In many statistical modeling frameworks, goodness-of-fit tests are typically administered to the estimated residuals. In the time series setting, whiteness of the residuals is assessed using the sample autocorrelation function. For many time series models, especially those used for financial time series, the key assumption on the residuals is that they are in fact independent and not just uncorrelated. In this paper, we apply the auto-distance covariance function (ADCV) to evaluate the serial dependence of the estimated residuals. Distance covariance can discriminate between dependence and independence of two random vectors. The limit behavior of the test statistic based on the ADCV is derived for a general class of time series models. One of the key aspects in this theory is adjusting for the dependence that arises due to parameter estimation. This adjustment has essentially the same form regardless of the model specification. We illustrate the results in simulated examples.

Additional Metadata
Keywords Distance covariance, Estimated residuals, Goodness-of-fit testing, Serial dependence, Time series models
JEL Econometrics (jel C01), Estimation (jel C13), Time-Series Models; Dynamic Quantile Regressions (jel C22)
Persistent URL dx.doi.org/10.1016/j.jeconom.2020.05.008, hdl.handle.net/1765/129520
Journal Journal of Econometrics
Citation
Wan, P. (Phyllis), & Davis, R.A. (Richard A.). (2020). Goodness-of-fit testing for time series models via distance covariance. Journal of Econometrics. doi:10.1016/j.jeconom.2020.05.008