Bootstrapping a powerful mixed portmanteau test for time series.

A new portmanteau test statistic is proposed for detecting nonlinearity in time series data. The new portmanteau statistic is calculated from the log of the determinant of a matrix comprised of the autocorrelations and cross-correlations of the residuals and squared residuals of a fitted time series. The asymptotic distribution of the proposed test statistic is derived as a linear combination of chi-square distributed random variables and can be approximated by a gamma distribution. A bootstrapping approach is shown to be robust when distributional assumptions are relaxed. The efficacy of the statistic is studied against linear and nonlinear dependency structures of some stationary time series models. It is shown that the new test can provide higher power than other tests in many situations. We demonstrate the advantages of the proposed test by investigating linear and nonlinear effects in an economic series and two environmental time series.