*
* Example TABLE6-8.DAT from pp 219-221
*
open data table6-8.dat
data(format=free,org=columns) 1 30 demand
*
* Single exponential smoothing
*
esmooth(alpha=0.15,smoothed=single) demand
*
* Brown's double exponential smoothing
*
esmooth(trend=linear,alpha=0.15,gamma=0.15,initial=start,smoothed=double,fitted=fitted) demand
set error = demand-fitted
*
* Note that, because of a different choice for the initial value of b (with
* INITIAL=START, ESMOOTH chooses Y(2)-Y(1), so the ES recursions hit the first
* two values exactly), the results are slightly different at the end of the
* sample, and more noticeably different at the start.
*
print(picture="*.###") / demand single double fitted error
graph(footer="Figure 6-4 Single and Double Exponential Smoothing",key=below) 4
# demand
# single
# double
# fitted
*
* Building table 6-9 requires a bit of programming. RATS can optimize parameter
* choices for the Holt model (next section in book), but not Brown's. Note, also,
* that the results are somewhat different, again because of the different choice
* for initializing the recursions. The minimum here is .10, though it's fairly
* flat for most of the range from .05 to .20.
*
* DOFOR loops over a set of instructions, with the values of an index being taken
* from a list. %rss is the sum of squared residuals, and %nobs is the number of
* observations, so the RSE is the square root of %rss/%nobs
*
dofor [real] alpha = .02 .05 .10 .12 .14 .15 .16 .18 .20 .25 .30 .70
   esmooth(trend=linear,alpha=alpha,gamma=alpha,initial=start,noprint) demand
   disp alpha sqrt(%rss/%nobs)
end dofor