*
* Exponential smoothing model, pp 367-369.
*
cal(m) 1973
open data exch.dat
data(format=prn,org=columns) 1973:1 1996:7 yen dm
*
set logyen = log(yen)
*
* Holt-Winters smoothing is done using the ESMOOTH instruction in RATS. The
* parameters are  three parameters are the series to be smoothed, followed by the
* estimation range. If you want (out-of-sample) forecasts, include the options
* FORECAST=series for forecasts and STEPS=number of forecast steps.
*
* The specific form of smoothing is determined by the TREND and SEASONAL options.
* TREND can take the choices NONE, LINEAR and EXPONENTIAL. SEASONAL can be NONE,
* ADDITIVE and MULTIPLICATIVE. TREND=NONE,SEASONAL=NONE (which is the default) is
* the basic exponential smoothing process described on page 355.
* TREND=LINEAR,SEASONAL=NONE is on page 356, and TREND=LINEAR,SEASONAL=ADDITIVE
* is on page 357.
*
* The TREND and SEASONAL options can also take the choice SELECT, which has
* ESMOOTH try all the possibilities (all 3x3 if you use SELECT for both), and
* choose the one which minimizes the Schwarz Criterion.
*
* You can either have ESMOOTH estimate the parameters (option ESTIMATE) or set
* them directly. Since RATS comes up with different parameters than shown in the
* text (EViews uses a grid search procedure, RATS uses a more sophisticated
* method) when it estimates, we'll show both. Note, by the way, that RATS uses
* "gamma" for the trend smoothing parameter which is "beta" in the text.
*
set forezone * 2010:12 = t>=1995:1
esmooth(trend=linear,estimate,constrain,initial=start,forecast=fsmooth,steps=18) logyen * 1994:12
*
graph(footer="Figure 12.18 Log Yen/Dollar Rate: History and Forecast",$
  subhead="Holt-Winters Smoothing",shading=forezone) 2
# logyen 1990:1 1994:12
# fsmooth 1995:1 1996:7
*
graph(footer="Figure 12.20 Log Yen/Dollar Rate: History, Forecast and Realization",$
  subhead="Holt-Winters Smoothing",shading=forezone) 2
# logyen 1990:1 1996:7
# fsmooth 1995:1 1996:7
*
esmooth(trend=linear,estimate,constrain,initial=start,forecast=fsmooth,steps=2010:12-1994:12) logyen * 1994:12
*
graph(footer="Figure 12.19 Log Yen/Dollar Rate: History and Long-Horizon Forecast",$
  subhead="Holt-Winters Smoothing",shading=forezone) 2
# logyen 1990:1 1994:12
# fsmooth 1995:1 2010:12
*
* Same long-horizon forecast, but with parameters set to the values used in the
* text.
*
esmooth(trend=linear,alpha=1.0,gamma=.09,forecast=fsmooth,steps=2010:12-1994:12) logyen * 1994:12
*
graph(footer="Figure 12.19 Log Yen/Dollar Rate: History and Long-Horizon Forecast",$
  subhead="Holt-Winters Smoothing",shading=forezone) 2
# logyen 1990:1 1994:12
# fsmooth 1995:1 2010:12