Realized Volatility Forecasting Research Articles

Can transformers transform financial forecasting?

PurposeThis study aims to critically evaluate the competitiveness of Transformer-based models in financial forecasting, specifically in the context of stock realized volatility forecasting. It seeks to challenge and extend upon the assertions of Zeng et al. (2023) regarding the purported limitations of these models in handling temporal information in financial time series.Design/methodology/approachEmploying a robust methodological framework, the study systematically compares a range of Transformer models, including first-generation and advanced iterations like Informer, Autoformer, and PatchTST, against benchmark models (HAR, NBEATSx, NHITS, and TimesNet). The evaluation encompasses 80 different stocks, four error metrics, four statistical tests, and three robustness tests designed to reflect diverse market conditions and data availability scenarios.FindingsThe research uncovers that while first-generation Transformer models, like TFT, underperform in financial forecasting, second-generation models like Informer, Autoformer, and PatchTST demonstrate remarkable efficacy, especially in scenarios characterized by limited historical data and market volatility. The study also highlights the nuanced performance of these models across different forecasting horizons and error metrics, showcasing their potential as robust tools in financial forecasting, which contradicts the findings of Zeng et al. (2023)Originality/valueThis paper contributes to the financial forecasting literature by providing a comprehensive analysis of the applicability of Transformer-based models in this domain. It offers new insights into the capabilities of these models, especially their adaptability to different market conditions and forecasting requirements, challenging the existing skepticism created by Zeng et al. (2023) about their utility in financial forecasting.

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.

Do short-term market swings improve realized volatility forecasts?

CBOE recently introduced a new volatility index, VIX1D. This paper aims to provide a concise evaluation of the effectiveness of this new index that reflects short-term market swings in predicting realized volatility. Similar to VIX, VIX1D exhibits a positive relationship with future realized volatility. When incorporated into HAR-RV, VIX1D demonstrates considerably enhanced predictive capability compared to VIX for one-day ahead predictions, as confirmed by various out-of-sample analyses. Additionally, the predictive capacity of VIX1D diminishes more rapidly compared to that of VIX. These findings validate that short-term swings significantly improve the forecast of short-term realized volatility.

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.

Novel optimization approach for realized volatility forecast of stock price index based on deep reinforcement learning model

Accurately predicting volatility has always been the focus of government decision-making departments, financial regulators and academia. Therefore, it is very crucial to precisely predict the realized volatility (RV) of the stock price index. In this paper, we take the RV sequences of Shanghai Stock Exchange Composite Index (SSEC), Standard & Poor 500 index (SPX) and Financial Times Stock Exchange Index (FTSE) as the research objects, and propose a predictive model based on optimized variational mode decomposition (VMD), deep learning models including deep belief network (DBN), long short-term memory network (LSTM) and gated recurrent unit (GRU), and reinforcement learning Q-learning algorithm. Firstly, the original RV sequence is decomposed by using the VMD ideal parameters optimized by grey wolf optimizer (GWO) to obtain the intrinsic mode functions (IMFs). Then, DBN, LSTM and GRU are used to predict same IMF simultaneously. Finally, the optimal weights of the above three models are determined by the Q-learning algorithm to construct an integrated model, and the final results are obtained after accumulating the predicted values of each IMF. The predictive performance of the model was evaluated by four loss functions: the mean average error (MAE), mean squared error (MSE), heterogeneous mean average error (HMAE), heterogeneous mean squared error (HMSE) and modified Diebold and Mariano test (MDM). The experimental results show that the constructed GVMD-Q-DBN-LSTM-GRU method has better performance that the comparison model in both emerging and developed markets.

Do extreme range estimators improve realized volatility forecasts? Evidence from G7 Stock Markets

This paper investigates whether range estimators contain important information in forecasting future realized volatility. We use widely applied range-based estimators: Parkinson, Garman-Klass, Roger-Satchell, and Yang-Zhang within a HAR-RV-X framework. Overnight volatility and close-to-close volatility estimators are also included, and the forecasting exercise is applied to G7 stock markets using a rolling window. Using QLIKE, HMSE and MCS forecast criteria, several noteworthy points are reported. The overall findings suggest that while no single model dominates, overnight return volatility achieves the most consistent performance. For example, HAR-RV model forecasts for CAC and DAX indices are improved only by overnight volatility, with some evidence also for SPX. For other indices, forecasts are improved by Parkinson and/or Garman-Klass volatility estimators. Of note, simpler range estimators outperform more complex range estimators. The findings could be important for investors in managing portfolio risk.

Forecasting the realized volatility of Energy Stock Market: A multimodel comparison

The realized volatility forecasting of energy sector stocks facilitates the establishment of corresponding risk warning mechanisms and investor decisions. In this paper, we collected two different energy sector indices and used different methods, namely principal component analysis (PCA) and sparse principal component analysis (SPCA), to extract features, and combined LSTM and GRU to construct 12 different models. The results show that the SPCA-LSTM model we constructed has the best forecasting performance in the realized volatility forecasting of energy indices, and SPCA has better forecasting results than PCA in the feature extraction stage. The results of the robustness test indicate that our results are robust.

Introducing NBEATSx to Realized Volatility Forecasting

Introducing NBEATSx to Realized Volatility Forecasting

Сравнение моделей прогноза волатильности криптовалют и фондового рынка

The article compares GARСH and HAR models for 1 day ahead forecasting performance of the realized volatility of financial series. As an example, the cryptocurrency with the largest capitalization, Bitcoin, was chosen. Its realized volatility is calculated from intraday (24 hours) data, using the closing values of five-minute trading intervals. The paper proposes a method for calculating realized volatility for the case of gaps in 5-minute intraday data. This makes it possible to achieve comparability of the daily values of the realized volatility of assets with different trading times. All days of the week are almost equally present among the days selected for forecasting. For comparison, a stock market asset was chosen, E-mini S&P 500, a futures contract that is traded 23 hours a day. We use data from 01/01/2018 to 12/29/2021. Since there could be (and were) structural changes in the markets in this interval, the models are evalua­ted in rolling windows 399 days long. For each series 810 GARCH models and 46312 HAR models are compared. The MCS test is used to select the best models (at the significance level of 0,01). It is shown that GARCH models are inferior to HAR models in the accuracy of forecasting both the realized volatility of Bitcoin and the E-mini S&P 500. At the same time, the relative accuracy of the forecast of the realized volatility of Bitcoin is higher than the accuracy of the forecast of the realized volatility of the E-mini S&P 500 futures. The smallest relative errors for Bitcoin and E-mini S&P 500 realized volatility forecasts are 29,51% and 36,12%, respectively.

Realized volatility forecast of financial futures using time-varying HAR latent factor models

We forecast realized volatilities by developing a time-varying heterogeneous autoregressive (HAR) latent factor model with dynamic model average (DMA) and dynamic model selection (DMS) approaches. The number of latent factors is determined using Chan and Grant's (2016) deviation information criteria. The predictors in our model include lagged daily, weekly, and monthly volatility variables, the corresponding volatility factors, and a speculation variable. In addition, the time-varying properties of the best-performing DMA(DMS)-HAR-2FX models, including size, inclusion probabilities, and coefficients, are examined. We find that the proposed DMA(DMS)-HAR-2FX model outperforms the competing models for both in-sample and out-of-sample forecasts. Furthermore, the speculation variable displays strong predictability for forecasting the realized volatility of financial futures in China.

Trading volume and realized volatility forecasting: Evidence from the China stock market

AbstractThe existing contradictory findings on the contribution of trading volume to volatility forecasting prompt us to seek new solutions to test the sequential information arrival hypothesis (SIAH). Departing from other empirical analyses that mainly focus on sophisticated testing methods, this research offers new insights into the volume‐volatility nexus by decomposing and reconstructing the trading activity into short‐run components that typically represent irregular information flow and long‐run components that denote extreme information flow in the stock market. We are the first to attempt at incorporating an improved empirical mode decomposition (EMD) method to investigate the volatility forecasting ability of trading volume along with the Heterogeneous Autoregressive (HAR) model. Previous trading volume is used to obtain the decompositions to forecast the future volatility to ensure an ex ante forecast, and both the decomposition and forecasting processes are carried out by the rolling window scheme. Rather than trading volume by itself, the results show that the reconstructed components are also able to significantly improve out‐of‐sample realized volatility (RV) forecasts. This finding is robust both in one‐step ahead and multiple‐step ahead forecasting horizons under different estimation windows. We thus fill the gap in studies by (1) extending the literature on the volume‐volatility linkage to EMD‐HAR analysis and (2) providing a clear view on how trading volume helps improve RV forecasting accuracy.

Using implied volatility jumps for realized volatility forecasting: Evidence from the Chinese market

This study examines the Chinese implied volatility index (iVIX) to determine whether jump information from the index is useful for volatility forecasting of the Shanghai Stock Exchange 50ETF. Specifically, we consider the jump sizes and intensities of the 50ETF and iVIX as well as cojumps. The findings show that both the jump size and intensity of the 50ETF can improve the forecasting accuracy of the 50ETF volatility. Moreover, we find that the jump size and intensity of the iVIX provide no significant predictive ability in any forecasting horizon. The cojump intensity of the 50ETF and iVIX is a powerful predictor for volatility forecasting of the 50ETF in all forecasting horizons, and the cojump size is helpful for forecasting in short forecasting horizon. In addition, for a one-day forecasting horizon, the iVIX jump size in the cojump is more predictive of future volatility than that of the 50ETF when simultaneous jumps occur. Our empirical results are robust and consistent. This work provides new insights into predicting asset volatility with greater accuracy.

HARNet: A Convolutional Neural Network for Realized Volatility Forecasting

HARNet: A Convolutional Neural Network for Realized Volatility Forecasting

Increasing the information content of realized volatility forecasts

Abstract Assuming N available calendar days, each with M intraday returns, the realized volatility literature suggests creating N end-of-day estimators by summing the M squared returns from each particular date. Instead of this “Calendar” [realized variance (RV)] approach, we propose a “Rolling” [rolling RV (RRV)] approach that simply sums trailing M returns at each timestamp, regardless if all M returns belong to the same calendar date. When estimating an out-of-sample 1-day realized volatility model, the former results in an ordinary least squares (OLS) regression with N−1 datapoints while the latter incorporates M(N−2)+1 datapoints, effectively lowering the standard errors, and potentially resulting in more accurate forecasts. We compare both models for the S&P 500 and 26 Dow Jones Industrial Average stocks; our results generally suggest that the Rolling approach yields both statistically and economically significant superior out-of-sample performance over the traditional Calendar approach.

Risk aversion and the predictability of crude oil market volatility: A forecasting experiment with random forests

We analyze the predictive power of time-varying risk aversion for the realized volatility of crude oil returns based on high-frequency data. Using random forests, and their extensions to quantile random forests and extreme random forests, we show that risk aversion improves out-of-sample accuracy of realized volatility forecasts. The predictive power of risk aversion is robust to various covariates including realized skewness and realized kurtosis, various measures of jump intensity, and leverage. Our findings highlight the importance of non-cash flow factors over commodity-market uncertainty with significant implications for the pricing and forecasting in these markets.

Out-of-sample realized volatility forecasting: does the support vector regression compete combination methods

ABSTRACT This article investigates whether the nonlinear support vector regression method under the Heterogeneous Auto-Regressive model (SVR-HAR) can compete for combination methods in terms of out-of-sample realized volatility forecasting. Empirical analyses are conducted based on the CSI 300 index high-frequency data, two new combination methods are employed and compared with the forecasting ability of the SVR method. The empirical results show that SVR-HAR models outperform individual models and all the combination methods, although the new combination methods are superior to other combination strategies. Specifically, HAR models with realized semi-variances as regressors obtains the lowest forecasting errors, confirming the strong forecasting ability of nonlinear SVR method and the realized semi-variances. The portfolio performance further confirms the highest economic value for models employing realized semi-variances and nonlinear SVR method in terms of volatility forecasting.

Does VPIN provide predictive information for realized volatility forecasting: evidence from Chinese stock index futures market

PurposeUsing intraday data, the authors explore the forecast ability of one high frequency order flow imbalance measure (OI) based on the volume-synchronized probability of informed trading metric (VPIN) for predicting the realized volatility of the index futures on the China Securities Index 300 (CSI 300).Design/methodology/approachThe authors employ the heterogeneous autoregressive model for realized volatility (HAR-RV) and compare the forecast ability of models with and without the predictive variable, OI.FindingsThe empirical results demonstrate that the augmented HAR model incorporating OI (HARX-RV) can generate more precise forecasts, which implies that the order imbalance measure contains substantial information for describing the volatility dynamics.Originality/valueThe study sheds light on the relation between high frequency trading behavior and volatility forecasting in China's index futures market and reveals the underlying market mechanisms of liquidity-induced volatility.

Sparse vector heterogeneous autoregressive modeling for realized volatility

We propose a sparse vector heterogeneous autoregressive (VHAR) model for realized volatility forecasting. As a multivariate extension of a heterogeneous autoregressive model, a VHAR model can consider the dynamics of multinational stock volatilities in a compact manner. A sparse VHAR is estimated using adaptive lasso and some theoretical properties are provided. In practice, our sparse VHAR model can improve forecasting performance and explicitly show the connectivity between stock markets. In particular, our empirical analysis shows that the NASDAQ market had the strongest influence on stock market volatility worldwide in the 2010s.

Realized volatility forecasting and volatility spillovers: Evidence from Chinese non‐ferrous metals futures

AbstractWe study the prediction of realized volatility of non‐ferrous metals futures traded on the Shanghai Futures Exchange from March 2011 to December 2017. A dynamic model averaging model is employed to combine multiple prediction models using time‐varying weights based on individual model performance. Empirical results also reveal that models incorporating volatility spillovers across metals are important for forecast combinations, and short‐term spillovers have a stronger impact than long‐term spillovers. This approach offers the best forecasting performance and allows users to identify the most dominant model at any given time and demonstrate when and how volatility transmission from another metal is valuable for forecasting. We also find evidence of distinct trading behaviours in emerging and developed markets.

Increasing the Information Dynamics of Realized Volatility Forecasts

This paper draws upon several distinct contributions to improve the out-of- sample forecasting performance of realized volatility models. More specifically, we retain the rolling-sample idea of Andreou and Ghysels (2002) to propose a new approach we call the Rolling Realized Volatility (RRV ), which samples consecutive high-frequency squared returns regardless of whether they originate from the same trading session like in the traditional approach. This new approach yields a sample approximately M times larger than the traditional approach, where M is the intraday sampling frequency. The new approach has at least two advantages. First, having more observations increases the informational dynamics of the OLS regression. Second, the Rolling method accounts for the serial correlation between the last returns in day t − 1 and the first returns in day t. We test competing out-of-sample forecast losses from the new approach against those of the traditional method for the S&P 500 and 26 Dow Jones Industrial Average stocks. Using several state-of-the-art realized volatility models, both a simulation and an empirical exercise strongly suggest the Rolling approach yields superior out-of-sample performance over the traditional approach.