Marc Hallin

The Generalized Dynamic-Factor Model: Identification and Estimation

This paper proposes a factor model with infinite dynamics and nonorthogonal idiosyncratic components. The model, which we call the generalized dynamic-factor model, is novel to the literature and generalizes the static approximate factor model of Chamberlain and Rothschild (1983), as well as the exact factor model la Sargent and Sims (1977). We provide identification conditions, propose an estimator of the common components, prove convergence as both time and cross-sectional size go to infinity at appropriate rates, and present simulation results. We use our model to construct a coincident index for the European Union. Such index is defined as the common component of real GDP within a model including several macroeconomic variables for each European country.

The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting

This article proposes a new forecasting method that makes use of information from a large panel of time series. Like earlier methods, our method is based on a dynamic factor model. We argue that our method improves on a standard principal component predictor in that it fully exploits all the dynamic covariance structure of the panel and also weights the variables according to their estimated signal-to-noise ratio. We provide asymptotic results for our optimal forecast estimator and show that in finite samples, our forecast outperforms the standard principal components predictor.

Determining the Number of Factors in the General Dynamic Factor Model

This article develops an information criterion for determining the number q of common shocks in the general dynamic factor model developed by Forni et al., as opposed to the restricted dynamic model considered by Bai and Ng and by Amengual and Watson. Our criterion is based on the fact that this number q is also the number of diverging eigenvalues of the spectral density matrix of the observations as the number n of series goes to infinity. We provide sufficient conditions for consistency of the criterion for large n and T (where T is the series length). We show how the method can be implemented and provide simulations and empirics illustrating its very good finite-sample performance. Application to real data adds a new empirical facet to an ongoing debate on the number of factors driving the U.S. economy.

Do Financial Variables Help Forecasting Inflation and Real Activity in the Euro Area

The Paper uses a large data set, consisting of 447 monthly macroeconomic time series concerning the main countries of the Euro area to simulate out-of-sample predictions of the Euro area industrial production and the harmonized inflation index and to evaluate the role of financial variables in forecasting. We considered two models which allow forecasting based on large panels of time series: Forni, Hallin, Lippi, and Reichlin (2000, 2001c) and Stock and Watson (1999). Performance of both models was compared to that of a simple univariate AR model. Results show that multivariate methods outperform univariate methods for forecasting inflation at one, three, six, and twelve months and industrial production at one and three months. We find that financial variables do help forecasting inflation, but do not help forecasting industrial production. (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.)

The generalized dynamic factor model consistency and rates

Abstract A factor model generalizing those proposed by Geweke (in: D.J. Aigner and A.S. Goldberger, Latent Variables in Socio-Economic Models, North-Holland, Amsterdam, 1977), Sargent and Sims (New Methods in Business Research, Federal Reserve Bank of Minneapolis, Minneapolis, 1977), Engle and Watson (J. Amer. Statist. Assoc. 76 (1981) 774) and Stock and Watson (J. Business. Econom. Statist. 20 (2002) 147) has been introduced in Forni et al. (Rev. Econ. Statist. 80 (2000) 540), 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 n2. 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.

Coincident and Leading Indicators for the Euro Area

This paper proposes a new way to compute a coincident and a leading indicator of economic activity. Our methodology, based on Forni, Hallin, Lippi and Reichlin (2000), reconciles dynamic principal components analysis with dynamic factor analysis. It allows us to extract indicators from a large panel of economic variables (many variables for many countries). The procedure is used to estimate coincident and leading indicators for the EURO area. Unlike other methods used in the literature, the procedure takes into consideration the cross-country as well as the within-country correlation structure and exploit all information on dynamic cross-correlation.(This abstract was borrowed from another version of this item.)

Asymptotic power of sphericity tests for high-dimensional data

This paper studies the asymptotic power of tests of sphericity against perturbations in a single unknown direction as both the dimensionality of the data and the number of observations go to infinity. We establish the convergence, under the null hypothesis and the alternative, of the log ratio of the joint densities of the sample covariance eigenvalues to a Gaussian process indexed by the norm of the perturbation. When the perturbation norm is larger than the phase transition threshold studied in Baik et al. (2005), the limiting process is degenerate and discrimination between the null and the alternative is asymptotically certain. When the norm is below the threshold, the process is non-degenerate, so that the joint eigenvalue densities under the null and alternative hypotheses are mutually contiguous. Using the asymptotic theory of statistical experiments, we obtain asymptotic power envelopes and derive the asymptotic power for various sphericity tests in the contiguity region. In particular, we show that the asymptotic power of the Tracy-Widom-type tests is trivial, whereas that of the eigenvalue-based likelihood ratio test is strictly larger than the size, and close to the power envelope.

Semiparametrically efficient rank-based inference for shape I. Optimal rank-based tests for sphericity

We propose a class of rank-based procedures for testing that the shape matrix V of an elliptical distribution (with unspecified center of symmetry, scale and radial density) has some fixed value V 0 ; this includes, for V 0 = I k , the problem of testing for sphericity as an important particular case. The proposed tests are invariant under translations, monotone radial transformations, rotations and reflections with respect to the estimated center of symmetry. They are valid without any moment assumption. For adequately chosen scores, they are locally asymptotically maximin (in the Le Cam sense) at given radial densities. They are strictly distribution-free when the center of symmetry is specified, and asymptotically so when it must be estimated. The multivariate ranks used throughout are those of the distances-in the metric associated with the null value V 0 of the shape matrix-between the observations and the (estimated) center of the distribution. Local powers (against elliptical alternatives) and asymptotic relative efficiencies (AREs) are derived with respect to the adjusted Mauchly test (a modified version of the Gaussian likelihood ratio procedure proposed by Muirhead and Waternaux [Biometrika 67 (1980) 31-43]) or, equivalently, with respect to (an extension of) the test for sphericity introduced by John [Biometrika 59 (1972) 169-173]. For Gaussian scores, these AREs are uniformly larger than one, irrespective of the actual radial density. Necessary and/or sufficient conditions for consistency under nonlocal, possibly nonelliptical alternatives are given. Finite sample performance is investigated via a Monte Carlo study.

Kernel density estimation for spatial processes: the L 1 theory

The purpose of this paper is to investigate kernel density estimators for spatial processes with linear or nonlinear structures. Sufficient conditions for such estimators to converge in L1 are obtained under extremely general, verifiable conditions. The results hold for mixing as well as for nonmixing processes. Potential applications include testing for spatial interaction, the spatial analysis of causality structures, the definition of leading/lagging sites, the construction of clusters of comoving sites, etc.

Local linear spatial quantile regression

Copyright @ 2009 International Statistical Institute / Bernoulli Society for Mathematical Statistics and Probability.