An I(2) Cointegration Model with Piecewise Linear Trends: Likelihood Analysis and Application

TY - UNPB

T1 - An I(2) Cointegration Model with Piecewise Linear Trends

T2 - Likelihood Analysis and Application

AU - Kurita, Takamitsu

AU - Nielsen, Heino Bohn

AU - Rahbek, Anders Christian

N1 - JEL classification: C32

PY - 2009

Y1 - 2009

N2 - This paper presents likelihood analysis of the I(2) cointegrated vector autoregression with piecewise linear deterministic terms. Limiting behavior of the maximum likelihood estimators are derived, which is used to further derive the limiting distribution of the likelihood ratio statistic for the cointegration ranks, extending the result for I(2) models with a linear trend in Nielsen and Rahbek (2007) and for I(1) models with piecewise linear trends in Johansen, Mosconi, and Nielsen (2000). The provided asymptotic theory extends also the results in Johansen, Juselius, Frydman, and Goldberg (2009) where asymptotic inference is discussed in detail for one of the cointegration parameters. To illustrate, an empirical analysis of US consumption, income and wealth, 1965 - 2008, is performed, emphasizing the importance of a change in nominal price trends after 1980.

AB - This paper presents likelihood analysis of the I(2) cointegrated vector autoregression with piecewise linear deterministic terms. Limiting behavior of the maximum likelihood estimators are derived, which is used to further derive the limiting distribution of the likelihood ratio statistic for the cointegration ranks, extending the result for I(2) models with a linear trend in Nielsen and Rahbek (2007) and for I(1) models with piecewise linear trends in Johansen, Mosconi, and Nielsen (2000). The provided asymptotic theory extends also the results in Johansen, Juselius, Frydman, and Goldberg (2009) where asymptotic inference is discussed in detail for one of the cointegration parameters. To illustrate, an empirical analysis of US consumption, income and wealth, 1965 - 2008, is performed, emphasizing the importance of a change in nominal price trends after 1980.

KW - Faculty of Social Sciences

KW - US consumption

M3 - Working paper

BT - An I(2) Cointegration Model with Piecewise Linear Trends

PB - Department of Economics, University of Copenhagen

ER -