1 2 3 4 5 6 7 8 9 10 11 12 13
Wts for 7MA   0.142857143 0.142857 0.142857 0.142857143 0.142857143 0.142857143 0.142857143            
Wts for 2x12MA   0.041666667 0.083333 0.083333 0.083333 0.083333 0.083333 0.083333 0.083333 0.083333 0.083333 0.083333 0.083333 0.041667 0.999996
Orig. Data Trend-Cycle
Yt 7MA Tt = 2x12MA Yt-Tt Month Sj(t) Et=Yt-Tt-St Note Sj(t) values calculated in pivot table.  
1 112         -18.5885221   See below. (G282)  
2 118         -22.69565205  
3 132         5.471035238  
4 129 127.8571       -3.231326905  
5 121 133       -4.195595952  
6 135 135.5714       23.69130867  
7 148 133.7143 126.7911973 21.2088 7 41.2031139 -19.99431124
8 148 130.1429 127.2495317 20.75047 8 38.37574086 -17.62527252
9 136 129.7143 127.957867 8.042133 9 11.18526314 -3.143130143
10 119 126.8571 128.582863 -9.58286 10 -16.15401171 6.571148714
11 104 123.7143 128.999525 -24.9995 11 -41.70757414 16.70804914
12 118 122.7143 129.7495283 -11.7495 12 -20.01709657 8.267568238
1 115 122.5714 131.249528 -16.2495 1 -18.5885221 2.338994095
2 126 123.4286 133.082854 -7.08285 2 -22.69565205 15.61279805
3 141 129.8571 134.916176 6.083824 3 5.471035238 0.612788762
4 135 137.2857 136.416163 -1.41616 4 -3.231326905 1.815163905
5 125 145.1429 137.4161533 -12.4162 5 -4.195595952 -8.220557381
6 149 149.7143 138.749488 10.25051 6 23.69130867 -13.44079667
7 170 148.5714 140.9161463 29.08385 7 41.2031139 -12.11926024
8 170 145.5714 143.16614 26.83386 8 38.37574086 -11.54188086
9 158 147.7143 145.7078037 12.2922 9 11.18526314 1.10693319
10 133 147.1429 148.4161227 -15.4161 10 -16.15401171 0.737889048
11 114 144.2857 151.54111 -37.5411 11 -41.70757414 4.166464143
12 140 145.4286 154.707769 -14.7078 12 -20.01709657 5.309327571
1 145 146.1429 157.124433 -12.1244 1 -18.5885221 6.464089095
2 150 151.7143 159.54109 -9.54109 2 -22.69565205 13.15456205
3 178 160.8571 161.832743 16.16726 3 5.471035238 10.69622176
4 163 169.2857 164.1243927 -1.12439 4 -3.231326905 2.106934238
5 172 177 166.6660433 5.333957 5 -4.195595952 9.529552619
6 178 181.8571 169.082708 8.917292 6 23.69130867 -14.77401667
7 199 179.5714 171.2493677 27.75063 7 41.2031139 -13.45248157
8 199 177.1429 173.582694 25.41731 8 38.37574086 -12.95843486
9 184 176.2857 175.4576933 8.542307 9 11.18526314 -2.642956476
10 162 175.2857 176.8326833 -14.8327 10 -16.15401171 1.321328381
11 146 172.5714 178.0410137 -32.041 11 -41.70757414 9.666560476
12 166 171.7143 180.166012 -14.166 12 -20.01709657 5.851084571
1 171 171.2857 183.124339 -12.1243 1 -18.5885221 6.464183095
2 180 174.2857 186.207662 -6.20766 2 -22.69565205 16.48799005
3 193 184.5714 189.040976 3.959024 3 5.471035238 -1.512011238
4 181 193.7143 191.2909603 -10.291 4 -3.231326905 -7.059633429
5 183 203.8571 193.582612 -10.5826 5 -4.195595952 -6.387016048
6 218 208 195.83261 22.16739 6 23.69130867 -1.523918667
7 230 207.7143 198.0409357 31.95906 7 41.2031139 -9.244049571
8 242 206.4286 199.7492637 42.25074 8 38.37574086 3.874995476
9 209 208 202.207596 6.792404 9 11.18526314 -4.392859143
10 191 204.8571 206.2492443 -15.2492 10 -16.15401171 0.904767381
11 172 200 210.4158937 -38.4159 11 -41.70757414 3.291680476
12 194 199.1429 213.3742233 -19.3742 12 -20.01709657 0.642873238
1 196 202.8571 215.8325523 -19.8326 1 -18.5885221 -1.244030238
2 196 208.2857 218.4992117 -22.4992 2 -22.69565205 0.196440381
3 236 218.4286 220.9158573 15.08414 3 5.471035238 9.613107429
4 235 228.4286 222.915842 12.08416 4 -3.231326905 15.3154849
5 229 239.2857 224.0824957 4.917504 5 -4.195595952 9.113100286
6 243 245.1429 224.7075003 18.2925 6 23.69130867 -5.398809
7 264 241.5714 225.3324987 38.6675 7 41.2031139 -2.535612571
8 272 233.7143 225.332496 46.6675 8 38.37574086 8.291763143
9 237 229.7143 224.957512 12.04249 9 11.18526314 0.857224857
10 211 224.1429 224.582512 -13.5825 10 -16.15401171 2.571499714
11 180 213.2857 224.4575127 -44.4575 11 -41.70757414 -2.749938524
12 201 208 225.540849 -24.5408 12 -20.01709657 -4.523752429
1 204 206.5714 227.9991823 -23.9992 1 -18.5885221 -5.410660238
2 188 209.8571 230.4575057 -42.4575 2 -22.69565205 -19.76185362
3 235 221.8571 232.2491537 2.750846 3 5.471035238 -2.720188905
4 227 236.2857 233.9158043 -6.9158 4 -3.231326905 -3.684477429
5 234 249 235.6241213 -1.62412 5 -4.195595952 2.571474619
6 264 259.1429 237.7491207 26.25088 6 23.69130867 2.559570667
7 302 258.2857 240.4991123 61.50089 7 41.2031139 20.29777376
8 293 254.8571 243.9574277 49.04257 8 38.37574086 10.66683148
9 259 254.1429 247.1657617 11.83424 9 11.18526314 0.64897519
10 229 251 250.2490817 -21.2491 10 -16.15401171 -5.095069952
11 203 241.1429 253.49907 -50.4991 11 -41.70757414 -8.791495857
12 229 237.4286 257.124068 -28.1241 12 -20.01709657 -8.106971429
1 242 238.8571 261.832397 -19.8324 1 -18.5885221 -1.243874905
2 233 244.7143 266.6657067 -33.6657 2 -22.69565205 -10.97005462
3 267 260.7143 271.1240107 -4.12401 3 5.471035238 -9.595045905
4 269 280 275.2073163 -6.20732 4 -3.231326905 -2.975989429
5 270 295 278.4989593 -8.49896 5 -4.195595952 -4.303363381
6 315 306.2857 281.95729 33.04271 6 23.69130867 9.351401333
7 364 307.2857 285.7489447 78.25106 7 41.2031139 37.04794143
8 347 302.7143 289.332261 57.66774 8 38.37574086 19.29199814
9 312 303.8571 293.2489243 18.75108 9 11.18526314 7.565812524
10 274 299.4286 297.165575 -23.1656 10 -16.15401171 -7.011563286
11 237 287 300.998894 -63.9989 11 -41.70757414 -22.29131986
12 278 282.7143 305.4572263 -27.4572 12 -20.01709657 -7.440129762 278
1 284 282.8571 309.957223 -25.9572 1 -18.5885221 -7.368700905 284
2 277 289.1429 314.4155343 -37.4155 2 -22.69565205 -14.71988229 277
3 317 308.7143 318.6238367 -1.62384 3 5.471035238 -7.094871905 317
4 313 328 321.7488097 -8.74881 4 -3.231326905 -5.517482762 313
5 318 345.2857 324.4987867 -6.49879 5 -4.195595952 -2.303190714 318
6 374 356.4286 327.0821223 46.91788 6 23.69130867 23.226569 374
7 413 354.8571           413
8 405 348.8571           405
9 355 347.1429           355
10 306             306
11 271             271
12 306             306
324.3846154
Value Month To calculate the Sj(t) values using a Pivot Table:    
21.20880267 7 1. Copy the Yt-Tt and Month columns into a clear area.    
20.75046833 8 2. Add the Headings (Value & Month) to identify the columns    
8.042133 9 3. Select Data/PivotTable    
-9.582863 10 4. At step 3 select Existing worksheet.    
-24.999525 11 5. Enter the position of the top left cell for the pivot table    
-11.7495283 12 6. Click Finish; the Pivot Table is then created    
-16.249528 1 7. The pivot table form is displayed    
-7.082854 2 8. Drag The Month button onto the Row Fields position    
6.083824 3 9. Drag the Value button into the main Data Fields Position    
-1.416163 4 10. Click the little "i" menu button in the Pivot Table form and select Average  
-12.4161533 5 11. The Total column gives the Sj values.    
10.250512 6 12 Copy these into the Sj(t) (blue) column, starting at G12..    
29.08385367 7 Average of Value  
26.83386 8 Month Total
12.29219633 9 1 -18.5885221
-15.4161227 10 2 -22.69565205
-37.54111 11 3 5.471035238
-14.707769 12 4 -3.231326905
-12.124433 1 5 -4.195595952
-9.54109 2 6 23.69130867
16.167257 3 7 41.2031139
-1.12439267 4 8 38.37574086
5.333956667 5 9 11.18526314
8.917292 6 10 -16.15401171
27.75063233 7 11 -41.70757414
25.417306 8 12 -20.01709657
8.542306667 9 Grand Total -0.555276468
-14.8326833 10
-32.0410137 11
-14.166012 12
-12.124339 1
-6.207662 2
3.959024 3
-10.2909603 4
-10.582612 5
22.16739 6
31.95906433 7
42.25073633 8
6.792404 9
-15.2492443 10
-38.4158937 11
-19.3742233 12
-19.8325523 1
-22.4992117 2
15.08414267 3
12.084158 4
4.917504333 5
18.29249967 6
38.66750133 7
46.667504 8
12.042488 9
-13.582512 10
-44.4575127 11
-24.540849 12
-23.9991823 1
-42.4575057 2
2.750846333 3
-6.91580433 4
-1.62412133 5
26.25087933 6
61.50088767 7
49.04257233 8
11.83423833 9
-21.2490817 10
-50.49907 11
-28.124068 12
-19.832397 1
-33.6657067 2
-4.12401067 3
-6.20731633 4
-8.49895933 5
33.04271 6
78.25105533 7
57.667739 8
18.75107567 9
-23.165575 10
-63.998894 11
-27.4572263 12
-25.957223 1
-37.4155343 2
-1.62383667 3
-8.74880967 4
-6.49878667 5
46.91787767 6