrix. |
S |
variance covariance matrix of the joint distribution. |
R.squared |
R-squared of the model. |
F.stat |
F-statistics of the model. |
ad |
Anderson-Darling test for Student's t distribution. |
Niraj Poudyal [email protected]
Poudyal, N. and Spanos, A. (2022), Model Validation and DSGE Modeling. Econometrics, 10 (2), 17.
Spanos, A. (1994), On Modeling Heteroskedasticity: the Student's t and Elliptical Linear Regression Models. Econometric Theory, 10: 286-315.
## StAR Model##### ## Random number seed set.seed(4093) ## Creating trend variable. t <- seq(1,50,1) # Generating data on y. y <- 0.004 + 0.0045*t - 0.09*t^2 + 50*rt(50,df=5) T <- length(y) # The trend matrix Trend <- cbind(1,poly(t,2,raw=TRUE)) # Estimating the model star <- StAR(y,lag=1,Trend=Trend,v=5,maxiter=2000) # Generate arbitrary dates dates <- seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "weeks") ## Plotting the variable y, its estimated trend and the fitted value. oldpar <- par(mfcol=c(3,1)) matplot(dates[2:T],cbind(y[2:T],star$fitted,star$trend),xlab="Months",type='l', lty=c(1,2,3),lwd=c(1,1,3),col=c("black","blue","black"),ylab=" ",xaxt="n") axis.Date(1, at = seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "months"),labels=TRUE) legend("bottomleft",legend=c("data","trend","fitted values"),lty=c(1,2,3),lwd=c(1,1,3), col=c("black","blue","black"),cex=.85) hist(star$res,main="",xlab="") ## Histogram of y matplot(dates[2:T],cbind(star$cvar),xlab="Months",type='l',lty=2,lwd=1, ylab="fitted variance",xaxt="n") axis.Date(1,at=seq(as.Date("2014/1/1"),as.Date("2016/1/1"),"months"),labels=TRUE) par(oldpar)## StAR Model##### ## Random number seed set.seed(4093) ## Creating trend variable. t <- seq(1,50,1) # Generating data on y. y <- 0.004 + 0.0045*t - 0.09*t^2 + 50*rt(50,df=5) T <- length(y) # The trend matrix Trend <- cbind(1,poly(t,2,raw=TRUE)) # Estimating the model star <- StAR(y,lag=1,Trend=Trend,v=5,maxiter=2000) # Generate arbitrary dates dates <- seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "weeks") ## Plotting the variable y, its estimated trend and the fitted value. oldpar <- par(mfcol=c(3,1)) matplot(dates[2:T],cbind(y[2:T],star$fitted,star$trend),xlab="Months",type='l', lty=c(1,2,3),lwd=c(1,1,3),col=c("black","blue","black"),ylab=" ",xaxt="n") axis.Date(1, at = seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "months"),labels=TRUE) legend("bottomleft",legend=c("data","trend","fitted values"),lty=c(1,2,3),lwd=c(1,1,3), col=c("black","blue","black"),cex=.85) hist(star$res,main="",xlab="") ## Histogram of y matplot(dates[2:T],cbind(star$cvar),xlab="Months",type='l',lty=2,lwd=1, ylab="fitted variance",xaxt="n") axis.Date(1,at=seq(as.Date("2014/1/1"),as.Date("2016/1/1"),"months"),labels=TRUE) par(oldpar)
Maximum likelihood estimation of Student's t dynamic linear regression model is the purpose of this function. It can be used to estimate the dynamic linear autoregressive function (conditional mean) and the quadratic autoskedastic function (conditional variance). Users can specify the model with deterministic variables such as trends and dummies in the matrix form.
StDLM(y,X,Trend=1,lag=1,v=1,maxiter=1000,meth="BFGS",hes="FALSE",init="na")StDLM(y,X,Trend=1,lag=1,v=1,maxiter=1000,meth="BFGS",hes="FALSE",init="na")
y |
A vector representing dependent variable. Cannot be empty. |
X |
A data matrix whose columns represent exogenous variables. Cannot be empty. |
Trend |
A matrix with columns representing deterministic variables like trends and dummies. If 1 (default), model with only constant intercept is estimated. If 0, the model is estimated without an intercept term. |
lag |
A non-negative integer (default value is 1) as lag length. If lag=0, a static model is estimated. |
v |
A scalar (default value is 1) greater than or equal to 1. Degrees of freedom parameter. |
maxiter |
Maximum number of iteration. Must be an integer bigger than 10. |
meth |
One of the optimization method from |
hes |
Logical (default value is FALSE). If TRUE produces estimated hessian matrix and the standard errors of estimates. |
init |
If na (default), initial values for optimization are generated from a uniform distribution. A vector of initial values can also be used (not recommended). The length of the init vector must be equal to the number of parameters of the joint distribution. |
For the functional form of the autoregressive function and the autoskedastic function, see Spanos (1994) and Poudyal (2012).
beta |
coefficients of the dynamic linear regression model including the coefficients of trends in matrix form with standard errors and p-values. If some of the standard errors are
NA's, the |
var.coef |
coefficients of the autoskedastic function, standard errors and p-values if if |
like |
maximum log likelihood value. |
sigma |
contemporary variance covariance matrix. |
cvar |
|
trend |
estimated trend in the variable y. |
res |
non-standardized residuals |
fitted |
fitted values of the autoregressive function. |
init |
estimates of the joint distribution parameters. It can be used as new initial value |
S |
variance covariance matrix of the joint distribution. |
R.squared |
R-squared of the model. |
F.stat |
F-statistics of the model. |
ad |
Anderson-Darling test for Student's t distribution. |
Niraj Poudyal [email protected]
Poudyal, N. and Spanos, A. (2022), Model Validation and DSGE Modeling. Econometrics, 10 (2), 17.
Spanos, A. (1994), On Modeling Heteroskedasticity: the Student's t and Elliptical Linear Regression Models. Econometric Theory, 10: 286-315.
## StDLM Model##### ## Random number seed set.seed(7504) ## Creating trend variable. t <- seq(1,100,1) ut <- rt(100,df=5) # Generating data on y, x and z. y <- 0.004 + 0.0045*t - 0.09*t^2 + 0.001*t^3 + 50*ut x <- 0.05 - 0.005*t + 0.09*t^2 - 0.001*t^3 + 40*ut z <- 0.08 - 0.006*t + 0.08*t^2 - 0.001*t^3 + 30*ut # The trend matrix Trend <- cbind(1,poly(t,3,raw=TRUE)) # Estimating the model stdlrm <- StDLM(y,cbind(x,z),lag=1,Trend=Trend,v=5,maxiter=2000) # Generate arbitrary dates dates <- seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "weeks") ## Plotting the variable y, its estimated trend and the fitted value. lag <- 1 oldpar <- par(mfcol=c(3,1)) matplot(dates[(lag+1):length(y)],cbind(y[(lag+1):length(y)],stdlrm$fit,stdlrm$trend), xlab="Months",type='l',lty=c(1,2,3),lwd=c(1,1,3),col=c("black","blue","black"),ylab=" ",xaxt="n") axis.Date(1, at = seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "months"),labels=TRUE) legend("bottomleft",legend=c("data","trend","fitted values"),lty=c(1,2,3),lwd=c(1,1,3), col=c("black","blue","black"),cex=.85) hist(stdlrm$res,main="",xlab="") ## Histogram of y matplot(dates[2:length(y)],cbind(stdlrm$cvar),xlab="Months",type='l',lty=2,lwd=1, ylab="fitted variance",xaxt="n") axis.Date(1, at = seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "months"),labels=TRUE) par(oldpar)## StDLM Model##### ## Random number seed set.seed(7504) ## Creating trend variable. t <- seq(1,100,1) ut <- rt(100,df=5) # Generating data on y, x and z. y <- 0.004 + 0.0045*t - 0.09*t^2 + 0.001*t^3 + 50*ut x <- 0.05 - 0.005*t + 0.09*t^2 - 0.001*t^3 + 40*ut z <- 0.08 - 0.006*t + 0.08*t^2 - 0.001*t^3 + 30*ut # The trend matrix Trend <- cbind(1,poly(t,3,raw=TRUE)) # Estimating the model stdlrm <- StDLM(y,cbind(x,z),lag=1,Trend=Trend,v=5,maxiter=2000) # Generate arbitrary dates dates <- seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "weeks") ## Plotting the variable y, its estimated trend and the fitted value. lag <- 1 oldpar <- par(mfcol=c(3,1)) matplot(dates[(lag+1):length(y)],cbind(y[(lag+1):length(y)],stdlrm$fit,stdlrm$trend), xlab="Months",type='l',lty=c(1,2,3),lwd=c(1,1,3),col=c("black","blue","black"),ylab=" ",xaxt="n") axis.Date(1, at = seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "months"),labels=TRUE) legend("bottomleft",legend=c("data","trend","fitted values"),lty=c(1,2,3),lwd=c(1,1,3), col=c("black","blue","black"),cex=.85) hist(stdlrm$res,main="",xlab="") ## Histogram of y matplot(dates[2:length(y)],cbind(stdlrm$cvar),xlab="Months",type='l',lty=2,lwd=1, ylab="fitted variance",xaxt="n") axis.Date(1, at = seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "months"),labels=TRUE) par(oldpar)
Maximum likelihood estimation of Student's t linear regression model is the purpose of this function. It can be used to estimate the linear regression function (conditional mean) and the quadratic skedastic function (conditional variance). Users can specify the model with deterministic variables such as trends and dummies in the matrix form.
StLM(y,X,Trend=1,v=1,maxiter=1000,meth="BFGS",hes="FALSE",init="na")StLM(y,X,Trend=1,v=1,maxiter=1000,meth="BFGS",hes="FALSE",init="na")
y |
A vector representing dependent variable. Cannot be empty. |
X |
A data matrix whose columns represent exogenous variables. Cannot be empty. |
Trend |
A matrix with columns representing deterministic variables like trends and dummies. If 1 (default), model with only constant intercept is estimated. If 0, the model is estimated without an intercept term. |
v |
A scalar (default value is 1) greater than or equal to 1. Degrees of freedom parameter. |
maxiter |
Maximum number of iteration. Must be an integer bigger than 10. |
meth |
One of the optimization method from |
hes |
Logical (default value is FALSE). If TRUE produces estimated hessian matrix and the standard errors of estimates. |
init |
If na (default), initial values for optimization are generated from a uniform distribution. A vector of initial values can also be used (not recommended). The length of the init vector must be equal to the number of parameters of the joint distribution. |
For the functional form of the regression function and the skedastic function, see Spanos (1994) and Poudyal (2012).
beta |
coefficients of the regression function including the coefficients of trends in matrix form with standard errors and p-values. If some of the standard errors are
NA's, the |
var.coef |
coefficients of the skedastic function, standard errors and p-values if if |
like |
maximum log likelihood value. |
sigma |
contemporary variance covariance matrix. |
cvar |
|
trend |
estimated trend in the variable y. |
res |
non-standardized residuals |
fitted |
fitted values of the regression function. |
init |
estimates of the joint distribution parameters. It can be used as new initial value |
S |
variance covariance matrix of the joint distribution. |
R.squared |
R-squared of the model. |
F.stat |
F-statistics of the model. |
ad |
Anderson-Darling test for Student's t distribution. |
Niraj Poudyal [email protected]
Poudyal, N. and Spanos, A. (2022), Model Validation and DSGE Modeling. Econometrics, 10 (2), 17.
Spanos, A. (1994), On Modeling Heteroskedasticity: the Student's t and Elliptical Linear Regression Models. Econometric Theory, 10: 286-315.
## stlm Model##### ## Random number seed set.seed(7504) ## Creating trend variable. t <- seq(1,50,1) # Generating data on y, x and z. x <- rt(50,df=5) ; set.seed(7505) z <- 5*rt(50,df=5) ; set.seed(7506) y <- 4 + 0.045*t + 2*x + 5*z + rt(50,25,df=5) # The trend matrix Trend <- cbind(1,poly(t,1,raw=FALSE)) colnames(Trend) <- c("const","t") # Estimating the model stlrm <- StLM(y,cbind(x,z),Trend=Trend,v=5,maxiter=2000) # Generate arbitrary dates dates <- seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "weeks") ## Plotting the variable y, its estimated trend and the fitted value. oldpar <- par(mfcol=c(3,1)) matplot(dates[1:length(y)],cbind(y[1:length(y)],stlrm$fit,stlrm$trend),xlab="Months", type='l',lty=c(1,2,3),lwd=c(1,1,3),col=c("black","blue","black"),ylab=" ",xaxt="n") axis.Date(1, at = seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "months"),labels=TRUE) legend("bottomleft",legend=c("data","trend","fitted values"),lty=c(1,2,3),lwd=c(1,1,3), col=c("black","blue","black"),cex=.85) hist(stlrm$res,main="",xlab="") ## Histogram of y matplot(dates[1:length(y)],cbind(stlrm$cvar),xlab="Months",type='l',lty=2,lwd=1, ylab="fitted variance",xaxt="n") axis.Date(1, at = seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "months"),labels=TRUE) par(oldpar)## stlm Model##### ## Random number seed set.seed(7504) ## Creating trend variable. t <- seq(1,50,1) # Generating data on y, x and z. x <- rt(50,df=5) ; set.seed(7505) z <- 5*rt(50,df=5) ; set.seed(7506) y <- 4 + 0.045*t + 2*x + 5*z + rt(50,25,df=5) # The trend matrix Trend <- cbind(1,poly(t,1,raw=FALSE)) colnames(Trend) <- c("const","t") # Estimating the model stlrm <- StLM(y,cbind(x,z),Trend=Trend,v=5,maxiter=2000) # Generate arbitrary dates dates <- seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "weeks") ## Plotting the variable y, its estimated trend and the fitted value. oldpar <- par(mfcol=c(3,1)) matplot(dates[1:length(y)],cbind(y[1:length(y)],stlrm$fit,stlrm$trend),xlab="Months", type='l',lty=c(1,2,3),lwd=c(1,1,3),col=c("black","blue","black"),ylab=" ",xaxt="n") axis.Date(1, at = seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "months"),labels=TRUE) legend("bottomleft",legend=c("data","trend","fitted values"),lty=c(1,2,3),lwd=c(1,1,3), col=c("black","blue","black"),cex=.85) hist(stlrm$res,main="",xlab="") ## Histogram of y matplot(dates[1:length(y)],cbind(stlrm$cvar),xlab="Months",type='l',lty=2,lwd=1, ylab="fitted variance",xaxt="n") axis.Date(1, at = seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "months"),labels=TRUE) par(oldpar)
Maximum likelihood estimation of Student's t vector autoregression (VAR) model is the purpose of this function. It can be used to estimate the linear autoregressive function (conditional mean) and the quadratic autoskedastic function (conditional variance). Users can specify the model with deterministic variables such as trends and dummies in the matrix form.
StVAR(Data,Trend=1,lag=1,v=1,maxiter=1000,meth="BFGS",hes="FALSE",init="na")StVAR(Data,Trend=1,lag=1,v=1,maxiter=1000,meth="BFGS",hes="FALSE",init="na")
Data |
A data matrix with at least two columns. Cannot be empty. |
Trend |
A matrix with columns representing deterministic variables like trends and dummies. If 1 (default), model with only constant intercept is estimated. If 0, the model is estimated without the intercept term. |
lag |
A positive integer (default value is 1) as lag length. |
v |
A scalar (default value is 1) greater than or equal to 1. Degrees of freedom parameter. |
maxiter |
Maximum number of iteration. Must be an integer bigger than 10. |
meth |
One of the optimization method from |
hes |
Logical (default value is FALSE). If TRUE produces estimated hessian matrix and the standard errors of estimates. |
init |
If na (default), initial values for optimization are generated from a uniform distribution. A vector of initial values can also be used (not recommended). The length of the init vector must be equal to the number of parameters of the joint distribution. |
For the functional form of the autoregressive function and the autoskedastic function, see Spanos (1994) and Poudyal (2012).
beta |
coefficients of the autoregressive function including the coefficients of trends in matrix form with standard errors and p-values. If some of the standard errors are
NA's, the |
var.coef |
coefficients of the autoskedastic (conditional variance) function, standard errors and p-values. |
like |
maximum log likelihood value. |
sigma |
contemporary variance-covariance matrix. |
cvar |
|
trends |
estimated trends in the variables. |
res |
non-standardized residuals. |
fitted |
fitted values of the autoregressive function. |
init |
estimates of the joint distribution parameters. It can be used as new initial value |
hes |
the estimated hessian matrix if |
S |
variance covariance matrix of the joint distribution. |
R.squared |
R-squared of each equation of the model. |
F.stat |
F-statistics of each equation of the model. |
ad |
Anderson-Darling test for Student's t distribution. |
Niraj Poudyal [email protected]
Poudyal, N. and Spanos, A. (2022), Model Validation and DSGE Modeling. Econometrics, 10 (2), 17.
Spanos, A. (1994), On Modeling Heteroskedasticity: the Student's t and Elliptical Linear Regression Models. Econometric Theory, 10: 286-315.
## StVAR Model##### ## Random number seed set.seed(7504) ## Creating trend variable. t <- seq(1,50,1) y <- x <- vector(length=50) y[1] <- x[1] <- 0 # Generating data on y and x. ut <- rt(50,df=5) for(i in 2:50) { y[i] <- 0.004 + 0.0045*t[i] - 0.9*y[i-1] + .2*x[i-1] + ut[i] x[i] <- 0.05 - 0.005*t[i] + 0.8*x[i-1] + 1*y[i-1] + ut[i] } # The trend matrix Trend <- cbind(1,t) # Estimating the model stvar <- StVAR(cbind(y,x),lag=1,Trend=Trend,v=6,maxiter=2000,hes=TRUE) # Generate arbitrary dates dates <- seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "weeks") ## Plotting the variable y, its estimated trend and the fitted value. oldpar <- par(mfcol=c(3,1)) matplot(dates[2:length(y)],cbind(y[2:length(y)],stvar$fit[,1],stvar$trend[,1]),xlab="Months", type='l',lty=c(1,2,3), lwd=c(1,1,3),col=c("black","blue","black"),ylab=" ",xaxt="n") axis.Date(1, at = seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "months"),labels=TRUE) legend("bottomleft",legend=c("data","trend","fitted values"),lty=c(1,2,3),lwd=c(1,1,3), col=c("black","blue","black"),cex=.85) hist(stvar$res[,1],main="",xlab="") ## Histogram of y matplot(dates[2:length(y)],cbind(stvar$cvar),xlab="Months",type='l',lty=2,lwd=1, ylab="fitted variance",xaxt="n") axis.Date(1, at = seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "months"),labels=TRUE) par(oldpar) ## Plotting the variable x, its estimated trend and the fitted value. oldpar <- par(mfcol=c(3,1)) matplot(dates[2:length(x)],cbind(x[2:length(x)],stvar$fit[,2],stvar$trend[,2]), xlab="Months",type='l',lty=c(1,2,3),lwd=c(1,1,3),col=c("black","blue","black"),ylab=" ",xaxt="n") axis.Date(1, at = seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "months"),labels=TRUE) legend("bottomleft",legend=c("data","trend","fitted values"),lty=c(1,2,3),lwd=c(1,1,3), col=c("black","blue","black"),cex=.85) hist(stvar$res[,2],main="",xlab="") ## Histogram of x matplot(dates[2:length(x)],cbind(stvar$cvar),xlab="Months",type='l',lty=2,lwd=1, ylab="fitted variance",xaxt="n") axis.Date(1,at=seq(as.Date("2014/1/1"),as.Date("2016/1/1"),"months"),labels=TRUE) par(oldpar)## StVAR Model##### ## Random number seed set.seed(7504) ## Creating trend variable. t <- seq(1,50,1) y <- x <- vector(length=50) y[1] <- x[1] <- 0 # Generating data on y and x. ut <- rt(50,df=5) for(i in 2:50) { y[i] <- 0.004 + 0.0045*t[i] - 0.9*y[i-1] + .2*x[i-1] + ut[i] x[i] <- 0.05 - 0.005*t[i] + 0.8*x[i-1] + 1*y[i-1] + ut[i] } # The trend matrix Trend <- cbind(1,t) # Estimating the model stvar <- StVAR(cbind(y,x),lag=1,Trend=Trend,v=6,maxiter=2000,hes=TRUE) # Generate arbitrary dates dates <- seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "weeks") ## Plotting the variable y, its estimated trend and the fitted value. oldpar <- par(mfcol=c(3,1)) matplot(dates[2:length(y)],cbind(y[2:length(y)],stvar$fit[,1],stvar$trend[,1]),xlab="Months", type='l',lty=c(1,2,3), lwd=c(1,1,3),col=c("black","blue","black"),ylab=" ",xaxt="n") axis.Date(1, at = seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "months"),labels=TRUE) legend("bottomleft",legend=c("data","trend","fitted values"),lty=c(1,2,3),lwd=c(1,1,3), col=c("black","blue","black"),cex=.85) hist(stvar$res[,1],main="",xlab="") ## Histogram of y matplot(dates[2:length(y)],cbind(stvar$cvar),xlab="Months",type='l',lty=2,lwd=1, ylab="fitted variance",xaxt="n") axis.Date(1, at = seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "months"),labels=TRUE) par(oldpar) ## Plotting the variable x, its estimated trend and the fitted value. oldpar <- par(mfcol=c(3,1)) matplot(dates[2:length(x)],cbind(x[2:length(x)],stvar$fit[,2],stvar$trend[,2]), xlab="Months",type='l',lty=c(1,2,3),lwd=c(1,1,3),col=c("black","blue","black"),ylab=" ",xaxt="n") axis.Date(1, at = seq(as.Date("2014/1/1"), as.Date("2016/1/1"), "months"),labels=TRUE) legend("bottomleft",legend=c("data","trend","fitted values"),lty=c(1,2,3),lwd=c(1,1,3), col=c("black","blue","black"),cex=.85) hist(stvar$res[,2],main="",xlab="") ## Histogram of x matplot(dates[2:length(x)],cbind(stvar$cvar),xlab="Months",type='l',lty=2,lwd=1, ylab="fitted variance",xaxt="n") axis.Date(1,at=seq(as.Date("2014/1/1"),as.Date("2016/1/1"),"months"),labels=TRUE) par(oldpar)