Just want to know how we can use the below estimation equation using MS-Excel.
CLOSE = C(1)*D(CLOSE) + [AR(3)=C(2),MA(3)=C(3),BACKCAST=1/29/2016,ESTSMPL="1/29/2016 5/27/2016"]
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Let's begin by fleshing out what the EViews code is saying.
The EViews code says that the variable CLOSE depends on its first difference and there is also an ARMA(3,3) error term included in the model. Supposedly, the ARMA error process is to whiten the residuals, which can be, and has been, argued against as a modelling strategy. It's also worth noting that there is no constant term in the equation. The reference to BACKCAST indicates how the MA process is initialized - the details of which can be found in the EViews documentation. ESTSMPL typically refers to the estimation sample.
Having understood the EViews code, the question is now: how does one estimate a linear regression model with ARMA errors using MS-Excel?
The easiest solution would be to find an existing add-in that provides this feature. An alternative method would be to write the code yourself using the MS-Excel programming language (VBA). Beware though, what makes this application tricky is the MA term; AR processes are easier to program and more common in certain fields, e.g. VAR models appear more frequently in economics than VARMA models. Another approach, if you are willing to delve into some code, would be to look at some R source code (either base code or from some time-series package) to get a sense of the task ahead if you do decide to program from scratch. Programming this from scratch seems like overkill, though, as this sort of estimation has been around for decades. Why bother if all you're interested in are the estimated parameters and not the underlying routines? It doesn't answer your question, but my advice would be to use R if EViews is not available to you. Or, seek out an MS-Excel add-in that will do the job for you.
A useful thread from the EViews forum is here: http://forums.eviews.com/viewtopic.php?f=7&t=465. Note: "Estimation, and forecasting of MA processes is complicated, especially when backcasting is used to obtain starting observations for the error terms."