Goodness-of-fit testing for time series models via distance covariance

Phyllis Wan and Richard A. Davis

Journal of Econometrics, 2022, vol. 227, issue 1, 4-24

Abstract: 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.

Keywords: Distance covariance; Time series models; Estimated residuals; Goodness-of-fit testing; Serial dependence (search for similar items in EconPapers)
JEL-codes: C01 C13 C22 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:227:y:2022:i:1:p:4-24

DOI: 10.1016/j.jeconom.2020.05.008

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