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st: forecasting a short multivariate time series


From   "Dimitriy V. Masterov" <dvmaster@gmail.com>
To   Statalist <statalist@hsphsun2.harvard.edu>
Subject   st: forecasting a short multivariate time series
Date   Tue, 13 Mar 2012 14:49:08 -0400

I need to forecast the following 4 variables for the 29th unit of
time. I have roughly 2 years worth of historical data, where 1 and 14
and 27 are all the same period (or time of year).

time	W	wd	wc	p
1	4.920725	4.684342	4.065288	.5962985
2	4.956172	4.73998	4.092179	.6151785
3	4.85532	4.725982	4.002519	.6028712
4	4.754887	4.674568	3.988028	.5943888
5	4.862039	4.758899	4.045568	.5925704
6	5.039032	4.791101	4.071131	.590314
7	4.612594	4.656253	4.136271	.529247
8	4.722339	4.631588	3.994956	.5801989
9	4.679251	4.647347	3.954906	.5832723
10	4.736177	4.679152	3.974465	.5843731
11	4.738954	4.759482	4.037036	.5868722
12	4.571325	4.707446	4.110281	.556147
13	4.883891	4.750031	4.168203	.602057
14	4.652408	4.703114	4.042872	.6059471
15	4.677363	4.744875	4.232081	.5672519
16	4.695732	4.614248	3.998735	.5838578
17	4.633575	4.6025	3.943488	.5914644
18	4.61025	4.67733	4.066427	.548952
19	4.678374	4.741046	4.060458	.5416393
20	4.48309	4.609238	4.000201	.5372143
21	4.477549	4.583907	3.94821	.5515663
22	4.555191	4.627404	3.93675	.5542806
23	4.508585	4.595927	3.881685	.5572687
24	4.467037	4.619762	3.909551	.5645944
25	4.326283	4.544351	3.877583	.5738906
26	4.672741	4.599463	3.953772	.5769604
27	4.53551	4.506167	3.808779	.5831352
28	4.528004	4.622972	3.90481	.5968299

I believe that W is approximately p*wd + (1 - p)*wc plus measurement error.

Here are my 2 questions. Are there any time-series methods that (1)
perform better in the face of "micro-numerosity" and (2) would be able
to exploit the link between the variables? My first thought was to try
vector autoregression on these variables and an exogenous time or
period variable:

var W wd wc p, exog(time) lag(1 2) dfk

The moduli of the eigenvalues are all less than 1, so I don't think I
need to worry about stationarity (thought the dfuller test suggest
otherwise). The forecast seems on the high side, but reasonable. Does
that seem like a good idea?

DVM
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