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.
This paper considers monitoring an anomaly from sequentially observed time series with heteroscedastic conditional volatilities based on the cumulative sum (CUSUM) method combined with support vector regression (SVR). The proposed online monitoring process is designed to detect a significant change in volatility of financial time series. The tuning parameters are optimally chosen using particle swarm optimization (PSO). We conduct Monte Carlo simulation experiments to illustrate the validity of the proposed method. A real data analysis with the S&P 500 index, Korea Composite Stock Price Index (KOSPI), and the stock price of Microsoft Corporation is presented to demonstrate the versatility of our model.
This study develops a statistical process control (SPC) chart that simultaneously monitors the mean and variance of general location‐scale time series models. Integrating the one‐class classification (OCC) technique (the support vector data description (SVDD) particularly), we formulate a nonlinear boundary to enclose in‐control observations for detecting structural anomalies. The control limits obtained from SVDD can capture a more sophisticated structural change and are also controllable. We particularly propose a control chart formulated using location‐scale residuals. This further enhances our ability to detect shifts in the mean, variance, and various model parameters. The proposed OCC control chart is compared with some traditional charts and is validated by conducting simulations under various circumstances. Moreover, we consolidate applicability in a real data analysis by demonstrating its functionality with the S&P 500 index.
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