Distribution of the Residual Autocorrelations in Multivariate Arma Time Series Models

Abstract

Summary The large‐sample distribution of the multivariate residual autocorrelations in the vector arma model is derived. This result is somewhat less complicated for the vector autoregressive model. A new multivariate portmanteau test for checking the adequacy of fitted vector arma models is developed. A simulation study shows that a simple modification of the portmanteau test improves its accuracy in small samples.

An automatic Portmanteau test for serial correlation

“…For convenience, let us call p the number of considered autocorrelations. The basic Box-Pierce statistic has been slightly modified to improve its finite sample performance, see Davies et al (1977), Ljung and Box (1978), Davies and Newbold (1979) or Li and McLeod (1981). However, it still presents two main limitations: first, from a theoretical point of view, the test was developed under the independence assumption; second, from a practical point of view, the selection of the employed number of autocorrelations p is arbitrary.…”

Residual autocorrelation testing for vector error correction models

“…They are, for example, available in commercial econometric software such as EViews and PcGive. The theoretical properties of these tests are well explored for stationary DGPs (see, e.g., Ahn, 1988;Hosking, 1980Hosking, , 1981aLi and McLeod, 1981;or Lu¨tkepohl, 1991 for a textbook exposition with more references and Edgerton and Shukur, 1999, for a large scale small sample comparison of various tests). An explicit treatment of the properties of residual ACs of vector error correction models (VECMs) for cointegrated variables does not seem to be available, however.…”

On the Dynamic Linkages Among International Emerging Currencies

“…In our study, we refer to the most broadly used diagnostic tests, namely the Hosking's and Li and McLeod's Multivariate Portmanteau statistics on both standardized and squared standardized residuals. According to Hosking (1980), Li and McLeod (1981) and McLeod and Li (1983) autocorrelation test results reported in Table 3 (Panel B), the multivariate diagnostic tests allow accepting the null hypothesis of no serial correlation on both standardized and squared standardized residuals and thus there is no evidence of statistical misspecification.…”