[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.
.
.
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