Seminar of the Thematic project (2023/01728-0) Econometric Modelling and Forecasting in High-Dimensional Models (HDEN&For)

Speaker: Maddalena Cavicchioli: Associate Professor of Economic Statistics University of Modena and Reggio Emilia, Italy

Title: Topics in Markov switching vector autoregressive models: statistical inference and applications

Abstract: This talk covers different topics of interest for a class of nonlinear multivariate time series, namely, Markov Switching Vector Autoregressive models (MS VAR).

Firstly, we show that the ordinary least squares estimates of population parameters MS VAR models coincide with the maximum likelihood estimates. Then, we propose an algorithm in matrix form for the estimation of model parameters, and derive an explicit expression for the asymptotic covariance matrix of the estimators of such models.

Secondly, we propose a new method to compute various impulse response functions for MS VAR models in terms of neat matrix expressions. The key is to derive a suitable closed form representation for MS VAR models using a state-space representation.

Thirdly, we derive the optimal forecasts for MS VAR models, where optimality means that the trace of the mean square forecast error matrix is minimized by using suitable weighting observations. Then we provide neat analytic expressions for the optimal weights in terms of the matrices involved in a state space representation of the considered process.

Finally, we illustrate the feasibility of the proposed approaches with numerical simulations and some  empirical evidences which demonstrate the relevance of accommodating asymmetries in economic contexts.