Modified Breusch-Godfrey Test for Restricted Higher Order Autocorrelation in Dynamic Linear Model – A Distance Based Approach

In business, dynamic models often provide valuable insights into the complex interactions between variablesover time. But recent research contends that the lagged dependent variable specification is too problematic foruse in most situations. More specifically, if residuals autocorrelation is present in a dynamic equation wherelagged values of the dependent variable appear as regressors, Ordinary least squares (OLS) estimates are biasedand generally inconsistent. For this reason it is important to have available tests against autocorrelation,particularly when it is a dynamic model. The Breusch-Godfrey (BG) test is the most appropriate test in thepresence of stochastic regressors such as lagged values of the dependent variable for higher order autocorrelation,which is asymptotically equivalent to the Durbin-Watson h test for first order autocorrelation. But Durbin htest is not applicable for second or higher order autocorrelation. Moreover these existing tests are not suitable forone-sided higher order autoregressive schemes. Whenever the sign of the parameters are known of aneconometric model, usual two-sided tests are no longer valid. In this situation, we propose a distance-basedone-sided Lagrange Multiplier (DLM) test, a likelihood based test, to test one-sided alternative. Monte Carlosimulations are conducted to compare power properties of the proposed DLM test with the BG test. It is foundthat the DLM test shows substantially improved power than two-sided counterparts for most of the casesconsidered.

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