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We discuss the development of dynamic factor models for multivariate nancial time series, and the incorporation of stochastic volatility components for latent factor processes. Bayesian inference and computation is developed and explored in a study of the dynamic factor structure of daily spot exchange rates for a selection of international currencies. The models are direct generalisations of univariate stochastic volatility models, and represent speci c varieties of models recently discussed in the growing multivariate stochastic volatility literature. We also discuss connections and comparisons with the much simpler method of dynamic variance discounting that, for over a decade, has been a standard approach in applied nancial econometrics in the Bayesian forecasting world. We review empirical ndings in applying these models to the exchange rate series, including aspects of model performance in dynamic portfolio allocation. We conclude with comments on the potential practical utility of structured factor models and future potential developments and model extensions.

The locally most powerful test is derived for the hypothesis that the regression coefficients are constant over time against the alternative that they vary according to the random walk process. When the regression equation contains the constant term only, comparisons are made with the tests suggested by LaMotte and McWhorter (1978). These are based on exact powers and on three different types of asymptotic efficiencies including the classical Pitman and Bahadur approaches and the new one due to Gregory (1980). The concept of the Bahadur efficiency is extended to cover also the random slopes. Suggestions are made for choosing the test.

We propose a generalization of existing business cycle models which allows us to decompose recessions into permanent and transitory components. We find that the transitory component of recessions accounts for between 77% and 96% of the observed variance of monthly indicator series. Our results suggest the following three phase characterization of the business cycle: recession, high-growth recovery during which output partially reverts to its previous peak, and normal growth following the recovery. In addition, we find significant timing differences between the permanent and transitory components of recessions; most notably the lack of the usual high-growth recovery phase following the 1990-91 recession. JEL Codes: C32, E32 Kim: Department of Economics, Korea University, Seoul, 136-701, Korea (cjkim@kuccnx.korea.ac.kr); Murray: (Corresponding author) Department of Economics, University of Houston, Houston, TX 77204-5882 (cjmurray@uh.edu), Tel: 713-743-3835, Fax: 713-743-3798 1 1. In...

In a series of papers, Donoho and Johnstone develop a powerful theory based on wavelets for extracting nonsmooth signals from noisy data. Several nonlinear smoothing algorithms are presented which provide high performance for removing Gaussian noise from a wide range of spatially inhomogeneous signals. However, like other methods based on the linear wavelet transform, these algorithms are very sensitive to certain types of non-Gaussian noise, such as outliers. In this paper, we develop outlier resistant wavelet transforms. In these transforms, outliers and outlier patches are localized to just a few scales. By using the outlier resistant wavelet transforms, we improve upon the Donoho and Johnstone nonlinear signal extraction methods. The outlier resistant wavelet algorithms are included with the S+Wavelets object-oriented toolkit for wavelet analysis. 1 INTRODUCTION The introduction of wavelets in the late 1980's has spawned a flurry of research activity, exploring new techniques for ...

seasonal adjustment, dynamic harmonic regression This paper describes in detail a flexible approach to nonstationary time series analysis based on a Dynamic Harmonic Regression (DHR) model of the Unobserved Components (UC) type, formulated with a stochastic state space setting. The model is particularly useful for adaptive seasonal adjustment, signal extraction and interpolation over gaps, as well as forecasting or backcasting. The Kalman Filter and Fixed Interval Smoothing algorithms are exploited for estimating the various components, with the Noise Variance Ratio and other hyper-parameters in the stochastic state space model estimated by a novel optimisation method in the frequency domain. Unlike other approaches of this general type, which normally exploit Maximum Likelihood methods, this optimisation procedure is based on a cost function defined in terms of the difference between the logarithmic pseudo-spectrum of the DHR model and the logarithmic autoregressive spectrum of the time series. This cost function not only seems to yield improved convergence characteristics when compared with the alternative ML cost function, but it also has much reduced numerical requirements. 1.

The mixture model likelihood function is invariant with respect to permutation of the components of the mixture. If functions of interest are permutation sensitive, as in classification applications, then interpretation of the likelihood function requires valid inequality constraints and a very large sample may be required to resolve ambiguities. If functions of interest are permutation invariant, as in prediction applications, then there are no such problems of interpretation. Contrary to assessments in some recent publications, simple and widely used Markov chain Monte Carlo (MCMC) algorithms with data augmentation reliably recover the entire posterior distribution. 1 1

This paper discusses formal quantitative algorithms that can be used to identify business cycle turning points. An intuitive, graphical derivation of these algorithms is presented along with a description of how they can be implemented making very minimal distributional assumptions. We also provide the intuition and detailed description of these algorithms for both simple parametric univariate inference as well as latent-variable multiple-indicator inference using a state-space Markov-switching approach. We illustrate the promise of this approach by reconstructing the inferences that would have been generated if parameters had to be estimated and inferences drawn based on data as they were originally released at each historical date. Our recommendation is that one should wait until one extra quarter of GDP growth is reported or one extra month of the monthly indicators released before making a call of a business cycle turning point. We introduce two new measures for dating business cycle turning points, which we call the “quarterly real-time GDP-based recession probability index ” and the “monthly real-time multiple-indicator recession probability index ” that incorporate these principles. Both indexes perform quite well in simulation with real-time data bases. We also discuss some of the potential complicating factors one might want to consider for such an analysis, such as the reduced volatility of output growth rates since 1984 and the changing cyclical behavior of employment. Although such re…nements can improve the inference, we nevertheless recommend the simpler speci…cations which perform very well historically and may be more robust for recognizing future business cycle turning points of unknown character. JEL classi…cation: E32

Abstract: We review the past 25 years of research into time series forecasting. In this silver jubilee issue, we naturally highlight results published in journals managed by the International Institute of Forecasters (Journal of Forecasting 1982–1985; International Journal of Forecasting 1985–2005). During this period, over one third of all papers published in these journals concerned time series forecasting. We also review highly influential works on time series forecasting that have been published elsewhere during this period. Enormous progress has been made in many areas, but we find that there are a large number of topics in need of further development. We conclude with comments on

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