Residual-based tests for factorial cointegration: A Monte Carlo study (Q2740042)

The data considered are described by the model \( y_t=\alpha+\beta x_t+\gamma t+u_t,\) where \(x_t\) and \(y_t\) are observed \(I(1)\) series (i.e., \(\Delta x_t\) and \(\Delta y_t\) are stationary with finite positive spectral density at \(0\)); \(\alpha\), \(\beta\) and \(\gamma\) are unknown parameters, and \(u_t\) is a long memory \(I(d)\)-process (i.e., the spectral density of \(u_t\) is \(\sim\lambda^{-2d}\) as \(\lambda\to 0\), \(0<d\leq 1\)).NEWLINENEWLINENEWLINEThe author considers six tests for the hypothesis \(H_0\): \(u_t\) is \(I(1)\) for any \(\alpha,\beta,\gamma\in R\). In this case it is said that \(x\) and \(y\) are not cointegrated. The alternative is that \(u_t\) is \(I(d)\) for some \(d<1\) (\(x\) and \(y\) are cointegrated). The considered tests (Geweke-Porter-Hudak test; modified rescaled range test; Phillips-Perron \(t-\) and \(\rho-\)tests; augmented Dickey-Fuller test; Lobato-Robinson LM-test) are applied to the residuals of ordinary least squares regression of \(y_t\) on \(x_t\). A Monte-Carlo study is used to compare the size and power of these tests.