Estimating structural VARMA models with uncorrelated but non-independent error terms

The asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of vector autoregressive moving-average (VARMA) models are derived under the assumption that the errors are uncorrelated but not necessarily independent. Relaxing the independence assumption considerably extends the range of application of the VARMA models, and allows to cover linear representations of general nonlinear processes. Conditions are given for the consistency and asymptotic normality of the QMLE. A particular attention is given to the estimation of the asymptotic variance matrix, which may be very different from that obtained in the standard framework. Modified versions of the Wald, Lagrange Multiplier and Likelihood Ratio tests are proposed for testing linear restrictions on the parameters

Estimating structural VARMA models with uncorrelated but non-independent error terms

The asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of vector autoregressive moving-average (VARMA) models are derived under the assumption that the errors are uncorrelated but not necessarily independent. Relaxing the independence assumption considerably extends the range of application of the VARMA models, and allows to cover linear representations of general nonlinear processes. Conditions are given for the consistency and asymptotic normality of the QMLE. A particular attention is given to the estimation of the asymptotic variance matrix, which may be very different from that obtained in the standard framework. Modified versions of the Wald, Lagrange Multiplier and Likelihood Ratio tests are proposed for testing linear restrictions on the parameters

Estimating structural VARMA models with uncorrelated but non-independent error terms

The asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of vector autoregressive moving-average (VARMA) models are derived under the assumption that the errors are uncorrelated but not necessarily independent. Relaxing the independence assumption considerably extends the range of application of the VARMA models, and allows to cover linear representations of general nonlinear processes. Conditions are given for the consistency and asymptotic normality of the QMLE. A particular attention is given to the estimation of the asymptotic variance matrix, which may be very different from that obtained in the standard framework. Modified versions of the Wald, Lagrange Multiplier and Likelihood Ratio tests are proposed for testing linear restrictions on the parameters

Selection of weak VARMA models by Akaïke's information criteria

This article considers the problem of orders selections of vector autoregressive moving-average (VARMA) models and the sub-class of vector autoregressive (VAR) models under the assumption that the errors are uncorrelated but not necessarily independent. We relax the standard independence assumption to extend the range of application of the VARMA models, and allow to cover linear representations of general nonlinear processes. We propose a modified criterion to the corrected AIC (Akaïke information criterion) version (AICc) introduced by Tsai and Hurvich (1989). This modified criterion is an approximately unbiased estimator of the Kullback-Leibler discrepancy, originally used to derive AIC-based criteria. Moreover, this criterion requires the estimation of the matrice involved in the asymptotic variance of the quasi-maximum likelihood (QML) estimator of the models, which provide an additional information about models. Monte carlo experiments show that the proposed modified criterion estimates the models orders more accurately than the standard AIC and AICc in large samples and often in small samples.AIC, discrepancy, Kullback-Leibler information, QMLE/LSE, order selection, structural representation, weak VARMA models.

A Review of Nonfundamentalness and Identification in Structural VAR Models

We review, under a historical perspective, the developement of the problem of non- fundamentalness of Moving Average (MA) representations of economic models, starting from the work by Hansen and Sargent [1980]. Nonfundamentalness typically arises when agents' information space is larger than the econometrican's one. Therefore it is impos- sible for the latter to use standard econometric techniques, as Vector AutoRegression (VAR), to estimate economic models. We re-state the conditions under which it is pos- sible to invert an MA representation in order to get an ordinary VAR, and we consider how the latter is used in the literature to assess the validity of Dynamic Stochastic Gen- eral Equilibrium models, providing some interesting examples. We believe that possible nonfundamental representations of considered models are too often neglected in the liter- ature. We consider how factor models can be seen as an alternative to VAR for assessing the validity of an economic model without having to deal with the problem of nonfun- damentalness. We then review the works by Lippi and Reichlin [1993] and Lippi and Reichlin [1994] which are the first attempts to give to nonfundamental representations the economic relevance that they deserve, and to outline a method to obtain such repre- sentations starting from an estimated VAR.Nonfundamentalness, Structural VAR, Dynamic Stochastic General Equilibrium Models, Factor Models

A method to generate structural impulse-responses for measuring the effects of shocks in structural macro models

We develop a technique for analyzing the response dynamics of economic variables to structural shocks in linear rational expectations models. Our work differs fromstandard SVARs since we allow expectations of future variables to enter structural equations. We show how to estimate the variance-covariance matrix of fundamental and non-fundamental shocks and we construct point estimates and confidence bounds for impulse response functions. Our technique can handle both determinate and indeterminate equilibria. We provide an application to U.S. monetary policy under pre and post Volcker monetary policy rules. JEL Classification: C39, C62, D51, E52, E58Identification, indeterminacy, rational expectations models

Forecasting Aggregated Time Series Variables: A Survey

Aggregated times series variables can be forecasted in different ways. For example, they may be forecasted on the basis of the aggregate series or forecasts of disaggregated variables may be obtained first and then these forecasts may be aggregated. A number of forecasts are presented and compared. Classical theoretical results on the relative efficiencies of different forecasts are reviewed and some complications are discussed which invalidate the theoretical results. Contemporaneous as well as temporal aggregation are considered.Autoregressive moving-average process, temporal aggregation, contemporaneous aggregation, vector autoregressive moving-average process