Generalized Portmanteau Tests Based on Subspace Methods

The problem of diagnostic checking is tackled from the perspective of the subspace methods. Two statistics are presented and their asymptotic distributions are derived under the null hypothesis. The procedures are devised to deal with univariate and multivariate processes, are flexible and able to separately check regular and seasonal correlations. The performance in finite samples of the proposals is illustrated via Monte Carlo simulations and two examples with real data.