TY - JOUR

T1 - Nonstationary Cointegration in the Fractionally Cointegrated VAR Model

AU - Johansen, Søren

AU - Nielsen, Morten Ørregaard

PY - 2019

Y1 - 2019

N2 - We consider the fractional cointegrated vector autoregressive (CVAR) model of Johansen and Nielsen (2012a) and make two distinct contributions. First, in their consistency proof, Johansen and Nielsen (2012a) imposed moment conditions on the errors that depend on the parameter space, such that when the parameter space is larger, stronger moment conditions are required. We show that these moment conditions can be relaxed, and for consistency we require just eight moments regardless of the parameter space. Second, Johansen and Nielsen (2012a) assumed that the cointegrating vectors are stationary, and we extend the analysis to include the possibility that the cointegrating vectors are non‐stationary. Both contributions require new analysis and results for the asymptotic properties of the likelihood function of the fractional CVAR model, which we provide. Finally, our analysis follows recent research and applies a parameter space large enough that the usual (non‐fractional) CVAR model constitutes an interior point and hence can be tested against the fractional model using a Chi‐squared‐test.

AB - We consider the fractional cointegrated vector autoregressive (CVAR) model of Johansen and Nielsen (2012a) and make two distinct contributions. First, in their consistency proof, Johansen and Nielsen (2012a) imposed moment conditions on the errors that depend on the parameter space, such that when the parameter space is larger, stronger moment conditions are required. We show that these moment conditions can be relaxed, and for consistency we require just eight moments regardless of the parameter space. Second, Johansen and Nielsen (2012a) assumed that the cointegrating vectors are stationary, and we extend the analysis to include the possibility that the cointegrating vectors are non‐stationary. Both contributions require new analysis and results for the asymptotic properties of the likelihood function of the fractional CVAR model, which we provide. Finally, our analysis follows recent research and applies a parameter space large enough that the usual (non‐fractional) CVAR model constitutes an interior point and hence can be tested against the fractional model using a Chi‐squared‐test.

KW - Faculty of Social Sciences

KW - Cointegration

KW - fractional integration

KW - likelihood inference

KW - vector autoregressive model

U2 - 10.1111/jtsa.12438

DO - 10.1111/jtsa.12438

M3 - Journal article

VL - 40

SP - 519

EP - 543

JO - Journal of Time Series Analysis

JF - Journal of Time Series Analysis

SN - 0143-9782

IS - 4

ER -