*
* ExampleFour.RPF
* RATS Introduction, Example from Section 1.5
*
open data ex152.xls
calendar(m) 1986:1
data(format=xls,org=columns) 1986:1 1995:10 hs6fr
*
* Computing filtered series using a 7-period moving average
* and the Hodrick-Prescott filter:
*
filter(type=centered,width=7) hs6fr / flat7
filter(type=hp) hs6fr / hpfilter
*
* Generate a graph comparing the original series and the
* two filtered series:
*
GRAPH(STYLE=LINE,FOOTER="Moving Average versus HP Filtering",KEY=UPRIGHT) 3
# HS6FR
# FLAT7
# HPFILTER
*
* Same thing, but over a limited range of observations:
*
GRAPH(STYLE=LINE,FOOTER="Moving Average versus HP Filtering",KEY=UPRIGHT) 3
# HS6FR 1990:1 1995:12
# FLAT7 1990:1 1995:12
# HPFILTER 1990:1 1995:12
*
* This filters out the trend component:
*
filter(remove=trend) hs6fr / detrend
*
* This save the removed trend into a new series by taking the difference
* of the original and detrended data:
*
set removed = hs6fr-detrend
*
* The ESMOOTH instruction is applied to the detrended series:
*
ESMOOTH(ALPHA=0.2,SMOOTHED=ESMOOTH) DETREND
*
* Then we replace ESMOOTH with the sum of its previous values and the
* trend component removed earlier:
*
set esmooth = esmooth+removed
*
* Graph the original, HP filter, and exponentially smoothed series:
*
GRAPH(STYLE=LINE,HEADER="Exponential Smoothing vs HP Filter",KEY=ABOVE,NOKBOX) 3
# HS6FR
# HPFILTER
# ESMOOTH
*
* This ESMOOTH command is applied to the original series (not the
* detrended version). It includes trend and seasonal components to
* produce a smoothed series as well as forecasts for 8 periods from the
* end of the original data:
*
ESMOOTH(TREND=LINEAR,SEASONAL=MULTIPLICATIVE,ESTIMATE,SMOOTHED=ESMOOTH,$
   FORECAST=ESMOOTH_FORE,STEPS=8) HS6FR
*
* This graphs the original series followed by the forecasts:
*
GRAPH(STYLE=LINE,HEADER="Exponential Smoothing Forecast",KEY=ABOVE,NOKBOX) 3
# HS6FR
# ESMOOTH
# ESMOOTH_FORE
*
* Seasonally adjusting data using ESMOOTH
*
esmooth(seasonal=multiplicative,estimate,$
        smoothed=smoothed,fitted=fitted) hs6fr
graph(header="Seasonally Adjusted Data",key=above,nokbox) 3
# hs6fr
# smoothed
# fitted
*
* OLS regression and forecast on seasonally adjusted data.
* First, define a time trend series:
*
SET TREND * 1996:12 = T
*
* Then regress on constant and trend:
*
linreg(define=forecast_eq) smoothed 1992:1 *
# constant trend

uforecast(from=1995:11,to=1996:12,equation=forecast_eq) hsfore

graph 3
# hs6fr 1992:1 *
# smoothed 1992:1 *
# hsfore
*
* Demonstrating the PRINT instruction
*
print
print 1990:1 1996:6 hs6fr esmooth esmooth_fore
print / hs6fr esmooth esmooth_fore
print(window="ESMOOTH Forecasts") / hs6fr esmooth_fore
print(picture="*.#") / hs6fr