We show that the ordinary least squares (OLS) estimates of population parameters for Markov switching vector autoregressive (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 in closed-form for the asymptotic covariance matrix of the OLS estimator of such models. The obtained characterization of the asymptotic variance is new to our knowledge. It is easier to program than the usual approach based on second derivatives, and more accurate. Our theorems generalize the classical results known for a linear VAR process, and complete those existing in the literature on the estimation of the asymptotic covariance matrix for multivariate stationary time series. Numerical simulations are provided to illustrate the obtained theoretical results. Finally, an application on energy use and economic growth in the Euro area gives some insights on the nonlinear nature of the corresponding time series, and reproduces the major stylized facts.

OLS estimation of Markov Switching VAR models: asymptotics and application to energy use / Cavicchioli, Maddalena. - In: ASTA ADVANCES IN STATISTICAL ANALYSIS. - ISSN 1863-8171. - 105:3(2021), pp. 431-449. [10.1007/s10182-020-00383-4]

### OLS estimation of Markov Switching VAR models: asymptotics and application to energy use

#### Abstract

We show that the ordinary least squares (OLS) estimates of population parameters for Markov switching vector autoregressive (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 in closed-form for the asymptotic covariance matrix of the OLS estimator of such models. The obtained characterization of the asymptotic variance is new to our knowledge. It is easier to program than the usual approach based on second derivatives, and more accurate. Our theorems generalize the classical results known for a linear VAR process, and complete those existing in the literature on the estimation of the asymptotic covariance matrix for multivariate stationary time series. Numerical simulations are provided to illustrate the obtained theoretical results. Finally, an application on energy use and economic growth in the Euro area gives some insights on the nonlinear nature of the corresponding time series, and reproduces the major stylized facts.
##### Scheda breve Scheda completa Scheda completa (DC)
2021
22-ott-2020
105
3
431
449
OLS estimation of Markov Switching VAR models: asymptotics and application to energy use / Cavicchioli, Maddalena. - In: ASTA ADVANCES IN STATISTICAL ANALYSIS. - ISSN 1863-8171. - 105:3(2021), pp. 431-449. [10.1007/s10182-020-00383-4]
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11380/1211842`