Dynamic Latent Class Model Averaging for Online Prediction

We consider the problem of online prediction when it is uncertain what the best prediction model to use is. We develop a method called dynamic latent class model averaging, which combines a state‐space model for the parameters of each of the candidate models of the system with a Markov chain model for the best model. We propose a polychotomous regression model for the transition weights to assume that the probability of a change in time depends on the past through the values of the most recent time periods and spatial correlation among the regions. The evolution of the parameters in each submodel is defined by exponential forgetting. This structure allows the ‘correct’ model to vary over both time and regions. In contrast to existing methods, the proposed model naturally incorporates clustering and prediction analysis in a single unified framework. We develop an efficient Gibbs algorithm for computation, and we demonstrate the value of our framework on simulated experiments and on a real‐world problem: forecasting IBM's corporate revenue. Copyright © 2014 John Wiley & Sons, Ltd.     

Forecasting under model uncertainty: Non-homogeneous hidden Markov models with Pòlya-Gamma data augmentation

We consider finite state-space non-homogeneous hidden Markov models for forecasting univariate time series. Given a set of predictors, the time series are modeled via predictive regressions with state-dependent coefficients and time-varying transition probabilities that depend on the predictors via a logistic/multinomial function. In a hidden Markov setting, inference for logistic regression coefficients becomes complicated and in some cases impossible due to convergence issues. In this paper, we aim to address this problem utilizing the recently proposed Pólya-Gamma latent variable scheme. Also, we allow for model uncertainty regarding the predictors that affect the series both linearly — in the mean — and non-linearly — in the transition matrix. Predictor selection and inference on the model parameters are based on an automatic Markov chain Monte Carlo scheme with reversible jump steps. Hence the proposed methodology can be used as a black box for predicting time series. Using simulation experiments, we illustrate the performance of our algorithm in various setups, in terms of mixing properties, model selection and predictive ability. An empirical study on realized volatility data shows that our methodology gives improved forecasts compared to benchmark models.     

Out‐of‐sample equity premium prediction: A scenario analysis approach

We propose two methods of equity premium prediction with single and multiple predictors respectively and evaluate their out‐of‐sample performance using US stock data with 15 popular predictors for equity premium prediction. The first method defines three scenarios in terms of the expected returns under the scenarios and assumes a Markov chain governing the occurrence of the scenarios over time. It employs predictive quantile regressions of excess return on a predictor for three quantiles to estimate the occurrence of the scenarios over an in‐sample period and the transition probabilities of the Markov chain, predicts the expected returns under the scenarios, and generates an equity premium forecast by combining the predicted expected returns under three scenarios with the estimated transition probabilities. The second method generates an equity premium forecast by combining the individual forecasts from the first method across all predictors. For most of predictors, the first method outperforms the benchmark method of historical average and the traditional predictive linear regression with a single predictor both statistically and economically, and the second method consistently performs better than several competing methods used in the literature. The performance of our methods is further examined under different scenarios and economic conditions, and is robust for two different out‐of‐sample periods and specifications of the scenarios.     

One-sided Simultaneous Prediction Intervals for AR(1) and MA(1) Processes with Exponential Innovations

This paper is concerned with the determination of simultaneous confidence regions for some types of time series models. We derive recursive formulas which allow the determination of the probability for an AR(1) stationary process based on exponential inputs to lie under any sequence of constants during N steps. Also, probabilities of the same form are derived for an MA(1) process, based on an exponentially distributed white noise. Numerical results are obtained and comparison of prediction regions for different values of ϕ or θ is made. The results show how the use of the correlation structure of the models can reduce the confidence regions area. © 1997 by John Wiley & Sons, Ltd.     

Wind power prediction based on wind speed forecast using hidden Markov model

This study examines a new approach for short-term wind speed and power forecasting based on the mixture of Gaussian hidden Markov models (MoG-HMMs). The proposed approach focuses on the characteristics of wind speed and power in the consecutive hours of previous days. The proposed method is carried out in two steps. In the first step, for the hourly prediction of wind speed, several wind speed features are employed in MoG-HMM, and in the second step, the results obtained from the first step along with their characteristics and wind power features are used to predict wind power estimation. To increase the prediction accuracy, the data used in each step are classified, and then for each class, one HMM with its specific parameters is used. The performance of the proposed approach is examined using real NREL data. The results show that the proposed method is more precise than other examined methods.     

Predictive power of Markovian models: Evidence from US recession forecasting

This paper provides extensions to the application of Markovian models in predicting US recessions. The proposed Markovian models, including the hidden Markov and Markov models, incorporate the temporal autocorrelation of binary recession indicators in a traditional but natural way. Considering interest rates and spreads, stock prices, monetary aggregates, and output as the candidate predictors, we examine the out‐of‐sample performance of the Markovian models in predicting the recessions 1–12 months ahead, through rolling window experiments as well as experiments based on the fixed full training set. Our study shows that the Markovian models are superior to the probit models in detecting a recession and capturing the recession duration. But sometimes the rolling window method may affect the models' prediction reliability as it could incorporate the economy's unsystematic adjustments and erratic shocks into the forecast. In addition, the interest rate spreads and output are the most efficient predictor variables in explaining business cycles.     

Forecasting stock prices using a hierarchical Bayesian approach

The Ohlson model is evaluated using quarterly data from stocks in the Dow Jones Index. A hierarchical Bayesian approach is developed to simultaneously estimate the unknown coefficients in the time series regression model for each company by pooling information across firms. Both estimation and prediction are carried out by the Markov chain Monte Carlo (MCMC) method. Our empirical results show that our forecast based on the hierarchical Bayes method is generally adequate for future prediction, and improves upon the classical method. Copyright © 2005 John Wiley & Sons, Ltd.     

The Predictive Performance Evaluation of Biased Regression Predictors With Correlated Errors

When the interdependence of disturbances is present in a regression model, the pattern of sample residuals contains information which is useful in the prediction of post‐sample drawings and when multicollinearity among regressors is also present, it is useful to use biased regression estimators. This information is exploited in the biased predictors derived here. Also, the predictive performance of various biased predictors with correlated errors is discussed and all pair‐wise comparisons are made among these predictors. The theoretical results are illustrated by a numerical example. Copyright © 2015 John Wiley & Sons, Ltd.     

Forecasting Forward Defaults with the Discrete‐Time Hazard Model

For predicting forward default probabilities of firms, the discrete‐time forward hazard model (DFHM) is proposed. We derive maximum likelihood estimates for the parameters in DFHM. To improve its predictive power in practice, we also consider an extension of DFHM by replacing its constant coefficients of firm‐specific predictors with smooth functions of macroeconomic variables. The resulting model is called the discrete‐time varying‐coefficient forward hazard model (DVFHM). Through local maximum likelihood analysis, DVFHM is shown to be a reliable and flexible model for forward default prediction. We use real panel datasets to illustrate these two models. Using an expanding rolling window approach, our empirical results confirm that DVFHM has better and more robust out‐of‐sample performance on forward default prediction than DFHM, in the sense of yielding more accurate predicted numbers of defaults and predicted survival times. Thus DVFHM is a useful alternative for studying forward default losses in portfolios. Copyright © 2013 John Wiley & Sons, Ltd.     

Enhancing survey‐based investment forecasts

We investigate the accuracy of capital investment predictors from a national business survey of South African manufacturing. Based on data available to correspondents at the time of survey completion, we propose variables that might inform the confidence that can be attached to their predictions. Having calibrated the survey predictors' directional accuracy, we model the probability of a correct directional prediction using logistic regression with the proposed variables. For point forecasting, we compare the accuracy of rescaled survey forecasts with time series benchmarks and some survey/time series hybrid models. In addition, using the same set of variables, we model the magnitude of survey prediction errors. Directional forecast tests showed that three out of four survey predictors have value but are biased and inefficient. For shorter horizons we found that survey forecasts, enhanced by time series data, significantly improved point forecasting accuracy. For longer horizons the survey predictors were at least as accurate as alternatives. The usefulness of the more accurate of the predictors examined is enhanced by auxiliary information, namely the probability of directional accuracy and the estimated error magnitude.     

Minimum variance prediction of bilinear time series: Direct and adaptive versions

Bilinear models of time series are considered. Minimum variance predictor for bilinear time series, homogeneous in the input and output, is proposed. Results of minimum variance prediction of bilinear time series are included. They are compared to the results of linear prediction of bilinear time series. A minimum variance prediction algorithm for bilinear time series of the general form is developed and an adaptive version of minimum variance algorithm is derived.     

Prediction of final data with use of preliminary and/or revised data

In the case of US national accounts the data are revised for the first few years and every decade, which implies that we do not really have the final data. In this paper we aim to predict the final data, using the preliminary data and/or the revised data. The following predictors are introduced and derived from a context of the non-linear filtering or smoothing problem, which are: (1) prediction of the final data of time t given the preliminary data up to time t- 1, (2) prediction of the final data of time t given the preliminary data up to time t, (3) prediction of the final data of time t given the preliminary data up to time T, (4) prediction of the final data of time t given the revised data up to time t -1 and the preliminary data up to time t- 1, and (5) prediction of the final data of time t given the revised data up to time t-1 and the preliminary data up to time t. It is shown that (5) is the best predictor but not too different from (3). The prediction problem is illustrated using US per capita consumption data.     

Prediction from the One‐Way Error Components Model with AR(1) Disturbances

In this paper we extend the works of Baillie and Baltagi (1999, in Analysis of Panels and Limited Dependent Variables Models, Hsiao C et al. (eds). Cambridge University Press: Cambridge, UK; 255–267) and generalize certain results from the Baltagi and Li (1992, Journal of Forecasting 11 : 561–567) paper accounting for AR(1) errors in the disturbance term. In particular, we derive six predictors for the one‐way error components model, as well as their associated asymptotic mean squared error of multi‐step prediction in the presence of AR(1) errors in the disturbance term. In addition, we also provide both theoretical and simulation evidence as to the relative efficiency of our alternative predictors. The adequacy of the prediction AMSE formula is also investigated by the use of Monte Carlo methods and indicates that the ordinary optimal predictor performs well for various accuracy criteria. Copyright © 2011 John Wiley & Sons, Ltd.     

Real time prediction of irregular periodic time series data

By means of a novel time-dependent cumulated variation penalty function, a new class of real-time prediction methods is developed to improve the prediction accuracy of time series exhibiting irregular periodic patterns: in particular, the breathing motion data of the patients during robotic radiation therapy. It is illustrated that for both simulated and empirical data involving changes in mean, trend, and amplitude, the proposed methods outperform existing forecasting methods based on support vector machines and artificial neural network in terms of prediction accuracy. Moreover, the proposed methods are designed so that real-time updates can be done efficiently with O(1) computational complexity upon the arrival of a new signal without scanning the old data repeatedly.     

Functional methods for time series prediction: a nonparametric approach

The problem of prediction in time series using nonparametric functional techniques is considered. An extension of the local linear method to regression with functional explanatory variable is proposed. This forecasting method is compared with the functional Nadaraya–Watson method and with finite‐dimensional nonparametric predictors for several real‐time series. Prediction intervals based on the bootstrap and conditional distribution estimation for those nonparametric methods are also compared. Copyright © 2010 John Wiley & Sons, Ltd.     

Volatility forecasting with double Markov switching GARCH models

This paper investigates inference and volatility forecasting using a Markov switching heteroscedastic model with a fat‐tailed error distribution to analyze asymmetric effects on both the conditional mean and conditional volatility of financial time series. The motivation for extending the Markov switching GARCH model, previously developed to capture mean asymmetry, is that the switching variable, assumed to be a first‐order Markov process, is unobserved. The proposed model extends this work to incorporate Markov switching in the mean and variance simultaneously. Parameter estimation and inference are performed in a Bayesian framework via a Markov chain Monte Carlo scheme. We compare competing models using Bayesian forecasting in a comparative value‐at‐risk study. The proposed methods are illustrated using both simulations and eight international stock market return series. The results generally favor the proposed double Markov switching GARCH model with an exogenous variable. Copyright © 2008 John Wiley & Sons, Ltd.     

Cryptocurrency volatility forecasting: A Markov regime-switching MIDAS approach

The primary purpose of this paper is to investigate whether a novel Markov regime-switching mixed-data sampling (MRS-MIADS) model we design can improve the prediction accuracy of the realized variance (RV) of Bitcoin. Moreover, to verify whether the importance of jumps for RV forecasting changes over time, we extend the standard MIDAS model to characterize two volatility regimes and introduce a jump-driven time-varying transition probability between the two regimes. Our results suggest that the proposed novel MRS-MIDAS model exhibits statistically significant improvement for forecasting the RV of Bitcoin. In addition, we find that jump occurrences significantly increase the persistence of the high-volatility regime and switch between high- and low-volatility regimes. A wide range of checks confirm the robustness of our results. Finally, the proposed model shows significant improvement for 2-week and 1-month horizon forecasts.     

Forecasting Elections

In this paper we assess opinion polls, prediction markets, expert opinion and statistical modelling over a large number of US elections in order to determine which perform better in terms of forecasting outcomes. In line with existing literature, we bias‐correct opinion polls. We consider accuracy, bias and precision over different time horizons before an election, and we conclude that prediction markets appear to provide the most precise forecasts and are similar in terms of bias to opinion polls. We find that our statistical model struggles to provide competitive forecasts, while expert opinion appears to be of value. Finally we note that the forecast horizon matters; whereas prediction market forecasts tend to improve the nearer an election is, opinion polls appear to perform worse, while expert opinion performs consistently throughout. We thus contribute to the growing literature comparing election forecasts of polls and prediction markets. Copyright © 2015 John Wiley & Sons, Ltd.     

Updating ARMA predictions for temporal aggregates

This article develops and extends previous investigations on the temporal aggregation of ARMA predications. Given a basic ARMA model for disaggregated data, two sets of predictors may be constructed for future temporal aggregates: predictions based on models utilizing aggregated data or on models constructed from disaggregated data for which forecasts are updated as soon as the new information becomes available. We show that considerable gains in efficiency based on mean‐square‐error‐type criteria can be obtained for short‐term predications when using models based on updated disaggregated data. However, as the prediction horizon increases, the gain in using updated disaggregated data diminishes substantially. In addition to theoretical results associated with forecast efficiency of ARMA models, we also illustrate our findings with two well‐known time series. Copyright © 2004 John Wiley & Sons, Ltd.     

Identifying US business cycle regimes using dynamic factors and neural network models

We use dynamic factors and neural network models to identify current and past states (instead of future) of the US business cycle. In the first step, we reduce noise in data by using a moving average filter. Dynamic factors are then extracted from a large-scale data set consisted of more than 100 variables. In the last step, these dynamic factors are fed into the neural network model for predicting business cycle regimes. We show that our proposed method follows US business cycle regimes quite accurately in-sample and out-of-sample without taking account of the historical data availability. Our results also indicate that noise reduction is an important step for business cycle prediction. Furthermore, using pseudo real time and vintage data, we show that our neural network model identifies turning points quite accurately and very quickly in real time.