Variance of the coefficient path

Takes an 'isat' object returned by the isat function as input and returns the coefficient path of the constant (and long-run equilibrium if 'lr' is specified) together with its approximate variance and standard errors. If mxfull and mxbreak are specified, then the function returns the coefficient path of the user-specified variable.

Usage

isatvar(x, lr=FALSE, conscorr=FALSE, effcorr=FALSE, mcor = 1, 
    mxfull = NULL, mxbreak=NULL)

Arguments

x: a 'gets' object obtained with the isat function
lr: logical. If TRUE and 'x' contains autoregressive elements, then isatvar also returns the long-run equilibrium coefficient path with its variance and standard deviation. See Pretis (2015).
conscorr: logical. If TRUE then the Johansen and Nielsen (2016) impulse-indicator consistency correction is applied to estimated residual variance.
effcorr: logical. If TRUE then the Johansen and Nielsen (2016) m-step efficiency correction is applied to estimated standard errors of `fixed' regressors.
mcor: integer. The m-step efficiency correction factor, where m=mcor.
mxfull: string. The name of the full-sample variable when constructing the coefficient path of user-specified break variables.
mxbreak: string. The name of the break variables used to construct the coefficient path of user-specified break variables.

Details

The function computes the approximate variance and standard errors of the intercept term with structural breaks determined by isat. This permits hypothesis testing and plotting of approximate confidence intervals for the intercept in the presence of structural breaks. For dynamic autoregressive models in isat the lr argument returns the time-varying long-run equilibrium together with its approximate variance and standard errors. If mxfull and mxbreak are specified, then the function returns the coefficient path of the user-specified variable, where mxfull denotes the ful-sample variable name, to which the mxbreak variables are added. To correct for the under-estimation of the residual variance, the argument conscorr implements the Johansen and Nielsen (2016) consistency correction, and effcorr adds the efficiency correction for standard errors on fixed regressors which are not selected over.

Value

If lr=FALSE: A Tx4 matrix (with T = number of observations) where the first column denotes the coefficient path relative to the full sample coefficient, the second column the coefficient path of the intercept, the third the approximate variance of the coefficient path, and the fourth column the approximate standard errors of the coefficient path. If lr=TRUE: A Tx7 matrix where the first four columns are identical to the lr=FALSE case, and the additional columns denote the long-run equilibrium coefficient path, together with the approximate variance and standard errors of the long-run equilibrium coefficient path.

References

Pretis, F. (2015): 'Testing for time-varying predictive accuracy using bias-corrected indicator saturation'. Oxford Department of Economics ???orking Paper.

Johansen, S., & Nielsen, B. (2016): 'Asymptotic theory of outlier detection algorithms for linear time series regression models.' Scandinavian Journal of Statistics, 43(2), 321-348.

Pretis, Felix, Reade, James and Sucarrat, Genaro (2018): 'Automated General-to-Specific (GETS) Regression Modeling and Indicator Saturation for Outliers and Structural Breaks'. Journal of Statistical Software 86, Number 3, pp. 1-44

Author

Felix Pretis, http://www.felixpretis.org/
James Reade, https://sites.google.com/site/jjamesreade/

Examples

##Variance in presence of a break
#nile <- as.zoo(Nile)
#isat.nile <- isat(nile, sis=TRUE, iis=FALSE, plot=FALSE, t.pval=0.005)
#var <- isatvar(isat.nile)

#plot(nile)
#lines(isat.nile$mean.fit, col="red")
#lines(isat.nile$mean.fit + 2*var$const.se, col="blue", lty=3)
#lines(isat.nile$mean.fit - 2*var$const.se, col="blue", lty=3)

##Variance when there is no break
#set.seed(1)
#x <- as.zoo(rnorm(100, 0, 1))
#isat.x <- isat(x, sis=TRUE, iis=FALSE, plot=TRUE, t.pval=0.005)
#var.x <- isatvar(isat.x)

#plot(x)
#lines(isat.x$mean.fit, col="red")
#lines(isat.x$mean.fit + 2*var.x[,2], col="blue", lty=3)
#lines(isat.x$mean.fit - 2*var.x[,2], col="blue", lty=3)

##Variance of the long-run equilibrium coefficient path

#nile <- as.zoo(Nile)
#isat.nile <- isat(nile, sis=TRUE, iis=FALSE, plot=TRUE, t.pval=0.005, ar=1:2)
#var <- isatvar(isat.nile, lr=TRUE)