/* Monthly Sales (in quantity units) of widgets at Fomby Inc from Jan 1998 to Aug 2014 */ 

data sales;
   input sales @@;
   date = intnx( 'month', '31dec96'd, _n_ );
   format date monyy.;
   datalines;
144549 137310 140151 132112
138168 145583 157878 162901
147584 144062 144366 154966
159913 143257 147846 139292
147088 160945 173467 177109
156385 153951 147881 153305
157254 142472 150043 142021
153513 156161 177992 173871
152222 151978 149841 159736
164325 147080 155481 146217
153231 162442 176816 179714
155223 154944 152794 169372
178329 156684 164174 153167
157370 173392 186434 186403
165035 163746 169085 183877
196372 162734 169157 156853
169332 180787 198930 196126
176265 166402 167099 184267
197835 173504 173193 159738
175236 188312 202682 206418
185572 175802 176172 191865
209692 186337 182849 169962
178069 186682 202255 204850
180751 179716 177506 188703
200005 188715 187464 168720
175734 189430 216776 215393
191485 178555 178550 195613
206467 179613 185553 172545
177806 202702 220373 210403
186838 181352 175570 195590
209403 180299 187687 172580
177147 186128 210584 205656
180662 172966 173377 184722
195579 172479 182488 170372
174392 191048 220165 229957
195604 182931 182949 212319
216632 189564 200107 181084
192217 209649 221245 229296
195198 190936 190380 199996
227856 198242 194970 184877
196790 205363 226722 226050
202499 194789 192427 219255
217470 192336 196834 186074
197315 215015 242672 225166
206692 197754 196432 213551
222749 194034 201849 189496
206074 225589 247915 247645
213008 203009 200258 220500
237600 216702 213838 195809
208180 232507 257235 267408
220023 210377 209394 232550
231343 219066 226436 207749
219803 235397 256744 258335
;

title 'Fomby Inc Monthly Sales of Widgets in quantity units';
symbol1 i=join  v=star;
proc gplot data=sales;
   plot sales * date = 1 / haxis= '1jan97'd to '1jan15'd by year;
run;

/* A presentation of the 12 step ahead forecasts produced by Additive Winters method.  */

Title 'Additive Winters Seasonal Model Results';  
proc esm data=sales out = result1 
         lead=12 print = all 
         plot=forecastsonly; 
   id date interval=month; 
   forecast sales / model=addseasonal; 
run;

/* Producing the sum of the first through two step-ahead forecasts and its standard
   error.  Use this in the calculation of the REORDER POINT FOR OPTIMAL INVENTORY
   CONTROL  */

proc esm data=sales out = result3 
         lead = 2 startsum = 1 print = all
         plot=forecastsonly; 
   id date interval=month; 
   forecast sales / model=addwinters; 
run;

/*  In addition to trend, there is seasonal variation in the data.
    This is indicated by the below Buys-Ballot plot and the nature
    of the autocorrelations of the differenced data at lags 12 and 24  */

/*  Buys-Ballot Plot of Season by Year */

data sales;
   set sales;
   
   series_yr = year(date);
   series_month = month(date);

   label series_yr = "Series Year";
run;
    

/*Creates the Seasons by Year Buys-Ballot seasonality graph*/

/*Set Options*/
goptions cback=white colors=(black) border reset=(axis symbol);

/*Sets the axis parameters*/
axis1 label=('Month') minor=none
      value=('Jan' 'Feb' 'Mar' 'Apr' 'May' 'Jun'
	  'Jul' 'Aug' 'Sep' 'Oct' 'Nov' 'Dec')
      order=(1 to 12 by 1)
      offset = (2)
      width = 3;
axis2 label=(angle=90 'Fomby Inc Monthly Sales Data')
      order=(120000 to 280000 by 10000);

/*Creates a Unique symbol and line for each of the 18 years*/
symbol1 color=black interpol=spline
        value=none;
symbol2 color=blue interpol=spline
        value=none;
symbol3 color=brown interpol=spline
        value=none;
symbol4 color=libg interpol=spline
        value=none;
symbol5 color=cyan interpol=spline
        value=none;
symbol6 color=gold interpol=spline
        value=none;
symbol7 color=gray interpol=spline
        value=none;
symbol8 color=green interpol=spline
        value=none;
symbol9 color=lilac interpol=spline
        value=none;
symbol10 color=steel interpol=spline
        value=none;
symbol11 color=magenta interpol=spline
        value=none;
symbol12 color=maroon interpol=spline
        value=none;
symbol13 color=olive interpol=spline
        value=none;
symbol14 color=tan interpol=spline
        value=none;
symbol15 color=salmon interpol=spline
        value=none;
symbol16 color=violet interpol=spline
        value=none;
symbol17 color=orange interpol=spline
        value=none;
symbol18 color=red interpol=spline
        value=none;

/* Graph the data - Seasons by Year */

title 'Fomby Inc Monthly Sales of Widgets';
title2 'Buys-Ballot "Seasons By Year" Plot';
legend1 position = (bottom center outside);

proc gplot data=sales;
   plot sales*series_month=series_yr / haxis=axis1
                     vaxis=axis2
                     vminor=1 legend=legend1;
run;

/*  Also there seems to be seasonality in the data because the differenced
    data is highly correlated at lags 12 and 24.  See below.  */

Title 'Autocorrelation Function of the Differenced Data';
proc arima data = sales;
  identify var = sales(1);
  run;