Building composite leading indexes in a dynamic factor model framework: a new proposal

One of the most problematic aspects in the work of policy makers and practitioners is having efficient forecasting tools combining two seemingly incompatible features: ease of use and completeness of the information set underlying the forecasts. Econometric literature provides different answers to these needs: Dynamic Factor Models (DFMs) optimally exploit the information coming from large datasets; composite leading indexes represent an immediate and flexible tool to anticipate the future evolution of a phenomenon. Curiously, the recent DFM literature has either ignored the construction of leading indexes or has made unsatisfactory choices as regards the criteria for aggregating the index components and the identification of factors that feed the index. This paper fills the gap and proposes a multi-step procedure for building composite leading indexes within a DFM framework. Once selected the target economic variable and estimated a DFM based on a large target-oriented dataset, we identify the common factor shocks through sign restrictions on the impact multipliers and simulate the structural form of the model. The Forecast Error Variance Decompositions obtained over a k steps-ahead simulation horizon define k sets of weights for aggregating factors (in a different way depending on the leading horizon) in order to get composite leading indexes. This procedure is used for a very preliminar empirical exercise aimed at forecasting crude nominal oil prices. The results seem to be encouraging and support the validity of the proposal: we generate a wide range of horizon-specific leading indexes with appreciable forecasting performances.

Comparing and evaluating Bayesian predictive distributions of assets returns

Bayesian inference in a time series model provides exact, out-of-sample predictive distributions that fully and coherently incorporate parameter uncertainty. This study compares and evaluates Bayesian predictive distributions from alternative models, using as an illustration five alternative models of asset returns applied to daily S&P 500 returns from 1976 through 2005. The comparison exercise uses predictive likelihoods and is inherently Bayesian. The evaluation exercise uses the probability integral transform and is inherently frequentist. The illustration shows that the two approaches can be complementary, each identifying strengths and weaknesses in models that are not evident using the other. JEL Classification: C11, C53forecasting, GARCH, inverse probability transform, Markov mixture, predictive likelihood, S&P 500 returns, stochastic volatility

Analysis of variance for bayesian inference

This paper develops a multi-way analysis of variance for non-Gaussian multivariate distributions and provides a practical simulation algorithm to estimate the corresponding components of variance. It specifically addresses variance in Bayesian predictive distributions, showing that it may be decomposed into the sum of extrinsic variance, arising from posterior uncertainty about parameters, and intrinsic variance, which would exist even if parameters were known. Depending on the application at hand, further decomposition of extrinsic or intrinsic variance (or both) may be useful. The paper shows how to produce simulation-consistent estimates of all of these components, and the method demands little additional effort or computing time beyond that already invested in the posterior simulator. It illustrates the methods using a dynamic stochastic general equilibrium model of the US economy, both before and during the global financial crisis. JEL Classification: C11, C53Analysis of variance, Bayesian inference, posterior simulation, predictive distributions

Hierarchical Markov normal mixture models with applications to financial asset returns

With the aim of constructing predictive distributions for daily returns, we introduce a new Markov normal mixture model in which the components are themselves normal mixtures. We derive the restrictions on the autocovariances and linear representation of integer powers of the time series in terms of the number of components in the mixture and the roots of the Markov process. We use the model prior predictive distribution to study its implications for some interesting functions of returns. We apply the model to construct predictive distributions of daily S&P500 returns, dollarpound returns, and one- and ten-year bonds. We compare the performance of the model with ARCH and stochastic volatility models using predictive likelihoods. The model's performance is about the same as its competitors for the bond returns, better than its competitors for the S&P 500 returns, and much better for the dollar-pound returns. Validation exercises identify some potential improvements. JEL Classification: C53, G12, C11, C14Asset returns, Bayesian, forecasting, MCMC, mixture models

Imperfect predictability and mutual fund dynamics. How managers use predictors in changing systematic risk.

Suppose a fund manager uses predictors in changing port-folio allocations over time. How does predictability translate into portfolio decisions? To answer this question we derive a new model within the Bayesian framework, where managers are assumed to modulate the systematic risk in part by observing how the benchmark returns are related to some set of imperfect predictors, and in part on the basis of their own information set. In this portfolio allocation process, managers concern themselves with the potential benefits arising from the market timing generated by benchmark predictors and by private information. In doing this, we impose a structure on fund returns, betas, and bench-mark returns that help to analyse how managers really use predictors in changing investments over time. The main findings of our empirical work are that beta dynamics are significantly affected by economic variables, even though managers do not care about bench-mark sensitivities towards the predictors in choosing their instrument exposure, and that persistence and leverage effects play a key role as well. Conditional market timing is virtually absent, if not negative, over the period 1990-2005. However such anomalous negative timing ability is offset by the leverage effect, which in turn leads to an increase in mutual fund extra performance. JEL Classification: C11, C13, G12, G13Bayesian analysis, conditional asset pricing models, Equity mutual funds, time-varying beta

Optimal Prediction Pools

A prediction model is any statement of a probability distribution for an outcome not yet observed. This study considers the properties of weighted linear combinations of n prediction models, or linear pools, evaluated using the conventional log predictive scoring rule. The log score is a concave function of the weights and, in general, an optimal linear combination will include several models with positive weights despite the fact that exactly one model has limiting posterior probability one. The paper derives several interesting formal results: for example, a prediction model with positive weight in a pool may have zero weight if some other models are deleted from that pool. The results are illustrated using S&P 500 returns with prediction models from the ARCH, stochastic volatility and Markov mixture families. In this example models that are clearly inferior by the usual scoring criteria have positive weights in optimal linear pools, and these pools substantially outperform their best components.forecasting; GARCH; log scoring; Markov mixture; model combination; S&P 500 returns; stochastic volatility

Exact likelihood computation for nonlinear DSGE models with heteroskedastic innovations

Phenomena such as the Great Moderation have increased the attention of macro-economists towards models where shock processes are not (log-)normal. This paper studies a class of discrete-time rational expectations models where the variance of exogenous innovations is subject to stochastic regime shifts. We first show that, up to a second-order approximation using perturbation methods, regime switching in the variances has an impact only on the intercept coefficients of the decision rules. We then demonstrate how to derive the exact model likelihood for the second-order approximation of the solution when there are as many shocks as observable variables. We illustrate the applicability of the proposed solution and estimation methods in the case of a small DSGE model. JEL Classification: E0, C63DSGE Models, Regime switching, second-order approximation, time-varying volatility

Optimal Prediction Pools

A prediction model is any statement of a probability distribution for an outcome not yet observed. This study considers the properties of weighted linear combinations of n prediction models, or linear pools, evaluated using the conventional log predictive scoring rule. The log score is a concave function of the weights and, in general, an optimal linear combination will include several models with positive weights despite the fact that exactly one model has limiting posterior probability one. The paper derives several interesting formal results: for example, a prediction model with positive weight in a pool may have zero weight if some other models are deleted from that pool. The results are illustrated using S&P 500 returns with prediction models from the ARCH, stochastic volatility and Markov mixture families. In this example models that are clearly inferior by the usual scoring criteria have positive weights in optimal linear pools, and these pools substantially outperform their best components. JEL Classification: C11, C53forecasting, GARCH, log scoring, Markov mixture, model combination

Euro area inflation persistence in an estimated nonlinear DSGE model

We estimate the approximate nonlinear solution of a small DSGE model on euro area data, using the conditional particle filter to compute the model likelihood. Our results are consistent with previous findings, based on simulated data, suggesting that this approach delivers sharper inference compared to the estimation of the linearised model. We also show that the nonlinear model can account for richer economic dynamics: the impulse responses to structural shocks vary depending on initial conditions selected within our estimation sample. JEL Classification: C11, C15, E31, E32, E52Bayesian estimation, DSGE Models, Inflation persistence, second order approximations, sequential Monte Carlo

Money growth and inflation: a regime switching approach

We develop a time-varying transition probabilities Markov Switching model in which inflation is characterised by two regimes (high and low inflation). Using Bayesian techniques, we apply the model to the euro area, Germany, the US, the UK and Canada for data from the 1960s up to the present. Our estimates suggest that a smoothed measure of broad money growth, corrected for real-time estimates of trend velocity and potential output growth, has important leading indicator properties for switches between inflation regimes. Thus money growth provides an important early warning indicator for risks to price stability. JEL Classification: C11, C53, E31Bayesian inference, early warning, inflation regimes, Markov Switching model, money growth, time varying transition probabilities