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.     

Time‐Varying Parameter Realized Volatility Models

In this paper, we introduce the functional coefficient to heterogeneous autoregressive realized volatility (HAR‐RV) models to make the parameters change over time. A nonparametric statistic is developed to perform a specification test. The simulation results show that our test displays reliable size and good power. Using the proposed test, we find a significant time variation property of coefficients to the HAR‐RV models. Time‐varying parameter (TVP) models can significantly outperform their constant‐coefficient counterparts for longer forecasting horizons. The predictive ability of TVP models can be improved by accounting for VIX information. Copyright © 2016 John Wiley & Sons, Ltd.     

Comparison of Realized Measure and Implied Volatility in Forecasting Volatility

This paper compares the information content of realized measures constructed from high‐frequency data and implied volatilities from options in the context of forecasting volatility. The comparison is based on within‐sample and out‐of‐sample (over horizons of 1–22 days) forecasts of daily S&P 500 index return volatility. The paper adds to the findings of previous studies, by considering recent developments in the related practice and the literature. It is shown that, for within‐sample fitting, the realized measure is more informative than the implied volatility. In contrast, the implied volatility is more informative than the realized measure for out‐of‐sample forecasting, in particular for multi‐step‐ahead forecasting. Moreover, we show that it is helpful to use all the information provided by the realized measure and the implied volatility for the within‐sample fitting. For multi‐step‐ahead forecasting, however, it is better to use only the implied volatility. Copyright © 2013 John Wiley & Sons, Ltd.     

A Multiplicative Error Model with Heterogeneous Components for Forecasting Realized Volatility

To forecast realized volatility, this paper introduces a multiplicative error model that incorporates heterogeneous components: weekly and monthly realized volatility measures. While the model captures the long‐memory property, estimation simply proceeds using quasi‐maximum likelihood estimation. This paper investigates its forecasting ability using the realized kernels of 34 different assets provided by the Oxford‐Man Institute's Realized Library. The model outperforms benchmark models such as ARFIMA, HAR, Log‐HAR and HEAVY‐RM in within‐sample fitting and out‐of‐sample (1‐, 10‐ and 22‐step) forecasts. It performed best in both pointwise and cumulative comparisons of multi‐step‐ahead forecasts, regardless of loss function (QLIKE or MSE). Copyright © 2015 John Wiley & Sons, Ltd.     

Modeling Realized Volatility Dynamics with a Genetic Algorithm

The heterogeneous autoregressive model of realized volatility (HAR‐RV) is inspired by the heterogeneous market hypothesis and characterizes realized volatility dynamics through a linear function of lagged daily, weekly and monthly realized volatilities with a (1, 5, 22) lag structure. Considering that different markets can have different heterogeneous structures and a market's heterogeneous structure can vary over time, we build an adaptive heterogeneous autoregressive model of realized volatility (AHAR‐RV), whose lag structure is optimized with a genetic algorithm. Using nine common loss functions and the superior predictive ability test, we find that our AHAR‐RV model and its extensions provide significantly better out‐of‐sample volatility forecasts for the CSI 300 index than the corresponding HAR models. Furthermore, the AHAR‐RV model significantly outperforms all the other models under most loss functions. Besides, we confirm that Chinese stock markets' heterogeneous structure varies over time and the (1, 5, 22) lag structure is not the optimal choice. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Moving beyond Volatility Index (VIX): HARnessing the term structure of implied volatility

This paper considers how information from the implied volatility (IV) term structure can be harnessed to improve stock return volatility forecasting within the state-of-the-art HAR model. Factors are extracted from the IV term structure and included as exogenous variables in the HAR framework. We found that including slope and curvature factors leads to significant forecast improvements over the HAR benchmark at a range of forecast horizons, compared with the standard HAR model and HAR model with VIX as IV information set.     

Realized Volatility Forecasting of Agricultural Commodity Futures Using Long Memory and Regime Switching

We investigate the dynamic properties of the realized volatility of five agricultural commodity futures by employing the high‐frequency data from Chinese markets and find that the realized volatility exhibits both long memory and regime switching. To capture these properties simultaneously, we utilize a Markov switching autoregressive fractionally integrated moving average (MS‐ARFIMA) model to forecast the realized volatility by combining the long memory process with regime switching component, and compare its forecast performances with the competing models at various horizons. The full‐sample estimation results show that the dynamics of the realized volatility of agricultural commodity futures are characterized by two levels of long memory: one associated with the low‐volatility regime and the other with the high‐volatility regime, and the probability to stay in the low‐volatility regime is higher than that in the high‐volatility regime. The out‐of‐sample volatility forecast results show that the combination of long memory with switching regimes improves the performance of realized volatility forecast, and the proposed model represents a superior out‐of‐sample realized volatility forecast to the competing models. Copyright © 2016 John Wiley & Sons, Ltd.     

Combination of Forecasts across Estimation Windows: An Application to Air Travel Demand

This paper applies combining forecasts of air travel demand generated from the same model but over different estimation windows. The combination approach used resorts to Pesaran and Pick (Journal of Business Economics and Statistics 2011; 29 : 307–318), but the empirical application is extended in several ways. The forecasts are based on a seasonal Box–Jenkins model (SARIMA), which is adequate to forecast monthly air travel demand with distinct seasonal patterns at the largest German airport: Frankfurt am Main. Furthermore, forecasts with forecast horizons from 1 to 12 months ahead, which are based on different average estimation windows, expanding windows and single rolling windows, are compared with baseline forecasts based on an expanding window of the observations after a structural break. The forecast exercise shows that the average window forecasts mostly outperform the alternative single window forecasts. Copyright © 2016 John Wiley & Sons, Ltd.     

On the Modelling and Forecasting of Multivariate Realized Volatility: Generalized Heterogeneous Autoregressive (GHAR) Model

Recent multivariate extensions of the popular heterogeneous autoregressive model (HAR) for realized volatility leave substantial information unmodelled in residuals. We propose to employ a system of seemingly unrelated regressions to model and forecast a realized covariance matrix to capture this information. We find that the newly proposed generalized heterogeneous autoregressive (GHAR) model outperforms competing approaches in terms of economic gains, providing better mean–variance trade‐off, while, in terms of statistical precision, GHAR is not substantially dominated by any other model. Our results provide a comprehensive comparison of the performance when realized covariance, subsampled realized covariance and multivariate realized kernel estimators are used. We study the contribution of the estimators across different sampling frequencies, and show that the multivariate realized kernel and subsampled realized covariance estimators deliver further gains compared to realized covariance estimated on a 5‐minute frequency. In order to show economic and statistical gains, a portfolio of various sizes is used. Copyright © 2016 John Wiley & Sons, Ltd.     

Measuring the market risk of freight rates: A forecast combination approach

This paper addresses the issue of freight rate risk measurement via value at risk (VaR) and forecast combination methodologies while focusing on detailed performance evaluation. We contribute to the literature in three ways: First, we reevaluate the performance of popular VaR estimation methods on freight rates amid the adverse economic consequences of the recent financial and sovereign debt crisis. Second, we provide a detailed and extensive backtesting and evaluation methodology. Last, we propose a forecast combination approach for estimating VaR. Our findings suggest that our combination methods produce more accurate estimates for all the sectors under scrutiny, while in some cases they may be viewed as conservative since they tend to overestimate nominal VaR.