Introduction |

Vector Time Series Analysis |

The VARMAX procedure enables you to model the dynamic relationship both between the dependent variables and between the dependent and independent variables. The VARMAX procedure includes the following features:

several modeling features:

vector autoregressive model

vector autoregressive model with exogenous variables

vector autoregressive and moving-average model

Bayesian vector autoregressive model

vector error correction model

Bayesian vector error correction model

GARCH-type multivariate conditional heteroscedasticity models

criteria for automatically determining AR and MA orders:

Akaike information criterion (AIC)

corrected AIC (AICC)

Hannan-Quinn (HQ) criterion

final prediction error (FPE)

Schwarz Bayesian criterion (SBC), also known as Bayesian information criterion (BIC)

AR order identification aids:

partial cross-correlations

Yule-Walker estimates

partial autoregressive coefficients

partial canonical correlations

testing the presence of unit roots and cointegration:

Dickey-Fuller tests

Johansen cointegration test for nonstationary vector processes of integrated order one

Stock-Watson common trends test for the possibility of cointegration among nonstationary vector processes of integrated order one

Johansen cointegration test for nonstationary vector processes of integrated order two

model parameter estimation methods:

least squares (LS)

maximum likelihood (ML)

model checks and residual analysis using the following tests:

Durbin-Watson (DW) statistics

test for autoregressive conditional heteroscedastic (ARCH) disturbance

test for AR disturbance

Jarque-Bera normality test

Portmanteau test

seasonal deterministic terms

subset models

multiple regression with distributed lags

dead-start model that does not have present values of the exogenous variables

Granger-causal relationships between two distinct groups of variables

infinite order AR representation

impulse response function (or infinite order MA representation)

decomposition of the predicted error covariances

roots of the characteristic functions for both the AR and MA parts to evaluate the proximity of the roots to the unit circle

contemporaneous relationships among the components of the vector time series

forecasts

conditional covariances for GARCH models

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