MA(1)


MA(1)

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Edward
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I'm at wit's end here.

I have a MA(1) model: y_t = .64 + e_t + 0.599*e_[t-1]

Here is the first few lags from my data:
lag Y
1 0.63
2 0.67
3 0.56
4 0.59

I cannot for the life of me calculate the first forecasted MA(1) value. Can someone provide me with the predicted values and residuals based on just the first 4 lags? I'm basically stuck on calculating the residuals despite going through the book, notes, and this message board. I'm sure the answer is somewhere, but I apparently failed to find... in any case, I'm at wit's end here. Any help is greatly appreciated.

[NEAS: Calculate both the expected values and the actual values for each period. The residual is the difference. From the MA(1) equation, calculate the next expected value.]


Edward
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The expected value of an MA(1) process is simply delta, in my model 0.64.

So is the expected value of every period is 0.64?

So provided that the actual Y at lag 1 is 0.63, would the forecasted value at lag 2 = .64 + 0.599*e_[t-1] = 0.64 + 0.599*(0.63 - 0.64) = 0.64 + 0.599*(-0.01) = .63401?

[NEAS: The expected value depends on the previous residual as well as delta.]


Edward
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Is the first residual 0?

[NEAS: A common assumption for fitting ARIMA processes is that the first residual is zero. An alternative assumption is to ingore the first and second values for a minimum least squiares analysis.]


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