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Version 2.6 of BEWIstat included a new version of the Durbin-Watson statistic in linear regression analysis (6a). A statistical test for this Durbin-Watson statistic allows a better distinction between dependent and independent cases than the classical DW statistic. This test has been available in StatXact for a long time, and it is included in the package of R. In this article we provide a short introduction to the newly developed DW statistic in linear regression, and we describe some of the features of the BEWIstat package. The DW statistic as a measure for the presence of auto-correlation The DW statistic can be understood as a measure of the presence of auto-correlation in a time series. The DW statistic is built on the assumption that, over a finite time interval, the time series can be described as an auto-regressive process. In the linear regression model the DW statistic is the first component of the error variance in the AR(1) model To illustrate this in Figure 1 we show a time series with a linear regression model The error variance is the sum of the variances of the disturbances of the model: The DW statistic is the first of the squared errors Note that, since the time series is not independent from itself, the DW statistic is always non-negative, unlike the DW statistic of the ARMA model (figure 2). An interesting consequence of the DW statistic in the linear regression model is that a positive DW statistic always implies a positive DW statistic for the ARMA model. Figure 2: DW statistic of an AR(1) process with parameters (1,0.5,0.5). The numbers above the lines show the DW statistic of the ARMA(1,1) process, i.e. the first DW statistic of the ARMA model and the second DW statistic of the AR(1) model. Another property of the DW statistic in the linear regression model is that the DW statistic of a stationary time series will not change. This can be demonstrated by the following example. As Figure 3 shows, the linear regression model has the same DW statistic as the AR(1) model The DW statistic of the linear regression model is The first components of the two squared errors in both models are the same. Figure 3: DW statistic of a stationary linear regression model with coefficients (1,0
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