Title: New methods for model diagnostics in multiplicative error models
Authors: Indeewara Perera - University of Sheffield (United Kingdom) [presenting]
Mervyn Silvapulle - Monash University (Australia)
Abstract: The recent literature on financial time series analysis has devoted considerable attention to non-negative random variables, such as the duration between trades at a stock exchange, realized volatility, volume transactions and squared or absolute returns. The class of models, referred to as the multiplicative error models, is particularly suited to model such non-negative time series. A multiplicative error model (mem) decomposes the non-negative time-series variable of interest into the product of its conditional mean and a multiplicative error term. Kolmogorov-Smirnov type tests are developed for testing the parametric specification of a given mem which consists of separate parametric models for the conditional mean and the error distribution. The limiting distributions of the test statistics are model-dependent and not free of nuisance parameters, and hence critical values cannot be tabulated for general use. A bootstrap method is proposed for computing the p-values of the tests, and is shown to be consistent. To this end, a new general result on asymptotic uniform expansions is established for a class of randomly weighted residual empirical processes. This is a useful result in its own right. The proposed tests are shown to have nontrivial asymptotic power against a class of root-n local alternatives. The tests performed well in a simulation study, and are illustrated using a data example on realized volatility.