[EMAIL PROTECTED] (Jennifer Bo) wrote in message news:<[EMAIL PROTECTED]>... > Hi, > > does anyone know, which critical values I should use for > Durbin-Watson's d-test when I have more than 100 cases and more than 5 > variables? > > In fact, I have about 4000 cases and 19 variables. I can't find any > tables for the critical values. Is it possible to calculate them? SPSS > doesn't do it and I have no alternatives. I am getting a value of > d=1,549. > > Best regards, > > Jennifer Borck
Jennifer, The limit values for the DW statistic is 1.78 for alpha=.05 and 1.65 for alpha=.01 The statistic is largely ignored by the statistical community as it is quite dated (1951) and leads to some very false conclusions regarding model augmentation strategies. Having said that you should know that the DW statistic is essentially meaningless as it assumes that the evidented serial autocorrelation can be remedied by an ARIMA model of order 1 ( aka a first order autoregressivee model ) Durbin and Watson A common problem that often arises with the following model y(t) = a + b*x(t) + e(t), is that you often find that e(t) has large, positive serial correlation. Ignoring this results in a badly mis-specified model. Durbin suggested that one study the auto-regressive structure of the errors and finding a significant correlation between e(t) and e(t-1) one should rather entertain the larger model y(t) = a + b*x(t) + e(t) e(t) = rho*e(t-1) + a(t) an ARIMA model (1,0,0) culminating in an a(t) process that was normal,independent and identically generated , N.I.I.D. for short. Durbin and Watson developed a test statistic and paved the way for empirical model restructuring via diagnostic checking. The problem however was that they were testing for significant autocorrelation of the e(t)'s at lag 1 and inferring cause. Significant autocorrelation of lag 1 in an error process can arise in a number of ways. 1.Another ARIMA model might be more appropriate 2.Additional lags of X might be needed to fully capture the impact of X. When additional lags are needed one gets a "false signal" from the autocorrelation function . 3.Outliers may exist at successive points in time causing a "false signal" from the autocorrelation function since these successive values create the impression of autoregressive structure . 4.The variance of the errors e(t) might be changing over time. 5.The parameters of the model might be changing over time. Thus the na�ve augmentation strategy of Durbin and Watson did not necessarily address itself to the cause. Other researchers, notably Hildreth and Liu made contributions in the 60's but it was all like an appetizer to the rigorous approach incorporated into the Box-Jenkins approach. Namely 1. the acf of the tentatively identified errors is examined to suggest the ARIMA form 2. the cross-correlation of these e(t) with lags of X to detect needed lag structure in X and 3. the need for Pulses, Level Shifts , Seasonal Pulses and/or Local Time Trends to guarantee that the mean of the error is zero everywhere or equivalently that the mean of the errors doesn't differ significantly from zero for all subsets of time. Hope this helps you and others that lean on this very ineffective model diagnostic tool. Dave Reilly Automatic Forecasting Systems http://www.autobox.com P.S. The correct approach is to examine all three avenues of model augmentation ..thus eight combinations ... and see which approach is best for the particular problem at hand. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
