StVAR: Student's t Vector Autoregression (StVAR)

In StVAR: Student's t Vector Autoregression (StVAR)

Description

Maximum likelihood estimation of StVAR model is the purpose of this function. It can be used to estimate the linear autoregressive function (conditional mean) and the quadratic autosckedastic function (conditional variance). Users can specify the model with deterministic variables such as trends and dummies in the matrix form.

Usage

StVAR(Data, Trend=1, lag=1, v=1, maxiter=1000, meth="BFGS", hes="FALSE", init="na")

Arguments

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 optim function (default value is BFGS). See details of optim function.
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.

Details

For the functional form of the autoregressive function and the autoskedastic function, see Spanos (1994) and Poudyal (2012).

Value

beta	coefficients of the autoregressive function including the coefficients of trends in matrix form.
coef	coefficients of the autoregressive function, standard errors and p-values. If some of the standard errors are NA's, the StVAR() function has to be run again.
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	(v/(v+lag*l-2))*sigma*cvar is the fitted value of the autoskedastic function where l is the rank of Data
trends	estimated trends in the variables.
res	nonstandardized residuals
fitted	fitted values of the autoregressive function.
init	estimates of the joint distribution parameters. It can be used as new initial value init in StVAR() to improve optimization further.
hes	the estiamted hessian matrix if hes=TRUE.
S	variance covariance matrix of the joint distribution.
ad	Anderson-Darling test for Student's t distribution.

Author(s)

Niraj Poudyal [e-mail]

References

Poudyal, N. (2012), Confronting Theory with Data: the Case of DSGE Modeling. Doctoral dissertation, Virginia Tech.

Spanos, A. (1994), On Modeling Heteroskedasticity: the Student's t and Elliptical Linear Regression Models. Econometric Theory, 10: 286-315.

Examples

## StVAR Model#####
## Random number seed
set.seed(7504)

## Creating trend variable.
t <- seq(1,100,1)

# Generating data on y and x. 
y <-  0.004 + 0.0045*t - 0.09*t^2 + 0.001*t^3 + 50*rt(100,df=5)
x <-  0.05 - 0.005*t + 0.09*t^2 - 0.001*t^3 + 50*rt(100,df=5)

# The trend matrix
Trend <- cbind(1,poly(t,3,raw=TRUE))

# Estimating the model
stvar <- StVAR(cbind(y,x),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.
d <- dates[2:length(y)]; Y <-  cbind(y[2:length(y)],stvar$fit[,1],stvar$trend[,1])
color <- c("black","blue","black") ; legend <- c("data","trend","fitted values")
cvar <- cbind(stvar$cvar) 
par(mfcol=c(3,1))
matplot(d,Y,xlab="Months",type='l',lty=c(1,2,3),lwd=c(1,1,3),col=color,ylab=" ",xaxt="n")
axis.Date(1,at=seq(as.Date("2014/1/1"), as.Date("2016/1/1"),"months"),labels=TRUE)
legend("bottomleft",legend=legend,lty=c(1,2,3),lwd=c(1,1,3), col=color,cex=.85)
hist(stvar$res[,1],main="Residuals",xlab="",ylab="frequency") ## Histogram of y
matplot(d,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)

Example output

initial  value 8371.417206 
iter  10 value 6378.361607
iter  20 value 4382.841397
iter  30 value 2973.318898
final  value 2562.598461 
converged

StVAR documentation built on May 1, 2019, 8:22 p.m.