Heterogeneous Autoregressive Model Research Articles

Forecasting global stock market volatilities: A shrinkage heterogeneous autoregressive (HAR) model with a large cross-market predictor set

We propose a shrinkage heterogeneous autoregressive (HAR) model to explore the predictability of global stock market volatilities. To this end, we construct a big data environment using international stock market data, which comprises over 200 cross-market predictors, including realized variances (RVs), continuous components, jumps, leverages, overnight returns, and uncertainty indices. Two shrinkage models (LASSO and ENet) are considered for volatility modeling and forecasting. The results demonstrate that these models, notably LASSO, consistently improve predictive performance across global stock markets and daily, weekly, and monthly horizons. Their superiority extends to directional and density forecasting as well as asset allocation. There are several empirical findings of shrinkage: (i) the shrinkage degree varies significantly across forecast horizons, with longer horizons implying more predictors are needed for accurate estimation; (ii) no country/region's predictors show absolute superiority and utilize cross-market information leads to larger predictive gains, particularly for longer horizons; (iii) the predictors except for RVs and continuous components are more powerful, especially over longer horizons; and (iv) the uncertainty indices are the strongest predictors for all horizons.

Oil Price Volatility Prediction Using Out-Of-Sample Analysis – Prediction Efficiency of Individual Models, Combination Methods, And Machine Learning Based Shrinkage Methods

In this study, we compare the efficacy of forecast combination methods against machine learning-based shrinkage techniques in predicting oil price volatility. Our analysis is based on heterogeneous autoregressive (HAR) model framework. We employ eight individual HAR models and their variations, alongside five distinct combination methods for aggregating forecasts derived from HAR models and their variants. Additionally, we incorporate two widely recognized machine learning-based shrinkage methods, namely the elastic net and the lasso. Machine learning (ML) techniques, including elastic net and lasso, exhibit promise in estimating individual extended HAR models and combination sampled approaches. Meanwhile, model confidence set (MCS) estimation techniques demonstrate notably superior out-of-sample forecasting performance for the chosen sample. Our empirical findings reveal that both the elastic net and the lasso exhibit superior out-of-sample prediction accuracy in comparison to the individual HAR models and their variants, as well as the five combination techniques. Furthermore, we provide statistical evidence demonstrating the notably higher directional accuracy achieved by the elastic net and lasso methodologies. Importantly, our results remain statistically consistent across a range of robustness analyses. These findings hold significance for investors and policymakers, as they suggest potential economic benefits derived from allocating portfolios in alignment with oil price volatility estimates.

Forecasting the Chinese crude oil futures volatility using jump intensity and Markov-regime switching model

This study examines the predictive ability of nine high-frequency jumps on the Chinese crude oil futures volatility using a series of the Heterogeneous Autoregressive (HAR) models. Out-of-sample empirical results indicate that among the nine high-frequency jump tests, the JO jump component is powerful because the prediction model including this component demonstrates superior predictive performance. Compared to other competing models, the model incorporating JO jump component, jump intensity, and Markov-regime achieves higher predictive accuracy. During the outbreak of the COVID-19 pandemic and periods of high volatility, this new model continues to exhibit strong predictive capability for volatility in the Chinese oil futures market. This study provides novel insights into forecasting volatility in the Chinese oil market under the presence of extreme shocks.

Sentiment and energy price volatility: A nonlinear high frequency analysis

This study investigates the volatility dynamics of oil and gas prices in an environment characterized by post-coronavirus disease 2019 recovery, uncertainty, high inflation, and geopolitical tensions. Unlike previous studies, we examine a long-run series of high-frequency data on gas and oil prices from July 2007 to May 2022, which provides more than one million observations with which to analyze volatility. We compute realized volatility (RV) and decompose it into continuous volatility and jumps. We then investigate the relationship between uncertainty, investor sentiment, and RV, as well as its main components. Econometrically, we extend the heterogeneous autoregressive model of Corsi (2009) while considering not only disaggregate proxies for volatility (jumps and continuous volatility) and introducing uncertainty and heterogeneous investor sentiment, but also by allowing the model to include asymmetry, nonlinearity, and time variation according to the regime under consideration. Our results present three main findings. First, we find significant evidence of volatility decomposition, suggesting that both markets are characterized by significant jumps. Second, we show that trading volume, extra-financial news (uncertainty, investor sentiment), and jumps appear to drive commodity price volatility. Third, we find evidence of nonlinearity and threshold effects on energy price volatility. These findings are relevant for policymakers, regulators, investors, and portfolio managers, as they enable them to better characterize and forecast changes in commodity prices.

Forecasting the realized volatility of agricultural commodity prices: Does sentiment matter?

AbstractWe analyze the out‐of‐sample predictive power of sentiment for the realized volatility of agricultural commodity price returns. We use high‐frequency intra‐day data covering the period from 2009 to 2020 to estimate realized volatility. Our baseline forecasting model is a heterogeneous autoregressive (HAR) model, which we extend to include sentiment. We further enhance this model by incorporating various key realized moments such as leverage, realized skewness, realized kurtosis, realized upside (“good”) volatility, realized downside (“bad”) volatility, realized jumps, realized upside tail risk, and realized downside tail risk. In order to setup a forecasting model, we use (i) forward and backward stepwise predictor selection and (ii) a model‐based averaging algorithm. The forecasting models constructed through these algorithms outperform both the baseline HAR‐RV model and the HAR‐RV‐sentiment model. We conclude that, for the agricultural commodities studied in our research, realized moments play a more significant role in forecasting realized volatility compared to sentiment.

Energy price shocks and stock market volatility in an energy-importing country

We examine volatility dynamics in the Korean market using heterogeneous autoregressive models with exogenous covariates. The COVID-19 pandemic and the Russia–Ukraine War have caused substantial fluctuations in energy prices. We assess how these energy shocks affect stock market-implied volatility in Korea, a representative energy-importing country. During the pre-pandemic period, domestic and U.S. market factors affect Korea's volatility dynamics, whereas crude oil and natural gas futures prices have little explanatory power for these dynamics. In contrast, during the pandemic (war), oil (natural gas) futures prices become the key explanatory variable, and other market factors lose their explanatory power.

Forecasting of clean energy market volatility: The role of oil and the technology sector

This study is the first to explore whether the well-known relationship between the clean energy sector, oil prices, and technology stocks can be leveraged to enhance the accuracy of realized volatility forecasts for individual clean energy sub-sectors. Based on intraday data and various decompositions of daily realized volatility, we account for the heterogeneity across clean energy sub-sectors using the dynamic common correlated effect heterogeneous autoregressive (DCCE-HAR) model. Our findings reveal that, in the short term, price variations in technology shares are more informative for future clean energy volatility than fluctuations in oil prices. In an out-of-sample analysis, we individually forecast the volatility of each clean energy sub-index using Lasso, Ridge, and random forest approaches. We identify sub-indices that systematically benefit from technology sector price variation (e.g. Smart Grid, Operators, Energy Management), sub-indices that benefit from oil price variation (e.g. Bio Fuel, Wind and Geothermal), while also sub-indices that show limited sensitivity to price variation in the technology and oil markets.

Assessing the Risk of Bitcoin Futures Market: New Evidence

AbstractThe main objective of this paper is to forecast the realized volatility (RV) of Bitcoin futures (BTCF) market. To serve our purpose, we propose an augmented heterogenous autoregressive (HAR) model to consider the information on time-varying jumps observed in BTCF returns. Specifically, we estimate the jump-induced volatility using the GARCH-jump process and then consider this information in the HAR model. Both the in-sample and out-of-sample analyses show that jumps offer added information which is not provided by the existing HAR models. In addition, a novel finding is that the jump-induced volatility offers incremental information relative to the Bitcoin implied volatility index. In sum, our results indicate that the HAR-RV process comprising the leverage effects and jump volatility would predict the RV more precisely compared to the standard HAR-type models. These findings have important implications to cryptocurrency investors.

A hybrid econometrics and machine learning based modeling of realized volatility of natural gas

Determining which variables affect price realized volatility has always been challenging. This paper proposes to explain how financial assets influence realized volatility by developing an optimal day-to-day forecast. The methodological proposal is based on using the best econometric and machine learning models to forecast realized volatility. In particular, the best forecasting from heterogeneous autoregressive and long short-term memory models are used to determine the influence of the Standard and Poor’s 500 index, euro–US dollar exchange rate, price of gold, and price of Brent crude oil on the realized volatility of natural gas. These financial assets influenced the realized volatility of natural gas in 87.4% of the days analyzed; the euro–US dollar exchange rate was the primary financial asset and explained 40.1% of the influence. The results of the proposed daily analysis differed from those of the methodology used to study the entire period. The traditional model, which studies the entire period, cannot determine temporal effects, whereas the proposed methodology can. The proposed methodology allows us to distinguish the effects for each day, week, or month rather than averages for entire periods, with the flexibility to analyze different frequencies and periods. This methodological capability is key to analyzing influences and making decisions about realized volatility.

A Hybrid Model for Forecasting Realized Volatility Based on Heterogeneous Autoregressive Model and Support Vector Regression

In this study, we proposed two types of hybrid models based on the heterogeneous autoregressive (HAR) model and support vector regression (SVR) model to forecast realized volatility (RV). The first model is a residual-type model, where the RV is first predicted using the HAR model, and the residuals are used to train the SVR model. The residual component is then predicted using the SVR model, and the results from both the HAR and SVR models are combined to obtain the final prediction. The second model is a weight-based model, which is a combination of the HAR and SVR models and uses the same independent variables and dependent variables as the HAR model; we adjust the contribution of the two models to the predicted values by giving different weights to each model. In particular, four volatility models are used in RV forecasting as basic models. For empirical analysis, the RV of returns of the Tokyo stock price index and five individual stocks of TOPIX 30 is used as the dataset. The empirical results reveal that according to the model confidence set test, the weight-type model outperforms the HAR model and the residual-type HAR–SVR model.

Stabilizing global foreign exchange markets in the time of COVID-19: The role of vaccinations

By restoring economic openness, mitigating economic policy uncertainty, and regaining macroeconomic stability, the mass deployment of COVID-19 vaccinations should stabilize foreign exchange (FX) markets. This paper empirically examines the impact of COVID-19 vaccinations on the realized volatility of exchange rates in 30 countries/regions from January 1, 2020, to September 29, 2021. Using the heterogeneous autoregressive model with measurement errors, we find that the COVID-19 vaccine rollout stabilizes global FX markets; this result holds through a series of robustness checks. The stabilizing effect is asymmetric across the quantile levels of FX volatility distribution. Furthermore, the stabilizing effect is more pronounced in emerging markets, countries with high economic policy uncertainty, and nations with greater vaccine confidence.

"Investor attention fluctuation and stock market volatility: Evidence from China".

This paper examines the linkage between Chinese stock market volatility and investor attention fluctuation. In Heterogeneous autoregressive (HAR) model, first, we analyzed the linkage between both decomposed and undecomposed stock market realized volatility and investor attention fluctuations across full-sample and two-year moving window sub-samples. Second, we compare the predictive power of four models in short-, medium-, and long-term volatility forecasting. Empirical results show large positive attention fluctuation amplified Chinese stock market volatility after the outbreak of COVID-19, and negative small attention fluctuation significantly stabilized stock market volatility before COVID-19, and the impact dwindled in after COVID-19. The model incorporating decomposed realized volatility and decomposed attention fluctuation performs better in volatility Forecasting. This research underscores a shift in the dynamics between stock market volatility and investor attention fluctuations, and investor attention fluctuation improves the volatility forecasting accuracy of the Chinese stock market.

Air pollution, weather factors, and realized volatility forecasts of agricultural commodity futures

AbstractThis study investigates the potential effects of environmental factors on fluctuations in agricultural commodity futures markets, by constructing a new category of daily exogenous predictors related to air pollution, weather, climate change, and investor attention. The empirical results from out‐of‐sample analyses suggest that the heterogeneous autoregressive (HAR) model incorporating all these exogenous predictors is more likely to outperform other HAR‐type models. Additionally, economic evaluations demonstrate the superior performance of models incorporating investors' attention to climate change or extreme weather as predictors. While not all exogenous predictors are equally important for volatility forecasts, adopting appropriate variable selection methods to handle different sets of exogenous predictors can lead to better performance than the HAR benchmark. With the inclusion of air pollution or weather factors in the HAR model, a portfolio with an annualized average excess return of 16.2068% or a Sharpe ratio of 10.0431 can be achieved for the wheat futures, respectively.

Forecast combination puzzle in the HAR model

AbstractThe heterogeneous autoregressive (HAR) model has become the benchmark model for predicting realized volatility, given its simplicity and consistent empirical performance. Many modifications and extensions to the original model have been proposed that often only provide incremental forecast improvements. In this paper, we take a step back and view the HAR model as a forecast combination that combines three predictors: previous day realization (or random walk forecast), previous week average, and previous month average. When applying the ordinary least squares (OLS) to combine the predictors, the HAR model uses optimal weights that are known to be problematic in the forecast combination literature. In fact, an average of simpler HAR‐style models, and a simple average forecast often outperforms the optimal combination in many empirical applications. We investigate the performance of these simple combination forecasts for the realized volatility of the Dow Jones Industrial Average equity index, and a sample of individual constituent stocks, as well as across a range of other assets, commodities, exchange rates, and a range of global equity market indices. In all cases, we find dramatic improvements in forecast accuracy across all horizons and different time periods. The combinations also perform well relative to the logarithmic form of the HAR model and when using a volatility timing strategy in portfolio allocation. Thisis the first time the forecast combination puzzle is identified in this context.

Forecasting volatility with investor pessimism index: Exploring the predictive power of search queries

AbstractThis paper discusses whether investor sentiment contains useful information to predict volatility by constructing investor pessimism index based on Baidu, which is the largest search engine in China. We discover that the investor pessimism index is significantly negatively correlated with contemporaneous returns but predicts following days' returns reversals. Furthermore, the heterogeneous autoregressive model of realized volatility (HAR‐RV) with investor pessimism index performs better than other HAR‐RV‐type benchmark models. We perform a series of robustness tests, which include alternative construction of investor pessimism index, crisis subsample, alternative predictive model, alternative measures of volatility, and considering the role of institutional investor. Our results remain robust. Taken together, investor pessimism index constructed in this paper seem to be a suitable proxy to measure investor sentiment in China and can enhance the accuracy of volatility forecasting in the Chinese stock market.

What Should be Taken into Consideration when Forecasting Oil Implied Volatility Index?

This study forecasts the oil volatility index (OVX) incorporating information from other implied volatility (IV) indices. We provide evidence for the existence of long memory in the OVX in order to justify the use of the Heterogeneous AutoRegressive (HAR) model. We extend the HAR model by implementing a dynamic model averaging (DMA) method in order to allow for IV indices from other asset classes to be applicable at different time periods. Apart from the statistical evaluation, a straddle options trading strategy validates our results from an economic point of view. The IV of Dow Jones is highly significant for short- and mid-run forecasting horizons, whereas, at longer horizons, the IV of Energy Sector provides accurate forecasts but only from an economic point of view.

The effect of uncertainty on stock market volatility and correlation

In this study, we use an extension of the heterogeneous autoregressive model to investigate the influence of time-varying risk aversion and macroeconomic, financial, and economic policy uncertainty measures on stock market volatility and correlation. Based on the findings, there is a stronger predictive ability of these variables at the monthly frequency than at the daily frequency. We also highlight the importance of risk aversion, which, alongside fundamental factors, reflects investor sentiment in predicting stock market volatility. Meanwhile, although uncertainty variables, such as economic uncertainty and financial uncertainty, are important, the widely used variable, economic policy uncertainty, is not helpful for predicting stock market volatility. Moreover, there is evidence of higher economic value and reduced portfolio risk when including risk aversion and economic uncertainty in international portfolio analysis.

VIX futures pricing based on high‐frequency VIX: A hybrid approach combining SVR with parametric models

AbstractWe propose a novel hybrid approach for volatility index (VIX) futures pricing by combining support vector regression (SVR) with parametric models. Realized semivariances calculated based on high‐frequency VIX are used to characterize the asymmetric shocks of VIX, and the direct pricing framework of the heterogeneous autoregressive model is extended by incorporating realized semivariances. VIX futures prices are first obtained via parametric models, then the predicted prices and realized semivariances are input into SVR to obtain the final predicted values. Empirical results indicate that the combination of SVR with parametric models significantly improves the pricing ability. This indicates the important information of high‐frequency VIX and the necessity of combining machine learning methods with parametric models to obtain more accurate predictions.

Forecasting realized volatility of Bitcoin: The informative role of price duration

AbstractMotivated by the relationship between trading intensity and volatility and the attractiveness of duration‐based volatility estimators, this paper investigates the ability of price duration to forecast realized volatility of Bitcoin. Using high‐frequency transaction data, trading intensity is measured by price duration and incorporated in the class of heterogeneous autoregressive (HAR) models. Results provide compelling evidence that trading intensity improves the forecasting performance of a highly competitive set of HAR models, commonly used in the literature. HAR extensions that incorporate price duration systematically deliver the lowest forecast errors and generate economically significant gains in volatility targeting exercise over multiple horizons. However, results show no evidence in favor of a unique duration‐augmented model. The predictive ability of price duration is supported by a number of robustness checks, including alternative estimation windows, bull and bear market states, and alternative thresholds that define price events.

Sample frequency robustness and accuracy in forecasting Value-at-Risk for Brent Crude Oil futures

In this paper we examine how sensitive Value-at-Risk (VaR) forecasts based on simple linear quantile regressions are to the sampling frequency used to calculate realized volatility. We use sampling frequencies from one to 108 min for ICE Brent Crude Oil futures and test the out-of-sample performance of a set of quantile regression models using formal coverage tests. The results show that a one-factor model performs exceptionally well for most sampling frequencies used to calculate realized volatility. In comparison with the well-known Heterogeneous Auto-regressive Model of Realized Volatility (HAR-RV) and a quantile regression version of the HAR model (HAR-QREG), we also find that the one-factor model is much less sensitive to the sampling frequency used to calculate realized volatility.