Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 29 Dec 2010 22:33:08 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/29/t1293661916zjykw53n265dnvp.htm/, Retrieved Fri, 03 May 2024 11:20:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117184, Retrieved Fri, 03 May 2024 11:20:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [Unemployment] [2010-11-30 13:37:23] [b98453cac15ba1066b407e146608df68]
- R  D    [Exponential Smoothing] [Exponential Smoot...] [2010-12-27 15:14:01] [17d39bb3ec485d4ce196f61215d11ba1]
-             [Exponential Smoothing] [] [2010-12-29 22:33:08] [a7b2a0c11f64eef3aa1d49ba29ffb331] [Current]
Feedback Forum

Post a new message
Dataseries X:
206010
198112
194519
185705
180173
176142
203401
221902
197378
185001
176356
180449
180144
173666
165688
161570
156145
153730
182698
200765
176512
166618
158644
159585
163095
159044
155511
153745
150569
150605
179612
194690
189917
184128
175335
179566
181140
177876
175041
169292
166070
166972
206348
215706
202108
195411
193111
195198
198770
194163
190420
189733
186029
191531
232571
243477
227247
217859
208679
213188
216234
213586
209465
204045
200237
203666
241476
260307
243324
244460
233575
237217
235243
230354
227184
221678
217142
219452
256446
265845
248624
241114
229245
231805
219277
219313
212610
214771
211142
211457
240048
240636
230580
208795
197922
194596
194581
185686
178106
172608
167302
168053
202300
202388
182516
173476
166444
171297
169701
164182
161914
159612
151001
158114
186530
187069
174330
169362
166827
178037
186413
189226
191563
188906
186005
195309
223532
226899
214126
206903
204442
220375
214320
212588
205816
202196
195722
198563
229139
229527
211868
203555
195770




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117184&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117184&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117184&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.786721671208313
beta0.155737227444672
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.786721671208313 \tabularnewline
beta & 0.155737227444672 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117184&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.786721671208313[/C][/ROW]
[ROW][C]beta[/C][C]0.155737227444672[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117184&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117184&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.786721671208313
beta0.155737227444672
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13180144192256.77590812-12112.7759081197
14173666174646.428106398-980.428106397972
15165688164180.8073711891507.19262881079
16161570159602.1658100851967.83418991519
17156145154188.6069701651956.39302983464
18153730152119.1230186181610.876981382
19182698179952.3484015222745.65159847779
20200765200442.561219332322.43878066825
21176512176164.427462601347.572537398606
22166618164082.6938745692535.30612543123
23158644157564.6031125531079.39688744742
24159585162699.575040561-3114.57504056091
25163095157033.5205933096061.47940669145
26159044158060.686855114983.31314488608
27155511151876.2857412733634.7142587268
28153745151536.0705339142208.92946608641
29150569148805.6999799911763.30002000884
30150605148982.9099334371622.09006656322
31179612179540.64902107171.3509789286763
32194690199556.121835498-4866.12183549814
33189917172711.69245961417205.307540386
34184128177934.6383742186193.36162578195
35175335178007.834878517-2672.83487851685
36179566182860.56067138-3294.56067137973
37181140182552.108246814-1412.10824681402
38177876179243.047588603-1367.04758860334
39175041174113.551861832927.448138168431
40169292173346.182184128-4054.18218412847
41166070166832.87427879-762.874278789735
42166972165922.4910065951049.50899340483
43206348196558.7952843899789.20471561115
44215706225216.873886494-9510.87388649379
45202108200907.00696911200.99303089993
46195411190710.8561367064700.14386329381
47193111187055.8402206396055.15977936087
48195198199049.339913742-3851.33991374171
49198770199042.997871195-272.997871194704
50194163197117.930776858-2954.93077685832
51190420191512.249043426-1092.24904342552
52189733188129.6788898931603.32111010666
53186029187498.596717085-1469.59671708476
54191531187061.5533571314469.44664286863
55232571223314.1931842789256.80681572173
56243477248433.712722975-4956.71272297547
57227247231545.874832777-4298.8748327769
58217859218649.86048071-790.860480710166
59208679211171.888635608-2492.88863560779
60213188213488.229628964-300.229628963629
61216234216634.512356744-400.512356744439
62213586213617.211916038-31.2119160378934
63209465210647.255498067-1182.25549806724
64204045207696.056936062-3651.05693606209
65200237201559.353700862-1322.35370086171
66203666201806.3581361041859.64186389593
67241476236008.6293294945467.3706705058
68260307253632.9740701646674.02592983609
69243324245978.104966728-2654.10496672837
70244460235268.2824712649191.71752873648
71233575236647.931624633-3072.93162463326
72237217240271.635200018-3054.63520001838
73235243242188.15269305-6945.15269304995
74230354234257.517648547-3903.51764854678
75227184227677.911670693-493.911670693138
76221678224508.313359515-2830.31335951484
77217142219381.134929036-2239.13492903588
78219452219340.37877907111.621220930218
79256446252477.5642737673968.43572623306
80265845268537.035194257-2692.03519425693
81248624249733.664875926-1109.66487592596
82241114241164.041968422-50.0419684217777
83229245229923.595156388-678.595156388124
84231805232994.616274153-1189.61627415262
85219277233336.866000632-14059.866000632
86219313217374.1832982211938.81670177865
87212610213750.413699221-1140.41369922119
88214771207127.0340285987643.96597140183
89211142209202.7514305291939.24856947092
90211457212298.996501291-841.996501291229
91240048244740.097239513-4692.09723951275
92240636250736.072567318-10100.072567318
93230580223704.945028596875.05497141043
94208795219884.192553618-11089.1925536177
95197922196713.5364857461208.46351425373
96194596198279.950262193-3683.95026219264
97194581190729.0900505413851.9099494589
98185686191278.927945051-5592.92794505131
99178106179159.00117226-1053.00117226044
100172608172574.58126733.4187330002605
101167302164610.4379122582691.56208774194
102168053164961.7541554063091.2458445938
103202300197414.3760947654885.62390523477
104202388208703.725659621-6315.72565962127
105182516187645.695259936-5129.69525993612
106173476168453.7592840085022.24071599171
107166444160459.7414514655984.25854853509
108171297165203.6710899516093.32891004876
109169701168613.7145560091087.28544399096
110164182166297.126878904-2115.12687890409
111161914159630.5798763512283.4201236488
112159612158060.5395547431551.46044525696
113151001154201.424991103-3200.42499110274
114158114151624.5621344896489.43786551084
115186530189171.601050889-2641.60105088935
116187069193266.148679688-6197.1486796877
117174330173684.922388921645.077611079469
118169362163039.4116295686322.58837043165
119166827158271.002348838555.99765117007
120178037167373.95077015310663.049229847
121186413176183.81580852710229.1841914731
122189226184368.8393573164857.16064268383
123191563188972.4008920332590.59910796714
124188906192372.294027709-3466.2940277087
125186005187821.724755109-1816.72475510943
126195309192839.2157924012469.78420759932
127223532229223.087110721-5691.08711072078
128226899233733.22180034-6834.2218003402
129214126218605.044575765-4479.04457576541
130206903208006.298620989-1103.29862098879
131204442199829.4202577164612.57974228362
132220375207753.52926872812621.4707312718
133214320219725.686840237-5405.68684023729
134212588214263.16287187-1675.16287187007
135205816212242.323659017-6426.32365901687
136202196205149.962306198-2953.96230619837
137195722199310.402816273-3588.40281627342
138198563201587.356456262-3024.356456262
139229139228974.239624871164.760375128622
140229527235630.86822827-6103.8682282705
141211868219452.446170661-7584.4461706613
142203555204622.969306616-1067.96930661576
143195770195189.669246087580.330753913237

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 180144 & 192256.77590812 & -12112.7759081197 \tabularnewline
14 & 173666 & 174646.428106398 & -980.428106397972 \tabularnewline
15 & 165688 & 164180.807371189 & 1507.19262881079 \tabularnewline
16 & 161570 & 159602.165810085 & 1967.83418991519 \tabularnewline
17 & 156145 & 154188.606970165 & 1956.39302983464 \tabularnewline
18 & 153730 & 152119.123018618 & 1610.876981382 \tabularnewline
19 & 182698 & 179952.348401522 & 2745.65159847779 \tabularnewline
20 & 200765 & 200442.561219332 & 322.43878066825 \tabularnewline
21 & 176512 & 176164.427462601 & 347.572537398606 \tabularnewline
22 & 166618 & 164082.693874569 & 2535.30612543123 \tabularnewline
23 & 158644 & 157564.603112553 & 1079.39688744742 \tabularnewline
24 & 159585 & 162699.575040561 & -3114.57504056091 \tabularnewline
25 & 163095 & 157033.520593309 & 6061.47940669145 \tabularnewline
26 & 159044 & 158060.686855114 & 983.31314488608 \tabularnewline
27 & 155511 & 151876.285741273 & 3634.7142587268 \tabularnewline
28 & 153745 & 151536.070533914 & 2208.92946608641 \tabularnewline
29 & 150569 & 148805.699979991 & 1763.30002000884 \tabularnewline
30 & 150605 & 148982.909933437 & 1622.09006656322 \tabularnewline
31 & 179612 & 179540.649021071 & 71.3509789286763 \tabularnewline
32 & 194690 & 199556.121835498 & -4866.12183549814 \tabularnewline
33 & 189917 & 172711.692459614 & 17205.307540386 \tabularnewline
34 & 184128 & 177934.638374218 & 6193.36162578195 \tabularnewline
35 & 175335 & 178007.834878517 & -2672.83487851685 \tabularnewline
36 & 179566 & 182860.56067138 & -3294.56067137973 \tabularnewline
37 & 181140 & 182552.108246814 & -1412.10824681402 \tabularnewline
38 & 177876 & 179243.047588603 & -1367.04758860334 \tabularnewline
39 & 175041 & 174113.551861832 & 927.448138168431 \tabularnewline
40 & 169292 & 173346.182184128 & -4054.18218412847 \tabularnewline
41 & 166070 & 166832.87427879 & -762.874278789735 \tabularnewline
42 & 166972 & 165922.491006595 & 1049.50899340483 \tabularnewline
43 & 206348 & 196558.795284389 & 9789.20471561115 \tabularnewline
44 & 215706 & 225216.873886494 & -9510.87388649379 \tabularnewline
45 & 202108 & 200907.0069691 & 1200.99303089993 \tabularnewline
46 & 195411 & 190710.856136706 & 4700.14386329381 \tabularnewline
47 & 193111 & 187055.840220639 & 6055.15977936087 \tabularnewline
48 & 195198 & 199049.339913742 & -3851.33991374171 \tabularnewline
49 & 198770 & 199042.997871195 & -272.997871194704 \tabularnewline
50 & 194163 & 197117.930776858 & -2954.93077685832 \tabularnewline
51 & 190420 & 191512.249043426 & -1092.24904342552 \tabularnewline
52 & 189733 & 188129.678889893 & 1603.32111010666 \tabularnewline
53 & 186029 & 187498.596717085 & -1469.59671708476 \tabularnewline
54 & 191531 & 187061.553357131 & 4469.44664286863 \tabularnewline
55 & 232571 & 223314.193184278 & 9256.80681572173 \tabularnewline
56 & 243477 & 248433.712722975 & -4956.71272297547 \tabularnewline
57 & 227247 & 231545.874832777 & -4298.8748327769 \tabularnewline
58 & 217859 & 218649.86048071 & -790.860480710166 \tabularnewline
59 & 208679 & 211171.888635608 & -2492.88863560779 \tabularnewline
60 & 213188 & 213488.229628964 & -300.229628963629 \tabularnewline
61 & 216234 & 216634.512356744 & -400.512356744439 \tabularnewline
62 & 213586 & 213617.211916038 & -31.2119160378934 \tabularnewline
63 & 209465 & 210647.255498067 & -1182.25549806724 \tabularnewline
64 & 204045 & 207696.056936062 & -3651.05693606209 \tabularnewline
65 & 200237 & 201559.353700862 & -1322.35370086171 \tabularnewline
66 & 203666 & 201806.358136104 & 1859.64186389593 \tabularnewline
67 & 241476 & 236008.629329494 & 5467.3706705058 \tabularnewline
68 & 260307 & 253632.974070164 & 6674.02592983609 \tabularnewline
69 & 243324 & 245978.104966728 & -2654.10496672837 \tabularnewline
70 & 244460 & 235268.282471264 & 9191.71752873648 \tabularnewline
71 & 233575 & 236647.931624633 & -3072.93162463326 \tabularnewline
72 & 237217 & 240271.635200018 & -3054.63520001838 \tabularnewline
73 & 235243 & 242188.15269305 & -6945.15269304995 \tabularnewline
74 & 230354 & 234257.517648547 & -3903.51764854678 \tabularnewline
75 & 227184 & 227677.911670693 & -493.911670693138 \tabularnewline
76 & 221678 & 224508.313359515 & -2830.31335951484 \tabularnewline
77 & 217142 & 219381.134929036 & -2239.13492903588 \tabularnewline
78 & 219452 & 219340.37877907 & 111.621220930218 \tabularnewline
79 & 256446 & 252477.564273767 & 3968.43572623306 \tabularnewline
80 & 265845 & 268537.035194257 & -2692.03519425693 \tabularnewline
81 & 248624 & 249733.664875926 & -1109.66487592596 \tabularnewline
82 & 241114 & 241164.041968422 & -50.0419684217777 \tabularnewline
83 & 229245 & 229923.595156388 & -678.595156388124 \tabularnewline
84 & 231805 & 232994.616274153 & -1189.61627415262 \tabularnewline
85 & 219277 & 233336.866000632 & -14059.866000632 \tabularnewline
86 & 219313 & 217374.183298221 & 1938.81670177865 \tabularnewline
87 & 212610 & 213750.413699221 & -1140.41369922119 \tabularnewline
88 & 214771 & 207127.034028598 & 7643.96597140183 \tabularnewline
89 & 211142 & 209202.751430529 & 1939.24856947092 \tabularnewline
90 & 211457 & 212298.996501291 & -841.996501291229 \tabularnewline
91 & 240048 & 244740.097239513 & -4692.09723951275 \tabularnewline
92 & 240636 & 250736.072567318 & -10100.072567318 \tabularnewline
93 & 230580 & 223704.94502859 & 6875.05497141043 \tabularnewline
94 & 208795 & 219884.192553618 & -11089.1925536177 \tabularnewline
95 & 197922 & 196713.536485746 & 1208.46351425373 \tabularnewline
96 & 194596 & 198279.950262193 & -3683.95026219264 \tabularnewline
97 & 194581 & 190729.090050541 & 3851.9099494589 \tabularnewline
98 & 185686 & 191278.927945051 & -5592.92794505131 \tabularnewline
99 & 178106 & 179159.00117226 & -1053.00117226044 \tabularnewline
100 & 172608 & 172574.581267 & 33.4187330002605 \tabularnewline
101 & 167302 & 164610.437912258 & 2691.56208774194 \tabularnewline
102 & 168053 & 164961.754155406 & 3091.2458445938 \tabularnewline
103 & 202300 & 197414.376094765 & 4885.62390523477 \tabularnewline
104 & 202388 & 208703.725659621 & -6315.72565962127 \tabularnewline
105 & 182516 & 187645.695259936 & -5129.69525993612 \tabularnewline
106 & 173476 & 168453.759284008 & 5022.24071599171 \tabularnewline
107 & 166444 & 160459.741451465 & 5984.25854853509 \tabularnewline
108 & 171297 & 165203.671089951 & 6093.32891004876 \tabularnewline
109 & 169701 & 168613.714556009 & 1087.28544399096 \tabularnewline
110 & 164182 & 166297.126878904 & -2115.12687890409 \tabularnewline
111 & 161914 & 159630.579876351 & 2283.4201236488 \tabularnewline
112 & 159612 & 158060.539554743 & 1551.46044525696 \tabularnewline
113 & 151001 & 154201.424991103 & -3200.42499110274 \tabularnewline
114 & 158114 & 151624.562134489 & 6489.43786551084 \tabularnewline
115 & 186530 & 189171.601050889 & -2641.60105088935 \tabularnewline
116 & 187069 & 193266.148679688 & -6197.1486796877 \tabularnewline
117 & 174330 & 173684.922388921 & 645.077611079469 \tabularnewline
118 & 169362 & 163039.411629568 & 6322.58837043165 \tabularnewline
119 & 166827 & 158271.00234883 & 8555.99765117007 \tabularnewline
120 & 178037 & 167373.950770153 & 10663.049229847 \tabularnewline
121 & 186413 & 176183.815808527 & 10229.1841914731 \tabularnewline
122 & 189226 & 184368.839357316 & 4857.16064268383 \tabularnewline
123 & 191563 & 188972.400892033 & 2590.59910796714 \tabularnewline
124 & 188906 & 192372.294027709 & -3466.2940277087 \tabularnewline
125 & 186005 & 187821.724755109 & -1816.72475510943 \tabularnewline
126 & 195309 & 192839.215792401 & 2469.78420759932 \tabularnewline
127 & 223532 & 229223.087110721 & -5691.08711072078 \tabularnewline
128 & 226899 & 233733.22180034 & -6834.2218003402 \tabularnewline
129 & 214126 & 218605.044575765 & -4479.04457576541 \tabularnewline
130 & 206903 & 208006.298620989 & -1103.29862098879 \tabularnewline
131 & 204442 & 199829.420257716 & 4612.57974228362 \tabularnewline
132 & 220375 & 207753.529268728 & 12621.4707312718 \tabularnewline
133 & 214320 & 219725.686840237 & -5405.68684023729 \tabularnewline
134 & 212588 & 214263.16287187 & -1675.16287187007 \tabularnewline
135 & 205816 & 212242.323659017 & -6426.32365901687 \tabularnewline
136 & 202196 & 205149.962306198 & -2953.96230619837 \tabularnewline
137 & 195722 & 199310.402816273 & -3588.40281627342 \tabularnewline
138 & 198563 & 201587.356456262 & -3024.356456262 \tabularnewline
139 & 229139 & 228974.239624871 & 164.760375128622 \tabularnewline
140 & 229527 & 235630.86822827 & -6103.8682282705 \tabularnewline
141 & 211868 & 219452.446170661 & -7584.4461706613 \tabularnewline
142 & 203555 & 204622.969306616 & -1067.96930661576 \tabularnewline
143 & 195770 & 195189.669246087 & 580.330753913237 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117184&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]180144[/C][C]192256.77590812[/C][C]-12112.7759081197[/C][/ROW]
[ROW][C]14[/C][C]173666[/C][C]174646.428106398[/C][C]-980.428106397972[/C][/ROW]
[ROW][C]15[/C][C]165688[/C][C]164180.807371189[/C][C]1507.19262881079[/C][/ROW]
[ROW][C]16[/C][C]161570[/C][C]159602.165810085[/C][C]1967.83418991519[/C][/ROW]
[ROW][C]17[/C][C]156145[/C][C]154188.606970165[/C][C]1956.39302983464[/C][/ROW]
[ROW][C]18[/C][C]153730[/C][C]152119.123018618[/C][C]1610.876981382[/C][/ROW]
[ROW][C]19[/C][C]182698[/C][C]179952.348401522[/C][C]2745.65159847779[/C][/ROW]
[ROW][C]20[/C][C]200765[/C][C]200442.561219332[/C][C]322.43878066825[/C][/ROW]
[ROW][C]21[/C][C]176512[/C][C]176164.427462601[/C][C]347.572537398606[/C][/ROW]
[ROW][C]22[/C][C]166618[/C][C]164082.693874569[/C][C]2535.30612543123[/C][/ROW]
[ROW][C]23[/C][C]158644[/C][C]157564.603112553[/C][C]1079.39688744742[/C][/ROW]
[ROW][C]24[/C][C]159585[/C][C]162699.575040561[/C][C]-3114.57504056091[/C][/ROW]
[ROW][C]25[/C][C]163095[/C][C]157033.520593309[/C][C]6061.47940669145[/C][/ROW]
[ROW][C]26[/C][C]159044[/C][C]158060.686855114[/C][C]983.31314488608[/C][/ROW]
[ROW][C]27[/C][C]155511[/C][C]151876.285741273[/C][C]3634.7142587268[/C][/ROW]
[ROW][C]28[/C][C]153745[/C][C]151536.070533914[/C][C]2208.92946608641[/C][/ROW]
[ROW][C]29[/C][C]150569[/C][C]148805.699979991[/C][C]1763.30002000884[/C][/ROW]
[ROW][C]30[/C][C]150605[/C][C]148982.909933437[/C][C]1622.09006656322[/C][/ROW]
[ROW][C]31[/C][C]179612[/C][C]179540.649021071[/C][C]71.3509789286763[/C][/ROW]
[ROW][C]32[/C][C]194690[/C][C]199556.121835498[/C][C]-4866.12183549814[/C][/ROW]
[ROW][C]33[/C][C]189917[/C][C]172711.692459614[/C][C]17205.307540386[/C][/ROW]
[ROW][C]34[/C][C]184128[/C][C]177934.638374218[/C][C]6193.36162578195[/C][/ROW]
[ROW][C]35[/C][C]175335[/C][C]178007.834878517[/C][C]-2672.83487851685[/C][/ROW]
[ROW][C]36[/C][C]179566[/C][C]182860.56067138[/C][C]-3294.56067137973[/C][/ROW]
[ROW][C]37[/C][C]181140[/C][C]182552.108246814[/C][C]-1412.10824681402[/C][/ROW]
[ROW][C]38[/C][C]177876[/C][C]179243.047588603[/C][C]-1367.04758860334[/C][/ROW]
[ROW][C]39[/C][C]175041[/C][C]174113.551861832[/C][C]927.448138168431[/C][/ROW]
[ROW][C]40[/C][C]169292[/C][C]173346.182184128[/C][C]-4054.18218412847[/C][/ROW]
[ROW][C]41[/C][C]166070[/C][C]166832.87427879[/C][C]-762.874278789735[/C][/ROW]
[ROW][C]42[/C][C]166972[/C][C]165922.491006595[/C][C]1049.50899340483[/C][/ROW]
[ROW][C]43[/C][C]206348[/C][C]196558.795284389[/C][C]9789.20471561115[/C][/ROW]
[ROW][C]44[/C][C]215706[/C][C]225216.873886494[/C][C]-9510.87388649379[/C][/ROW]
[ROW][C]45[/C][C]202108[/C][C]200907.0069691[/C][C]1200.99303089993[/C][/ROW]
[ROW][C]46[/C][C]195411[/C][C]190710.856136706[/C][C]4700.14386329381[/C][/ROW]
[ROW][C]47[/C][C]193111[/C][C]187055.840220639[/C][C]6055.15977936087[/C][/ROW]
[ROW][C]48[/C][C]195198[/C][C]199049.339913742[/C][C]-3851.33991374171[/C][/ROW]
[ROW][C]49[/C][C]198770[/C][C]199042.997871195[/C][C]-272.997871194704[/C][/ROW]
[ROW][C]50[/C][C]194163[/C][C]197117.930776858[/C][C]-2954.93077685832[/C][/ROW]
[ROW][C]51[/C][C]190420[/C][C]191512.249043426[/C][C]-1092.24904342552[/C][/ROW]
[ROW][C]52[/C][C]189733[/C][C]188129.678889893[/C][C]1603.32111010666[/C][/ROW]
[ROW][C]53[/C][C]186029[/C][C]187498.596717085[/C][C]-1469.59671708476[/C][/ROW]
[ROW][C]54[/C][C]191531[/C][C]187061.553357131[/C][C]4469.44664286863[/C][/ROW]
[ROW][C]55[/C][C]232571[/C][C]223314.193184278[/C][C]9256.80681572173[/C][/ROW]
[ROW][C]56[/C][C]243477[/C][C]248433.712722975[/C][C]-4956.71272297547[/C][/ROW]
[ROW][C]57[/C][C]227247[/C][C]231545.874832777[/C][C]-4298.8748327769[/C][/ROW]
[ROW][C]58[/C][C]217859[/C][C]218649.86048071[/C][C]-790.860480710166[/C][/ROW]
[ROW][C]59[/C][C]208679[/C][C]211171.888635608[/C][C]-2492.88863560779[/C][/ROW]
[ROW][C]60[/C][C]213188[/C][C]213488.229628964[/C][C]-300.229628963629[/C][/ROW]
[ROW][C]61[/C][C]216234[/C][C]216634.512356744[/C][C]-400.512356744439[/C][/ROW]
[ROW][C]62[/C][C]213586[/C][C]213617.211916038[/C][C]-31.2119160378934[/C][/ROW]
[ROW][C]63[/C][C]209465[/C][C]210647.255498067[/C][C]-1182.25549806724[/C][/ROW]
[ROW][C]64[/C][C]204045[/C][C]207696.056936062[/C][C]-3651.05693606209[/C][/ROW]
[ROW][C]65[/C][C]200237[/C][C]201559.353700862[/C][C]-1322.35370086171[/C][/ROW]
[ROW][C]66[/C][C]203666[/C][C]201806.358136104[/C][C]1859.64186389593[/C][/ROW]
[ROW][C]67[/C][C]241476[/C][C]236008.629329494[/C][C]5467.3706705058[/C][/ROW]
[ROW][C]68[/C][C]260307[/C][C]253632.974070164[/C][C]6674.02592983609[/C][/ROW]
[ROW][C]69[/C][C]243324[/C][C]245978.104966728[/C][C]-2654.10496672837[/C][/ROW]
[ROW][C]70[/C][C]244460[/C][C]235268.282471264[/C][C]9191.71752873648[/C][/ROW]
[ROW][C]71[/C][C]233575[/C][C]236647.931624633[/C][C]-3072.93162463326[/C][/ROW]
[ROW][C]72[/C][C]237217[/C][C]240271.635200018[/C][C]-3054.63520001838[/C][/ROW]
[ROW][C]73[/C][C]235243[/C][C]242188.15269305[/C][C]-6945.15269304995[/C][/ROW]
[ROW][C]74[/C][C]230354[/C][C]234257.517648547[/C][C]-3903.51764854678[/C][/ROW]
[ROW][C]75[/C][C]227184[/C][C]227677.911670693[/C][C]-493.911670693138[/C][/ROW]
[ROW][C]76[/C][C]221678[/C][C]224508.313359515[/C][C]-2830.31335951484[/C][/ROW]
[ROW][C]77[/C][C]217142[/C][C]219381.134929036[/C][C]-2239.13492903588[/C][/ROW]
[ROW][C]78[/C][C]219452[/C][C]219340.37877907[/C][C]111.621220930218[/C][/ROW]
[ROW][C]79[/C][C]256446[/C][C]252477.564273767[/C][C]3968.43572623306[/C][/ROW]
[ROW][C]80[/C][C]265845[/C][C]268537.035194257[/C][C]-2692.03519425693[/C][/ROW]
[ROW][C]81[/C][C]248624[/C][C]249733.664875926[/C][C]-1109.66487592596[/C][/ROW]
[ROW][C]82[/C][C]241114[/C][C]241164.041968422[/C][C]-50.0419684217777[/C][/ROW]
[ROW][C]83[/C][C]229245[/C][C]229923.595156388[/C][C]-678.595156388124[/C][/ROW]
[ROW][C]84[/C][C]231805[/C][C]232994.616274153[/C][C]-1189.61627415262[/C][/ROW]
[ROW][C]85[/C][C]219277[/C][C]233336.866000632[/C][C]-14059.866000632[/C][/ROW]
[ROW][C]86[/C][C]219313[/C][C]217374.183298221[/C][C]1938.81670177865[/C][/ROW]
[ROW][C]87[/C][C]212610[/C][C]213750.413699221[/C][C]-1140.41369922119[/C][/ROW]
[ROW][C]88[/C][C]214771[/C][C]207127.034028598[/C][C]7643.96597140183[/C][/ROW]
[ROW][C]89[/C][C]211142[/C][C]209202.751430529[/C][C]1939.24856947092[/C][/ROW]
[ROW][C]90[/C][C]211457[/C][C]212298.996501291[/C][C]-841.996501291229[/C][/ROW]
[ROW][C]91[/C][C]240048[/C][C]244740.097239513[/C][C]-4692.09723951275[/C][/ROW]
[ROW][C]92[/C][C]240636[/C][C]250736.072567318[/C][C]-10100.072567318[/C][/ROW]
[ROW][C]93[/C][C]230580[/C][C]223704.94502859[/C][C]6875.05497141043[/C][/ROW]
[ROW][C]94[/C][C]208795[/C][C]219884.192553618[/C][C]-11089.1925536177[/C][/ROW]
[ROW][C]95[/C][C]197922[/C][C]196713.536485746[/C][C]1208.46351425373[/C][/ROW]
[ROW][C]96[/C][C]194596[/C][C]198279.950262193[/C][C]-3683.95026219264[/C][/ROW]
[ROW][C]97[/C][C]194581[/C][C]190729.090050541[/C][C]3851.9099494589[/C][/ROW]
[ROW][C]98[/C][C]185686[/C][C]191278.927945051[/C][C]-5592.92794505131[/C][/ROW]
[ROW][C]99[/C][C]178106[/C][C]179159.00117226[/C][C]-1053.00117226044[/C][/ROW]
[ROW][C]100[/C][C]172608[/C][C]172574.581267[/C][C]33.4187330002605[/C][/ROW]
[ROW][C]101[/C][C]167302[/C][C]164610.437912258[/C][C]2691.56208774194[/C][/ROW]
[ROW][C]102[/C][C]168053[/C][C]164961.754155406[/C][C]3091.2458445938[/C][/ROW]
[ROW][C]103[/C][C]202300[/C][C]197414.376094765[/C][C]4885.62390523477[/C][/ROW]
[ROW][C]104[/C][C]202388[/C][C]208703.725659621[/C][C]-6315.72565962127[/C][/ROW]
[ROW][C]105[/C][C]182516[/C][C]187645.695259936[/C][C]-5129.69525993612[/C][/ROW]
[ROW][C]106[/C][C]173476[/C][C]168453.759284008[/C][C]5022.24071599171[/C][/ROW]
[ROW][C]107[/C][C]166444[/C][C]160459.741451465[/C][C]5984.25854853509[/C][/ROW]
[ROW][C]108[/C][C]171297[/C][C]165203.671089951[/C][C]6093.32891004876[/C][/ROW]
[ROW][C]109[/C][C]169701[/C][C]168613.714556009[/C][C]1087.28544399096[/C][/ROW]
[ROW][C]110[/C][C]164182[/C][C]166297.126878904[/C][C]-2115.12687890409[/C][/ROW]
[ROW][C]111[/C][C]161914[/C][C]159630.579876351[/C][C]2283.4201236488[/C][/ROW]
[ROW][C]112[/C][C]159612[/C][C]158060.539554743[/C][C]1551.46044525696[/C][/ROW]
[ROW][C]113[/C][C]151001[/C][C]154201.424991103[/C][C]-3200.42499110274[/C][/ROW]
[ROW][C]114[/C][C]158114[/C][C]151624.562134489[/C][C]6489.43786551084[/C][/ROW]
[ROW][C]115[/C][C]186530[/C][C]189171.601050889[/C][C]-2641.60105088935[/C][/ROW]
[ROW][C]116[/C][C]187069[/C][C]193266.148679688[/C][C]-6197.1486796877[/C][/ROW]
[ROW][C]117[/C][C]174330[/C][C]173684.922388921[/C][C]645.077611079469[/C][/ROW]
[ROW][C]118[/C][C]169362[/C][C]163039.411629568[/C][C]6322.58837043165[/C][/ROW]
[ROW][C]119[/C][C]166827[/C][C]158271.00234883[/C][C]8555.99765117007[/C][/ROW]
[ROW][C]120[/C][C]178037[/C][C]167373.950770153[/C][C]10663.049229847[/C][/ROW]
[ROW][C]121[/C][C]186413[/C][C]176183.815808527[/C][C]10229.1841914731[/C][/ROW]
[ROW][C]122[/C][C]189226[/C][C]184368.839357316[/C][C]4857.16064268383[/C][/ROW]
[ROW][C]123[/C][C]191563[/C][C]188972.400892033[/C][C]2590.59910796714[/C][/ROW]
[ROW][C]124[/C][C]188906[/C][C]192372.294027709[/C][C]-3466.2940277087[/C][/ROW]
[ROW][C]125[/C][C]186005[/C][C]187821.724755109[/C][C]-1816.72475510943[/C][/ROW]
[ROW][C]126[/C][C]195309[/C][C]192839.215792401[/C][C]2469.78420759932[/C][/ROW]
[ROW][C]127[/C][C]223532[/C][C]229223.087110721[/C][C]-5691.08711072078[/C][/ROW]
[ROW][C]128[/C][C]226899[/C][C]233733.22180034[/C][C]-6834.2218003402[/C][/ROW]
[ROW][C]129[/C][C]214126[/C][C]218605.044575765[/C][C]-4479.04457576541[/C][/ROW]
[ROW][C]130[/C][C]206903[/C][C]208006.298620989[/C][C]-1103.29862098879[/C][/ROW]
[ROW][C]131[/C][C]204442[/C][C]199829.420257716[/C][C]4612.57974228362[/C][/ROW]
[ROW][C]132[/C][C]220375[/C][C]207753.529268728[/C][C]12621.4707312718[/C][/ROW]
[ROW][C]133[/C][C]214320[/C][C]219725.686840237[/C][C]-5405.68684023729[/C][/ROW]
[ROW][C]134[/C][C]212588[/C][C]214263.16287187[/C][C]-1675.16287187007[/C][/ROW]
[ROW][C]135[/C][C]205816[/C][C]212242.323659017[/C][C]-6426.32365901687[/C][/ROW]
[ROW][C]136[/C][C]202196[/C][C]205149.962306198[/C][C]-2953.96230619837[/C][/ROW]
[ROW][C]137[/C][C]195722[/C][C]199310.402816273[/C][C]-3588.40281627342[/C][/ROW]
[ROW][C]138[/C][C]198563[/C][C]201587.356456262[/C][C]-3024.356456262[/C][/ROW]
[ROW][C]139[/C][C]229139[/C][C]228974.239624871[/C][C]164.760375128622[/C][/ROW]
[ROW][C]140[/C][C]229527[/C][C]235630.86822827[/C][C]-6103.8682282705[/C][/ROW]
[ROW][C]141[/C][C]211868[/C][C]219452.446170661[/C][C]-7584.4461706613[/C][/ROW]
[ROW][C]142[/C][C]203555[/C][C]204622.969306616[/C][C]-1067.96930661576[/C][/ROW]
[ROW][C]143[/C][C]195770[/C][C]195189.669246087[/C][C]580.330753913237[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117184&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117184&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13180144192256.77590812-12112.7759081197
14173666174646.428106398-980.428106397972
15165688164180.8073711891507.19262881079
16161570159602.1658100851967.83418991519
17156145154188.6069701651956.39302983464
18153730152119.1230186181610.876981382
19182698179952.3484015222745.65159847779
20200765200442.561219332322.43878066825
21176512176164.427462601347.572537398606
22166618164082.6938745692535.30612543123
23158644157564.6031125531079.39688744742
24159585162699.575040561-3114.57504056091
25163095157033.5205933096061.47940669145
26159044158060.686855114983.31314488608
27155511151876.2857412733634.7142587268
28153745151536.0705339142208.92946608641
29150569148805.6999799911763.30002000884
30150605148982.9099334371622.09006656322
31179612179540.64902107171.3509789286763
32194690199556.121835498-4866.12183549814
33189917172711.69245961417205.307540386
34184128177934.6383742186193.36162578195
35175335178007.834878517-2672.83487851685
36179566182860.56067138-3294.56067137973
37181140182552.108246814-1412.10824681402
38177876179243.047588603-1367.04758860334
39175041174113.551861832927.448138168431
40169292173346.182184128-4054.18218412847
41166070166832.87427879-762.874278789735
42166972165922.4910065951049.50899340483
43206348196558.7952843899789.20471561115
44215706225216.873886494-9510.87388649379
45202108200907.00696911200.99303089993
46195411190710.8561367064700.14386329381
47193111187055.8402206396055.15977936087
48195198199049.339913742-3851.33991374171
49198770199042.997871195-272.997871194704
50194163197117.930776858-2954.93077685832
51190420191512.249043426-1092.24904342552
52189733188129.6788898931603.32111010666
53186029187498.596717085-1469.59671708476
54191531187061.5533571314469.44664286863
55232571223314.1931842789256.80681572173
56243477248433.712722975-4956.71272297547
57227247231545.874832777-4298.8748327769
58217859218649.86048071-790.860480710166
59208679211171.888635608-2492.88863560779
60213188213488.229628964-300.229628963629
61216234216634.512356744-400.512356744439
62213586213617.211916038-31.2119160378934
63209465210647.255498067-1182.25549806724
64204045207696.056936062-3651.05693606209
65200237201559.353700862-1322.35370086171
66203666201806.3581361041859.64186389593
67241476236008.6293294945467.3706705058
68260307253632.9740701646674.02592983609
69243324245978.104966728-2654.10496672837
70244460235268.2824712649191.71752873648
71233575236647.931624633-3072.93162463326
72237217240271.635200018-3054.63520001838
73235243242188.15269305-6945.15269304995
74230354234257.517648547-3903.51764854678
75227184227677.911670693-493.911670693138
76221678224508.313359515-2830.31335951484
77217142219381.134929036-2239.13492903588
78219452219340.37877907111.621220930218
79256446252477.5642737673968.43572623306
80265845268537.035194257-2692.03519425693
81248624249733.664875926-1109.66487592596
82241114241164.041968422-50.0419684217777
83229245229923.595156388-678.595156388124
84231805232994.616274153-1189.61627415262
85219277233336.866000632-14059.866000632
86219313217374.1832982211938.81670177865
87212610213750.413699221-1140.41369922119
88214771207127.0340285987643.96597140183
89211142209202.7514305291939.24856947092
90211457212298.996501291-841.996501291229
91240048244740.097239513-4692.09723951275
92240636250736.072567318-10100.072567318
93230580223704.945028596875.05497141043
94208795219884.192553618-11089.1925536177
95197922196713.5364857461208.46351425373
96194596198279.950262193-3683.95026219264
97194581190729.0900505413851.9099494589
98185686191278.927945051-5592.92794505131
99178106179159.00117226-1053.00117226044
100172608172574.58126733.4187330002605
101167302164610.4379122582691.56208774194
102168053164961.7541554063091.2458445938
103202300197414.3760947654885.62390523477
104202388208703.725659621-6315.72565962127
105182516187645.695259936-5129.69525993612
106173476168453.7592840085022.24071599171
107166444160459.7414514655984.25854853509
108171297165203.6710899516093.32891004876
109169701168613.7145560091087.28544399096
110164182166297.126878904-2115.12687890409
111161914159630.5798763512283.4201236488
112159612158060.5395547431551.46044525696
113151001154201.424991103-3200.42499110274
114158114151624.5621344896489.43786551084
115186530189171.601050889-2641.60105088935
116187069193266.148679688-6197.1486796877
117174330173684.922388921645.077611079469
118169362163039.4116295686322.58837043165
119166827158271.002348838555.99765117007
120178037167373.95077015310663.049229847
121186413176183.81580852710229.1841914731
122189226184368.8393573164857.16064268383
123191563188972.4008920332590.59910796714
124188906192372.294027709-3466.2940277087
125186005187821.724755109-1816.72475510943
126195309192839.2157924012469.78420759932
127223532229223.087110721-5691.08711072078
128226899233733.22180034-6834.2218003402
129214126218605.044575765-4479.04457576541
130206903208006.298620989-1103.29862098879
131204442199829.4202577164612.57974228362
132220375207753.52926872812621.4707312718
133214320219725.686840237-5405.68684023729
134212588214263.16287187-1675.16287187007
135205816212242.323659017-6426.32365901687
136202196205149.962306198-2953.96230619837
137195722199310.402816273-3588.40281627342
138198563201587.356456262-3024.356456262
139229139228974.239624871164.760375128622
140229527235630.86822827-6103.8682282705
141211868219452.446170661-7584.4461706613
142203555204622.969306616-1067.96930661576
143195770195189.669246087580.330753913237







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
144198652.315847294188946.127403196208358.504291392
145192306.353232724179187.823603683205424.882861766
146188010.821329436171506.694169215204514.948489657
147182618.374637994162670.698972004202566.050303985
148178433.51109528154949.581220205201917.440970355
149172255.700582968145126.928102233199384.473063704
150175388.800333884144499.251040267206278.3496275
151204118.502515189169349.186597036238887.818433341
152207571.683921272168802.85614486246340.511697684
153194890.525319291152002.96560706237778.085031523
154187357.973538483140233.710876445234482.236200521
155179187.517956563127710.236010507230664.799902619

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
144 & 198652.315847294 & 188946.127403196 & 208358.504291392 \tabularnewline
145 & 192306.353232724 & 179187.823603683 & 205424.882861766 \tabularnewline
146 & 188010.821329436 & 171506.694169215 & 204514.948489657 \tabularnewline
147 & 182618.374637994 & 162670.698972004 & 202566.050303985 \tabularnewline
148 & 178433.51109528 & 154949.581220205 & 201917.440970355 \tabularnewline
149 & 172255.700582968 & 145126.928102233 & 199384.473063704 \tabularnewline
150 & 175388.800333884 & 144499.251040267 & 206278.3496275 \tabularnewline
151 & 204118.502515189 & 169349.186597036 & 238887.818433341 \tabularnewline
152 & 207571.683921272 & 168802.85614486 & 246340.511697684 \tabularnewline
153 & 194890.525319291 & 152002.96560706 & 237778.085031523 \tabularnewline
154 & 187357.973538483 & 140233.710876445 & 234482.236200521 \tabularnewline
155 & 179187.517956563 & 127710.236010507 & 230664.799902619 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117184&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]144[/C][C]198652.315847294[/C][C]188946.127403196[/C][C]208358.504291392[/C][/ROW]
[ROW][C]145[/C][C]192306.353232724[/C][C]179187.823603683[/C][C]205424.882861766[/C][/ROW]
[ROW][C]146[/C][C]188010.821329436[/C][C]171506.694169215[/C][C]204514.948489657[/C][/ROW]
[ROW][C]147[/C][C]182618.374637994[/C][C]162670.698972004[/C][C]202566.050303985[/C][/ROW]
[ROW][C]148[/C][C]178433.51109528[/C][C]154949.581220205[/C][C]201917.440970355[/C][/ROW]
[ROW][C]149[/C][C]172255.700582968[/C][C]145126.928102233[/C][C]199384.473063704[/C][/ROW]
[ROW][C]150[/C][C]175388.800333884[/C][C]144499.251040267[/C][C]206278.3496275[/C][/ROW]
[ROW][C]151[/C][C]204118.502515189[/C][C]169349.186597036[/C][C]238887.818433341[/C][/ROW]
[ROW][C]152[/C][C]207571.683921272[/C][C]168802.85614486[/C][C]246340.511697684[/C][/ROW]
[ROW][C]153[/C][C]194890.525319291[/C][C]152002.96560706[/C][C]237778.085031523[/C][/ROW]
[ROW][C]154[/C][C]187357.973538483[/C][C]140233.710876445[/C][C]234482.236200521[/C][/ROW]
[ROW][C]155[/C][C]179187.517956563[/C][C]127710.236010507[/C][C]230664.799902619[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117184&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117184&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
144198652.315847294188946.127403196208358.504291392
145192306.353232724179187.823603683205424.882861766
146188010.821329436171506.694169215204514.948489657
147182618.374637994162670.698972004202566.050303985
148178433.51109528154949.581220205201917.440970355
149172255.700582968145126.928102233199384.473063704
150175388.800333884144499.251040267206278.3496275
151204118.502515189169349.186597036238887.818433341
152207571.683921272168802.85614486246340.511697684
153194890.525319291152002.96560706237778.085031523
154187357.973538483140233.710876445234482.236200521
155179187.517956563127710.236010507230664.799902619



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')