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I am working with time series data and fitting an autoregressive model using OLS. For reference, here is my price data for the commodity (I am not sure how to better format data for this site):

15.6
16.25
16.25
16.25
18.1
18.25
17.9
17.65
17.5
17
17.8
18
18
18.05
18.25
16.25
17.87
18.25
17.9
18.25
18.25
18.25
18.25
18.25
18
18.06
18.25
18.25
18.25
18.37
18.5
18.25
18.25
18.25
18.25
18.25
18.25
18.25
18
17.5
17.5
17.3
17.5
16.8
16.22
16.25
19
22.5
22.5
22.69
23.62
26.75
27.5
26.9
24.25
21.1
19.44
18.5
18.35
18.12
17.02
16.75
16.63
16.63
16.63
16.63
16.65
16.93
18.12
20
21
23
23.25
22.44
22.13
21.9
21.5
21.5
20.75
20.75
20.5
20.2
20
20
19.87
19.25
19
19
19
19
19
19
19
19
19
19
18.81
18.75
18.31
18
18
18.66
18.94
19.68
20.6
21.87
21.25
21.49
21.69
21.5
21.63
22.13
22.25
24.33
25.25
24.5
23
21.75
20.75
20.75
20.75
20.75
20.75
20.75
20.75
20.75
20.75
20.75
19.75
18.25
16.5
16
14.5
14.5
11.5
11.5
11.75
12.5
11.75
12.13
11.5
14.25
14.25
14.25
14.08
14
14
13.25
12.75
12.75
12.75
12.75
12.75
12.75
12.75
12.75
13.75
13
14.25
15
16
16.5
19
21
22.25
24.25
24.5
25
25
25
25.5
27
25
25
20
18
16.5
16
15
15
15
15
15.5
15
15
15
16
16.5
18
20
21
24
23
22
22
22
22
22.5
23
24
25.5
25.5
25.75
25.75
25.75
25.75
25.75
26.25
26.25
26.25
26.25
26.25
26.75
26.75
27.25
27.25
27.25
28
28.25
31.25
39.88
43.75
46.15
47
48.05
48.75
48.75
48.75
49.125
49.5
50.25
52.125
52.25
52.25
49.75
47.5
46.08333333
43.5625
41.8125
41.25
40
36.5625
37.5
34.625
32.13
31
30.63
30.5
31.06
34.5
36.33
37.06
38.5
39
40
40
40
40
39.5
38.85
38.75
37.8125
37.25
36.875
35.13
34.75
34.75
34.25
34.15
34.25
34.25
34.5
34.5
34.9
34.91
34.79
33.94
33.5
33
32.95
32.75
32.75
32.75
32.5
31.94
31.75
31.75
31.75
37

However, this question applies to any data set. I am currently working in STATA, but have seen from a coleague that his R code to predict future prices is:

fit=ar.ols(lg, aic=F, order.max=3,demean=F, intercept=T)
fore = predict(fit, n.ahead=12)

Predicting 12 periods ahead, he obtains the following results:

>[1] 39.10485 40.71541 41.58133 42.04069 42.20034 42.16457 41.99738 41.74455
>[9] 41.43697 41.09589 40.73577 40.36645

I have seen this similar question posed, however, no clear answer, or answers given do not work for me: when I predict future periods, I only obtain results for one period ahead.

For example:

tsappend, add(12) 
g lag1 = lg[_n-1]
g lag2 = lg[_n-2]
g lag3 = lg[_n-3]
reg lg L1.lg L2.lg L3.lg
predict xb, xb

Note, I created my own lags because someone postulated that predict was not working well with the lag operator L. However, the only prediction I get back is:

39.10485

which is in fact the same as the R result. However, no matter what I try I cannot obtain more than a single prediction. I have also tried using STATA's forecast, which gave me the same and single forecasted number.

How can I obtain the forecasted models for more than a single period in STATA?

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First, reg may not be the best option for regressing a time series, since they will tend to be autocorrelated. In Stata, you have quite a few options to deal with this, including prais, and arima.

Try arima,

arima lg L1.lg L2.lg L3.lg

Make sure you have 12 rows at the end of your data with a blank lg, which you want to predict. Then look at predict arima, specifically the dyn option. You are wanting a dynamic prediction (where prior predictions are carried forward as lagged independent values) rather than a non-dynamic prediction where you specify the independent variables a priori. If you were using non-lagged independent variables, you'd obviously have to have values for them in the 12 rows.

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  • $\begingroup$ Hi @Wayne, I agree regarding the use of OLS versus ARIMA. However, I was trying to recreate my colleague's code. Thank you for your answer, while I thought I had already tried dynamic forecasting, typing: arima lg L(1/3).lg and then predict fore, dyn(290) actually provides the same result as the R code. $\endgroup$ – Nox Jan 27 '15 at 21:19
  • $\begingroup$ Great to hear! I'm an R guy myself, though I do like Stata a lot. It's a bit less flexible (or perhaps it requires more rigorous specifications) than R. I'm surprised that your R colleague got a dynamic forecast from a non-arima. My guess is his input data was a ts with a bunch of NA's at the end or something. $\endgroup$ – Wayne Jan 27 '15 at 21:21
  • $\begingroup$ I was surprised too. His data looks exactly as I pasted on here, reads it in normally (i.e. rm(list=ls(all=TRUE)) jmin=read.table("where data is saved") lg=jmin[,1]) and then just goes ahead to fit the autoregressive ols and predict ahead 12 periods. $\endgroup$ – Nox Jan 27 '15 at 21:48
  • $\begingroup$ If you happen to see this - I do have a follow up question which is if you know a way of collecting the standard errors for the dynamically predicted values. Usually, you could collect s.e. with predict e, stdp but it does not seem to work alongside of the dyn option. Thanks again! $\endgroup$ – Nox Jan 27 '15 at 21:56
  • $\begingroup$ @Nox: I think you want mse not stdp. Does that work? $\endgroup$ – Wayne Jan 27 '15 at 22:01

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