StDLRM: Student's t Dynamic Linear Regression Model (StDLRM)

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

Description

Maximum likelihood estimation of StDLRM model is the purpose of this function. It can be used to estimate the dynamc 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

StDLRM(y, X, Trend=1, lag=1, v=1, maxiter=1000, meth="BFGS", hes="FALSE", init="na")

Arguments

y	A vector representing dependent variable. Cannot be empty.
X	A data matrix whose columns represent exogeneous 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 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 hes=TRUE. If some of the standard errors are NA's, the StVAR() function has to be run again.
var.coef	coefficients of the autoskedastic function, standard errors and p-values if if hes=TRUE
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
trend	estimated trend in the variable y.
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.
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

## StDLRM 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)
z <-  0.08 - 0.006*t + 0.08*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
stdlrm <- StDLRM(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. 
d <- dates[2:length(y)] ; Y <- cbind(y[2:length(y)],stdlrm$fit,stdlrm$trend)
color <- c("black","blue","black") ; legend <- c("data","trend","fitted values")
cvar <- cbind(stdlrm$cvar)
par(mfcol=c(3,1))
matplot(d,Y,xlab="Months",type='l',lty=c(1,2,3),lwd=c(1,1,3),col=color,ylab=" ",xaxt="n")
axis.Date(1,at=seq(as.Date("2014/1/1"), as.Date("2016/1/1"),"months"),labels=TRUE)
legend("bottomleft",legend=legend,lty=c(1,2,3),lwd=c(1,1,3),col=color,cex=.85)
hist(stdlrm$res,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 9774.851659 
iter  10 value 7794.556597
iter  20 value 5384.000090
final  value 4810.234469 
converged

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