Time Series MT 2.0 Update

New Single series unit root tests

DFGLS
The GAUSS dfgls unit root test procedure follows the methodology proposed by Elliot, Rothenberg and Stock (1996). The testing parameter is given for the case including a time trend and for the case including only a constant.

KPSS
Tests the null hypothesis of stationarity against the unit root alternative, expanding unit root analysis. This addition to GAUSS’s unit root testing capabilities is useful as a stand-alone test or as a complementary tool with other unit root tests for confirmatory analysis.

The GAUSS kpss procedure:

  • Calculates the KPSS Lagrange Multiplier score statistic and a vector of critical values.
  • Adaptable to model all deterministic components and data frequencies.
  • Allows users to control the long run variance estimation kernel
  • Option to utilize the Newey-West, automatic bandwidth selection methodology

New Panel series unit root tests

The latest GAUSS TSMT update broadens GAUSS’s unit root testing applications to include cross sectional data. Three new panel series unit root testing procedures provide flexible unit root testing capabilities across a variety of cross-sectional applications.

Breitung
The Breitung z statistic tests the null hypothesis that all series contain a unit root against the alternative that all series are stationary. It assumes that the autoregressive parameter is constant across all panels.

In addition, the GAUSS implementation of the Breitung test assumes uncorrelated error terms across panels. The Breitung test builds on the LLC or IPS procedures, with the inclusion of a preliminary pre-adjustment to data prior to ADF testing to address biased estimation.

The GAUSS breitung procedure:

  • Allows users to specify deterministic terms
  • Provides the option to remove cross-sectional means from all series
  • Allows users to specify panel specific lags for ADF regressions.

Im-Pesaran-Shin
The IPS test is less restrictive than the LLC test, as it tests the null hypothesis that all series contain a unit root against the alternative that at least one series is stationary. In addition, the IPS panel root test allows for heterogeneous autoregressive behavior across panels.

The GAUSS ips procedure:

  • Allows users to specify deterministic terms
  • Provides the option to remove cross-sectional means
  • Allows users to specify panel specific lags for ADF regressions

Levin-Lin-Chu
The LLC is the most restrictive of the panel series unit root tests and assumes a homogenous autoregressive parameter and independently distributed error terms across all series.

The GAUSS llc procedure:

  • Allows users to specify deterministic terms
  • Provides the option to remove cross-sectional means from all series
  • Allows users to specify panel specific lags for ADF regressions and to control the long run variance estimation kernel

New Unit root test with structural breaks

Zivot-Andrews
The Zivot and Andrews unit root testing procedure widens GAUSS’s unit root testing abilities to cover series with a single, innovative structural breaks in the intercept, trend, or both.

The procedure tests the null hypothesis that the series contains a unit root and no structural break. The Zivot-Andrews test requires no knowledge of the break location, but rather estimates the time of the break.

The GAUSS zandrews procedure:

  • Allows users to specify which deterministic terms include a structural break
  • Allows users to specify panel specific lags for ADF regressions

Now includes GARCH

GJR GARCH
A model with asymmetrical effects of the conditional variance proposed by Glosten, Jagannathan and Runkle (1993).

IGARCH
The IGARCH(p,q) model is a GARCH(p,q) model with a unit root.

GARCH-in-mean
For the GARCHM, or GARCH-­in-­mean, model the time series equation is modified to include the square root of the conditional variance.

Distributions: Gaussian, Student’s t and Skew Generalized t

Also includes

Estimating long-run variance
The GAUSS getlrv procedure estimates the heteroscedasticity and autocorrelation covariance (HAC) of time series data based on a user specified kernel and bandwidth length.

This new GAUSS feature provides a useful tool for a variety of time series modeling and estimation needs. Kernel options include the Parzen, Bartlett, and Quadratic Spectral density.

Adjusted R-Squared
The adjrsq procedure providers a user level tool to find the adjusted R-Squared statistic following the estimation of a linear regression model. It requires both the original data and the residuals from the estimate as inputs.