Likelihood Based Inference for an Identifiable Fractional Vector Error Correction Model

Tinbergen Institute Discussion Paper 2018-085/III

40 Pages Posted: 10 Dec 2018

See all articles by Federico Carlini

Federico Carlini

Dipartimento di Economia e Finanza

Katarzyna Lasak

VU Amsterdam; Tinbergen Institute

Date Written: November 16, 2018

Abstract

We consider the Fractional Vector Error Correction model proposed in Avarucci (2007), which is characterized by a richer lag structure than the models proposed in Granger (1986) and Johansen (2008, 2009). In particular, we discuss the properties of the model of Avarucci (2007) (FECM) in comparison to the model of Johansen (2008, 2009) (FCVAR). Both models generate the same class of processes, but the properties of the two models are different. First, opposed to the model of Johansen (2008, 2009), the model of Avarucci has a convenient nesting structure, which allows for testing the number of lags and the cointegration rank exactly in the same way as in the standard I(1) cointegration framework of Johansen (1995) and hence might be attractive for econometric practice. Second, we find that the model of Avarucci (2007) is almost free from identification problems, contrary to the model of Johansen (2008, 2009) and Johansen and Nielsen (2012), which identification problems are discussed in Carlini and Santucci de Magistris (2017).

However, due to a larger number of parameters, the estimation of the FECM model of Avarucci (2007) turns out to be more complicated. Therefore, we propose a 4-step estimation procedure for this model that is based on the switching algorithm employed in Carlini and Mosconi (2014), together with the GLS procedure of Mosconi and Paruolo (2014). We check the performance of the proposed estimation procedure in finite samples by means of a Monte Carlo experiment and we prove the asymptotic distribution of the estimators of all the parameters. The solution of the model has been previously derived in Avarucci (2007), while testing for the rank has been discussed in Lasak and Velasco (for cointegration strength >0.5) and Avarucci and Velasco (for cointegration strength <0.5). Therefore our paper fills in the gap for a complete inference based on Avarucci (2007) model.

Keywords: Error correction model, Gaussian VAR model, Fractional Cointegration, Estimation algorithm, Maximum likelihood estimation, Switching Algorithm, Reduced Rank Regression

JEL Classification: C13, C32

Suggested Citation

Carlini, Federico and Lasak, Katarzyna, Likelihood Based Inference for an Identifiable Fractional Vector Error Correction Model (November 16, 2018). Tinbergen Institute Discussion Paper 2018-085/III, Available at SSRN: https://ssrn.com/abstract=3285821 or http://dx.doi.org/10.2139/ssrn.3285821

Federico Carlini (Contact Author)

Dipartimento di Economia e Finanza ( email )

Rome
Rome, ID Rome
Italy

Katarzyna Lasak

VU Amsterdam ( email )

Department of Econometrics, FEWEB
De Boelelaan 1105
Amsterdam, 1081 HV
Netherlands

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

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