Abstract
This study considers the problem of detecting a change in the conditional variance of time series with time-varying volatilities based on the cumulative sum (CUSUM) of squares test using the residuals from support vector regression (SVR)-generalized autoregressive conditional heteroscedastic (GARCH) models. To compute the residuals, we first fit SVR-GARCH models with different tuning parameters utilizing a time series of training set. We then obtain the best SVR-GARCH model with the optimal tuning parameters via a time series of the validation set. Subsequently, based on the selected model, we obtain the residuals, as well as the estimates of the conditional volatility and employ these to construct the residual CUSUM of squares test. We conduct Monte Carlo simulation experiments to illustrate its validity with various linear and nonlinear GARCH models. A real data analysis with the S&P 500 index, Korea Composite Stock Price Index (KOSPI), and Korean won/U.S. dollar (KRW/USD) exchange rate datasets is provided to exhibit its scope of application.
Highlights
We aim to develop a method to detect a significant change in the conditional variance of time series with time-varying volatility using the cumulative sum (CUSUM) of squares test based on the support vector regression (SVR)-generalized autoregressive conditional heteroscedastic (GARCH) residuals
As the SVR-ARMA models cannot capture volatility in financial time series and the CUSUM test based on them is highly affected by volatility and misidentifies the change point (Lee, Lee and Moon [38]), we aim to develop a CUSUM test based on the SVR-GARCH models
We proposed the CUSUM of squares test based on the residuals obtained with the SVR-GARCH model in order to detect a parameter change in the volatility of time series
Summary
We aim to develop a method to detect a significant change in the conditional variance of time series with time-varying volatility using the cumulative sum (CUSUM) of squares test based on the support vector regression (SVR)-generalized autoregressive conditional heteroscedastic (GARCH) residuals. In this task, obtaining accurate predictions of volatilities is crucial because the residuals are obtained as the ratios of the observations and the forecasts of volatility. The GARCH model, proposed by Engle [1] and Bollerslev [2], is the most popular model for measuring the volatility of financial time series. Several GARCH variants have been developed to better capture these properties, e.g., the asymmetric GARCH model proposed by Engle [3], the exponential GARCH (EGARCH) model proposed by Nelson [4], the threshold
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