*
* Example of exponential smoothing from pp 153-160
*
open data invent15.dat
data(format=free,org=columns) 1 24 e15
*
* In order to estimate the parameters, use the option ESTIMATE.
*
esmooth(trend=none,estimate,fit=sesfit) e15
@uforeerrors(title="Simple Exponential Smoothing") e15 sesfit 10 24
*
* To get Holt's model, use the option TREND=LINEAR. The default method used by
* RATS to get the initial value of the trend is to estimate the trend rate over
* the full sample. To get results which match those in the text, include the
* option INITIAL=START. (This isn't necessary for SES, since the smoothed value
* is always set to hit the first data point exactly). The option CONSTRAIN forces
* the estimated parameters into the range of [0.0,1.0). (The exponential
* smoothing recursions are stable outside of that range, so RATS allows such
* values to be considered).
*
esmooth(trend=linear,estimate,constrain,initial=start,fit=holtfit) e15
@uforeerrors(title="Holt's Model") e15 holtfit 10 24
*
* To get out-of-sample forecasts, include options FORECAST=series for forecasts
* and STEPS=# of forecast steps
*
esmooth(trend=linear,estimate,constrain,initial=start,forecast=holtfore,steps=6) e15
print / holtfore