Abstract
This study considers support vector regression (SVR) and twin SVR (TSVR) for the time series of counts, wherein the hyper parameters are tuned using the particle swarm optimization (PSO) method. For prediction, we employ the framework of integer-valued generalized autoregressive conditional heteroskedasticity (INGARCH) models. As an application, we consider change point problems, using the cumulative sum (CUSUM) test based on the residuals obtained from the PSO-SVR and PSO-TSVR methods. We conduct Monte Carlo simulation experiments to illustrate the methods’ validity with various linear and nonlinear INGARCH models. Subsequently, a real data analysis, with the return times of extreme events constructed based on the daily log-returns of Goldman Sachs stock prices, is conducted to exhibit its scope of application.
Highlights
We developed a forecasting method for the time series of counts based on support vector regression (SVR) with particle swarm optimization (PSO), and used it to detect a change in the conditional mean of the time series based on the cumulative sum (CUSUM) test that is calculated from integer-valued autoregressive conditional heteroscedastic (INGARCH) residuals
The basic theories and analytical tools for these models are quite well developed in the literature, as seen in [11,12,13,14,15], a restriction on their usage exists because both integer-valued autoregressive (INAR) and INGARCH models are mostly assumed to have a linear structure in their conditional mean
As misspecification can potentially lead to false conclusions in real situations, we considered SVR as a nonparametric algorithm for forecasting the time series of counts
Summary
We developed a forecasting method for the time series of counts based on support vector regression (SVR) with particle swarm optimization (PSO), and used it to detect a change in the conditional mean of the time series based on the cumulative sum (CUSUM) test that is calculated from integer-valued autoregressive conditional heteroscedastic (INGARCH) residuals. The authors of the recent reference [43,53] developed a simplistic residual-based CUSUM test for location-scale time series models, based on which the authors of [21,22] designated a hybridization of the SVR and CUSUM methods for handling the change point problem for AR and GARCH time series and demonstrated its superiority over classical models Their approach is not directly applicable and requires a new modification for effective performance, especially on the proxies used for the GARCH prediction, as seen, as simple or exponential moving average type proxies conventionally used for SVR-GARCH models [22] would not work adequately in our current study.
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