Lagrange‐Multiplier Tests of Multivariate Time‐Series Models

SUMMARY Generalizing Hosking (1980a), the Lagrange-multiplier test procedure is applied to hypotheses concerning multivariate autoregressive moving-average time-series models. The portmanteau and Quenouille goodness-of-fit tests for multivariate processes are derived in this manner and three other tests are obtained for multivariate moving-average models.

[1]  M. S. Bartlett,et al.  Extensions of Quenouille's Test for Autoregressive Schemes , 1950 .

[2]  D. Poskitt,et al.  Diagnostic Tests for Multiple Time Series Models , 1982 .

[3]  Calyampudi R. Rao.  Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation , 1948, Mathematical Proceedings of the Cambridge Philosophical Society.

[4]  H. Neudecker.  Some Theorems on Matrix Differentiation with Special Reference to Kronecker Matrix Products , 1969 .

[5]  M. Bartlett,et al.  Goodness of Fit Tests for Simultaneous Autoregressive Series , 1953 .

[6]  Leslie Godfrey,et al.  Testing the adequacy of a time series model , 1979 .

[7]  M. H. Quenouille.  A Large‐Sample Test for the Goodness of Fit of Autoregressive Schemes , 1947 .

[8]  Ratnam V. Chitturi.  Distribution of Residual Autocorrelations in Multiple Autoregressive Schemes , 1974 .

[9]  R. Kohn,et al.  Asymptotic properties of time domain gaussian estimators , 1978, Advances in Applied Probability.

[10]  D. Lindley,et al.  The existence of Bartlett-Rajalakshman goodness of fit G -tests for multivariate autoregressive processes with finitely dependent residuals , 1958 .

[11]  J. Hosking.  A Unified Derivation of the Asymptotic Distributions of Goodness‐Of‐Fit Statistics for Autoregressive Time‐Series Models , 1978 .

[12]  J. R. M. Hosking,et al.  The Multivariate Portmanteau Statistic , 1980 .

[13]  A. M. Walker.  Note on a Generalization of the Large Sample Goodness of Fit Test for Linear Autoregressive Schemes , 1950 .

[14]  A. I. McLeod,et al.  Distribution of the Residual Autocorrelations in Multivariate Arma Time Series Models , 1981 .

[15]  Robert Kohn,et al.  Asymptotic Estimation and Hypothesis Testing Results for Vector Linear Time Series Models , 1979 .

[16]  E. J. Hannan,et al.  Vector linear time series models , 1976, Advances in Applied Probability.

[17]  A. I. McLeod,et al.  On the Distribution of Residual Autocorrelations in Box–Jenkins Models , 1978 .