Question

If the Durbin-Watson statistic has a value close to 0, which assumption is violated? In other words, which assumption is the Durbin-Watson statistic checking to see is violated?
a - Independence of errors
b- Normality of errors
c- Homoscedasticity
d- none of the above

Answer 1

Answer:

Null Hypothesis: No first order autocorrelation

Alternative hypothesis: first order correlation exists

The assumptions to run this test are:

1) Errors are normally distributed with mean 0

2) Errors follows an stationary process

3) Independence condition between the erros

The statistic is defined as:

$DW = \frac{\sum_{t=2}^ T (e_t -e_{t-1})^2}{\sum_{t=1}^T e^2_t}$

And if the value for the DW is near to 0 we can conclude that the assumption of Independence is not satisfied.

Step-by-step explanation:

The Durbin Watson test is a way to check autocorrelation in residuals for a time seeries or a regression.

We need to remember that the autocorrelation is the similarity of the time series in successive intervals. When we conduct this type of test we are checking if the time series can be modeled with and AR(1) process autoregressive.

The system of hypothesis on this case are:

Null Hypothesis: No first order autocorrelation

Alternative hypothesis: First order correlation exists

The assumptions to run this test are:

1) Errors are normally distributed with mean 0

2) Errors follows an stationary process

3) Independence condition between the errors

The statistic is defined as:

$DW = \frac{\sum_{t=2}^ T (e_t -e_{t-1})^2}{\sum_{t=1}^T e^2_t}$

And if the value for the DW is near to 0 we can conclude that the assumption of Independence is not satisfied.