A threshold factor multivariate stochastic volatility model

A new multivariate stochastic volatility model is developed in this paper. The main feature of this model is to allow threshold asymmetry in a factor covariance structure. The new model provides a parsimonious characterization of volatility and correlation asymmetry in response to market news. Statistical inferences are drawn from Markov chain Monte Carlo methods. We introduce news impact analysis to analyze volatility asymmetry with a factor structure. This analysis helps us to study different responses of volatility to historical market information in a multivariate volatility framework. Our model is successful when applied to an extensive empirical study of twenty stocks. Copyright © 2009 John Wiley & Sons, Ltd.     

Forecasting volatility by means of threshold models

The aim of this paper is to compare the forecasting performance of competing threshold models, in order to capture the asymmetric effect in the volatility. We focus on examining the relative out‐of‐sample forecasting ability of the SETAR‐Threshold GARCH (SETAR‐TGARCH) and the SETAR‐Threshold Stochastic Volatility (SETAR‐THSV) models compared to the GARCH model and Stochastic Volatility (SV) model. However, the main problem in evaluating the predictive ability of volatility models is that the ‘true’ underlying volatility process is not observable and thus a proxy must be defined for the unobservable volatility. For the class of nonlinear state space models (SETAR‐THSV and SV), a modified version of the SIR algorithm has been used to estimate the unknown parameters. The forecasting performance of competing models has been compared for two return time series: IBEX 35 and S&P 500. We explore whether the increase in the complexity of the model implies that its forecasting ability improves. Copyright © 2007 John Wiley & Sons, Ltd.     

Detrending economic time series: a Bayesian generalization of the Hodrick–Prescott filter

This article develops a new method for detrending time series. It is shown how, in a Bayesian framework, a generalized version of the Hodrick–Prescott filter is obtained by specifying prior densities on the signal‐to‐noise ratio (q) in the underlying unobserved components model. This helps ensure an appropriate degree of smoothness in the estimated trend while allowing for uncertainty in q. The article discusses the important issue of prior elicitation for time series recorded at different frequencies. By combining prior expectations with the likelihood, the Bayesian approach permits detrending in a way that is more consistent with the properties of the series. The method is illustrated with some quarterly and annual US macroeconomic series. Copyright © 2006 John Wiley & Sons, Ltd.     

A Bayesian threshold nonlinearity test for financial time series

We propose in this paper a threshold nonlinearity test for financial time series. Our approach adopts reversible‐jump Markov chain Monte Carlo methods to calculate the posterior probabilities of two competitive models, namely GARCH and threshold GARCH models. Posterior evidence favouring the threshold GARCH model indicates threshold nonlinearity or volatility asymmetry. Simulation experiments demonstrate that our method works very well in distinguishing GARCH and threshold GARCH models. Sensitivity analysis shows that our method is robust to misspecification in error distribution. In the application to 10 market indexes, clear evidence of threshold nonlinearity is discovered and thus supporting volatility asymmetry. Copyright © 2005 John Wiley & Sons, Ltd.     

Forecasting time‐varying covariance with a robust Bayesian threshold model

This paper proposes a robust multivariate threshold vector autoregressive model with generalized autoregressive conditional heteroskedasticities and dynamic conditional correlations to describe conditional mean, volatility and correlation asymmetries in financial markets. In addition, the threshold variable for regime switching is formulated as a weighted average of endogenous variables to eliminate excessively subjective belief in the threshold variable decision and to serve as the proxy in deciding which market should be the price leader. The estimation is performed using Markov chain Monte Carlo methods. Furthermore, several meaningful criteria are introduced to assess the forecasting performance in the conditional covariance matrix. The proposed methodology is illustrated using daily S&P500 futures and spot prices. Copyright © 2010 John Wiley & Sons, Ltd.     

Nowcasting quarterly GDP growth in a monthly coincident indicator model

This paper presents an extension of the Stock and Watson coincident indicator model that allows one to include variables available at different frequencies while taking care of missing observations at any time period. The proposed procedure provides estimates of the unobserved common coincident component, of the unobserved monthly series underlying any included quarterly indicator, and of any missing values in the series. An application to a coincident indicator model for the Portuguese economy is presented. We use monthly indicators from business surveys whose results are published with a very short delay. By using the available data for the monthly indicators and for quarterly real GDP, it becomes possible to produce simultaneously a monthly composite index of coincident indicators and an estimate of the latest quarter real GDP growth well ahead of the release of the first official figures. Copyright © 2005 John Wiley & Son, 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.     

Finding good predictors for inflation: a Bayesian model averaging approach

We consider a Bayesian model averaging approach for the purpose of forecasting Swedish consumer price index inflation using a large set of potential indicators, comprising some 80 quarterly time series covering a wide spectrum of Swedish economic activity. The paper demonstrates how to efficiently and systematically evaluate (almost) all possible models that these indicators in combination can give rise to. The results, in terms of out‐of‐sample performance, suggest that Bayesian model averaging is a useful alternative to other forecasting procedures, in particular recognizing the flexibility by which new information can be incorporated. Copyright © 2004 John Wiley & Sons, Ltd.     

Subset threshold autoregression

We develop in this paper an efficient way to select the best subset threshold autoregressive model. The proposed method uses a stochastic search idea. Differing from most conventional approaches, our method does not require us to fix the delay or the threshold parameters in advance. By adopting the Markov chain Monte Carlo techniques, we can identify the best subset model from a very large of number of possible models, and at the same time estimate the unknown parameters. A simulation experiment shows that the method is very effective. In its application to the US unemployment rate, the stochastic search method successfully selects lag one as the time delay and five best models from more than 4000 choices. Copyright © 2003 John Wiley & Sons, Ltd.     

Evaluating volatility dynamics and the forecasting ability of Markov switching models

This paper uses Markov switching models to capture volatility dynamics in exchange rates and to evaluate their forecasting ability. We identify that increased volatilities in four euro‐based exchange rates are due to underlying structural changes. Also, we find that currencies are closely related to each other, especially in high‐volatility periods, where cross‐correlations increase significantly. Using Markov switching Monte Carlo approach we provide evidence in favour of Markov switching models, rejecting random walk hypothesis. Testing in‐sample and out‐of‐sample Markov trading rules based on Dueker and Neely (Journal of Banking and Finance, 2007) we find that using econometric methodology is able to forecast accurately exchange rate movements. When applied to the Euro/US dollar and the euro/British pound daily returns data, the model provides exceptional out‐of‐sample returns. However, when applied to the euro/Brazilian real and the euro/Mexican peso, the model loses power. Higher volatility exercised in the Latin American currencies seems to be a critical factor for this failure. Copyright © 2009 John Wiley & Sons, Ltd.     

A multi-country dynamic factor model with stochastic volatility for euro area business cycle analysis

This paper develops a dynamic factor model that uses euro area country-specific information on output and inflation to estimate an area-wide measure of the output gap. Our model assumes that output and inflation can be decomposed into country-specific stochastic trends and a common cyclical component. Comovement in the trends is introduced by imposing a factor structure on the shocks to the latent states. We moreover introduce flexible stochastic volatility specifications to control for heteroscedasticity in the measurement errors and innovations to the latent states. Carefully specified shrinkage priors allow for pushing the model towards a homoscedastic specification, if supported by the data. Our measure of the output gap closely tracks other commonly adopted measures, with small differences in magnitudes and timing. To assess whether the model-based output gap helps in forecasting inflation, we perform an out-of-sample forecasting exercise. The findings indicate that our approach yields superior inflation forecasts, both in terms of point and density predictions.     

Forecasting real‐time data allowing for data revisions

A modeling approach to real‐time forecasting that allows for data revisions is shown. In this approach, an observed time series is decomposed into stochastic trend, data revision, and observation noise in real time. It is assumed that the stochastic trend is defined such that its first difference is specified as an AR model, and that the data revision, obtained only for the latest part of the time series, is also specified as an AR model. The proposed method is applicable to the data set with one vintage. Empirical applications to real‐time forecasting of quarterly time series of US real GDP and its eight components are shown to illustrate the usefulness of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Term Structure Forecasting of Government Bond Yields with Latent and Macroeconomic Factors: Do Macroeconomic Factors Imply Better Out‐of‐Sample Forecasts?

This study empirically examines the role of macroeconomic and stock market variables in the dynamic Nelson–Siegel framework with the purpose of fitting and forecasting the term structure of interest rate on the Japanese government bond market. The Nelson–Siegel type models in state‐space framework considerably outperform the benchmark simple time series forecast models such as an AR(1) and a random walk. The yields‐macro model incorporating macroeconomic factors leads to a better in‐sample fit of the term structure than the yields‐only model. The out‐of‐sample predictability of the former for short‐horizon forecasts is superior to the latter for all maturities examined in this study, and for longer horizons the former is still compatible to the latter. Inclusion of macroeconomic factors can dramatically reduce the autocorrelation of forecast errors, which has been a common phenomenon of statistical analysis in previous term structure models. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

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.     

Affine Term Structure Model with Macroeconomic Factors: Do No‐Arbitrage Restriction and Macroeconomic Factors Imply Better Out‐of‐Sample Forecasts?

This study extends the affine dynamic Nelson–Siegel model for the inclusion of macroeconomic variables. Five macroeconomic variables are included in affine term structure model, derived under the arbitrage‐free restriction, to evaluate their role in the in‐sample fitting and out‐of‐sample forecasting of the term structure. We show that the relationship between the macroeconomic factors and yield data has an intuitive interpretation, and that there is interdependence between the yield and macroeconomic factors. Moreover, the macroeconomic factors significantly improve the forecast performance of the model. The affine Nelson–Siegel type models outperform the benchmark simple time series forecast models. The out‐of‐sample predictability of the affine Nelson–Siegel model with macroeconomic factors for the short horizon is superior to the simple affine yield model for all maturities, and for longer horizons the former is still compatible to the latter, particularly for medium and long maturities. Copyright © 2015 John Wiley & Sons, Ltd.     

Modelling and forecasting time series sampled at different frequencies

This paper discusses how to specify an observable high‐frequency model for a vector of time series sampled at high and low frequencies. To this end we first study how aggregation over time affects both the dynamic components of a time series and their observability, in a multivariate linear framework. We find that the basic dynamic components remain unchanged but some of them, mainly those related to the seasonal structure, become unobservable. Building on these results, we propose a structured specification method built on the idea that the models relating the variables in high and low sampling frequencies should be mutually consistent. After specifying a consistent and observable high‐frequency model, standard state‐space techniques provide an adequate framework for estimation, diagnostic checking, data interpolation and forecasting. An example using national accounting data illustrates the practical application of this method. Copyright © 2008 John Wiley & Sons, Ltd.     

Multivariate GARCH Models with Correlation Clustering

A new clustered correlation multivariate generalized autoregressive conditional heteroskedasticity (CC‐MGARCH) model that allows conditional correlations to form clusters is proposed. This model generalizes the time‐varying correlation structure of Tse and Tsui (2002, Journal of Business and Economic Statistics 20 : 351–361) by classifying the correlations among the series into groups. To estimate the proposed model, Markov chain Monte Carlo methods are adopted. Two efficient sampling schemes for drawing discrete indicators are also developed. Simulations show that these efficient sampling schemes can lead to substantial savings in computation time in Monte Carlo procedures involving discrete indicators. Empirical examples using stock market and exchange rate data are presented in which two‐cluster and three‐cluster models are selected using posterior probabilities. This implies that the conditional correlation equation is likely to be governed by more than one set of decaying parameters. Copyright © 2011 John Wiley & Sons, Ltd.     

Space‐Time Model versus VAR Model: Forecasting Electricity demand in Japan

This paper examined the forecasting performance of disaggregated data with spatial dependency and applied it to forecasting electricity demand in Japan. We compared the performance of the spatial autoregressive ARMA (SAR‐ARMA) model with that of the vector autoregressive (VAR) model from a Bayesian perspective. With regard to the log marginal likelihood and log predictive density, the VAR(1) model performed better than the SAR‐ARMA( 1,1) model. In the case of electricity demand in Japan, we can conclude that the VAR model with contemporaneous aggregation had better forecasting performance than the SAR‐ARMA model. Copyright © 2011 John Wiley & Sons, Ltd.     

Modelling a traffic network with missing data

Whitlock and Queen (1998) developed a dynamic graphical model for forecasting traffic flows at a number of sites at a busy traffic junction in Kent, UK. Some of the data collection sites at this junction have been faulty over the data collection period and so there are missing series in the multivariate problem. Here we adapt the model developed in Whitlock and Queen ( 1998 ) to accommodate these missing data. Markov chain Monte Carlo methods are used to provide forecasts of the missing series, which in turn are used to produce forecasts for some of the other series. The methods are used on part of the network and shown to be very promising. Copyright © 2000 John Wiley & Sons, Ltd.