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Testing the Fit of a Vector Autoregressive Moving Average Model
Author(s) -
Paparoditis Efstathios
Publication year - 2005
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2005.00419.x
Subject(s) - mathematics , test statistic , autoregressive model , goodness of fit , statistical hypothesis testing , nonparametric statistics , parametric model , parametric statistics , null distribution , closeness
. A new procedure for testing the fit of multivariate time series model is proposed. The method evaluates in a certain way the closeness of the sample spectral density matrix of the observed process to the spectral density matrix of the parametric model postulated under the null and uses for this purpose nonparametric estimation techniques. The asymptotic distribution of the test statistic is established and an alternative, bootstrap‐based method is developed in order to estimate more accurately this distribution under the null hypothesis. Goodness‐of‐fit diagnostics useful in understanding the test results and identifying sources of model inadequacy are introduced. The applicability of the testing procedure and its capability to detect lacks of fit is demonstrated by means of some real data examples.