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Replicating a MA(1) forecast in Excel

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New Contributor
Posts: 2

Replicating a MA(1) forecast in Excel

This is seamingly a trivial question, but several have looked at my question and are also perplexed.  I created a simple moving average prediction based on 100 data points in JMP.  I would like someone's assistantce in replicating, in Excel, the forecast provided by JMP using the coefficients provided by JMP.  Writing out the equation using actual numbers would be perfect for my needs. I have looked for sources with more than generalized formulas for hours now. The coefficients are as follows:

TermLagEstimateStd Errort RatioProb>|t|Constant Estimate
MA11-0.998490.433763-2.30.02350.179165
Intercept00.1791650.2483440.720.4724

The first 10 data points, forecast and residuals are provided below:

ObservationActual YPredicted YResidual Y
11.29170.17921.1125
23.50040.73542.7649
32.15952.02250.1370
42.24760.28191.9657
52.27911.75170.5274
62.35010.61871.7315
71.24911.6633-0.4141
80.9596-0.18321.1428
91.20701.19500.0120
100.16680.1899-0.0231

Could someone provide the math using the numbers in the tables that yields the Predicted Y for Observation 5 and 9 as an example?  Thank you!

Super User
Posts: 18,601

Re: Replicating a MA(1) forecast in Excel

You should post this in the statistics portion of the forum Smiley Happy

Super Contributor
Posts: 339

Re: Replicating a MA(1) forecast in Excel

I'm not a JMP-User and can offer only a part of the answer (at best). If you put your 1st 10 observations into proc arima:

Data A;
  Input Observation Actual;
  Datalines;
1 1.2917
2 3.5004
3 2.1595
4 2.2476
5 2.2791
6 2.3501
7 1.2491
8 0.9596
9 1.2070
10 0.1668
;
Run;

Proc ARIMA Data=A;
  Identify Var=Actual;
  Estimate q=1;
  Forecast Lead=0 Out=Result_ARIMA (Keep=Actual Forecast Residual);
Run;

The Result is: My=1.67681, MA1=-0.25377 and

Actual  Forecast       Residual
1.2917 1.6768075816 -0.385107582
3.5004 1.5790802232 1.9213197768
2.1595 2.164373954 -0.004873954
2.2476 1.6755707359 0.5720292641
2.2791 1.8219693795 0.4571306205
2.3501 1.7928119662 0.5572880338
1.2491 1.8182285508 -0.569128551
0.9596 1.5323818872 -0.572781887
1.207 1.5314547933 -0.324454793
0.1668 1.594471862 -1.427671862

The results calculate as I think they should: 1.579=1,6768-(-0.25377)*-0.3851, etc.

If you double-check your JMP-Input?

New Contributor
Posts: 2

Re: Replicating a MA(1) forecast in Excel

Thank you.  I'm getting different predicted values from JMP, which likely is the source of my confusion, no doubt caused by me.

Super User
Posts: 18,601

Re: Replicating a MA(1) forecast in Excel

Can you post the full data so someone can replicate the results/model?

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