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.     

On forecasting counts

Forecasting for a time series of low counts, such as forecasting the number of patents to be awarded to an industry, is an important research topic in socio‐economic sectors. Recently (2004), Freeland and McCabe introduced a Gaussian type stationary correlation model‐based forecasting which appears to work well for the stationary time series of low counts. In practice, however, it may happen that the time series of counts will be non‐stationary and also the series may contain over‐dispersed counts. To develop the forecasting functions for this type of non‐stationary over‐dispersed data, the paper provides an extension of the stationary correlation models for Poisson counts to the non‐stationary correlation models for negative binomial counts. The forecasting methodology appears to work well, for example, for a US time series of polio counts, whereas the existing Bayesian methods of forecasting appear to encounter serious convergence problems. Further, a simulation study is conducted to examine the performance of the proposed forecasting functions, which appear to work well irrespective of whether the time series contains small or large counts. Copyright © 2008 John Wiley & Sons, Ltd.     

Bootstrap prediction intervals for autoregressive models of unknown or infinite lag order

Recent studies on bootstrap prediction intervals for autoregressive (AR) model provide simulation findings when the lag order is known. In practical applications, however, the AR lag order is unknown or can even be infinite. This paper is concerned with prediction intervals for AR models of unknown or infinite lag order. Akaike's information criterion is used to estimate (approximate) the unknown (infinite) AR lag order. Small‐sample properties of bootstrap and asymptotic prediction intervals are compared under both normal and non‐normal innovations. Bootstrap prediction intervals are constructed based on the percentile and percentile‐t methods, using the standard bootstrap as well as the bootstrap‐after‐bootstrap. It is found that bootstrap‐after‐bootstrap prediction intervals show small‐sample properties substantially better than other alternatives, especially when the sample size is small and the model has a unit root or near‐unit root. Copyright © 2002 John Wiley & Sons, Ltd.     

A Bayesian nonlinear support vector machine error correction model

The use of linear error correction models based on stationarity and cointegration analysis, typically estimated with least squares regression, is a common technique for financial time series prediction. In this paper, the same formulation is extended to a nonlinear error correction model using the idea of a kernel‐based implicit nonlinear mapping to a high‐dimensional feature space in which linear model formulations are specified. Practical expressions for the nonlinear regression are obtained in terms of the positive definite kernel function by solving a linear system. The nonlinear least squares support vector machine model is designed within the Bayesian evidence framework that allows us to find appropriate trade‐offs between model complexity and in‐sample model accuracy. From straightforward primal–dual reasoning, the Bayesian framework allows us to derive error bars on the prediction in a similar way as for linear models and to perform hyperparameter and input selection. Starting from the results of the linear modelling analysis, the Bayesian kernel‐based prediction is successfully applied to out‐of‐sample prediction of an aggregated equity price index for the European chemical sector. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

A Robust Data‐Mining Approach to Bankruptcy Prediction

In this study, new variants of genetic programming (GP), namely gene expression programming (GEP) and multi‐expression programming (MEP), are utilized to build models for bankruptcy prediction. Generalized relationships are obtained to classify samples of 136 bankrupt and non‐bankrupt Iranian corporations based on their financial ratios. An important contribution of this paper is to identify the effective predictive financial ratios on the basis of an extensive bankruptcy prediction literature review and upon a sequential feature selection analysis. The predictive performance of the GEP and MEP forecasting methods is compared with the performance of traditional statistical methods and a generalized regression neural network. The proposed GEP and MEP models are effectively capable of classifying bankrupt and non‐bankrupt firms and outperform the models developed using other methods. Copyright © 2011 John Wiley & Sons, Ltd.     

Statistical estimation of optimal portfolios for non‐Gaussian dependent returns of assets

This paper discusses the asymptotic efficiency of estimators for optimal portfolios when returns are vector‐valued non‐Gaussian stationary processes. We give the asymptotic distribution of portfolio estimators ? for non‐Gaussian dependent return processes. Next we address the problem of asymptotic efficiency for the class of estimators ?. First, it is shown that there are some cases when the asymptotic variance of ? under non‐Gaussianity can be smaller than that under Gaussianity. The result shows that non‐Gaussianity of the returns does not always affect the efficiency badly. Second, we give a necessary and sufficient condition for ? to be asymptotically efficient when the return process is Gaussian, which shows that ? is not asymptotically efficient generally. From this point of view we propose to use maximum likelihood type estimators for g, which are asymptotically efficient. Furthermore, we investigate the problem of predicting the one‐step‐ahead optimal portfolio return by the estimated portfolio based on ? and examine the mean squares prediction error. Copyright © 2008 John Wiley & Sons, Ltd.     

Stochastic Multivariate Mixture Covariance Model

Stochastic covariance models have been explored in recent research to model the interdependence of assets in financial time series. The approach uses a single stochastic model to capture such interdependence. However, it may be inappropriate to assume a single coherence structure at all time t. In this paper, we propose the use of a mixture of stochastic covariance models to generalize the approach and offer greater flexibility in real data applications. Parameter estimation is performed by Bayesian analysis with Markov chain Monte Carlo sampling schemes. We conduct a simulation study on three different model setups and evaluate the performance of estimation and model selection. We also apply our modeling methods to high‐frequency stock data from Hong Kong. Model selection favors a mixture rather than non‐mixture model. In a real data study, we demonstrate that the mixture model is able to identify structural changes in market risk, as evidenced by a drastic change in mixture proportions over time. Copyright © 2016 John Wiley & Sons, Ltd.     

Empirical Bayesian Density Forecasting in Iowa and Shrinkage for the Monte Carlo Era

The track record of a 20‐year history of density forecasts of state tax revenue in Iowa is studied, and potential improvements sought through a search for better‐performing ‘priors’ similar to that conducted three decades ago for point forecasts by Doan, Litterman and Sims (Econometric Reviews, 1984). Comparisons of the point and density forecasts produced under the flat prior are made to those produced by the traditional (mixed estimation) ‘Bayesian VAR’ methods of Doan, Litterman and Sims, as well as to fully Bayesian ‘Minnesota Prior’ forecasts. The actual record and, to a somewhat lesser extent, the record of the alternative procedures studied in pseudo‐real‐time forecasting experiments, share a characteristic: subsequently realized revenues are in the lower tails of the predicted distributions ‘too often’. An alternative empirically based prior is found by working directly on the probability distribution for the vector autoregression parameters—the goal being to discover a better‐performing entropically tilted prior that minimizes out‐of‐sample mean squared error subject to a Kullback–Leibler divergence constraint that the new prior not differ ‘too much’ from the original. We also study the closely related topic of robust prediction appropriate for situations of ambiguity. Robust ‘priors’ are competitive in out‐of‐sample forecasting; despite the freedom afforded the entropically tilted prior, it does not perform better than the simple alternatives. Copyright © 2014 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.     

A threshold stochastic volatility model

This article introduces a new model to capture simultaneously the mean and variance asymmetries in time series. Threshold non‐linearity is incorporated into the mean and variance specifications of a stochastic volatility model. Bayesian methods are adopted for parameter estimation. Forecasts of volatility and Value‐at‐Risk can also be obtained by sampling from suitable predictive distributions. Simulations demonstrate that the apparent variance asymmetry documented in the literature can be due to the neglect of mean asymmetry. Strong evidence of the mean and variance asymmetries was detected in US and Hong Kong data. Asymmetry in the variance persistence was also discovered in the Hong Kong stock market. Copyright © 2002 John Wiley & Sons, Ltd.     

An outlier robust hierarchical Bayes model for forecasting: the case of Hong Kong

This paper introduces a Bayesian forecasting model that accommodates innovative outliers. The hierarchical specification of prior distributions allows an identification of observations contaminated by these outliers and endogenously determines the hyperparameters of the Minnesota prior. Estimation and prediction are performed using Markov chain Monte Carlo (MCMC) methods. The model forecasts the Hong Kong economy more accurately than the standard V AR and performs in line with other complicated BV AR models. It is also shown that the model is capable of finding most of the outliers in various simulation experiments. Copyright © 2004 John Wiley & Sons, Ltd.     

The Effect of Nonlinearity between Credit Conditions and Economic Activity on Density Forecasts

This paper examines the effect of nonlinearities on density forecasting. It focuses on the relationship between credit markets and the rest of the economy. The possible nonlinearity of this relationship is captured by a threshold vector autoregressive model estimated on US data using Bayesian methods. Density forecasts thus account for the uncertainty in all model parameters and possible future regime changes. It is shown that considering nonlinearity can improve the probabilistic assessment of the economic outlook. Moreover, three illustrative examples are discussed to shed some light on the possible practical applicability of density forecasts derived from non‐linear models. Copyright © 2015 John Wiley & Sons, Ltd.     

Bayesian Forecasting for Time Series of Categorical Data

Time series of categorical data is not a widely studied research topic. Particularly, there is no available work on the Bayesian analysis of categorical time series processes. With the objective of filling that gap, in the present paper we consider the problem of Bayesian analysis including Bayesian forecasting for time series of categorical data, which is modelled by Pegram's mixing operator, applicable for both ordinal and nominal data structures. In particular, we consider Pegram's operator‐based autoregressive process for the analysis. Real datasets on infant sleep status are analysed for illustrations. We also illustrate that the Bayesian forecasting is more accurate than the corresponding frequentist's approach when we intend to forecast a large time gap ahead. Copyright © 2016 John Wiley & Sons, Ltd.     

On a dynamic mixture GARCH model

This paper proposes a new mixture GARCH model with a dynamic mixture proportion. The mixture Gaussian distribution of the error can vary from time to time. The Bayesian Information Criterion and the EM algorithm are used to estimate the number of parameters as well as the model parameters and their standard errors. The new model is applied to the S&P500 Index and Hang Seng Index and compared with GARCH models with Gaussian error and Student's t error. The result shows that the IGARCH effect in these index returns could be the result of the mixture of one stationary volatility component with another non‐stationary volatility component. The VaR based on the new model performs better than traditional GARCH‐based VaRs, especially in unstable stock markets. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting regional house price inflation: a comparison between dynamic factor models and vector autoregressive models

This paper uses the dynamic factor model framework, which accommodates a large cross‐section of macroeconomic time series, for forecasting regional house price inflation. In this study, we forecast house price inflation for five metropolitan areas of South Africa using principal components obtained from 282 quarterly macroeconomic time series in the period 1980:1 to 2006:4. The results, based on the root mean square errors of one to four quarters ahead out‐of‐sample forecasts over the period 2001:1 to 2006:4 indicate that, in the majority of the cases, the Dynamic Factor Model statistically outperforms the vector autoregressive models, using both the classical and the Bayesian treatments. We also consider spatial and non‐spatial specifications. Our results indicate that macroeconomic fundamentals in forecasting house price inflation are important. Copyright © 2010 John Wiley & Sons, Ltd.     

Testing for the usefulness of forecasts

Ashley (Journal of Forecasting 1983; 2 (3): 211–223) proposes a criterion (known as Ashley's index) to judge whether the external macroeconomic variables are well forecast to serve as explanatory variables in forecasting models, which is crucial for policy makers. In this article, we try to extend Ashley's work by providing three testing procedures, including a ratio‐based test, a difference‐based test, and the Bayesian approach. The Bayesian approach has the advantage of allowing the flexibility of adapting all possible information content within a decision‐making environment such as the change of variable's definition due to the evolving system of national accounts. We demonstrate the proposed methods by applying six macroeconomic forecasts in the Survey of Professional Forecasters. Researchers or practitioners can thus formally test whether the external information is helpful. Copyright © 2010 John Wiley & Sons, Ltd.     

A forecasting comparison of classical and Bayesian methods for modelling logistic diffusion

A Bayesian procedure for forecasting S‐shaped growth is introduced and compared to classical methods of estimation and prediction using three variants of the logistic functional form and annual times series of the diffusion of music compact discs in twelve countries. The Bayesian procedure was found not only to improve forecast accuracy, using the medians of the predictive densities as point forecasts, but also to produce intervals with a width and asymmetry more in accord with the outcomes than intervals from the classical alternative. While the analysis in this paper focuses on logistic growth, the problem is set up so that the methods are transportable to other characterizations of the growth process. Copyright © 2001 John Wiley & Sons, Ltd.     

Application of Machine Learning Methods to Risk Assessment of Financial Statement Fraud: Evidence from China

This study presents a method of assessing financial statement fraud risk. The proposed approach comprises a system of financial and non‐financial risk factors, and a hybrid assessment method that combines machine learning methods with a rule‐based system. Experiments are performed using data from Chinese companies by four classifiers (logistic regression, back‐propagation neural network, C5.0 decision tree and support vector machine) and an ensemble of those classifiers. The proposed ensemble of classifiers outperform each of the four classifiers individually in accuracy and composite error rate. The experimental results indicate that non‐financial risk factors and a rule‐based system help decrease the error rates. The proposed approach outperforms machine learning methods in assessing the risk of financial statement fraud. Copyright © 2014 John Wiley & Sons, Ltd.     

Short‐term forecasting of industrial electricity consumption in Brazil

This paper presents short‐term forecasting methods applied to electricity consumption in Brazil. The focus is on comparing the results obtained after using two distinct approaches: dynamic non‐linear models and econometric models. The first method, that we propose, is based on structural statistical models for multiple time series analysis and forecasting. It involves non‐observable components of locally linear trends for each individual series and a shared multiplicative seasonal component described by dynamic harmonics. The second method, adopted by the electricity power utilities in Brazil, consists of extrapolation of the past data and is based on statistical relations of simple or multiple regression type. To illustrate the proposed methodology, a numerical application is considered with real data. The data represents the monthly industrial electricity consumption in Brazil from the three main power utilities: Eletropaulo, Cemig and Light, situated at the major energy‐consuming states, Sao Paulo, Rio de Janeiro and Minas Gerais, respectively, in the Brazilian Southeast region. The chosen time period, January 1990 to September 1994, corresponds to an economically unstable period just before the beginning of the Brazilian Privatization Program. Implementation of the algorithms considered in this work was made via the statistical software S‐PLUS. Copyright © 1999 John Wiley & Sons, Ltd.