Abstract
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.
Highlights
We study the cumulative sum (CUSUM) monitoring procedure to sequentially detect a significant change in time series with conditional volatilities
We considered a novel monitoring process for detecting a significant change of conditional volatilities in time series
We proposed a procedure based on a CUSUM
Summary
We study the cumulative sum (CUSUM) monitoring procedure to sequentially detect a significant change in time series with conditional volatilities. In SPC, a control chart is a primary component that graphically describes the behavior of sequentially observed time series. Instead of the conventional control charts, some authors, such as [7], alternatively took the approach of controlling type I errors in probability instead of controlling ARL to deal with the monitoring process in autoregressive time series. This design of the sequential monitoring method has merit in its ability to attain a lower false alarm rate, as seen in [8], who took a similar approach to dealing with generalized autoregressive conditional heteroscedastic (GARCH) time series
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