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.     

Modeling and forecasting aggregate stock market volatility in unstable environments using mixture innovation regressions

We perform Bayesian model averaging across different regressions selected from a set of predictors that includes lags of realized volatility, financial and macroeconomic variables. In our model average, we entertain different channels of instability by either incorporating breaks in the regression coefficients of each individual model within our model average, breaks in the conditional error variance, or both. Changes in these parameters are driven by mixture distributions for state innovations (MIA) of linear Gaussian state‐space models. This framework allows us to compare models that assume small and frequent as well as models that assume large but rare changes in the conditional mean and variance parameters. Results using S&P 500 monthly and quarterly realized volatility data from 1960 to 2014 suggest that Bayesian model averaging in combination with breaks in the regression coefficients and the error variance through MIA dynamics generates statistically significantly more accurate forecasts than the benchmark autoregressive model. However, compared to a MIA autoregression with breaks in the regression coefficients and the error variance, we fail to provide any drastic improvements.     

Modeling multivariate co integrated systems: Insights from non-linear dynamics

Johansen's test for co integration is applied to Litterman's original six-variable Bayesian vector auto regression (BVAR) model to obtain vector error correction mechanism (VECM) and Bayesian error correction (BECM) versions of the model. The Brock, Dechert, and Scheinkman (BDS) test for independence from the non-linear dynamics literature is then applied to the error structures of each estimated equation of the BECM and VECM models, plus two BVAR versions of the model. The results show that none of the models produce independent and identically distributed (IID) errors for all six equations. However, the BDS results suggest the elimination of the Bayesian prior from the BECM model, given that the univariate VECM errors are IID in five equations, compared to only two or three equations under the three Bayesian restricted models. These results combined with previous evidence regarding the superior forecasting performance of BECM over ECM models suggest future experimentation with less restrictive BVAR priors, BECM models corrected for heteroscedasticity, or hybrid specifications based on the nonlinear dynamics literature.     

Beating the random walk in Central and Eastern Europe

We compare the accuracy of vector autoregressive (VAR), restricted vector autoregressive (RVAR), Bayesian vector autoregressive (BVAR), vector error correction (VEC) and Bayesian error correction (BVEC) models in forecasting the exchange rates of five Central and Eastern European currencies (Czech Koruna, Hungarian Forint, Slovak Koruna, Slovenian Tolar and Polish Zloty) against the US Dollar and the Euro. Although these models tend to outperform the random walk model for long‐term predictions (6 months ahead and beyond), even the best models in terms of average prediction error fail to reject the test of equality of forecasting accuracy against the random walk model in short‐term predictions. Copyright © 2005 John Wiley & Sons, Ltd.     

Assessment of agricultural energy consumption of Turkey by MLR and Bayesian optimized SVR and GPR models

Agricultural productivity highly depends on the cost of energy required for cultivation. Thus prior knowledge of energy consumption is an important step for energy planning and policy development in agriculture. The aim of the present study is to evaluate the application potential of multiple linear regression (MLR) and machine learning tools such as support vector regression (SVR) and Gaussian process regression (GPR) to forecast the agricultural energy consumption of Turkey. In the development of the models, widespread indicators such as agricultural value-added, total arable land, gross domestic product share of agriculture, and population data were used as input parameters. Twenty-eight-year historical data from 1990 to 2017 were utilized for the training and testing stages of the models. A Bayesian optimization method was applied to improve the prediction capability of SVR and GPR models. The performance of the models was measured by various statistical tools. The results indicated that the Bayesian optimized GPR (BGPR) model with exponential kernel function showed a superior prediction capability over MLR and Bayesian optimized SVR model. The root mean square error, mean absolute deviation, mean absolute percentage error, and coefficient of determination (R²) values for the BGPR model were determined as 0.0022, 0.0005, 0.2041, and 0.9999 in the training phase and 0.0452, 0.0310, 7.7152, and 0.9677 in the testing phase, respectively. As a result, it can be concluded that the proposed BGPR model is an efficient technique and has the potential to predict agricultural energy consumption with high accuracy.     

Forecasting the Term Structure of Interest Rates Using Integrated Nested Laplace Approximations

This article discusses the use of Bayesian methods for inference and forecasting in dynamic term structure models through integrated nested Laplace approximations (INLA). This method of analytical approximation allows accurate inferences for latent factors, parameters and forecasts in dynamic models with reduced computational cost. In the estimation of dynamic term structure models it also avoids some simplifications in the inference procedures, such as the inefficient two‐step ordinary least squares (OLS) estimation. The results obtained in the estimation of the dynamic Nelson–Siegel model indicate that this method performs more accurate out‐of‐sample forecasts compared to the methods of two‐stage estimation by OLS and also Bayesian estimation methods using Markov chain Monte Carlo (MCMC). These analytical approaches also allow efficient calculation of measures of model selection such as generalized cross‐validation and marginal likelihood, which may be computationally prohibitive in MCMC estimations. Copyright © 2014 John Wiley & Sons, Ltd.     

Time series forecasting using functional partial least square regression with stochastic volatility,GARCH, and exponential smoothing

We propose a method for improving the predictive ability of standard forecasting models used in financial economics. Our approach is based on the functional partial least squares (FPLS) model, which is capable of avoiding multicollinearity in regression by efficiently extracting information from the high‐dimensional market data. By using its well‐known ability, we can incorporate auxiliary variables that improve the predictive accuracy. We provide an empirical application of our proposed methodology in terms of its ability to predict the conditional average log return and the volatility of crude oil prices via exponential smoothing, Bayesian stochastic volatility, and GARCH (generalized autoregressive conditional heteroskedasticity) models, respectively. In particular, what we call functional data analysis (FDA) traces in this article are obtained via the FPLS regression from both the crude oil returns and auxiliary variables of the exchange rates of major currencies. For forecast performance evaluation, we compare out‐of‐sample forecasting accuracy of the standard models with FDA traces to the accuracy of the same forecasting models with the observed crude oil returns, principal component regression (PCR), and least absolute shrinkage and selection operator (LASSO) models. We find evidence that the standard models with FDA traces significantly outperform our competing models. Finally, they are also compared with the test for superior predictive ability and the reality check for data snooping. Our empirical results show that our new methodology significantly improves predictive ability of standard models in forecasting the latent average log return and the volatility of financial time series.     

Forecasting US inflation by Bayesian model averaging

Recent empirical work has considered the prediction of inflation by combining the information in a large number of time series. One such method that has been found to give consistently good results consists of simple equal‐weighted averaging of the forecasts from a large number of different models, each of which is a linear regression relating inflation to a single predictor and a lagged dependent variable. In this paper, I consider using Bayesian model averaging for pseudo out‐of‐sample prediction of US inflation, and find that it generally gives more accurate forecasts than simple equal‐weighted averaging. This superior performance is consistent across subsamples and a number of inflation measures. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting with panel data

This paper gives a brief survey of forecasting with panel data. It begins with a simple error component regression model and surveys the best linear unbiased prediction under various assumptions of the disturbance term. This includes various ARMA models as well as spatial autoregressive models. The paper also surveys how these forecasts have been used in panel data applications, running horse races between heterogeneous and homogeneous panel data models using out‐of‐sample forecasts. Copyright © 2008 John Wiley & Sons, Ltd.     

Optimal Hedge Ratio Estimation and Effectiveness Using ARCD

This paper examines the importance of forecasting higher moments for optimal hedge ratio estimation. To this end, autoregressive conditional density (ARCD) models are employed which allow for time variation in variance, skewness and kurtosis. The performance of ARCD models is evaluated against that of GARCH and of other conventional hedge ratio estimation methodologies based on exponentially weighted moving averages, ordinary least squares and error correction, respectively. An empirical application using spot and futures data on the DJI, FTSE and DAX equity indices compares the in‐sample and out‐of‐sample hedging effectiveness of each approach in terms of risk minimization. The results show that the ARCD approach has the best performance, thus suggesting that forecasting higher moments is of practical importance for futures hedging. Copyright © 2012 John Wiley & Sons, Ltd.     

Prediction intervals for exponential smoothing using two new classes of state space models

Three general classes of state space models are presented, using the single source of error formulation. The first class is the standard linear model with homoscedastic errors, the second retains the linear structure but incorporates a dynamic form of heteroscedasticity, and the third allows for non‐linear structure in the observation equation as well as heteroscedasticity. These three classes provide stochastic models for a wide variety of exponential smoothing methods. We use these classes to provide exact analytic (matrix) expressions for forecast error variances that can be used to construct prediction intervals one or multiple steps ahead. These formulas are reduced to non‐matrix expressions for 15 state space models that underlie the most common exponential smoothing methods. We discuss relationships between our expressions and previous suggestions for finding forecast error variances and prediction intervals for exponential smoothing methods. Simpler approximations are developed for the more complex schemes and their validity examined. The paper concludes with a numerical example using a non‐linear model. Copyright © 2005 John Wiley & Sons, Ltd.     

Local to unity,long‐horizon forecasting thresholds for model selection in the AR(1)

This article introduces a novel framework for analysing long‐horizon forecasting of the near non‐stationary AR(1) model. Using the local to unity specification of the autoregressive parameter, I derive the asymptotic distributions of long‐horizon forecast errors both for the unrestricted AR(1), estimated using an ordinary least squares (OLS) regression, and for the random walk (RW). I then identify functions, relating local to unity ‘drift’ to forecast horizon, such that OLS and RW forecasts share the same expected square error. OLS forecasts are preferred on one side of these ‘forecasting thresholds’, while RW forecasts are preferred on the other. In addition to explaining the relative performance of forecasts from these two models, these thresholds prove useful in developing model selection criteria that help a forecaster reduce error. Copyright © 2004 John Wiley & Sons, Ltd.     

Linear constraints,robust-weighting and efficient composite modeling

Recent studies have shown that composite forecasting produces superior forecasts when compared to individual forecasts. This paper extends the existing literature by employing linear constraints and robust regression techniques in composite model building. Security analysts forecasts may be improved when combined with time series forecasts for a diversified sample of 261 firms with a 1980-1982 post-sample estimation period. The mean square error of analyst forecasts may be reduced by combining analyst and univariate time series model forecasts in constrained and unconstrained ordinary least squares regression models. These reductions are very interesting when one finds that the univariate time series model forecasts do not substantially deviate from those produced by ARIMA (0,1,1) processes. Moreover, security analysts' forecast errors may be significantly reduced when constrained and unconstrained robust regression analyses are employed.     

A hybrid model considering cointegration for interval-valued pork price forecasting in China

Compared with point forecasting, interval forecasting is believed to be more effective and helpful in decision making, as it provides more information about the data generation process. Based on the well-established “linear and nonlinear” modeling framework, a hybrid model is proposed by coupling the vector error correction model (VECM) with artificial intelligence models which consider the cointegration relationship between the lower and upper bounds (Coin-AIs). VECM is first employed to fit the original time series with the residual error series modeled by Coin-AIs. Using pork price as a research sample, the empirical results statistically confirm the superiority of the proposed VECM-CoinAIs over other competing models, which include six single models and six hybrid models. This result suggests that considering the cointegration relationship is a workable direction for improving the forecast performance of the interval-valued time series. Moreover, with a reasonable data transformation process, interval forecasting is proven to be more accurate than point forecasting.     

Testing Interval Forecasts: A GMM‐Based Approach

This paper proposes a new evaluation framework for interval forecasts. Our model‐free test can be used to evaluate interval forecasts and high‐density regions, potentially discontinuous and/or asymmetric. Using a simple J‐statistic, based on the moments defined by the orthonormal polynomials associated with the binomial distribution, this new approach presents many advantages. First, its implementation is extremely easy. Second, it allows for a separate test for unconditional coverage, independence and conditional coverage hypotheses. Third, Monte Carlo simulations show that for realistic sample sizes our GMM test has good small‐sample properties. These results are corroborated by an empirical application on SP500 and Nikkei stock market indexes. It confirms that using this GMM test leads to major consequences for the ex post evaluation of interval forecasts produced by linear versus nonlinear models. Copyright © 2011 John Wiley & Sons, Ltd.     

Model specification and forecasting foreign exchange rates with vector autoregressions

This study examines the forecasting accuracy of alternative vector autoregressive models each in a seven‐variable system that comprises in turn of daily, weekly and monthly foreign exchange (FX) spot rates. The vector autoregressions (VARs) are in non‐stationary, stationary and error‐correction forms and are estimated using OLS. The imposition of Bayesian priors in the OLS estimations also allowed us to obtain another set of results. We find that there is some tendency for the Bayesian estimation method to generate superior forecast measures relatively to the OLS method. This result holds whether or not the data sets contain outliers. Also, the best forecasts under the non‐stationary specification outperformed those of the stationary and error‐correction specifications, particularly at long forecast horizons, while the best forecasts under the stationary and error‐correction specifications are generally similar. The findings for the OLS forecasts are consistent with recent simulation results. The predictive ability of the VARs is very weak. Copyright © 2001 John Wiley & Sons, Ltd.     

Estimating and Forecasting APARCH‐Skew‐t Model by Wavelet Support Vector Machines

This paper concentrates on comparing estimation and forecasting ability of quasi‐maximum likelihood (QML) and support vector machines (SVM) for financial data. The financial series are fitted into a family of asymmetric power ARCH (APARCH) models. As the skewness and kurtosis are common characteristics of the financial series, a skew‐t distributed innovation is assumed to model the fat tail and asymmetry. Prior research indicates that the QML estimator for the APARCH model is inefficient when the data distribution shows departure from normality, so the current paper utilizes the semi‐parametric‐based SVM method and shows that it is more efficient than the QML under the skewed Student's‐t distributed error. As the SVM is a kernel‐based technique, we further investigate its performance by applying separately a Gaussian kernel and a wavelet kernel. The results suggest that the SVM‐based method generally performs better than QML for both in‐sample and out‐of‐sample data. The outcomes also highlight the fact that the wavelet kernel outperforms the Gaussian kernel with lower forecasting error, better generation capability and more computation efficiency. Copyright © 2014 John Wiley & Sons, Ltd.     

Can forecasting performance be improved by considering the steady state? An application to Swedish inflation and interest rate

This paper investigates whether the forecasting performance of Bayesian autoregressive and vector autoregressive models can be improved by incorporating prior beliefs on the steady state of the time series in the system. Traditional methodology is compared to the new framework—in which a mean‐adjusted form of the models is employed—by estimating the models on Swedish inflation and interest rate data from 1980 to 2004. Results show that the out‐of‐sample forecasting ability of the models is practically unchanged for inflation but significantly improved for the interest rate when informative prior distributions on the steady state are provided. The findings in this paper imply that this new methodology could be useful since it allows us to sharpen our forecasts in the presence of potential pitfalls such as near unit root processes and structural breaks, in particular when relying on small samples. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecast performance of nonlinear error‐correction models with multiple regimes

In this paper we investigate the forecast performance of nonlinear error‐correction models with regime switching. In particular, we focus on threshold and Markov switching error‐correction models, where adjustment towards long‐run equilibrium is nonlinear and discontinuous. Our simulation study reveals that the gains from using a correctly specified nonlinear model can be considerable, especially if disequilibrium adjustment is strong and/or the magnitude of parameter changes is relatively large. Copyright © 2005 John Wiley & Sons, Ltd.     

Bias‐corrected bootstrap prediction regions for vector autoregression

This paper examines small sample properties of alternative bias‐corrected bootstrap prediction regions for the vector autoregressive (VAR) model. Bias‐corrected bootstrap prediction regions are constructed by combining bias‐correction of VAR parameter estimators with the bootstrap procedure. The backward VAR model is used to bootstrap VAR forecasts conditionally on past observations. Bootstrap prediction regions based on asymptotic bias‐correction are compared with those based on bootstrap bias‐correction. Monte Carlo simulation results indicate that bootstrap prediction regions based on asymptotic bias‐correction show better small sample properties than those based on bootstrap bias‐correction for nearly all cases considered. The former provide accurate coverage properties in most cases, while the latter over‐estimate the future uncertainty. Overall, the percentile‐t bootstrap prediction region based on asymptotic bias‐correction is found to provide highly desirable small sample properties, outperforming its alternatives in nearly all cases. Copyright © 2004 John Wiley & Sons, Ltd.