A practical guide to heavy tails: statistical techniques and applications
A practical guide to heavy tails: statistical techniques and applications
A nonparametric test of serial independence for time series and residuals
Journal of Multivariate Analysis
Time Series Analysis, Forecasting and Control
Time Series Analysis, Forecasting and Control
Trimmed portmanteau test for linear processes with infinite variance
Journal of Multivariate Analysis
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The paper proposes new procedures for diagnostic checking of fitted models under the assumption of infinite-variance errors which are in the domain of attraction of a stable law. These procedures are functional of residual-based empirical processes. First, the asymptotic distributions of the empirical processes based on residuals are derived. Then two important applications in time series diagnostics are discussed. A goodness-of-fit test is developed using a functional of the empirical process based on residuals. Tests of independence of innovations are also considered. The finite-sample behavior of these tests are studied by simulation and comparison with the classical Portmanteau tests for ARMA models with infinite-variance developed recently by Lin and McLeod (2008) [25] is provided.