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

Rumana Rois, Tapati Basak, Mohd Muzibur Rahman, Ajit Kumar Majumder


In business, dynamic models often provide valuable insights into the complex interactions between variables
over time. But recent research contends that the lagged dependent variable specification is too problematic for
use in most situations. More specifically, if residuals autocorrelation is present in a dynamic equation where
lagged values of the dependent variable appear as regressors, Ordinary least squares (OLS) estimates are biased
and 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 the
presence 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 h
test is not applicable for second or higher order autocorrelation. Moreover these existing tests are not suitable for
one-sided higher order autoregressive schemes. Whenever the sign of the parameters are known of an
econometric model, usual two-sided tests are no longer valid. In this situation, we propose a distance-based
one-sided Lagrange Multiplier (DLM) test, a likelihood based test, to test one-sided alternative. Monte Carlo
simulations are conducted to compare power properties of the proposed DLM test with the BG test. It is found
that the DLM test shows substantially improved power than two-sided counterparts for most of the cases

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