Volatility forecasting for stock market incorporating macroeconomic variables based on GARCH-MIDAS and deep learning models

Empirical experiments have shown that macroeconomic variables can affect the volatility of stock market. However, the frequencies of macroeconomic variables are low and different from the stock market volatility, and few literature considers the low-frequency macroeconomic variables as input indicators for deep learning models. In this paper, we forecast the stock market volatility incorporating low-frequency macroeconomic variables based on a hybrid model integrating the deep learning method with generalized autoregressive conditional heteroskedasticity and mixed data sampling (GARCH-MIDAS) model to process the mixing frequency data. This paper firstly takes macroeconomic variables as exogenous variables then uses the GARCH-MIDAS model to deal with the problem of different frequencies between the macroeconomic variables and stock market volatility and to forecast the short-term volatility and finally takes the predicted short-term volatility as the input indicator into machine learning and deep learning models to forecast the realized volatility of stock market. It is found that adding macroeconomic variables can significantly improve the forecasting ability in the comparison of the forecasting effects of the same model before and after adding the macroeconomic variables. Additionally, in the comparison of the forecasting effects among different models, it is also found that the forecasting effect of the deep learning model is the best, the machine learning model is worse, and the traditional econometric model is the worst.     

Forecasting volatility of emerging stock markets: linear versus non‐linear GARCH models

ARCH and GARCH models are substantially used for modelling volatility of time series data. It is proven by many studies that if variables are significantly skewed, linear versions of these models are not sufficient for both explaining the past volatility and forecasting the future volatility. In this paper, we compare the linear(GARCH(1,1)) and non‐linear(EGARCH) versions of GARCH model by using the monthly stock market returns of seven emerging countries from February 1988 to December 1996. We find that for emerging stock markets GARCH(1,1) model performs better than EGARCH model, even if stock market return series display skewed distributions. Copyright © 2000 John Wiley & Sons, Ltd.     

Are industry‐level indicators more helpful to forecast industrial stock volatility? Evidence from Chinese manufacturing purchasing managers index

Effectively explaining and accurately forecasting industrial stock volatility can provide crucial references to develop investment strategies, prevent market risk and maintain the smooth running of national economy. This paper aims to discuss the roles of industry‐level indicators in industrial stock volatility. Selecting Chinese manufacturing purchasing managers index (PMI) and its five component PMI as the proxies of industry‐level indicators, we analyze the contributions of PMI on industrial stock volatility and further compare the volatility forecasting performances of PMI, macroeconomic fundamentals and economic policy uncertainty (EPU), by constructing the individual and combination GARCH‐MIDAS models. The empirical results manifest that, first, most of the PMI has significant negative effects on industrial stock volatility. Second, PMI which focuses on the industrial sector itself is more helpful to forecast industrial stock volatility compared with the commonly used macroeconomic fundamentals and economic policy uncertainty. Finally, the combination GARCH‐MIDAS approaches based on DMA technique demonstrate more excellent predictive abilities than the individual GARCH‐MIDAS models. Our major conclusions are robust through various robustness checks.     

Predictive ability and economic gains from volatility forecast combinations

The availability of numerous modeling approaches for volatility forecasting leads to model uncertainty for both researchers and practitioners. A large number of studies provide evidence in favor of combination methods for forecasting a variety of financial variables, but most of them are implemented on returns forecasting and evaluate their performance based solely on statistical evaluation criteria. In this paper, we combine various volatility forecasts based on different combination schemes and evaluate their performance in forecasting the volatility of the S&P 500 index. We use an exhaustive variety of combination methods to forecast volatility, ranging from simple techniques to time-varying techniques based on the past performance of the single models and regression techniques. We then evaluate the forecasting performance of single and combination volatility forecasts based on both statistical and economic loss functions. The empirical analysis in this paper yields an important conclusion. Although combination forecasts based on more complex methods perform better than the simple combinations and single models, there is no dominant combination technique that outperforms the rest in both statistical and economic terms.     

Model Uncertainty and Forecast Combination in High‐Dimensional Multivariate Volatility Prediction

In multivariate volatility prediction, identifying the optimal forecasting model is not always a feasible task. This is mainly due to the curse of dimensionality typically affecting multivariate volatility models. In practice only a subset of the potentially available models can be effectively estimated, after imposing severe constraints on the dynamic structure of the volatility process. It follows that in most applications the working forecasting model can be severely misspecified. This situation leaves scope for the application of forecast combination strategies as a tool for improving the predictive accuracy. The aim of the paper is to propose some alternative combination strategies and compare their performances in forecasting high‐dimensional multivariate conditional covariance matrices for a portfolio of US stock returns. In particular, we will consider the combination of volatility predictions generated by multivariate GARCH models, based on daily returns, and dynamic models for realized covariance matrices, built from intra‐daily returns. Copyright © 2015 John Wiley & Sons, Ltd.     

Predicting returns and volatility with macroeconomic variables: evidence from tests of encompassing

Tests of forecast encompassing are used to evaluate one‐step‐ahead forecasts of S&P Composite index returns and volatility. It is found that forecasts over the 1990s made from models that include macroeconomic variables tend to be encompassed by those made from a benchmark model which does not include macroeconomic variables. However, macroeconomic variables are found to add significant information to forecasts of returns and volatility over the 1970s. Often in empirical research on forecasting stock index returns and volatility, in‐sample information criteria are used to rank potential forecasting models. Here, none of the forecasting models for the 1970s that include macroeconomic variables are, on the basis of information criteria, preferred to the relevant benchmark specification. Thus, had investors used information criteria to choose between the models used for forecasting over the 1970s considered in this paper, the predictability that tests of encompassing reveal would not have been exploited. Copyright © 2005 John Wiley & Sons, Ltd.     

Forecasting Daily Variations of Stock Index Returns with a Multifractal Model of Realized Volatility

Multifractal models have recently been introduced as a new type of data‐generating process for asset returns and other financial data. Here we propose an adaptation of this model for realized volatility. We estimate this new model via generalized method of moments and perform forecasting by means of best linear forecasts derived via the Levinson–Durbin algorithm. Its out‐of‐sample performance is compared against other popular time series specifications. Using an intra‐day dataset for five major international stock market indices, we find that the the multifractal model for realized volatility improves upon forecasts of its earlier counterparts based on daily returns and of many other volatility models. While the more traditional RV‐ARFIMA model comes out as the most successful model (in terms of the number of cases in which it has the best forecasts for all combinations of forecast horizons and evaluation criteria), the new model performs often significantly better during the turbulent times of the recent financial crisis. Copyright © 2014 John Wiley & Sons, Ltd.     

Stock market volatility and the forecasting performance of stock index futures

This study attempts to apply the general equilibrium model of stock index futures with both stochastic market volatility and stochastic interest rates to the TAIFEX and the SGX Taiwan stock index futures data, and compares the predictive power of the cost of carry and the general equilibrium models. This study also represents the first attempt to investigate which of the five volatility estimators can enhance the forecasting performance of the general equilibrium model. Additionally, the impact of the up‐tick rule and other various explanatory factors on mispricing is also tested using a regression framework. Overall, the general equilibrium model outperforms the cost of carry model in forecasting prices of the TAIFEX and the SGX futures. This finding indicates that in the higher volatility of the Taiwan stock market incorporating stochastic market volatility into the pricing model helps in predicting the prices of these two futures. Furthermore, the comparison results of different volatility estimators support the conclusion that the power EWMA and the GARCH(1,1) estimators can enhance the forecasting performance of the general equilibrium model compared to the other estimators. Additionally, the relaxation of the up‐tick rule helps reduce the degree of mispricing. Copyright © 2008 John Wiley & Sons, Ltd.     

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

The 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.     

Does Information Help Intra‐Day Volatility Forecasts?

While much research related to forecasting return volatility does so in a univariate setting, this paper includes proxies for information flows to forecast intra‐day volatility for the IBEX 35 futures market. The belief is that volume or the number of transactions conveys important information about the market that may be useful in forecasting. Our results suggest that augmenting a variety of GARCH‐type models with these proxies lead to improved forecasts across a range of intra‐day frequencies. Furthermore, our results present an interesting picture whereby the PARCH model generally performs well at the highest frequencies and shorter forecasting horizons, whereas the component model performs well at lower frequencies and longer forecast horizons. Both models attempt to capture long memory; the PARCH model allows for exponential decay in the autocorrelation function, while the component model captures trend volatility, which dominates over a longer horizon. These characteristics are likely to explain the success of each model. Copyright © 2013 John Wiley & Sons, Ltd.     

Non‐linear forecasts of stock returns

Following recent non‐linear extensions of the present‐value model, this paper examines the out‐of‐sample forecast performance of two parametric and two non‐parametric nonlinear models of stock returns. The parametric models include the standard regime switching and the Markov regime switching, whereas the non‐parametric are the nearest‐neighbour and the artificial neural network models. We focused on the US stock market using annual observations spanning the period 1872–1999. Evaluation of forecasts was based on two criteria, namely forecast accuracy and forecast encompassing. In terms of accuracy, the Markov and the artificial neural network models produce at least as accurate forecasts as the other models. In terms of encompassing, the Markov model outperforms all the others. Overall, both criteria suggest that the Markov regime switching model is the most preferable non‐linear empirical extension of the present‐value model for out‐of‐sample stock return forecasting. Copyright © 2003 John Wiley & Sons, Ltd.     

Is implied volatility more informative for forecasting realized volatility: An international perspective

Inspired by the commonly held view that international stock market volatility is equivalent to cross-market information flow, we propose various ways of constructing two types of information flow, based on realized volatility (RV) and implied volatility (IV), in multiple international markets. We focus on the RVs derived from the intraday prices of eight international stock markets and use a heterogeneous autoregressive framework to forecast the future volatility of each market for 1 day to 22 days ahead. Our Diebold-Mariano tests provide strong evidence that information flow with IV enhances the accuracy of forecasting international RVs over all of the prediction horizons. The results of a model confidence set test show that a market's own IV and the first principal component of the international IVs exhibit the strongest predictive ability. In addition, the use of information flows with IV can further increase economic returns. Our results are supported by the findings of a wide range of robustness checks.     

Forecasting and trading currency volatility: an application of recurrent neural regression and model combination

In this paper, we examine the use of non‐parametric Neural Network Regression (NNR) and Recurrent Neural Network (RNN) regression models for forecasting and trading currency volatility, with an application to the GBP/USD and USD/JPY exchange rates. Both the results of the NNR and RNN models are benchmarked against the simpler GARCH alternative and implied volatility. Two simple model combinations are also analysed. The intuitively appealing idea of developing a nonlinear nonparametric approach to forecast FX volatility, identify mispriced options and subsequently develop a trading strategy based upon this process is implemented for the first time on a comprehensive basis. Using daily data from December 1993 through April 1999, we develop alternative FX volatility forecasting models. These models are then tested out‐of‐sample over the period April 1999–May 2000, not only in terms of forecasting accuracy, but also in terms of trading efficiency: in order to do so, we apply a realistic volatility trading strategy using FX option straddles once mispriced options have been identified. Allowing for transaction costs, most trading strategies retained produce positive returns. RNN models appear as the best single modelling approach yet, somewhat surprisingly, model combination which has the best overall performance in terms of forecasting accuracy, fails to improve the RNN‐based volatility trading results. Another conclusion from our results is that, for the period and currencies considered, the currency option market was inefficient and/or the pricing formulae applied by market participants were inadequate. Copyright © 2002 John Wiley & Sons, Ltd.     

Realized Volatility Forecast of Stock Index Under Structural Breaks

We investigate the realized volatility forecast of stock indices under the structural breaks. We utilize a pure multiple mean break model to identify the possibility of structural breaks in the daily realized volatility series by employing the intraday high‐frequency data of the Shanghai Stock Exchange Composite Index and the five sectoral stock indices in Chinese stock markets for the period 4 January 2000 to 30 December 2011. We then conduct both in‐sample tests and out‐of‐sample forecasts to examine the effects of structural breaks on the performance of ARFIMAX‐FIGARCH models for the realized volatility forecast by utilizing a variety of estimation window sizes designed to accommodate potential structural breaks. The results of the in‐sample tests show that there are multiple breaks in all realized volatility series. The results of the out‐of‐sample point forecasts indicate that the combination forecasts with time‐varying weights across individual forecast models estimated with different estimation windows perform well. In particular, nonlinear combination forecasts with the weights chosen based on a non‐parametric kernel regression and linear combination forecasts with the weights chosen based on the non‐negative restricted least squares and Schwarz information criterion appear to be the most accurate methods in point forecasting for realized volatility under structural breaks. We also conduct an interval forecast of the realized volatility for the combination approaches, and find that the interval forecast for nonlinear combination approaches with the weights chosen according to a non‐parametric kernel regression performs best among the competing models. Copyright © 2014 John Wiley & Sons, Ltd.     

Predicting stock index volatility: can market volume help?

This paper explores a number of statistical models for predicting the daily stock return volatility of an aggregate of all stocks traded on the NYSE. An application of linear and non-linear Granger causality tests highlights evidence of bidirectional causality, although the relationship is stronger from volatility to volume than the other way around. The out-of-sample forecasting performance of various linear, GARCH, EGARCH, GJR and neural network models of volatility are evaluated and compared. The models are also augmented by the addition of a measure of lagged volume to form more general ex-ante forecasting models. The results indicate that augmenting models of volatility with measures of lagged volume leads only to very modest improvements, if any, in forecasting performance. © 1998 John Wiley & Sons, Ltd.     

Forecasting house prices in OECD economies

In this paper, we forecast real house price growth of 16 OECD countries using information from domestic macroeconomic indicators and global measures of the housing market. Consistent with the findings for the US housing market, we find that the forecasts from an autoregressive model dominate the forecasts from the random walk model for most of the countries in our sample. More importantly, we find that the forecasts from a bivariate model that includes economically important domestic macroeconomic variables and two global indicators of the housing market significantly improve upon the univariate autoregressive model forecasts. Among all the variables, the mean square forecast error from the model with the country's domestic interest rates has the best performance for most of the countries. The country's income, industrial production, and stock markets are also found to have valuable information about the future movements in real house price growth. There is also some evidence supporting the influence of the global housing price growth in out‐of‐sample forecasting of real house price growth in these OECD countries.     

Macroeconomic forecasting with mixed data sampling frequencies: Evidence from a small open economy

The aim of this study was to forecast the Singapore gross domestic product (GDP) growth rate by employing the mixed‐data sampling (MIDAS) approach using mixed and high‐frequency financial market data from Singapore, and to examine whether the high‐frequency financial variables could better predict the macroeconomic variables. We adopt different time‐aggregating methods to handle the high‐frequency data in order to match the sampling rate of lower‐frequency data in our regression models. Our results showed that MIDAS regression using high‐frequency stock return data produced a better forecast of GDP growth rate than the other models, and the best forecasting performance was achieved by using weekly stock returns. The forecasting result was further improved by performing intra‐period forecasting.     

Forecasting stock volatility in the presence of extreme shocks: Short-term and long-term effects

This paper introduces a novel generalized autoregressive conditional heteroskedasticity–mixed data sampling–extreme shocks (GARCH-MIDAS-ES) model for stock volatility to examine whether the importance of extreme shocks changes in different time ranges. Based on different combinations of the short- and long-term effects caused by extreme events, we extend the standard GARCH-MIDAS model to characterize the different responses of the stock market for short- and long-term horizons, separately or in combination. The unique timespan of nearly 100 years of the Dow Jones Industrial Average (DJIA) daily returns allows us to understand the stock market volatility under extreme shocks from a historical perspective. The in-sample empirical results clearly show that the DJIA stock volatility is best fitted to the GARCH-MIDAS-SLES model by including the short- and long-term impacts of extreme shocks for all forecasting horizons. The out-of-sample results and robustness tests emphasize the significance of decomposing the effect of extreme shocks into short- and long-term effects to improve the accuracy of the DJIA volatility forecasts.     

Forecasting value‐at‐risk with a parsimonious portfolio spillover GARCH (PS‐GARCH) model

Accurate modelling of volatility (or risk) is important in finance, particularly as it relates to the modelling and forecasting of value‐at‐risk (VaR) thresholds. As financial applications typically deal with a portfolio of assets and risk, there are several multivariate GARCH models which specify the risk of one asset as depending on its own past as well as the past behaviour of other assets. Multivariate effects, whereby the risk of a given asset depends on the previous risk of any other asset, are termed spillover effects. In this paper we analyse the importance of considering spillover effects when forecasting financial volatility. The forecasting performance of the VARMA‐GARCH model of Ling and McAleer (2003), which includes spillover effects from all assets, the CCC model of Bollerslev (1990), which includes no spillovers, and a new Portfolio Spillover GARCH (PS‐GARCH) model, which accommodates aggregate spillovers parsimoniously and hence avoids the so‐called curse of dimensionality, are compared using a VaR example for a portfolio containing four international stock market indices. The empirical results suggest that spillover effects are statistically significant. However, the VaR threshold forecasts are generally found to be insensitive to the inclusion of spillover effects in any of the multivariate models considered. Copyright © 2008 John Wiley & Sons, Ltd.     

The role of jumps in the agricultural futures market on forecasting stock market volatility: New evidence

In this study, we explore the effect of cojumps within the agricultural futures market, and cojumps between the agricultural futures market and the stock market, on stock volatility forecasting. Also, we take into account large and small components of cojumps. We have several noteworthy findings. First, large jumps may lead to more substantial fluctuations and are more powerful than small jumps. The effect of cojumps and their decompositions on future volatility are mixed. Second, a model including large and small cojumps between the agricultural futures market and the stock market can achieve a higher forecasting accuracy, implying that large and small cojumps contain more useful predictive information than cojumps themselves. Third, our conclusions are robust based on various robustness tests such as the realized kernel, expanding forecasts, different forecasting windows, different jump tests, and different threshold values.