# Time series-Minitab-fixing Autocorrelation problem using first difference

I am studying time series. I have the following data:

The Model for this Data is given by: $Revenue= \beta_0+\beta_1{X_{1t}}+\beta_2({X_{S1,t}})+\beta_3({X_{S2,t}}) + \beta_4({X_{S3,t1t}})$

or equivalently :

$Revenue= \beta_0+\beta_1{X_{1t}}+\beta_2(Qrt1)+\beta_3(Qrt2) + \beta_4(Qrt3)$

(I am not sure if it is correct)

Because it is a Time series data, autocorrelation is a problem. I am trying to overcome the autocorrelation problem and I found that I could use first difference. I have some examples but none use Dummy variables.

I also saw that applying this method to overcome autocorrelation will give a stationary process, which I think that we are removing Trend and seasonality

I then used MINITAB and obtained:

Then I run a normal regression analysis selecting DiffY, DiffQrt1, DiffQrt2 and DiffQrt3 and do not select the Difft as it is the trend and the values are always 1. (If I include Difft I receive the following message: * ERROR * Continuous predictors must have more than one distinct value.)

Also I do not include the constant term, as I think that doing first difference we should force the Regression through the origin.

I obtained the following results:

Analyzing the results after fixing the Autocorrelation problem the Durbin test shows a negative autocorrelation.

However I am not really sure if I am doing this in the right way as I cannot find any example using this kind of data.

I need to overcome the Autocorrelation problem in this time series and analise the Durbin-Watson test to check the autocorrelation.

I am also confused, because if we are using first difference to solve the autocorrelation problem why do we still have a Durbin-value of 2.21590 which indicates a negative autocorrelation?

Can anyone help on this?

Thanks

To deal with autocorrelated errors, you may fit a regression with ARMA errors. (This can be done using auto.arima function in R and putting the regressor matrix in the argument xreg. I do not know how to do it in Minitab, though.) Alternatively, you may include lags of variables as regressors in the model.