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Fractional cointegration in the presence of linear trends
Author(s) -
Hassler Uwe,
Marmol Francesc,
Velasco Carlos
Publication year - 2008
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2008.00597.x
Subject(s) - mathematics , asymptotic distribution , cointegration , estimator , bivariate analysis , econometrics , rate of convergence , statistics , series (stratigraphy) , limiting , ordinary least squares , normality , mechanical engineering , paleontology , channel (broadcasting) , electrical engineering , biology , engineering
. We consider bivariate regressions of nonstationary fractionally integrated variables dominated by linear time trends. The asymptotic behaviour of the ordinary least square (OLS) estimators in this case allows limiting normality to arise at a faster rate of convergence than if the individual series were detrended, increasing in this way the power of the tests for fractional cointegration. We also show that the limiting distribution of the t ‐ratio of the slope coefficient depends upon the presence or not of a deterministic trend in the conditional regressor. We introduce the concept of local fractional trend to explain the apparently diverging asymptotic theories that apply when a trend is either present or absent in our set‐up.