Simultaneous Statistical Inference in Dynamic Factor Models

REVISTA BRASILEIRA DE BIOMETRIA

The multivariate t models are symmetric and have heavier tail than the normal distribution and produce robust inference procedures for applications. In this paper, the Bayesian estimation of a dynamic factor model is presented, where the factors follow a multivariate autoregressive model, using the multivariate t distribution. Since the multivariate t distribution is complex, it was represented in this work as a mix of the multivariate normal distribution and a square root of a chi-square distribution. This method allowed the complete dene of all the posterior distributions. The inference on the parameters was made taking a sample of the posterior distribution through a Gibbs Sampler. The convergence was veried through graphical analysis and the convergence diagnostics of Geweke (1992) and Raftery and Lewis (1992).

2012

This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We establish not only consistency but also the rate of convergence and the limiting distributions. Five different sets of identification conditions are considered. We show that the distributions of the MLE estimators depend on the identification restrictions. Unlike the principal components approach, the maximum likelihood estimator explicitly allows heteroskedasticities, which are jointly estimated with other parameters. Efficiency of MLE relative to the principal components method is also considered.

2008

We present new results for the likelihood-based analysis of the dynamic factor model that possibly includes intercepts and explanatory variables. The latent factors are modelled by stochastic processes. The idiosyncratic disturbances are specified as autoregressive processes with mutually correlated innovations. The new results lead to computationally efficient procedures for the estimation of the factors and parameter estimation by maximum likelihood

2013

We derive computationally simple and intuitive expressions for score tests of neglected serial correlation in common and idiosyncratic factors in dynamic factor models using frequency domain techniques. The implied time domain orthogonality conditions are analogous to the conditions obtained by treating the smoothed estimators of the innovations in the latent factors as if they were observed, but they account for their final estimation errors. Monte Carlo exercises confirm the finite sample reliability and power of our proposed tests. Finally, we illustrate their empirical usefulness in an application that constructs a monthly coincident indicator for the US from four macro series.

Journal of Econometrics, 2004

A factor model generalizing those proposed by , , has been introduced in Forni, , where consistent (as the number n of series and the number T of observations both tend to infinity along appropriate paths (n, T (n))) estimation methods for the common component are proposed. Rates of convergence associated with these methods are obtained here as functions of the paths (n, T (n)) along which n and T go to infinity. These results show that, under suitable assumptions, consistency requires T (n) to be at least of the same order as n, whereas an optimal rate of √ n is reached for T (n) of the order of n 2 . If convergence to the space of common components is considered, consistency holds irrespective of the path (T (n) thus can be arbitrarily slow); the optimal rate is still √ n, but only requires T (n) to be of the order of n. * Research supported by an A.R.C. contract of the Communauté française de Belgique, the Fonds d'Encouragementà la Recherche de l'Université Libre de Bruxelles, and the European Commission under the Training and Mobility of Researchers Programme (Contract ERBFMRX-CT98-0213). JEL subject classification : C13, C33, C43.

SSRN Electronic Journal, 2019

This paper considers multiple changes in the factor loadings of a high dimensional factor model occurring at dates that are unknown but common to all subjects. Since the factors are unobservable, the problem is converted to estimating and testing structural changes in the second moments of the pseudo factors. We consider both joint and sequential estimation of the change points and show that the distance between the estimated and the true change points is O p (1). We …nd that the estimation error contained in the estimated pseudo factors has no e¤ect on the asymptotic properties of the estimated change points as the cross-sectional dimension N and the time dimension T go to in…nity jointly. No N-T ratio condition is needed. We also propose (i) tests for the null of no change versus the alternative of l changes (ii) tests for the null of l changes versus the alternative of l + 1 changes, and show that using estimated factors asymptotically has no e¤ect on their limit distributions if p T =N ! 0. These tests allow us to make inference on the presence and number of structural changes. Simulation results show good performance of the proposed procedure. In an application to US quarterly macroeconomic data we detect two possible breaks.

Journal of Econometrics, 2001

We investigate several important inference issues for factor models with dynamic heteroskedasticity in the common factors. First, we show that such models are identi…ed if we take into account the time-variation in the variances of the factors. Our results also apply to dynamic versions of the APT, dynamic factor models, and vector autoregressions. Secondly, we propose a consistent two-step estimation procedure which does not rely on knowledge of any factor estimates, and explain how to compute correct standard errors. Thirdly, we develop a simple preliminary LM test for the presence of arch e¤ects in the common factors. Finally, we conduct a Monte Carlo analysis of the …nite sample properties of the proposed estimators and hypothesis tests.

The Annals of Statistics, 2012

This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We establish not only consistency but also the rate of convergence and the limiting distributions. Five different sets of identification conditions are considered. We show that the distributions of the MLE estimators depend on the identification restrictions. Unlike the principal components approach, the maximum likelihood estimator explicitly allows heteroskedasticities, which are jointly estimated with other parameters. Efficiency of MLE relative to the principal components method is also considered.

2009

From time to time, economies undergo far-reaching structural changes. In this paper we investigate the consequences of structural breaks in the factor loadings for the specification and estimation of factor models based on principal components and suggest test procedures for structural breaks. It is shown that structural breaks severely inflate the number of factors identified by the usual information criteria. Based on the strict factor model the hypothesis of a structural break is tested by using Likelihood-Ratio, Lagrange-Multiplier and Wald statistics. The LM test which is shown to perform best in our Monte Carlo simulations, is generalized to factor models where the common factors and idiosyncratic components are serially correlated. We also apply the suggested test procedure to a US dataset used in Stock and Watson (2005) and a euro-area dataset described in Altissimo et al. (2007). We find evidence that the beginning of the so-called Great Moderation in the US as well as the Maastricht treaty and the handover of monetary policy from the European national central banks to the ECB coincide with structural breaks in the factor loadings. Ignoring these breaks may yield misleading results if the empirical analysis focuses on the interpretation of common factors or on the transmission of common shocks to the variables of interest.

Review of Economics and …, 2000

The Generalized Dynamic Factor Model: