Multivariate volatility forecasts for stock market indices

Volatility forecasts aim to measure future risk and they are key inputs for financial analysis. In this study, we forecast the realized variance as an observable measure of volatility for several major international stock market indices and accounted for the different predictive information present in jump, continuous, and option-implied variance components. We allowed for volatility spillovers in different stock markets by using a multivariate modeling approach. We used heterogeneous autoregressive (HAR)-type models to obtain the forecasts. Based an out-of-sample forecast study, we show that: (i) including option-implied variances in the HAR model substantially improves the forecast accuracy, (ii) lasso-based lag selection methods do not outperform the parsimonious day-week-month lag structure of the HAR model, and (iii) cross-market spillover effects embedded in the multivariate HAR model have long-term forecasting power.     

Stock market volatility forecasting: Do we need high-frequency data?

The general consensus in the volatility forecasting literature is that high-frequency volatility models outperform low-frequency volatility models. However, such a conclusion is reached when low-frequency volatility models are estimated from daily returns. Instead, we study this question considering daily, low-frequency volatility estimators based on open, high, low, and close daily prices. Our data sample consists of 18 stock market indices. We find that high-frequency volatility models tend to outperform low-frequency volatility models only for short-term forecasts. As the forecast horizon increases (up to one month), the difference in forecast accuracy becomes statistically indistinguishable for most market indices. To evaluate the practical implications of our results, we study a simple asset allocation problem. The results reveal that asset allocation based on high-frequency volatility model forecasts does not outperform asset allocation based on low-frequency volatility model forecasts.     

An accurate and fully-automated ensemble model for weekly time series forecasting

Many businesses and industries require accurate forecasts for weekly time series nowadays. However, the forecasting literature does not currently provide easy-to-use, automatic, reproducible and accurate approaches dedicated to this task. We propose a forecasting method in this domain to fill this gap, leveraging state-of-the-art forecasting techniques, such as forecast combination, meta-learning, and global modelling. We consider different meta-learning architectures, algorithms, and base model pools. Based on all considered model variants, we propose to use a stacking approach with lasso regression which optimally combines the forecasts of four base models: a global Recurrent Neural Network (RNN) model, Theta, Trigonometric Box–Cox ARMA Trend Seasonal (TBATS), and Dynamic Harmonic Regression ARIMA (DHR-ARIMA), as it shows the overall best performance across seven experimental weekly datasets on four evaluation metrics. Our proposed method also consistently outperforms a set of benchmarks and state-of-the-art weekly forecasting models by a considerable margin with statistical significance. Our method can produce the most accurate forecasts, in terms of mean sMAPE, for the M4 weekly dataset among all benchmarks and all original competition participants.     

Predictive financial models of the euro area: A new evaluation test

This paper investigates the predictive ability of financial variables for euro area growth. Our forecasts are built from univariate autoregressive and single equation models. Euro area aggregate forecasts are constructed both by employing aggregate variables and by aggregating country-specific forecasts. The forecast evaluation is based on a recently developed test for equal predictive ability between nested models. Employing a monthly dataset from the period between January 1988 and May 2005 and setting the out-of-sample period to be from 2001 onwards, we find that the single most powerful predictor on a country basis is the stock market returns, followed by money supply growth. However, for the euro area aggregate, the set of most powerful predictors includes interest rate variables as well. The forecasts from pooling individual country models outperform those from the aggregate itself for short run forecasts, while for longer horizons this pattern is reversed. Additional benefits are obtained when combining information from a range of variables or combining model forecasts.     

Forecasting crude oil futures market returns: A principal component analysis combination approach

To improve the predictability of crude oil futures market returns, this paper proposes a new combination approach based on principal component analysis (PCA). The PCA combination approach combines individual forecasts given by all PCA subset regression models that use all potential predictor subsets to construct PCA indexes. The proposed method can not only guard against over-fitting by employing the PCA technique but also reduce forecast variance due to extensive forecast combinations, thus benefiting from both the combination of information and the combination of forecasts. Showing impressive out-of-sample forecasting performance, the PCA combination approach outperforms a benchmark model and many related competing models. Furthermore, a mean–variance investor can realize sizeable utility gains by using the PCA combination forecasts relative to the competing forecasts from an asset allocation perspective.     

Revisiting dividend yield dynamics and returns predictability: Evidence from a time-varying ESTR model

Since the bubble of the late 1990s the dividend yield appears non-stationary indicating the breakdown of the equilibrium relationship between prices and dividends. Two lines of research have developed in order to explain this apparent breakdown. First, that the dividend yield is better characterised as a non-linear process and second, that it is subject to mean level shifts. This paper jointly models both of these characteristics by allowing non-linear reversion to a changing mean level. Results support stationarity of this model for eight international dividend yield series. This model is than applied to the forecast of monthly stock returns. Evidence supports our time-varying non-linear model over linear alternatives, particularly so on the basis of an out-of-sample R-squared measure and a trading rule exercise. More detailed examination of the trading rule measure suggests that investors could obtain positive returns, as the model forecasts do not imply excessive trading such that costs would not outweigh returns. Finally, the superior performance of the non-linear model largely arises from its ability to forecast negative returns, whereas linear models are unable to do.     

Time-varying higher-order conditional moments and forecasting intraday VaR and Expected Shortfall

We estimate several GARCH- and Extreme Value Theory (EVT)-based models to forecast intraday Value-at-Risk (VaR) and Expected Shortfall (ES) for S&P 500 stock index futures returns for both long and short positions. Among the GARCH-based models we consider is the so-called Autoregressive Conditional Density (ARCD) model, which allows time-variation in higher-order conditional moments. ARCD model with time-varying conditional skewness parameter has the best in-sample fit among the GARCH-based models. The EVT-based model and the GARCH-based models which take conditional skewness and kurtosis (time-varying or otherwise) into account provide accurate VaR forecasts. ARCD model with time-varying conditional skewness parameter seems to provide the most accurate ES forecasts.     

Forecasting the direction of the US stock market with dynamic binary probit models

Several empirical studies have documented that the signs of excess stock returns are, to some extent, predictable. In this paper, we consider the predictive ability of the binary dependent dynamic probit model in predicting the direction of monthly excess stock returns. The recession forecast obtained from the model for a binary recession indicator appears to be the most useful predictive variable, and once it is employed, the sign of the excess return is predictable in-sample. The new dynamic “error correction” probit model proposed in the paper yields better out-of-sample sign forecasts, with the resulting average trading returns being higher than those of either the buy-and-hold strategy or trading rules based on ARMAX models.     

Modelling and forecasting stock returns: exploiting the futures market,regime shifts and international spillovers

This paper proposes a vector equilibrium correction model of stock returns that exploits the information in the futures market, while allowing for both regime‐switching behaviour and international spillovers across stock market indices. Using data for three major stock market indices since 1989, we find that: (i) in sample, our model outperforms several alternative models on the basis of standard statistical criteria; (ii) in out‐of‐sample forecasting, our model does not produce significant gains in terms of point forecasts relative to more parsimonious alternative specifications, but it does so both in terms of market timing ability and in density forecasting performance. The economic value of the density forecasts is illustrated with an application to a simple risk management exercise. Copyright © 2005 John Wiley & Sons, Ltd.     

Complete subset regressions

This paper proposes a new method for combining forecasts based on complete subset regressions. For a given set of potential predictor variables we combine forecasts from all possible linear regression models that keep the number of predictors fixed. We explore how the choice of model complexity, as measured by the number of included predictor variables, can be used to trade off the bias and variance of the forecast errors, generating a setup akin to the efficient frontier known from modern portfolio theory. In an application to predictability of stock returns, we find that combinations of subset regressions can produce more accurate forecasts than conventional approaches based on equal-weighted forecasts (which fail to account for the dimensionality of the underlying models), combinations of univariate forecasts, or forecasts generated by methods such as bagging, ridge regression or Bayesian Model Averaging.     

Stock market and macroeconomic volatility comparison: an US approach

In 2007, as the US subprime mortgage market began to fall down, which reached its peak with the catastrophic collapse of the Lehman Brothers, no one was aware of that this was going to be the worst financial crisis since the Great Depression. Evaluating the advantages and disadvantages connected with financial globalization demands a pure understanding of the influence of financial volatility. Up to the present few researches focused on analyzing macroeconomic volatility of national economies. Therefore, the aim of the paper is to compare the forecast performance of stock market and macroeconomic volatility of US economy between 2007 and 2010. Accordingly, two different types of financial time series were generated, namely weekly stock returns and quarterly return on investment. Firstly, the appropriate model was determined via time series analysis. Secondly, the relevant ARCH-type model was implemented. Finally, conditional variance forecast performance of models was presented with respect to confidence interval. Furthermore, coefficient of correlation between squared residuals and coefficient of conditional variance was given.     

Trading and non-trading period realized market volatility: Does it matter for forecasting the volatility of US stocks?

We study the potential merits of using trading and non-trading period market volatilities to model and forecast the stock volatility over the next one to 22 days. We demonstrate the role of overnight volatility information by estimating heterogeneous autoregressive (HAR) model specifications with and without a trading period market risk factor using ten years of high-frequency data for the 431 constituents of the S&P 500 index. The stocks’ own overnight squared returns perform poorly across stocks and forecast horizons, as well as in the asset allocation exercise. In contrast, we find overwhelming evidence that the market-level volatility, proxied by S&P Mini futures, matters significantly for improving the model fit and volatility forecasting accuracy. The greatest model fit and forecast improvements are found for short-term forecast horizons of up to five trading days, and for the non-trading period market-level volatility. The documented increase in forecast accuracy is found to be associated with the stocks’ sensitivity to the market risk factor. Finally, we show that both the trading and non-trading period market realized volatilities are relevant in an asset allocation context, as they increase the average returns, Sharpe ratios and certainty equivalent returns of a mean–variance investor.     

The asymmetric predictability of high-yield bonds

This study examines the relationship between the high-yield bonds market and the stock market and indicates that stock returns lead high-yield bond returns. Specifically, this study further shows that this lead–lag relationship is more solid during bear market periods since a downward trend in the stock market implies a high likelihood of the exercise of the equity put in short position embedded in a high-yield bond at maturity. We also conducted out-of-sample forecast using a VAR model, an AR model and naïve estimation during bear market and non-bear market periods. Our results demonstrate that high-yield bond returns are better predicted by a VAR model that includes past stock returns than by an AR model or naive estimation during bear market periods, but such is not the case during non-bear market periods.     

Portfolio optimization based on GARCH-EVT-Copula forecasting models

This study uses GARCH-EVT-copula and ARMA-GARCH-EVT-copula models to perform out-of-sample forecasts and simulate one-day-ahead returns for ten stock indexes. We construct optimal portfolios based on the global minimum variance (GMV), minimum conditional value-at-risk (Min-CVaR) and certainty equivalence tangency (CET) criteria, and model the dependence structure between stock market returns by employing elliptical (Student-$t$ and Gaussian) and Archimedean (Clayton, Frank and Gumbel) copulas. We analyze the performances of 288 risk modeling portfolio strategies using out-of-sample back-testing. Our main finding is that the CET portfolio, based on ARMA-GARCH-EVT-copula forecasts, outperforms the benchmark portfolio based on historical returns. The regression analyses show that GARCH-EVT forecasting models, which use Gaussian or Student-$t$ copulas, are best at reducing the portfolio risk.     

Combining survey long-run forecasts and nowcasts with BVAR forecasts using relative entropy

This paper constructs hybrid forecasts that combine forecasts from vector autoregressive (VAR) model(s) with both short- and long-term expectations from surveys. Specifically, we use the relative entropy to tilt one-step-ahead and long-horizon VAR forecasts to match the nowcasts and long-horizon forecasts from the Survey of Professional Forecasters. We consider a variety of VAR models, ranging from simple fixed-parameter to time-varying parameters. The results across models indicate meaningful gains in multi-horizon forecast accuracy relative to model forecasts that do not incorporate long-term survey conditions. Accuracy improvements are achieved for a range of variables, including those that are not tilted directly but are affected through spillover effects from tilted variables. The accuracy gains for hybrid inflation forecasts from simple VARs are substantial, statistically significant, and competitive to time-varying VARs, univariate benchmarks, and survey forecasts. We view our proposal as an indirect approach to accommodating structural change and moving end points.     

The influence and predictive powers of mixed-frequency individual stock sentiment on stock returns

In this article, we construct mixed-frequency individual stock sentiment using MIDAS model. We first investigate the influence power of mixed-frequency individual stock sentiment on excess returns. The results indicate that the higher the frequency of individual stock sentiment is, the better it explains the variation of excess returns, that mixed-frequency individual stock sentiment, especially mixed high-frequency sentiment, exerts greater influence on excess returns than the same frequency one and that the mixed-frequency sentiment has a stronger explanatory power to the variation of excess returns than size factor, book-to-market factor, profitability factor and investment factor do. Then, we study the predictive content of mixed-frequency individual stock sentiment. The results show that the higher the frequency of individual stock sentiment is, the better the forecast performs. Moreover, by comparing the corresponding statistics in influence and predictive power models, we find that the influence power of mixed-frequency individual stock sentiment is more significant than its predictive power.     

The regime-switching risk premium in the gold futures market

A bivariate Markov-switching model identifies two regimes in the futures-price and risk-premium models. The persistent underlying states have very different implications for spot and risk-premium forecasts. In the “low” state, a positive bias predicts spot price appreciation. The “high” state is associated with lower spot appreciation and higher risk premiums. The regime-switching framework provides a new perspective on the intertemporal role of gold as a hedge or safe-haven asset. The gold spot-price appreciation regime is shown to be correlated with higher inflation rates and the complement regime is associated with high market returns and stock market risk premia. Since the state-space methodology procedure can be employed using only past data, forecasts of the persistent unobserved underlying state of the gold price appreciation regime will be augmented as more data becomes available.     

对上证指数波动性的实证分析

股票价格频繁波动是股票市场中最明显的特征之一。ARCH类模型可以成功的预测金融资产收益的方差。通过对我国股价指数的统计描述,表明我国金融资产收益率存在自回归条件异方差,并表现出非正态性。并且应用GARCH、TARCH、EGARCH模型理论,进一步分析了日收益率波动的条件异方差性、非对称性。     

Empirical modeling of high-income and emerging stock and Forex market return volatility using Markov-switching GARCH models

Using weekly data for stock and Forex market returns, a set of MS-GARCH models is estimated for a group of high-income (HI) countries and emerging market economies (EMEs) using algorithms proposed by Augustyniak (2014) and Ardia et al. (2018, 2019a,b), allowing for a variety of conditional variance and distribution specifications. The main results are: (i) the models selected using Ardia et al. (2018) have a better fit than those estimated by Augustyniak (2014), contain skewed distributions, and often require that the main coefficients be different in each regime; (ii) in Latam Forex markets, estimates of the heavy-tail parameter are smaller than in HI Forex and all stock markets; (iii) the persistence of the high-volatility regime is considerable and more evident in stock markets (especially in Latam EMEs); (iv) in (HI and Latam) stock markets, a single-regime GJR model (leverage effects) with skewed distributions is selected; but when using MS models, virtually no MS-GJR models are selected. However, this does not happen in Forex markets, where leverage effects are not found either in single-regime or MS-GARCH models.     

Testing for linear and nonlinear granger causality in the stock price-volume relation: Korean evidence

In this paper, linear and nonlinear Granger causality tests are used to examine the dynamic relationship between daily Korean stock returns and trading volume. We find evidence of significant bidirectional linear and nonlinear causality between these two series. ARCH-ype models are used to examine whether the nonlinear causal relations can be explained by stock returns and volume serving as proxies for information flow in the stochastic process generating volume and stock returns respectively. After controlling for volatility persistent in both series and filtering for linear dependence, we find evidence of nonlinear bidirectional causality between stock returns and volume series. The finding of strong bidirectional stock price-volume causal relationships implies that knowledge of current trading volume improves the ability to forecast stock prices. This evidence is not supportive of the efficient market hypothesis. Another finding is that the nonlinear relationship is sensitive to institutional, organizational, and structural factors. The results of this study should be useful to regulators, practitioners and derivative market participants whose success precariously depends on the ability to forecast stock price movements.