Forecasting Ability of a Periodic Component Extracted from Large‐Cap Index Time Series

We develop a method to extract periodic variations in a time series that are hidden in large non‐periodic and stochastic variations. This method relies on folding the time series many times and allows direct visualization of a hidden periodic component without resorting to any fitting procedure. Applying this method to several large‐cap stock time series in Europe, Japan and the USA yields a component with periodicity of 1 year. Out‐of‐sample tests on these large‐cap time series indicate that this periodic component is able to forecast long‐term (decade) behavior for large‐cap time series. Copyright © 2016 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.     

Comparison of forecasting performances: Does normalization and variance stabilization method beat GARCH(1,1)‐type models? Empirical evidence from the stock markets

In this paper, we present a comparison between the forecasting performances of the normalization and variance stabilization method (NoVaS) and the GARCH(1,1), EGARCH(1,1) and GJR‐GARCH(1,1) models. Hence the aim of this study is to compare the out‐of‐sample forecasting performances of the models used throughout the study and to show that the NoVaS method is better than GARCH(1,1)‐type models in the context of out‐of sample forecasting performance. We study the out‐of‐sample forecasting performances of GARCH(1,1)‐type models and NoVaS method based on generalized error distribution, unlike normal and Student's t‐distribution. Also, what makes the study different is the use of the return series, calculated logarithmically and arithmetically in terms of forecasting performance. For comparing the out‐of‐sample forecasting performances, we focused on different datasets, such as S&P 500, logarithmic and arithmetic B?ST 100 return series. The key result of our analysis is that the NoVaS method performs better out‐of‐sample forecasting performance than GARCH(1,1)‐type models. The result can offer useful guidance in model building for out‐of‐sample forecasting purposes, aimed at improving forecasting accuracy.     

Predicting Business Failure Using an RSF‐based Case‐Based Reasoning Ensemble Forecasting Method

Case‐based reasoning (CBR) is considered a vital methodology in the current business forecasting area because of its simplicity, competitive performance with modern methods, and ease of pattern maintenance. Business failure prediction (BFP) is an effective tool that helps business people and entrepreneurs make more precise decisions in the current crisis. Using CBR as a basis for BFP can improve the tool's utility because CBR has the potential advantage in making predictions as well as suggestions compared with other methods. Recent studies indicate that an ensemble of various techniques has the possibility of improving the performance of predictive model. This research focuses on an early investigation on predicting business failure using a CBR ensemble (CBRE) forecasting method constructed from the use of random similarity functions (RSF), dubbed RSF‐based CBRE. Four issues are discussed: (i) the reasons for the use of RSF as the basis in the CBRE forecasting method for BFP; (ii) the means to construct the RSF‐based CBRE forecasting method for BFP; (iii) the empirical test on sensitivity of the RSF‐based CBRE to the number of member CBR predictors; and (iv) performance assessment of the ensemble forecasting method. Results of the RSF‐based CBRE forecasting method were statistically validated by comparing them with those of multivariate discriminant analysis, logistic regression, single CBR, and a linear support vector machine. The results from Chinese hotel BFP indicate that the RSF‐based CBRE forecasting method could significantly improve CBR's upper limit of predictive capability. Copyright © 2011 John Wiley & Sons, Ltd.     

When are Direct Multi‐step and Iterative Forecasts Identical?

Although both direct multi‐step‐ahead forecasting and iterated one‐step‐ahead forecasting are two popular methods for predicting future values of a time series, it is not clear that the direct method is superior in practice, even though from a theoretical perspective it has lower mean squared error (MSE). A given model can be fitted according to either a multi‐step or a one‐step forecast error criterion, and we show here that discrepancies in performance between direct and iterative forecasting arise chiefly from the method of fitting, and is dictated by the nuances of the model's misspecification. We derive new formulas for quantifying iterative forecast MSE, and present a new approach for assessing asymptotic forecast MSE. Finally, the direct and iterative methods are compared on a retail series, which illustrates the strengths and weaknesses of each approach. Copyright © 2015 John Wiley & Sons, Ltd.     

A Time‐Simultaneous Prediction Box for a Multivariate Time Series

A sample‐based method in Kolsrud (Journal of Forecasting 2007; 26 (3): 171–188) for the construction of a time‐simultaneous prediction band for a univariate time series is extended to produce a variable‐ and time‐simultaneous prediction box for a multivariate time series. A measure of distance based on the L_∞ ‐norm is applied to a learning sample of multivariate time trajectories, which can be mean‐ and/or variance‐nonstationary. Based on the ranking of distances to the centre of the sample, a subsample of the most central multivariate trajectories is selected. A prediction box is constructed by circumscribing the subsample with a hyperrectangle. The fraction of central trajectories selected into the subsample can be calibrated by bootstrap such that the expected coverage of the box equals a prescribed nominal level. The method is related to the concept of data depth, and thence modified to increase coverage. Applications to simulated and empirical data illustrate the method, which is also compared to several other methods in the literature adapted to the multivariate setting. Copyright © 2015 John Wiley & Sons, Ltd.     

Bias‐corrected bootstrap prediction intervals for autoregressive model: new alternatives with applications to tourism forecasting

This paper proposes the use of the bias‐corrected bootstrap for interval forecasting of an autoregressive time series with an arbitrary number of deterministic components. We use the bias‐corrected bootstrap based on two alternative bias‐correction methods: the bootstrap and an analytic formula based on asymptotic expansion. We also propose a new stationarity‐correction method, based on stable spectral factorization, as an alternative to Kilian's method exclusively used in past studies. A Monte Carlo experiment is conducted to compare small‐sample properties of prediction intervals. The results show that the bias‐corrected bootstrap prediction intervals proposed in this paper exhibit desirable small‐sample properties. It is also found that the bootstrap bias‐corrected prediction intervals based on stable spectral factorization are tighter and more stable than those based on Kilian's stationarity‐correction. The proposed methods are applied to interval forecasting for the number of tourist arrivals in Hong Kong. Copyright © 2010 John Wiley & Sons, Ltd.     

The Accuracy of Non‐traditional versus Traditional Methods of Forecasting Lumpy Demand

Forecasting for inventory items with lumpy demand is difficult because of infrequent nonzero demands with high variability. This article developed two methods to forecast lumpy demand: an optimally weighted moving average method and an intelligent pattern‐seeking method. We compare them with a number of well‐referenced methods typically applied over the last 30 years in forecasting intermittent or lumpy demand. The comparison is conducted over about 200,000 forecasts (using 1‐day‐ahead and 5‐day‐ahead review periods) for 24 series of actual product demands across four different error measures. One of the most important findings of our study is that the two non‐traditional methods perform better overall than the traditional methods. We summarize results and discuss managerial implications. Copyright © 2011 John Wiley & Sons, Ltd.     

Assessing the Macroeconomic Forecasting Performance of Boosting: Evidence for the United States,the Euro Area and Germany

The use of large datasets for macroeconomic forecasting has received a great deal of interest recently. Boosting is one possible method of using high‐dimensional data for this purpose. It is a stage‐wise additive modelling procedure, which, in a linear specification, becomes a variable selection device that iteratively adds the predictors with the largest contribution to the fit. Using data for the United States, the euro area and Germany, we assess the performance of boosting when forecasting a wide range of macroeconomic variables. Moreover, we analyse to what extent its forecasting accuracy depends on the method used for determining its key regularization parameter: the number of iterations. We find that boosting mostly outperforms the autoregressive benchmark, and that K‐fold cross‐validation works much better as stopping criterion than the commonly used information criteria. Copyright © 2014 John Wiley & Sons, Ltd.     

An intelligent model selection and forecasting system

In this paper we present an intelligent decision‐support system based on neural network technology for model selection and forecasting. While most of the literature on the application of neural networks in forecasting addresses the use of neural network technology as an alternative forecasting tool, limited research has focused on its use for selection of forecasting methods based on time‐series characteristics. In this research, a neural network‐based decision support system is presented as a method for forecast model selection. The neural network approach provides a framework for directly incorporating time‐series characteristics into the model‐selection phase. Using a neural network, a forecasting group is initially selected for a given data set, based on a set of time‐series characteristics. Then, using an additional neural network, a specific forecasting method is selected from a pool of three candidate methods. The results of training and testing of the networks are presented along with conclusions. Copyright © 1999 John Wiley & Sons, Ltd.     

Forecasting Volatility with Many Predictors

This study investigates the forecasting performance of the GARCH(1,1) model by adding an effective covariate. Based on the assumption that many volatility predictors are available to help forecast the volatility of a target variable, this study shows how to construct a covariate from these predictors and plug it into the GARCH(1,1) model. This study presents a method of building a covariate such that the covariate contains the maximum possible amount of predictor information of the predictors for forecasting volatility. The loading of the covariate constructed by the proposed method is simply the eigenvector of a matrix. The proposed method enjoys the advantages of easy implementation and interpretation. Simulations and empirical analysis verify that the proposed method performs better than other methods for forecasting the volatility, and the results are quite robust to model misspecification. Specifically, the proposed method reduces the mean square error of the GARCH(1,1) model by 30% for forecasting the volatility of S&P 500 Index. The proposed method is also useful in improving the volatility forecasting of several GARCH‐family models and for forecasting the value‐at‐risk. Copyright © 2013 John Wiley & Sons, Ltd.     

Efficient forecasting in nearly non‐stationary processes

This paper proposes a procedure to make efficient predictions in a nearly non‐stationary process. The method is based on the adaptation of the theory of optimal combination of forecasts to nearly non‐stationary processes. The proposed combination method is simple to apply and has a better performance than classical combination procedures. It also has better average performance than a differenced predictor, a fractional differenced predictor, or an optimal unit‐root pretest predictor. In the case of a process that has a zero mean, only the non‐differenced predictor is slightly better than the proposed combination method. In the general case of a non‐zero mean, the proposed combination method has a better overall performance than all its competitors. Copyright © 2002 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.     

Moment tests for density forecast evaluation in the presence of parameter estimation uncertainty

Density forecast (DF) possesses appealing properties when it is correctly specified for the true conditional distribution. Although a number of parametric specification tests have been introduced for the DF evaluation (DFE) in the parameter‐free context, econometric DF models are typically parameter‐dependent. In this paper, we first use a generalized probability integral transformation‐based moment test to unify these existing tests, and then apply the Newey–Tauchen method (the West–McCracken method) to correct this unified test as a generalized full‐sample (out‐of‐sample) test in the parameter‐dependent context. Unlike the corrected tests, the uncorrected tests could be substantially undersized (oversized) when they are directly applied to the full‐sample (out‐of‐sample) DFE in the presence of parameter estimation uncertainty. We also use a simulation to show the usefulness of the corrected tests in rectifying the size distortion problem, and apply the corrected tests to an empirical study of stock index returns. Copyright © 2010 John Wiley & Sons, Ltd.     

Forecasting Simultaneously High‐Dimensional Time Series: A Robust Model‐Based Clustering Approach

This paper considers the problem of forecasting high‐dimensional time series. It employs a robust clustering approach to perform classification of the component series. Each series within a cluster is assumed to follow the same model and the data are then pooled for estimation. The classification is model‐based and robust to outlier contamination. The robustness is achieved by using the intrinsic mode functions of the Hilbert–Huang transform at lower frequencies. These functions are found to be robust to outlier contamination. The paper also compares out‐of‐sample forecast performance of the proposed method with several methods available in the literature. The other forecasting methods considered include vector autoregressive models with ∕ without LASSO, group LASSO, principal component regression, and partial least squares. The proposed method is found to perform well in out‐of‐sample forecasting of the monthly unemployment rates of 50 US states. Copyright © 2013 John Wiley & Sons, Ltd.     

Forecasting Aggregates with Disaggregate Variables: Does Boosting Help to Select the Most Relevant Predictors?

Including disaggregate variables or using information extracted from the disaggregate variables into a forecasting model for an economic aggregate may improve forecasting accuracy. In this paper we suggest using the boosting method to select the disaggregate variables, which are most helpful in predicting an aggregate of interest. We conduct a simulation study to investigate the variable selection ability of this method. To assess the forecasting performance a recursive pseudo‐out‐of‐sample forecasting experiment for six key euro area macroeconomic variables is conducted. The results suggest that using boosting to select relevant predictors is a feasible and competitive approach in forecasting an aggregate. Copyright © 2016 John Wiley & Sons, Ltd.     

Forecasting business failure in China using case‐based reasoning with hybrid case respresentation

Case‐based reasoning (CBR) is a very effective and easily understandable method for solving real‐world problems. Business failure prediction (BFP) is a forecasting tool that helps people make more precise decisions. CBR‐based BFP is a hot topic in today's global financial crisis. Case representation is critical when forecasting business failure with CBR. This research describes a pioneer investigation on hybrid case representation by employing principal component analysis (PCA), a feature extraction method, along with stepwise multivariate discriminant analysis (MDA), a feature selection approach. In this process, sample cases are represented with all available financial ratios, i.e., features. Next, the stepwise MDA is used to select optimal features to produce a reduced‐case representation. Finally, PCA is employed to extract the final information representing the sample cases. All data signified by hybrid case representation are recorded in a case library, and the k‐nearest‐neighbor algorithm is used to make the forecasting. Thus we constructed a hybrid CBR (HCBR) by integrating hybrid case representation into the forecasting tool. We empirically tested the performance of HCBR with data collected for short‐term BFP of Chinese listed companies. Empirical results indicated that HCBR can produce more promising prediction performance than MDA, logistic regression, classical CBR, and support vector machine. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

A nonparametric method for asymmetrically extending signal extraction filters

Two important problems in the X‐11 seasonal adjustment methodology are the construction of standard errors and the handling of the boundaries. We adapt the ‘implied model approach’ of Kaiser and Maravall to achieve both objectives in a nonparametric fashion. The frequency response function of an X‐11 linear filter is used, together with the periodogram of the differenced data, to define spectral density estimates for signal and noise. These spectra are then used to define a matrix smoother, which in turn generates an estimate of the signal that is linear in the data. Estimates of the signal are provided at all time points in the sample, and the associated time‐varying signal extraction mean squared errors are a by‐product of the matrix smoother theory. After explaining our method, it is applied to popular nonparametric filters such as the Hodrick–Prescott (HP), the Henderson trend, and ideal low‐pass and band‐pass filters, as well as X‐11 seasonal adjustment, trend, and irregular filters. Finally, we illustrate the method on several time series and provide comparisons with X‐12‐ARIMA seasonal adjustments. Copyright © 2010 John Wiley & Sons, Ltd.     

Exponentially Smoothing the Skewed Laplace Distribution for Value‐at‐Risk Forecasting

Value‐at‐risk (VaR) is a standard measure of market risk in financial markets. This paper proposes a novel, adaptive and efficient method to forecast both volatility and VaR. Extending existing exponential smoothing as well as GARCH formulations, the method is motivated from an asymmetric Laplace distribution, where skewness and heavy tails in return distributions, and their potentially time‐varying nature, are taken into account. The proposed volatility equation also involves novel time‐varying dynamics. Back‐testing results illustrate that the proposed method offers a viable, and more accurate, though conservative, improvement in forecasting VaR compared to a range of popular alternatives. Copyright © 2013 John Wiley & Sons, Ltd.