Abstract
With the large amounts of modern financial and econometric data available from disparate informational sources, it becomes increasingly critical to develop inferential tools for the impact of exogenous factors on volatility of financial time series. We develop a new Local Covariate Trend test (LOCOT) for the significance of an exogenous covariate in the autoregressive conditional heteroscedastic volatility model, where the covariate effect can be nonlinear. The new LOCOT statistic is based on an artificial high-dimensional one-way ANOVA where the number of factor levels increases with the sample size. We derive asymptotic properties of the new LOCOT statistic and show its competitive finite sample performance in a broad range of simulation studies. We illustrate utility of the new testing approach in application to volatility analysis of three major cryptoassets and their relationship with the prices of gold and the S&P500 index.
Highlights
Since its inception by Engle (1982), a family of Autoregressive Conditional Heteroscedasticity (ARCH) models remains the primary tool to model volatility of financial time series
The primary goal of this paper is to develop a hypothesis test for the significance of exogenous covariates in autoregressive conditional heteroscedastic volatility models where the effect of the covariate can be nonlinear
In this paper we introduce a new Local Covariate Trend testing (LOCOT) approach for the significance of an exogenous covariate in an ARCH volatility model, where the covariate effect is a nonparametric functional
Summary
Since its inception by Engle (1982), a family of Autoregressive Conditional Heteroscedasticity (ARCH) models remains the primary tool to model volatility of financial time series (see overviews by Beyaztas et al, 2018; Brenner et al, 1996; Fabozzi et al, 2014; May and Herce, 2002, and references therein). A natural question arises on whether we can test for the effects of exogenous factors in volatility. Addressing this important question allows us to assist in appropriate data and model selection as well as in improving volatility forecasting. Despite its high importance in applications, hypothesis testing and inference for exogenous covariates in conditional heteroscedastic models remain yet a substantially under-explored area. The primary goal of this paper is to develop a hypothesis test for the significance of exogenous covariates in autoregressive conditional heteroscedastic volatility models where the effect of the covariate can be nonlinear
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