Determination of lag threshold on the measure of collinearity

摘要

To date, theimplementation of lag selection procedures within the context of unit roottests is largely based on application of standard information criteria whichare well-known to have lag selection problem. In this paper, we propose a newlag selection procedure based on collinearity measures for an autoregression ofdifferenced lagged values. In empirical analysis, the conventional coefficientof multiple determination denoted by Rc2 has been widely used in statisticalliterature for the computation of standard collinearity measures such asvariance inflation factor (VIF) and tolerance index(ToL) but given thewell-known difference between the underlying assumptions of standard multiplelinear regression and a linear autoregression, the conventional coefficient ofmultiple determination which is used to compute VIF and ToL under the frameworkof standard multiple linear regression may not provide an appropriatecollinearity measures under a linear autoregression setting. Hence, the realizationof this obvious inadequacy motivated the introduction of our newly proposedstatistic called the coefficient of multiple determination for autoregressionof differenced lagged values of time series data. Unit root tests areimplemented on autoregression made up of differenced lagged values whichrequires an appropriate choice of optimal truncation lag. However, in thecurrent literature there is dearth of information on possibility of usingcollinearity statistics as criteria for lag truncation in unit root tests.Using the newly proposed coefficient of multiple determination forautoregression of differenced lagged series denoted by Rd2 , we generate a classof collinearity statistics called tolerance index and variance inflation factorfor differenced lagged series denoted by ToLd and VIFd respectively. We usedthese collinearity statistics as criteria for determining lag threshold forunit root tests. We employed augmented Dickey-Fuller(ADF) and generalizedDickey Fuller (DF-GLS) unit root tests to illustrate empirically theapplication of these collinearity criteria for lag selection and wedemonstrated that these criteria select lag-length that is parsimonious therebyavoiding the problem of over-specification of truncation lag-length that is commonlyassociated with classical lag selection techniques.