topic Re: Replicating a MA(1) forecast in Excel in Statistical Procedures

Replicating a MA(1) forecast in Excel

WilliamRoberts — Thu, 11 Dec 2014 21:22:45 GMT

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:

Term	Lag	Estimate	Std Error	t Ratio	Prob>\|t\|	Constant Estimate
MA1	1	-0.99849	0.433763	-2.3	0.0235	0.179165
Intercept	0	0.179165	0.248344	0.72	0.4724

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

Observation	Actual Y	Predicted Y	Residual Y
1	1.2917	0.1792	1.1125
2	3.5004	0.7354	2.7649
3	2.1595	2.0225	0.1370
4	2.2476	0.2819	1.9657
5	2.2791	1.7517	0.5274
6	2.3501	0.6187	1.7315
7	1.2491	1.6633	-0.4141
8	0.9596	-0.1832	1.1428
9	1.2070	1.1950	0.0120
10	0.1668	0.1899	-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!

Re: Replicating a MA(1) forecast in Excel

Reeza — Fri, 12 Dec 2014 02:01:41 GMT

You should post this in the statistics portion of the forum

Re: Replicating a MA(1) forecast in Excel

user24feb — Fri, 12 Dec 2014 09:40:38 GMT

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?

Re: Replicating a MA(1) forecast in Excel

WilliamRoberts — Wed, 17 Dec 2014 02:19:59 GMT

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

Re: Replicating a MA(1) forecast in Excel

Reeza — Wed, 17 Dec 2014 02:22:51 GMT

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