1. Introduction
Volatility plays an important role in risk management. However, there is an inherent problem with volatility: real volatility is latent and is not directly observable. Volatility can be estimated using other approaches, such as the autoregressive conditional heteroskedasticity (ARCH) and generalized autoregressive conditional heteroskedasticity (GARCH) models proposed by
Engle (
1982) and
Bollerslev (
1986). Such models have been developed and studied extensively; however, because GARCH models use open-to-close return data, they are still subject to unobserved latent volatility. To overcome this problem and take full advantage of information from high-frequency intraday data,
Andersen et al. (
2003) proposed a framework to compute the summation of the squared high-frequency intraday returns to construct realized volatility (RV) using high-frequency data for measuring, modeling, and forecasting latent volatility. When the measurement error of the RV is ignored, volatility essentially becomes “observable”.
For forecasting RV,
Corsi (
2009) introduced a simple and easy-to-implement model called the heterogeneous autoregressive (HAR) model. This model utilizes the past daily, weekly, and monthly RVs called 1, 5, and 22 lags, respectively, as variables to predict the future daily RV. The HAR model captures the long-term memory and persistence of essential features in financial data. The goal of (G)ARCH models is to estimate and forecast unobservable latent volatility, whereas RV is a nonparametric estimator of latent volatility, and autoregressive moving average (ARMA)-type models, including the HAR model, are used to predict observable estimators, which are distinguished from each other by the difference in the dependent variables
Guidolin and Pedio (
2018),
McAleer and Medeiros (
2008).
Since its introduction, the HAR model has been widely used and continuously refined.
Corsi and Renò (
2012) further developed the HAR model into the HAR with component jumps (HAR-CJ) model by decomposing RV into continuous and jump components. Building on the realized semivariance,
Patton and Sheppard (
2015) proposed a HAR-semivariance (HAR-SV) model and demonstrated that it is better than the HAR-CJ model.
Bollerslev et al. (
2016) considered the distribution of measurement error and realized quarticity (RQ) as an estimator of the variance in the measurement error to construct the HARQ model, which outperformed the other HAR series models in an empirical analysis.
Wen et al. (
2016) used alternative risk measures to construct a series of HAR-type models for predicting volatility in crude oil futures.
Audrino et al. (
2018) proposed the flexible HAR (1, 2, …,
p) model, which goes beyond the traditional HAR (1, 5, 22) model. This model treats all past p days of RV as estimators, using the least absolute shrinkage and selection operator (LASSO) method with a regularization term to estimate the model, which mitigates the problem of overfitting.
Lyócsa and Stašek (
2021) introduced a method to improve the predictive accuracy of the HAR model by combining multiple results from HAR models with different volatility estimators. This approach involves averaging the predictions of all the models by using different volatility estimators to derive the final prediction.
In recent years, several studies have used machine learning methods directly in financial forecasting or implementing time series models to improve forecasting accuracy. Various studies by
Gupta et al. (
2023),
Ramos-Pérez et al. (
2019),
Demirer et al. (
2020),
Carr et al. (
2019), and others have discussed the prediction of RV in financial markets using individual machine learning models such as artificial neural networks and support vector machine (SVM).
In addition to this, studies have combined machine learning models with financial time series models to better capture both linear and nonlinear patterns in time series.
Kim and Won (
2018) combined long short-term memory (LSTM)-based methods with a GARCH-type model to construct numerous hybrid models. The empirical results with returns data of the KOSPI 200 index revealed that the LSTM-based hybrid models are better than single GARCH-type models in prediction accuracy.
Zhang and Qiao (
2021) and
Sun and Yu (
2020) proposed HAR- and GARCH-type support vector regression (SVR) models, respectively. Their finding showed that SVR effectively improved the prediction accuracy of HAR-type and GARCH-type models.
Pai and Lin (
2005),
Li et al. (
2010), and
Zhu et al. (
2017) investigated a hybrid model based on the autoregressive integrated moving average (ARIMA) and SVR or SVM for time series forecasting in different fields, revealing that a hybrid model can improve on the ARIMA model in prediction accuracy.
However, in these studies, the researches did not consider the optimal hyperparameter setting of machine learning models when combining machine learning with financial time series models. Therefore, in this study, following
Huang (
2012), we use the genetic algorithm (GA) method to optimize the hyperparameters of the SVR model so that we can choose more appropriate hyperparameters. Based on this automated machine learning model, we propose two types of hybrid models that combine the HAR model with the SVR to predict the RV of stock indices and individual stocks returns. The first type predicts the residual of the HAR model predictions using the GA-optimized SVR model as a nonlinear component. Then, we use the sum of the two predicted components as the predicted value of volatility. The second is a weight-type model, where the predicted value
$\widehat{y}$ is described as
$\alpha {\widehat{y}}_{HAR}+(1-\alpha ){\widehat{y}}_{SVR}$, which captures the nonlinear component. We construct the two types hybrid models based on four basic HAR-type models. Then, we compare the performance of these models in out-of-sample forecasting. Additionally, we use other extensions of the HAR model, such as HAR-semivariance (HAR-SV), HAR-signed jumps (HAR-SJ), and HAR-RQ (HARQ), in this study and combine them with SVR. In the empirical analysis, we collect high-frequency intraday price data (and, thus, computing the returns) from the Tokyo stock price index (TOPIX) and five individual stocks of TOPIX 30 in the Japanese market from 2020 to 2022 as our dataset for an out-of-sample forecasting test to compare the performance of the hybrid models and basic HAR-type model. Our main contributions are as follows: (1) we propose that the problem of parameter tuning in RV prediction using machine learning models can be made more efficient using automatic machine learning models; (2) we apply the optimization algorithm not only for hyperparameter optimization but also in the selection of weights when combining different predictive values; and (3) we conduct an empirical study in the Japanese stock market and prove the effectiveness of this method.
The rest of this paper is structured as follows. First, in
Section 2 we introduce the volatility estimators that will be used in this study. Second, in
Section 3, we present all the base models employed in this study and the methodology that will be used to combine the models. Next, in
Section 4, we conduct an empirical analysis of our dataset and report and discuss the results. Finally, we present the conclusions in
Section 5.
5. Conclusions
This study proposed the use of HAR-X-SVR models, which are used for RV prediction, and tested their out-of-sample forecasting performance under TOPIX and five individual stocks datasets. It constructed two types of hybrid models by combining four basic HAR-X models with SVR using two different combining methods, and these two types of hybrid models were compared with basic HAR-X models. In the Japanese stock market, the empirical results revealed that although the first hybrid model is effective in improving model accuracy in the stock price prediction study by
Pai and Lin (
2005), the first hybrid model is not significantly effective in improving model accuracy in forecasting RV. However, our second hybrid model performs very well in all six datasets, especially when based on the HAR-SV and HARQ models. Based on the empirical results, we suggest that combining different machine learning models with time series models can be useful for improving prediction accuracy in the Japanese stock market. Nevertheless, confirming the feasibility and viability of such an approach in different markets requires a more comprehensive and meticulous investigation.
We have proposed the following recommendations for future research in order to more comprehensively examine the hybrid model’s credibility. In this study, we only considered hybrid models to enhance the forecasting ability of HAR models. Other volatility models, such as MEM models (
Engle and Gallo 2006), can be considered in subsequent work. Furthermore, automatic machine learning methods have developed rapidly in recent years, so the application of machine learning frameworks such as AutoGluon (
Erickson et al. 2020) can be considered in subsequent studies. Our approach can be generalized to multivariate analysis using multivariate models such as the multivariate-HARQ (M-HARQ) model (
Bollerslev et al. 2018) for multivariate forecasting while considering correlations between different markets.