This paper studies the residual autocorrelation functions (ACFs) of partially nonstationary multivariate autoregressive moving-average (ARMA) models. The limiting distributions of the full rank estimators and the Gaussian reduced rank estimators are derived. Using these results, we derive the limiting distributions of the residual ACFs under full rank and reduce rank estimations. Based on these limiting distributions, we construct the portmanteau statistics for model checking. It is shown that these statistics asymptotically follow \(\chi ^2\)-distributions. Simulations are carried out to assess their performances in finite samples and two real examples are given.
Limiting distributions Autoregressive model Autoregressive moving-average model Partially nonstationary Portmanteau statistics
Mathematics Subject Classification (2010)
Primary 91B84 37M10 Secondary 62M10
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