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on Econometric Time Series |
| By: | Monica Billio; Roberto Casarin |
| Abstract: | We propose a new class of Markov-switching (MS) models for business cycle analysis. As usually done in the literature, we assume that the MS latent factor is driving the dynamics of the business cycle but the transition probabilities can vary randomly over time. Transition probabilities are generated by random processes which may account for the stochastic duration of the regimes and for possible stochastic relations between the MS probabilities and some explanatory variables, such as autoregressive components and exogenous variables. The presence of latent factors and nonlinearities calls for the use of simulation-based inference methods. We propose a full Bayesian inference approach which can be naturally combined with Monte Carlo methods. We discuss the choice of the priors and a Markov-chain Monte Carlo (MCMC) algorithm for estimating the parameters and the latent variables. We provide an application of the model and of the MCMC procedure to data of Euro area. We also carry out a real-time comparison between different models by employing sequential Monte Carlo methods and some concordance statistics, which are widely used in business cycle analysis. |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:ubs:wpaper:1002&r=ets |
| By: | Alejandro Rodríguez; Esther Ruiz |
| Abstract: | Prediction intervals in State Space models can be obtained by assuming Gaussian innovations and using the prediction equations of the Kalman filter, where the true parameters are substituted by consistent estimates. This approach has two limitations. First, it does not incorporate the uncertainty due to parameter estimation. Second, the Gaussianity assumption of future innovations may be inaccurate. To overcome these drawbacks, Wall and Stoffer (2002) propose to obtain prediction intervals by using a bootstrap procedure that requires the backward representation of the model. Obtaining this representation increases the complexity of the procedure and limits its implementation to models for which it exists. The bootstrap procedure proposed by Wall and Stoffer (2002) is further complicated by fact that the intervals are obtained for the prediction errors instead of for the observations. In this paper, we propose a bootstrap procedure for constructing prediction intervals in State Space models that does not need the backward representation of the model and is based on obtaining the intervals directly for the observations. Therefore, its application is much simpler, without loosing the good behavior of bootstrap prediction intervals. We study its finite sample properties and compare them with those of the standard and the Wall and Stoffer (2002) procedures for the Local Level Model. Finally, we illustrate the results by implementing the new procedure to obtain prediction intervals for future values of a real time series. |
| Keywords: | NAIRU, Output gap, Parameter uncertainty, Prediction Intervals, State Space Models |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws100301&r=ets |
| By: | Massimiliano Caporin (Dipartimento di Scienze Economiche "Marco Fanno", Universita degli Studi di Padova); Michael McAleer (Erasmus School of Economics, Erasmus University Rotterdam and Tinbergen Institute) |
| Abstract: | The management and monitoring of very large portfolios of financial assets are routine for many individuals and organizations. The two most widely used models of conditional covariances and correlations in the class of multivariate GARCH models are BEKK and DCC. It is well known that BEKK suffers from the archetypal "curse of dimensionality", whereas DCC does not. It is argued in this paper that this is a misleading interpretation of the suitability of the two models for use in practice. The primary purpose of this paper is to analyze the similarities and dissimilarities between BEKK and DCC, both with and without targeting, on the basis of the structural derivation of the models, the availability of analytical forms for the sufficient conditions for existence of moments, sufficient conditions for consistency and asymptotic normality of the appropriate estimators, and computational tractability for ultra large numbers of financial assets. Based on theoretical considerations, the paper sheds light on how to discriminate between BEKK and DCC in practical applications. |
| Date: | 2010–02 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2010cf713&r=ets |
| By: | Thomas Conlon; Heather J. Ruskin; Martin Crane |
| Abstract: | The dynamics of the equal-time cross-correlation matrix of multivariate financial time series is explored by examination of the eigenvalue spectrum over sliding time windows. Empirical results for the S&P 500 and the Dow Jones Euro Stoxx 50 indices reveal that the dynamics of the small eigenvalues of the cross-correlation matrix, over these time windows, oppose those of the largest eigenvalue. This behaviour is shown to be independent of the size of the time window and the number of stocks examined. A basic one-factor model is then proposed, which captures the main dynamical features of the eigenvalue spectrum of the empirical data. Through the addition of perturbations to the one-factor model, (leading to a 'market plus sectors' model), additional sectoral features are added, resulting in an Inverse Participation Ratio comparable to that found for empirical data. By partitioning the eigenvalue time series, we then show that negative index returns, (drawdowns), are associated with periods where the largest eigenvalue is greatest, while positive index returns, (drawups), are associated with periods where the largest eigenvalue is smallest. The study of correlation dynamics provides some insight on the collective behaviour of traders with varying strategies. |
| Date: | 2010–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1002.0321&r=ets |
| By: | Alghalith, Moawia |
| Abstract: | We present a new method of estimating the asset stochastic volatility and return. In doing so, we overcome some of the limitations of the existing random walk models, such as the GARCH/ARCH models. |
| Keywords: | portfolio; investment; stock; stochastic volatility |
| JEL: | C13 G12 G0 |
| Date: | 2010–01–28 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:20303&r=ets |
| By: | Willert, Juliane |
| Abstract: | Atheoretical regression trees (ART) are applied to detect changes in the mean of a stationary long memory time series when location and number are unknown. It is shown that the BIC, which is almost always used as a pruning method, does not operate well in the long memory framework. A new method is developed to determine the number of mean shifts. A Monte Carlo Study and an application is given to show the performance of the method. |
| Keywords: | long memory, mean shift, regression tree, ART, BIC. |
| JEL: | C14 C22 |
| Date: | 2010–02 |
| URL: | http://d.repec.org/n?u=RePEc:han:dpaper:dp-437&r=ets |