Backcast of residuals in arima

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Backcast of residuals in arima

Postby Karaja1889 » Tue Mar 09, 2021 5:18 am

Hello! I want to repeat the Eviews' calculation of one step ahead forecast (i. e. fit) in MA(4) model with additional lagged values of dependent variable as regressors. I explored the Forum and found thread that explains the process of making fit with zero starting residuals, that afterwards converges to the fit provided with backcast performed in Eviews.


But, nevertheless, when I am trying to compare fit provided to me by Eviews (I mean static forecast in Eviews) and fit made by myself in Excel with starting sero residuals, I see that my fit in Excel is much worse and it actually has oscilatory gap with fit from Eviews (see pic. in xlsx attached). I see that one of the reason why this occures is that I have unstationary model, but Eviews still is able to calculate proper fit without oscilatory behaviour.

So I have some questions:

1) What is the algorithm that is used by Eviews in order to backcast residuals and fill starting values?
2) Where can I read about this algorithm?
3) Is it possible to repeat this algorithm in Excel?
4) Is the repetition of this unknown algorithm of backcasting in Excel enough to get the same values of fit as in static forecast in Eviews?

The key question is the second one. I was unable to find any algorithms of residuals backcasting in econometric textbooks and decided to ask the question on Forum. If you will guide me to the textbook with this method I will be very happy.

In addition I have attached files with Eviews model and Excel calculations,

thank you in advance.
Example in Excel.xlsx
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