Prediction from the regression model with two‐way error components

In this paper we extend the Baillie and Baltagi ( 1999 ) paper (Prediction from the regression model with one‐way error components. In Analysis of Panels and Limited Dependent Variables Models, Hsiao C, Lahiri K, Lee LF, Pesaran H (eds). Cambridge University Press, Cambridge, UK). In particular, we derive six predictors for the two‐way error components model, as well as their associated asymptotic mean squared error (AMSE) of multi‐step prediction. In addition, we also provide both theoretical and simulation evidence as to the relative efficiency of our six alternative predictors. The adequacy of the prediction AMSE formula is also investigated by the use of Monte Carlo methods which indicate that the ordinary optimal predictors perform well for various accuracy criteria. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

The effect of target function on the predictive performance of the two‐stage ridge estimator

The main thrust of this study is to consider the problem of simultaneous prediction of actual and average values of the simultaneous equations model through the target function of Shalabh (Bulletin of International Statistical Institute, 1995, 56, 1375–1390). We focus on the predictive performance of the two‐stage ridge estimator with the motivation for eliminating the disorder arising from multicollinearity. An optimal biasing parameter of the two‐stage ridge estimator is derived by a minimization process of prediction mean square error. In addition, an optimal estimator for the weight of observed value in target function is attained theoretically. The results inferred from a numerical example and a Monte Carlo experiment provide a dramatic improvement in the predictive ability of the two‐stage ridge estimator.     

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.     

Consistent forecast intervals when the forecast-period exogenous variables are stochastic

Derivation of prediction intervals in the k-variable regression model is problematic when future-period values of exogenous variables are not known with certainty. Even in the most favourable case when the forecasts of the exogenous variables are jointly normal, the distribution of the forecast error is non-normal, and thus traditional asymptotic normal theory does not apply. This paper presents an alternative bootstrap method. In contrast to the traditional predictor of the future value of the endogenous variable, which is known to be inconsistent, the bootstrap predictor converges weakly to the true value. Monte Carlo results show that the bootstrap prediction intervals can achieve approximately nominal coverage.     

Oil financialization and volatility forecast: Evidence from multidimensional predictors

Using the generalized dynamic factor model, this study constructs three predictors of crude oil price volatility: a fundamental (physical) predictor, a financial predictor, and a macroeconomic uncertainty predictor. Moreover, an event‐triggered predictor is constructed using data extracted from Google Trends. We construct GARCH‐MIDAS (generalized autoregressive conditional heteroskedasticity–mixed‐data sampling) models combining realized volatility with the predictors to predict oil price volatility at different forecasting horizons. We then identify the predictive power of the realized volatility and the predictors by the model confidence set (MCS) test. The findings show that, among the four indexes, the financial predictor has the most predictive power for crude oil volatility, which provides strong evidence that financialization has been the key determinant of crude oil price behavior since the 2008 global financial crisis. In addition, the fundamental predictor, followed by the financial predictor, effectively forecasts crude oil price volatility in the long‐run forecasting horizons. Our findings indicate that the different predictors can provide distinct predictive information at the different horizons given the specific market situation. These findings have useful implications for market traders in terms of managing crude oil price risk.     

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.     

基于粗糙集与灰色动态预测模型在电力负荷短期预测的应用

针对电力系统多因素负荷预测问题的复杂性,结合粗糙集理论与GM（1,N）模型各自的优势,提出一种基于粗糙集理论的GM（1,N）预测模型.采取粗糙集理论对影响负荷预测因素进行简约,利用GM（1,N）建立简约后的因素变量和负荷之间的关系建立模型,并与GM（1,1）预测模型进行了比较,结果反映基于粗糙集理论的GM（1,N）预测模型的优越性,精准度达到94.055%.     

A bootstrap simulation study in ARMA (p,q) structures

In 1979 Efron proposed a new general statistical procedure known as ‘Bootstrap’, a computer-intensive method used when finite-sample theory is impossible or difficult to derive, or when only asymptotic theory is available. It is recommended in the estimation of measures of both location and scale for any statistical model without making any distributional assumptions about the data. This technique has been successfully used in various applied statistical problems, although not many applications have been reported in the area of time series. In this paper we present a new application of Bootstrap to time series. We consider a simulation study where artificial time series corresponding to AR(1), AR(2), MA(1), MA(2) and ARMA(1, 1) structures were generated, covering important regions of the parameter space of each one of them. The conventional Box-Jenkins parametric estimators of the parameters are compared with the corresponding non-parametric Bootstrap estimators, obtained by 500 Bootstrap repetitions for each series.     

Time-series forecasting using fractional differencing

The main failure of ARIMA modelling as used in practice are the limiting constraints imposed by differencing to achieve stationarity. The use of fractional differencing opens up a much wider and realistic behaviour for the trend and seasonal components than traditional integer differencing. This paper shows several advantages of using fractional differencing for forecasting monthly data. These advantages are illustrated using a sample of previously modelled time-series data selected from the literature.     

Long‐memory forecasting of US monetary indices

Several studies have tested for long‐range dependence in macroeconomic and financial time series but very few have assessed the usefulness of long‐memory models as forecast‐generating mechanisms. This study tests for fractional differencing in the US monetary indices (simple sum and divisia) and compares the out‐of‐sample fractional forecasts to benchmark forecasts. The long‐memory parameter is estimated using Robinson's Gaussian semi‐parametric and multivariate log‐periodogram methods. The evidence amply suggests that the monetary series possess a fractional order between one and two. Fractional out‐of‐sample forecasts are consistently more accurate (with the exception of the M3 series) than benchmark autoregressive forecasts but the forecasting gains are not generally statistically significant. In terms of forecast encompassing, the fractional model encompasses the autoregressive model for the divisia series but neither model encompasses the other for the simple sum series. Copyright © 2006 John Wiley & Sons, Ltd.     

Regression tree model for prediction of demand with heterogeneity and censorship

In this research we analyze a new approach for prediction of demand. In the studied market of performing arts the observed demand is limited by capacity of the house. Then one needs to account for demand censorship to obtain unbiased estimates of demand function parameters. The presence of consumer segments with different purposes of going to the theater and willingness-to-pay for performance and ticket characteristics causes a heterogeneity in theater demand. We propose an estimator for prediction of demand that accounts for both demand censorship and preferences heterogeneity. The estimator is based on the idea of classification and regression trees and bagging prediction aggregation extended for prediction of censored data. Our algorithm predicts and combines predictions for both discrete and continuous parts of censored data. We show that our estimator performs better in terms of prediction accuracy compared with estimators which account either for censorship or heterogeneity only. The proposed approach is helpful for finding product segments and optimal price setting.     

Hybrid Forecasting with Estimated Temporally Aggregated Linear Processes

We introduce a new strategy for the prediction of linear temporal aggregates; we call it ‘hybrid’ and study its performance using asymptotic theory. This scheme consists of carrying out model parameter estimation with data sampled at the highest available frequency and the subsequent prediction with data and models aggregated according to the forecasting horizon of interest. We develop explicit expressions that approximately quantify the mean square forecasting errors associated with the different prediction schemes and that take into account the estimation error component. These approximate estimates indicate that the hybrid forecasting scheme tends to outperform the so‐called ‘all‐aggregated’ approach and, in some instances, the ‘all‐disaggregated’ strategy that is known to be optimal when model selection and estimation errors are neglected. Unlike other related approximate formulas existing in the literature, those proposed in this paper are totally explicit and require neither assumptions on the second‐order stationarity of the sample nor Monte Carlo simulations for their evaluation. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive prediction for stochastic processes with markov jump parameters

This paper is concerned with the adaptive prediction for stochastic processes with abruptly changing parameters modelled as a finite-state Markov chain. The Markov transition matrix is assumed to be known. For the coloured noise disturbance case, it is shown that the optimal prediction algorithm requires a bank of elemental predictors running in parallel with its number growing exponentially with time. If the noise disturbance is white, it is found that the number of the elemental predictors required increases exponentially with the prediction ahead step instead of time. A suboptimal predictor is proposed with substantial reduced storage and computational requirements. Simulation examples show the good performance of the proposed algorithms.     

Should fixed coefficients be re-estimated every period for extrapolation?

This paper demonstrates that forecast accuracy is not necessarily improved when fixed-coefficient models are sequentially re-estimated and used for prediction, after updating the database with the latest observation(s). It is argued that although sequential estimation may minimize the variances of predictors based on some classes of estimators, sequential estimation does not necessarily yield accurate predictions (i.e. predictions that are close to actual realizations). Minimizing the mean squared prediction error about the actual realization is a necessary condition for maximizing the probability that one predictor is more accurate than others. This minimization need not require, and may even exclude, the most recent data. It has been shown by an example that a prediction based on a nonsequential estimate of a stochastically varying coefficient model is superior to predictions based on several sequential estimates of the fixed-coefficient models, including a random walk model.     

A semiparametric method for predicting bankruptcy

Bankruptcy prediction methods based on a semiparametric logit model are proposed for simple random (prospective) and case–control (choice‐based; retrospective) data. The unknown parameters and prediction probabilities in the model are estimated by the local likelihood approach, and the resulting estimators are analyzed through their asymptotic biases and variances. The semiparametric bankruptcy prediction methods using these two types of data are shown to be essentially equivalent. Thus our proposed prediction model can be directly applied to data sampled from the two important designs. One real data example and simulations confirm that our prediction method is more powerful than alternatives, in the sense of yielding smaller out‐of‐sample error rates. Copyright © 2007 John Wiley & Sons, Ltd.     

Scalar BEKK and indirect DCC

The paper derives the scalar special case of the well‐known BEKK multivariate GARCH model using a multivariate extension of the random coefficient autoregressive (RCA) model. This representation establishes the relevant structural and asymptotic properties of the scalar BEKK model using the theoretical results available in the literature for general multivariate GARCH. Sufficient conditions for the (direct) DCC model to be consistent with a scalar BEKK representation are established. Moreover, an indirect DCC model that is consistent with the scalar BEKK representation is obtained, and is compared with the direct DCC model using an empirical example. The paper shows, within an asset allocation and risk measurement framework, that the two models are similar in terms of providing parameter estimates and forecasting value‐at‐risk thresholds for equally weighted and minimum variance portfolios. Copyright © 2008 John Wiley & Sons, Ltd.     

Bayesian Analysis of a Threshold Stochastic Volatility Model

This paper proposes a parsimonious threshold stochastic volatility (SV) model for financial asset returns. Instead of imposing a threshold value on the dynamics of the latent volatility process of the SV model, we assume that the innovation of the mean equation follows a threshold distribution in which the mean innovation switches between two regimes. In our model, the threshold is treated as an unknown parameter. We show that the proposed threshold SV model can not only capture the time‐varying volatility of returns, but can also accommodate the asymmetric shape of conditional distribution of the returns. Parameter estimation is carried out by using Markov chain Monte Carlo methods. For model selection and volatility forecast, an auxiliary particle filter technique is employed to approximate the filter and prediction distributions of the returns. Several experiments are conducted to assess the robustness of the proposed model and estimation methods. In the empirical study, we apply our threshold SV model to three return time series. The empirical analysis results show that the threshold parameter has a non‐zero value and the mean innovations belong to two separately distinct regimes. We also find that the model with an unknown threshold parameter value consistently outperforms the model with a known threshold parameter value. Copyright © 2016 John Wiley & Sons, Ltd.     

Using wavelets to obtain a consistent ordinary least squares estimator of the long‐memory parameter

We develop an ordinary least squares estimator of the long‐memory parameter from a fractionally integrated process that is an alternative to the Geweke and Porter‐Hudak (1983) estimator. Using the wavelet transform from a fractionally integrated process, we establish a log‐linear relationship between the wavelet coefficients' variance and the scaling parameter equal to the log‐memory parameter. This log‐linear relationship yields a consistent ordinary least squares estimator of the long‐memory parameter when the wavelet coefficients' population variance is replaced by their sample variance. We derive the small sample bias and variance of the ordinary least squares estimator and test it against the GPH estimator and the McCoy–Walden maximum likelihood wavelet estimator by conducting a number of Monte Carlo experiments. Based upon the criterion of choosing the estimator which minimizes the mean squared error, the wavelet OLS approach was superior to the GPH estimator, but inferior to the McCoy–Walden wavelet estimator for the processes simulated. However, given the simplicity of programming and running the wavelet OLS estimator and its statistical inference of the long‐memory parameter we feel the general practitioner will be attracted to the wavelet OLS estimator. Copyright © 1999 John Wiley & Sons, Ltd.     

Estimation procedures for structural time series models

A univariate structural time series model based on the traditional decomposition into trend, seasonal and irregular components is defined. A number of methods of computing maximum likelihood estimators are then considered. These include direct maximization of various time domain likelihood function. The asymptotic properties of the estimators are given and a comparison between the various methods in terms of computational efficiency and accuracy is made. The methods are then extended to models with explanatory variables.