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 computationMon, 14 Dec 2015 12:00:09 +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/2015/Dec/14/t1450094476uggr5njqjronvu2.htm/, Retrieved Thu, 16 May 2024 18:30:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286269, Retrieved Thu, 16 May 2024 18:30:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-12-14 12:00:09] [d108c84c57c191267df4a6d3f43a776a] [Current]
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Dataseries X:
529
567
747
719
707
728
758
746
725
725
555
526
612
570
597
666
677
651
736
757
708
601
569
526
538
525
668
692
762
693
775
843
578
708
434
489
528
505
576
805
895
707
803
834
645
745
637
588
429
552
598
735
831
720
691
670
649
586
559
374
442
396
555
707
616
473
289
183
204
183
140
201
203
201
290
256
169
174
192
170
169
170
124
152
163
114
208
176
191
230
258
356
375
339
291
150
187
163
162
206
168
138
183
128
148
133
103
122
123
140
157
149
171
139
169
172
162
138
124
140
128
112
154
159
176
245
168
242
246
138
199
232
198
219
243
218
203
211
267
233
223
211
267
248
244
265
268
242
244
276
371




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286269&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286269&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286269&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.588634381161722
beta0
gamma0.655289246109926

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.588634381161722 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.655289246109926 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286269&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]0.588634381161722[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.655289246109926[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286269&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286269&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
alpha0.588634381161722
beta0
gamma0.655289246109926







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13612641.112713675214-29.1127136752142
14570578.956738707835-8.95673870783548
15597597.456930258757-0.456930258757438
16666668.585401296095-2.58540129609548
17677679.169314434883-2.16931443488284
18651647.8314839390633.16851606093701
19736719.59401732722916.4059826727705
20757710.19024534926846.8097546507319
21708719.39151220787-11.3915122078696
22601717.666845699663-116.666845699663
23569478.97349840992190.0265015900788
24526503.94696169232122.0530383076787
25538595.727850136671-57.7278501366712
26525522.161336504182.83866349582001
27668549.895945159748118.104054840252
28692690.2397302601411.76026973985927
29762703.49381659647758.5061834035231
30693709.310554313123-16.3105543131231
31775773.1753745502251.82462544977466
32843763.38426054808279.6157394519183
33578776.207322734329-198.207322734329
34708636.13806339960671.8619366003943
35434564.136214355245-130.136214355245
36489441.19117120726747.808828792733
37528526.6267906160271.37320938397329
38505504.1757119335660.824288066434292
39576561.79592838361514.2040716163846
40805609.618577168696195.381422831304
41895752.141356317198142.858643682802
42707787.442993137833-80.4429931378329
43803818.445836852806-15.4458368528063
44834819.45837729421214.5416227057877
45645719.085629394487-74.0856293944867
46745724.87947187984520.1205281201546
47637567.96952912778669.0304708722139
48588610.228327118626-22.2283271186259
49429641.92032207416-212.92032207416
50552493.1807339818358.8192660181704
51598588.5454892203079.45451077969267
52735682.41117799990652.5888220000941
53831726.723100519614104.276899480386
54720679.12023297817340.8797670218269
55691799.05868328476-108.05868328476
56670753.639641721536-83.6396417215357
57649571.5833567141277.4166432858805
58586691.951184084463-105.951184084463
59559474.01543073888484.9845692611156
60374501.06532165019-127.06532165019
61442419.6430620615722.3569379384304
62396482.646823600083-86.6468236000826
63555479.0783026637375.9216973362701
64707623.69629711624283.3037028837575
65616700.021271866441-84.0212718664415
66473524.490075984913-51.4900759849129
67289549.908095993557-260.908095993557
68183421.099116455698-238.099116455698
69204191.53756457056712.462435429433
70183224.241844851885-41.241844851885
7114095.865536862617544.1344631373825
7220141.7087472246583159.291252775342
73203169.12459484333233.8754051566677
74201209.525090410819-8.52509041081933
75290295.764241551386-5.76424155138602
76256394.289002920363-138.289002920363
77169295.072192236735-126.072192236735
78174103.55760078864870.4423992113522
79192144.2978205104647.7021794895396
80170203.295927087458-33.2959270874582
81169161.8308142696997.16918573030071
82170176.942593845259-6.9425938452585
8312491.770337763296132.2296622367039
8415261.648036390660990.3519636093391
85163114.67631758734748.3236824126529
86114152.151941340626-38.1519413406255
87208221.69593340668-13.69593340668
88176279.827994211059-103.827994211059
89191204.189323897568-13.1893238975678
90230132.09462423635297.9053757636483
91258182.8705637145275.1294362854798
92356236.179166254457119.820833745543
93375295.75175926823279.2482407317681
94339349.487728562041-10.4877285620414
95291272.78809342998518.211906570015
96150250.082108149303-100.082108149303
97187179.6850582045747.31494179542571
98163169.710858417857-6.71085841785711
99162264.354599142377-102.354599142377
100206246.00281037665-40.0028103766498
101168232.366711797518-64.3667117975181
102138160.094314402364-22.0943144023636
103183134.09474932736348.905250672637
104128184.01406260824-56.0140626082404
105148129.14730141286718.8526985871329
106133123.1428392018319.85716079816889
10710366.155278554263236.8447214457368
10812222.52946408358599.470535916415
10912398.54628233515524.453717664845
11014094.879711953863545.1202880461365
111157194.250989227867-37.2509892278672
112149231.02918790177-82.0291879017697
113171186.087300877432-15.0873008774319
114139154.217553001521-15.2175530015215
115169151.40477498154217.5952250184585
116172154.61151692337217.3884830766278
117162163.133361437199-1.1333614371988
118138142.939548804757-4.93954880475656
11912484.516996550471639.4830034495284
12014059.325797199580.6742028005
121128104.05665398477923.9433460152214
122112105.6606136507066.33938634929351
123154159.999831832563-5.99983183256293
124159203.102969753735-44.1029697537348
125176198.53084578197-22.5308457819699
126245162.24446024347282.7555397565279
127168225.94713922979-57.9471392297898
128242184.63131826640257.3686817335984
129246211.69406966701634.3059303329841
130138211.335033554552-73.3350335545517
131199124.62724462538974.3727553746111
132232131.076995283523100.923004716477
133198172.43442665584325.5655733441571
134219170.24790071447448.752099285526
135243246.226497505096-3.22649750509618
136218280.690901429064-62.6909014290637
137203270.992338310591-67.9923383105912
138211236.327118284888-25.327118284888
139267198.48032688330368.5196731166968
140233262.692152154657-29.6921521546572
141223232.29102826736-9.29102826735959
142211177.25325207327133.7467479267289
143267193.3941048950373.6058951049696
144248206.54943247514541.4505675248554
145244192.58573217702251.4142678229779
146265211.86487681694653.135123183054
147268276.411941445723-8.41194144572313
148242291.794583944768-49.7945839447682
149244288.25816298607-44.2581629860703
150276279.064679163095-3.06467916309509
151371279.61999122321491.3800087767864

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 612 & 641.112713675214 & -29.1127136752142 \tabularnewline
14 & 570 & 578.956738707835 & -8.95673870783548 \tabularnewline
15 & 597 & 597.456930258757 & -0.456930258757438 \tabularnewline
16 & 666 & 668.585401296095 & -2.58540129609548 \tabularnewline
17 & 677 & 679.169314434883 & -2.16931443488284 \tabularnewline
18 & 651 & 647.831483939063 & 3.16851606093701 \tabularnewline
19 & 736 & 719.594017327229 & 16.4059826727705 \tabularnewline
20 & 757 & 710.190245349268 & 46.8097546507319 \tabularnewline
21 & 708 & 719.39151220787 & -11.3915122078696 \tabularnewline
22 & 601 & 717.666845699663 & -116.666845699663 \tabularnewline
23 & 569 & 478.973498409921 & 90.0265015900788 \tabularnewline
24 & 526 & 503.946961692321 & 22.0530383076787 \tabularnewline
25 & 538 & 595.727850136671 & -57.7278501366712 \tabularnewline
26 & 525 & 522.16133650418 & 2.83866349582001 \tabularnewline
27 & 668 & 549.895945159748 & 118.104054840252 \tabularnewline
28 & 692 & 690.239730260141 & 1.76026973985927 \tabularnewline
29 & 762 & 703.493816596477 & 58.5061834035231 \tabularnewline
30 & 693 & 709.310554313123 & -16.3105543131231 \tabularnewline
31 & 775 & 773.175374550225 & 1.82462544977466 \tabularnewline
32 & 843 & 763.384260548082 & 79.6157394519183 \tabularnewline
33 & 578 & 776.207322734329 & -198.207322734329 \tabularnewline
34 & 708 & 636.138063399606 & 71.8619366003943 \tabularnewline
35 & 434 & 564.136214355245 & -130.136214355245 \tabularnewline
36 & 489 & 441.191171207267 & 47.808828792733 \tabularnewline
37 & 528 & 526.626790616027 & 1.37320938397329 \tabularnewline
38 & 505 & 504.175711933566 & 0.824288066434292 \tabularnewline
39 & 576 & 561.795928383615 & 14.2040716163846 \tabularnewline
40 & 805 & 609.618577168696 & 195.381422831304 \tabularnewline
41 & 895 & 752.141356317198 & 142.858643682802 \tabularnewline
42 & 707 & 787.442993137833 & -80.4429931378329 \tabularnewline
43 & 803 & 818.445836852806 & -15.4458368528063 \tabularnewline
44 & 834 & 819.458377294212 & 14.5416227057877 \tabularnewline
45 & 645 & 719.085629394487 & -74.0856293944867 \tabularnewline
46 & 745 & 724.879471879845 & 20.1205281201546 \tabularnewline
47 & 637 & 567.969529127786 & 69.0304708722139 \tabularnewline
48 & 588 & 610.228327118626 & -22.2283271186259 \tabularnewline
49 & 429 & 641.92032207416 & -212.92032207416 \tabularnewline
50 & 552 & 493.18073398183 & 58.8192660181704 \tabularnewline
51 & 598 & 588.545489220307 & 9.45451077969267 \tabularnewline
52 & 735 & 682.411177999906 & 52.5888220000941 \tabularnewline
53 & 831 & 726.723100519614 & 104.276899480386 \tabularnewline
54 & 720 & 679.120232978173 & 40.8797670218269 \tabularnewline
55 & 691 & 799.05868328476 & -108.05868328476 \tabularnewline
56 & 670 & 753.639641721536 & -83.6396417215357 \tabularnewline
57 & 649 & 571.58335671412 & 77.4166432858805 \tabularnewline
58 & 586 & 691.951184084463 & -105.951184084463 \tabularnewline
59 & 559 & 474.015430738884 & 84.9845692611156 \tabularnewline
60 & 374 & 501.06532165019 & -127.06532165019 \tabularnewline
61 & 442 & 419.64306206157 & 22.3569379384304 \tabularnewline
62 & 396 & 482.646823600083 & -86.6468236000826 \tabularnewline
63 & 555 & 479.07830266373 & 75.9216973362701 \tabularnewline
64 & 707 & 623.696297116242 & 83.3037028837575 \tabularnewline
65 & 616 & 700.021271866441 & -84.0212718664415 \tabularnewline
66 & 473 & 524.490075984913 & -51.4900759849129 \tabularnewline
67 & 289 & 549.908095993557 & -260.908095993557 \tabularnewline
68 & 183 & 421.099116455698 & -238.099116455698 \tabularnewline
69 & 204 & 191.537564570567 & 12.462435429433 \tabularnewline
70 & 183 & 224.241844851885 & -41.241844851885 \tabularnewline
71 & 140 & 95.8655368626175 & 44.1344631373825 \tabularnewline
72 & 201 & 41.7087472246583 & 159.291252775342 \tabularnewline
73 & 203 & 169.124594843332 & 33.8754051566677 \tabularnewline
74 & 201 & 209.525090410819 & -8.52509041081933 \tabularnewline
75 & 290 & 295.764241551386 & -5.76424155138602 \tabularnewline
76 & 256 & 394.289002920363 & -138.289002920363 \tabularnewline
77 & 169 & 295.072192236735 & -126.072192236735 \tabularnewline
78 & 174 & 103.557600788648 & 70.4423992113522 \tabularnewline
79 & 192 & 144.29782051046 & 47.7021794895396 \tabularnewline
80 & 170 & 203.295927087458 & -33.2959270874582 \tabularnewline
81 & 169 & 161.830814269699 & 7.16918573030071 \tabularnewline
82 & 170 & 176.942593845259 & -6.9425938452585 \tabularnewline
83 & 124 & 91.7703377632961 & 32.2296622367039 \tabularnewline
84 & 152 & 61.6480363906609 & 90.3519636093391 \tabularnewline
85 & 163 & 114.676317587347 & 48.3236824126529 \tabularnewline
86 & 114 & 152.151941340626 & -38.1519413406255 \tabularnewline
87 & 208 & 221.69593340668 & -13.69593340668 \tabularnewline
88 & 176 & 279.827994211059 & -103.827994211059 \tabularnewline
89 & 191 & 204.189323897568 & -13.1893238975678 \tabularnewline
90 & 230 & 132.094624236352 & 97.9053757636483 \tabularnewline
91 & 258 & 182.87056371452 & 75.1294362854798 \tabularnewline
92 & 356 & 236.179166254457 & 119.820833745543 \tabularnewline
93 & 375 & 295.751759268232 & 79.2482407317681 \tabularnewline
94 & 339 & 349.487728562041 & -10.4877285620414 \tabularnewline
95 & 291 & 272.788093429985 & 18.211906570015 \tabularnewline
96 & 150 & 250.082108149303 & -100.082108149303 \tabularnewline
97 & 187 & 179.685058204574 & 7.31494179542571 \tabularnewline
98 & 163 & 169.710858417857 & -6.71085841785711 \tabularnewline
99 & 162 & 264.354599142377 & -102.354599142377 \tabularnewline
100 & 206 & 246.00281037665 & -40.0028103766498 \tabularnewline
101 & 168 & 232.366711797518 & -64.3667117975181 \tabularnewline
102 & 138 & 160.094314402364 & -22.0943144023636 \tabularnewline
103 & 183 & 134.094749327363 & 48.905250672637 \tabularnewline
104 & 128 & 184.01406260824 & -56.0140626082404 \tabularnewline
105 & 148 & 129.147301412867 & 18.8526985871329 \tabularnewline
106 & 133 & 123.142839201831 & 9.85716079816889 \tabularnewline
107 & 103 & 66.1552785542632 & 36.8447214457368 \tabularnewline
108 & 122 & 22.529464083585 & 99.470535916415 \tabularnewline
109 & 123 & 98.546282335155 & 24.453717664845 \tabularnewline
110 & 140 & 94.8797119538635 & 45.1202880461365 \tabularnewline
111 & 157 & 194.250989227867 & -37.2509892278672 \tabularnewline
112 & 149 & 231.02918790177 & -82.0291879017697 \tabularnewline
113 & 171 & 186.087300877432 & -15.0873008774319 \tabularnewline
114 & 139 & 154.217553001521 & -15.2175530015215 \tabularnewline
115 & 169 & 151.404774981542 & 17.5952250184585 \tabularnewline
116 & 172 & 154.611516923372 & 17.3884830766278 \tabularnewline
117 & 162 & 163.133361437199 & -1.1333614371988 \tabularnewline
118 & 138 & 142.939548804757 & -4.93954880475656 \tabularnewline
119 & 124 & 84.5169965504716 & 39.4830034495284 \tabularnewline
120 & 140 & 59.3257971995 & 80.6742028005 \tabularnewline
121 & 128 & 104.056653984779 & 23.9433460152214 \tabularnewline
122 & 112 & 105.660613650706 & 6.33938634929351 \tabularnewline
123 & 154 & 159.999831832563 & -5.99983183256293 \tabularnewline
124 & 159 & 203.102969753735 & -44.1029697537348 \tabularnewline
125 & 176 & 198.53084578197 & -22.5308457819699 \tabularnewline
126 & 245 & 162.244460243472 & 82.7555397565279 \tabularnewline
127 & 168 & 225.94713922979 & -57.9471392297898 \tabularnewline
128 & 242 & 184.631318266402 & 57.3686817335984 \tabularnewline
129 & 246 & 211.694069667016 & 34.3059303329841 \tabularnewline
130 & 138 & 211.335033554552 & -73.3350335545517 \tabularnewline
131 & 199 & 124.627244625389 & 74.3727553746111 \tabularnewline
132 & 232 & 131.076995283523 & 100.923004716477 \tabularnewline
133 & 198 & 172.434426655843 & 25.5655733441571 \tabularnewline
134 & 219 & 170.247900714474 & 48.752099285526 \tabularnewline
135 & 243 & 246.226497505096 & -3.22649750509618 \tabularnewline
136 & 218 & 280.690901429064 & -62.6909014290637 \tabularnewline
137 & 203 & 270.992338310591 & -67.9923383105912 \tabularnewline
138 & 211 & 236.327118284888 & -25.327118284888 \tabularnewline
139 & 267 & 198.480326883303 & 68.5196731166968 \tabularnewline
140 & 233 & 262.692152154657 & -29.6921521546572 \tabularnewline
141 & 223 & 232.29102826736 & -9.29102826735959 \tabularnewline
142 & 211 & 177.253252073271 & 33.7467479267289 \tabularnewline
143 & 267 & 193.39410489503 & 73.6058951049696 \tabularnewline
144 & 248 & 206.549432475145 & 41.4505675248554 \tabularnewline
145 & 244 & 192.585732177022 & 51.4142678229779 \tabularnewline
146 & 265 & 211.864876816946 & 53.135123183054 \tabularnewline
147 & 268 & 276.411941445723 & -8.41194144572313 \tabularnewline
148 & 242 & 291.794583944768 & -49.7945839447682 \tabularnewline
149 & 244 & 288.25816298607 & -44.2581629860703 \tabularnewline
150 & 276 & 279.064679163095 & -3.06467916309509 \tabularnewline
151 & 371 & 279.619991223214 & 91.3800087767864 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286269&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]612[/C][C]641.112713675214[/C][C]-29.1127136752142[/C][/ROW]
[ROW][C]14[/C][C]570[/C][C]578.956738707835[/C][C]-8.95673870783548[/C][/ROW]
[ROW][C]15[/C][C]597[/C][C]597.456930258757[/C][C]-0.456930258757438[/C][/ROW]
[ROW][C]16[/C][C]666[/C][C]668.585401296095[/C][C]-2.58540129609548[/C][/ROW]
[ROW][C]17[/C][C]677[/C][C]679.169314434883[/C][C]-2.16931443488284[/C][/ROW]
[ROW][C]18[/C][C]651[/C][C]647.831483939063[/C][C]3.16851606093701[/C][/ROW]
[ROW][C]19[/C][C]736[/C][C]719.594017327229[/C][C]16.4059826727705[/C][/ROW]
[ROW][C]20[/C][C]757[/C][C]710.190245349268[/C][C]46.8097546507319[/C][/ROW]
[ROW][C]21[/C][C]708[/C][C]719.39151220787[/C][C]-11.3915122078696[/C][/ROW]
[ROW][C]22[/C][C]601[/C][C]717.666845699663[/C][C]-116.666845699663[/C][/ROW]
[ROW][C]23[/C][C]569[/C][C]478.973498409921[/C][C]90.0265015900788[/C][/ROW]
[ROW][C]24[/C][C]526[/C][C]503.946961692321[/C][C]22.0530383076787[/C][/ROW]
[ROW][C]25[/C][C]538[/C][C]595.727850136671[/C][C]-57.7278501366712[/C][/ROW]
[ROW][C]26[/C][C]525[/C][C]522.16133650418[/C][C]2.83866349582001[/C][/ROW]
[ROW][C]27[/C][C]668[/C][C]549.895945159748[/C][C]118.104054840252[/C][/ROW]
[ROW][C]28[/C][C]692[/C][C]690.239730260141[/C][C]1.76026973985927[/C][/ROW]
[ROW][C]29[/C][C]762[/C][C]703.493816596477[/C][C]58.5061834035231[/C][/ROW]
[ROW][C]30[/C][C]693[/C][C]709.310554313123[/C][C]-16.3105543131231[/C][/ROW]
[ROW][C]31[/C][C]775[/C][C]773.175374550225[/C][C]1.82462544977466[/C][/ROW]
[ROW][C]32[/C][C]843[/C][C]763.384260548082[/C][C]79.6157394519183[/C][/ROW]
[ROW][C]33[/C][C]578[/C][C]776.207322734329[/C][C]-198.207322734329[/C][/ROW]
[ROW][C]34[/C][C]708[/C][C]636.138063399606[/C][C]71.8619366003943[/C][/ROW]
[ROW][C]35[/C][C]434[/C][C]564.136214355245[/C][C]-130.136214355245[/C][/ROW]
[ROW][C]36[/C][C]489[/C][C]441.191171207267[/C][C]47.808828792733[/C][/ROW]
[ROW][C]37[/C][C]528[/C][C]526.626790616027[/C][C]1.37320938397329[/C][/ROW]
[ROW][C]38[/C][C]505[/C][C]504.175711933566[/C][C]0.824288066434292[/C][/ROW]
[ROW][C]39[/C][C]576[/C][C]561.795928383615[/C][C]14.2040716163846[/C][/ROW]
[ROW][C]40[/C][C]805[/C][C]609.618577168696[/C][C]195.381422831304[/C][/ROW]
[ROW][C]41[/C][C]895[/C][C]752.141356317198[/C][C]142.858643682802[/C][/ROW]
[ROW][C]42[/C][C]707[/C][C]787.442993137833[/C][C]-80.4429931378329[/C][/ROW]
[ROW][C]43[/C][C]803[/C][C]818.445836852806[/C][C]-15.4458368528063[/C][/ROW]
[ROW][C]44[/C][C]834[/C][C]819.458377294212[/C][C]14.5416227057877[/C][/ROW]
[ROW][C]45[/C][C]645[/C][C]719.085629394487[/C][C]-74.0856293944867[/C][/ROW]
[ROW][C]46[/C][C]745[/C][C]724.879471879845[/C][C]20.1205281201546[/C][/ROW]
[ROW][C]47[/C][C]637[/C][C]567.969529127786[/C][C]69.0304708722139[/C][/ROW]
[ROW][C]48[/C][C]588[/C][C]610.228327118626[/C][C]-22.2283271186259[/C][/ROW]
[ROW][C]49[/C][C]429[/C][C]641.92032207416[/C][C]-212.92032207416[/C][/ROW]
[ROW][C]50[/C][C]552[/C][C]493.18073398183[/C][C]58.8192660181704[/C][/ROW]
[ROW][C]51[/C][C]598[/C][C]588.545489220307[/C][C]9.45451077969267[/C][/ROW]
[ROW][C]52[/C][C]735[/C][C]682.411177999906[/C][C]52.5888220000941[/C][/ROW]
[ROW][C]53[/C][C]831[/C][C]726.723100519614[/C][C]104.276899480386[/C][/ROW]
[ROW][C]54[/C][C]720[/C][C]679.120232978173[/C][C]40.8797670218269[/C][/ROW]
[ROW][C]55[/C][C]691[/C][C]799.05868328476[/C][C]-108.05868328476[/C][/ROW]
[ROW][C]56[/C][C]670[/C][C]753.639641721536[/C][C]-83.6396417215357[/C][/ROW]
[ROW][C]57[/C][C]649[/C][C]571.58335671412[/C][C]77.4166432858805[/C][/ROW]
[ROW][C]58[/C][C]586[/C][C]691.951184084463[/C][C]-105.951184084463[/C][/ROW]
[ROW][C]59[/C][C]559[/C][C]474.015430738884[/C][C]84.9845692611156[/C][/ROW]
[ROW][C]60[/C][C]374[/C][C]501.06532165019[/C][C]-127.06532165019[/C][/ROW]
[ROW][C]61[/C][C]442[/C][C]419.64306206157[/C][C]22.3569379384304[/C][/ROW]
[ROW][C]62[/C][C]396[/C][C]482.646823600083[/C][C]-86.6468236000826[/C][/ROW]
[ROW][C]63[/C][C]555[/C][C]479.07830266373[/C][C]75.9216973362701[/C][/ROW]
[ROW][C]64[/C][C]707[/C][C]623.696297116242[/C][C]83.3037028837575[/C][/ROW]
[ROW][C]65[/C][C]616[/C][C]700.021271866441[/C][C]-84.0212718664415[/C][/ROW]
[ROW][C]66[/C][C]473[/C][C]524.490075984913[/C][C]-51.4900759849129[/C][/ROW]
[ROW][C]67[/C][C]289[/C][C]549.908095993557[/C][C]-260.908095993557[/C][/ROW]
[ROW][C]68[/C][C]183[/C][C]421.099116455698[/C][C]-238.099116455698[/C][/ROW]
[ROW][C]69[/C][C]204[/C][C]191.537564570567[/C][C]12.462435429433[/C][/ROW]
[ROW][C]70[/C][C]183[/C][C]224.241844851885[/C][C]-41.241844851885[/C][/ROW]
[ROW][C]71[/C][C]140[/C][C]95.8655368626175[/C][C]44.1344631373825[/C][/ROW]
[ROW][C]72[/C][C]201[/C][C]41.7087472246583[/C][C]159.291252775342[/C][/ROW]
[ROW][C]73[/C][C]203[/C][C]169.124594843332[/C][C]33.8754051566677[/C][/ROW]
[ROW][C]74[/C][C]201[/C][C]209.525090410819[/C][C]-8.52509041081933[/C][/ROW]
[ROW][C]75[/C][C]290[/C][C]295.764241551386[/C][C]-5.76424155138602[/C][/ROW]
[ROW][C]76[/C][C]256[/C][C]394.289002920363[/C][C]-138.289002920363[/C][/ROW]
[ROW][C]77[/C][C]169[/C][C]295.072192236735[/C][C]-126.072192236735[/C][/ROW]
[ROW][C]78[/C][C]174[/C][C]103.557600788648[/C][C]70.4423992113522[/C][/ROW]
[ROW][C]79[/C][C]192[/C][C]144.29782051046[/C][C]47.7021794895396[/C][/ROW]
[ROW][C]80[/C][C]170[/C][C]203.295927087458[/C][C]-33.2959270874582[/C][/ROW]
[ROW][C]81[/C][C]169[/C][C]161.830814269699[/C][C]7.16918573030071[/C][/ROW]
[ROW][C]82[/C][C]170[/C][C]176.942593845259[/C][C]-6.9425938452585[/C][/ROW]
[ROW][C]83[/C][C]124[/C][C]91.7703377632961[/C][C]32.2296622367039[/C][/ROW]
[ROW][C]84[/C][C]152[/C][C]61.6480363906609[/C][C]90.3519636093391[/C][/ROW]
[ROW][C]85[/C][C]163[/C][C]114.676317587347[/C][C]48.3236824126529[/C][/ROW]
[ROW][C]86[/C][C]114[/C][C]152.151941340626[/C][C]-38.1519413406255[/C][/ROW]
[ROW][C]87[/C][C]208[/C][C]221.69593340668[/C][C]-13.69593340668[/C][/ROW]
[ROW][C]88[/C][C]176[/C][C]279.827994211059[/C][C]-103.827994211059[/C][/ROW]
[ROW][C]89[/C][C]191[/C][C]204.189323897568[/C][C]-13.1893238975678[/C][/ROW]
[ROW][C]90[/C][C]230[/C][C]132.094624236352[/C][C]97.9053757636483[/C][/ROW]
[ROW][C]91[/C][C]258[/C][C]182.87056371452[/C][C]75.1294362854798[/C][/ROW]
[ROW][C]92[/C][C]356[/C][C]236.179166254457[/C][C]119.820833745543[/C][/ROW]
[ROW][C]93[/C][C]375[/C][C]295.751759268232[/C][C]79.2482407317681[/C][/ROW]
[ROW][C]94[/C][C]339[/C][C]349.487728562041[/C][C]-10.4877285620414[/C][/ROW]
[ROW][C]95[/C][C]291[/C][C]272.788093429985[/C][C]18.211906570015[/C][/ROW]
[ROW][C]96[/C][C]150[/C][C]250.082108149303[/C][C]-100.082108149303[/C][/ROW]
[ROW][C]97[/C][C]187[/C][C]179.685058204574[/C][C]7.31494179542571[/C][/ROW]
[ROW][C]98[/C][C]163[/C][C]169.710858417857[/C][C]-6.71085841785711[/C][/ROW]
[ROW][C]99[/C][C]162[/C][C]264.354599142377[/C][C]-102.354599142377[/C][/ROW]
[ROW][C]100[/C][C]206[/C][C]246.00281037665[/C][C]-40.0028103766498[/C][/ROW]
[ROW][C]101[/C][C]168[/C][C]232.366711797518[/C][C]-64.3667117975181[/C][/ROW]
[ROW][C]102[/C][C]138[/C][C]160.094314402364[/C][C]-22.0943144023636[/C][/ROW]
[ROW][C]103[/C][C]183[/C][C]134.094749327363[/C][C]48.905250672637[/C][/ROW]
[ROW][C]104[/C][C]128[/C][C]184.01406260824[/C][C]-56.0140626082404[/C][/ROW]
[ROW][C]105[/C][C]148[/C][C]129.147301412867[/C][C]18.8526985871329[/C][/ROW]
[ROW][C]106[/C][C]133[/C][C]123.142839201831[/C][C]9.85716079816889[/C][/ROW]
[ROW][C]107[/C][C]103[/C][C]66.1552785542632[/C][C]36.8447214457368[/C][/ROW]
[ROW][C]108[/C][C]122[/C][C]22.529464083585[/C][C]99.470535916415[/C][/ROW]
[ROW][C]109[/C][C]123[/C][C]98.546282335155[/C][C]24.453717664845[/C][/ROW]
[ROW][C]110[/C][C]140[/C][C]94.8797119538635[/C][C]45.1202880461365[/C][/ROW]
[ROW][C]111[/C][C]157[/C][C]194.250989227867[/C][C]-37.2509892278672[/C][/ROW]
[ROW][C]112[/C][C]149[/C][C]231.02918790177[/C][C]-82.0291879017697[/C][/ROW]
[ROW][C]113[/C][C]171[/C][C]186.087300877432[/C][C]-15.0873008774319[/C][/ROW]
[ROW][C]114[/C][C]139[/C][C]154.217553001521[/C][C]-15.2175530015215[/C][/ROW]
[ROW][C]115[/C][C]169[/C][C]151.404774981542[/C][C]17.5952250184585[/C][/ROW]
[ROW][C]116[/C][C]172[/C][C]154.611516923372[/C][C]17.3884830766278[/C][/ROW]
[ROW][C]117[/C][C]162[/C][C]163.133361437199[/C][C]-1.1333614371988[/C][/ROW]
[ROW][C]118[/C][C]138[/C][C]142.939548804757[/C][C]-4.93954880475656[/C][/ROW]
[ROW][C]119[/C][C]124[/C][C]84.5169965504716[/C][C]39.4830034495284[/C][/ROW]
[ROW][C]120[/C][C]140[/C][C]59.3257971995[/C][C]80.6742028005[/C][/ROW]
[ROW][C]121[/C][C]128[/C][C]104.056653984779[/C][C]23.9433460152214[/C][/ROW]
[ROW][C]122[/C][C]112[/C][C]105.660613650706[/C][C]6.33938634929351[/C][/ROW]
[ROW][C]123[/C][C]154[/C][C]159.999831832563[/C][C]-5.99983183256293[/C][/ROW]
[ROW][C]124[/C][C]159[/C][C]203.102969753735[/C][C]-44.1029697537348[/C][/ROW]
[ROW][C]125[/C][C]176[/C][C]198.53084578197[/C][C]-22.5308457819699[/C][/ROW]
[ROW][C]126[/C][C]245[/C][C]162.244460243472[/C][C]82.7555397565279[/C][/ROW]
[ROW][C]127[/C][C]168[/C][C]225.94713922979[/C][C]-57.9471392297898[/C][/ROW]
[ROW][C]128[/C][C]242[/C][C]184.631318266402[/C][C]57.3686817335984[/C][/ROW]
[ROW][C]129[/C][C]246[/C][C]211.694069667016[/C][C]34.3059303329841[/C][/ROW]
[ROW][C]130[/C][C]138[/C][C]211.335033554552[/C][C]-73.3350335545517[/C][/ROW]
[ROW][C]131[/C][C]199[/C][C]124.627244625389[/C][C]74.3727553746111[/C][/ROW]
[ROW][C]132[/C][C]232[/C][C]131.076995283523[/C][C]100.923004716477[/C][/ROW]
[ROW][C]133[/C][C]198[/C][C]172.434426655843[/C][C]25.5655733441571[/C][/ROW]
[ROW][C]134[/C][C]219[/C][C]170.247900714474[/C][C]48.752099285526[/C][/ROW]
[ROW][C]135[/C][C]243[/C][C]246.226497505096[/C][C]-3.22649750509618[/C][/ROW]
[ROW][C]136[/C][C]218[/C][C]280.690901429064[/C][C]-62.6909014290637[/C][/ROW]
[ROW][C]137[/C][C]203[/C][C]270.992338310591[/C][C]-67.9923383105912[/C][/ROW]
[ROW][C]138[/C][C]211[/C][C]236.327118284888[/C][C]-25.327118284888[/C][/ROW]
[ROW][C]139[/C][C]267[/C][C]198.480326883303[/C][C]68.5196731166968[/C][/ROW]
[ROW][C]140[/C][C]233[/C][C]262.692152154657[/C][C]-29.6921521546572[/C][/ROW]
[ROW][C]141[/C][C]223[/C][C]232.29102826736[/C][C]-9.29102826735959[/C][/ROW]
[ROW][C]142[/C][C]211[/C][C]177.253252073271[/C][C]33.7467479267289[/C][/ROW]
[ROW][C]143[/C][C]267[/C][C]193.39410489503[/C][C]73.6058951049696[/C][/ROW]
[ROW][C]144[/C][C]248[/C][C]206.549432475145[/C][C]41.4505675248554[/C][/ROW]
[ROW][C]145[/C][C]244[/C][C]192.585732177022[/C][C]51.4142678229779[/C][/ROW]
[ROW][C]146[/C][C]265[/C][C]211.864876816946[/C][C]53.135123183054[/C][/ROW]
[ROW][C]147[/C][C]268[/C][C]276.411941445723[/C][C]-8.41194144572313[/C][/ROW]
[ROW][C]148[/C][C]242[/C][C]291.794583944768[/C][C]-49.7945839447682[/C][/ROW]
[ROW][C]149[/C][C]244[/C][C]288.25816298607[/C][C]-44.2581629860703[/C][/ROW]
[ROW][C]150[/C][C]276[/C][C]279.064679163095[/C][C]-3.06467916309509[/C][/ROW]
[ROW][C]151[/C][C]371[/C][C]279.619991223214[/C][C]91.3800087767864[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286269&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286269&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
13612641.112713675214-29.1127136752142
14570578.956738707835-8.95673870783548
15597597.456930258757-0.456930258757438
16666668.585401296095-2.58540129609548
17677679.169314434883-2.16931443488284
18651647.8314839390633.16851606093701
19736719.59401732722916.4059826727705
20757710.19024534926846.8097546507319
21708719.39151220787-11.3915122078696
22601717.666845699663-116.666845699663
23569478.97349840992190.0265015900788
24526503.94696169232122.0530383076787
25538595.727850136671-57.7278501366712
26525522.161336504182.83866349582001
27668549.895945159748118.104054840252
28692690.2397302601411.76026973985927
29762703.49381659647758.5061834035231
30693709.310554313123-16.3105543131231
31775773.1753745502251.82462544977466
32843763.38426054808279.6157394519183
33578776.207322734329-198.207322734329
34708636.13806339960671.8619366003943
35434564.136214355245-130.136214355245
36489441.19117120726747.808828792733
37528526.6267906160271.37320938397329
38505504.1757119335660.824288066434292
39576561.79592838361514.2040716163846
40805609.618577168696195.381422831304
41895752.141356317198142.858643682802
42707787.442993137833-80.4429931378329
43803818.445836852806-15.4458368528063
44834819.45837729421214.5416227057877
45645719.085629394487-74.0856293944867
46745724.87947187984520.1205281201546
47637567.96952912778669.0304708722139
48588610.228327118626-22.2283271186259
49429641.92032207416-212.92032207416
50552493.1807339818358.8192660181704
51598588.5454892203079.45451077969267
52735682.41117799990652.5888220000941
53831726.723100519614104.276899480386
54720679.12023297817340.8797670218269
55691799.05868328476-108.05868328476
56670753.639641721536-83.6396417215357
57649571.5833567141277.4166432858805
58586691.951184084463-105.951184084463
59559474.01543073888484.9845692611156
60374501.06532165019-127.06532165019
61442419.6430620615722.3569379384304
62396482.646823600083-86.6468236000826
63555479.0783026637375.9216973362701
64707623.69629711624283.3037028837575
65616700.021271866441-84.0212718664415
66473524.490075984913-51.4900759849129
67289549.908095993557-260.908095993557
68183421.099116455698-238.099116455698
69204191.53756457056712.462435429433
70183224.241844851885-41.241844851885
7114095.865536862617544.1344631373825
7220141.7087472246583159.291252775342
73203169.12459484333233.8754051566677
74201209.525090410819-8.52509041081933
75290295.764241551386-5.76424155138602
76256394.289002920363-138.289002920363
77169295.072192236735-126.072192236735
78174103.55760078864870.4423992113522
79192144.2978205104647.7021794895396
80170203.295927087458-33.2959270874582
81169161.8308142696997.16918573030071
82170176.942593845259-6.9425938452585
8312491.770337763296132.2296622367039
8415261.648036390660990.3519636093391
85163114.67631758734748.3236824126529
86114152.151941340626-38.1519413406255
87208221.69593340668-13.69593340668
88176279.827994211059-103.827994211059
89191204.189323897568-13.1893238975678
90230132.09462423635297.9053757636483
91258182.8705637145275.1294362854798
92356236.179166254457119.820833745543
93375295.75175926823279.2482407317681
94339349.487728562041-10.4877285620414
95291272.78809342998518.211906570015
96150250.082108149303-100.082108149303
97187179.6850582045747.31494179542571
98163169.710858417857-6.71085841785711
99162264.354599142377-102.354599142377
100206246.00281037665-40.0028103766498
101168232.366711797518-64.3667117975181
102138160.094314402364-22.0943144023636
103183134.09474932736348.905250672637
104128184.01406260824-56.0140626082404
105148129.14730141286718.8526985871329
106133123.1428392018319.85716079816889
10710366.155278554263236.8447214457368
10812222.52946408358599.470535916415
10912398.54628233515524.453717664845
11014094.879711953863545.1202880461365
111157194.250989227867-37.2509892278672
112149231.02918790177-82.0291879017697
113171186.087300877432-15.0873008774319
114139154.217553001521-15.2175530015215
115169151.40477498154217.5952250184585
116172154.61151692337217.3884830766278
117162163.133361437199-1.1333614371988
118138142.939548804757-4.93954880475656
11912484.516996550471639.4830034495284
12014059.325797199580.6742028005
121128104.05665398477923.9433460152214
122112105.6606136507066.33938634929351
123154159.999831832563-5.99983183256293
124159203.102969753735-44.1029697537348
125176198.53084578197-22.5308457819699
126245162.24446024347282.7555397565279
127168225.94713922979-57.9471392297898
128242184.63131826640257.3686817335984
129246211.69406966701634.3059303329841
130138211.335033554552-73.3350335545517
131199124.62724462538974.3727553746111
132232131.076995283523100.923004716477
133198172.43442665584325.5655733441571
134219170.24790071447448.752099285526
135243246.226497505096-3.22649750509618
136218280.690901429064-62.6909014290637
137203270.992338310591-67.9923383105912
138211236.327118284888-25.327118284888
139267198.48032688330368.5196731166968
140233262.692152154657-29.6921521546572
141223232.29102826736-9.29102826735959
142211177.25325207327133.7467479267289
143267193.3941048950373.6058951049696
144248206.54943247514541.4505675248554
145244192.58573217702251.4142678229779
146265211.86487681694653.135123183054
147268276.411941445723-8.41194144572313
148242291.794583944768-49.7945839447682
149244288.25816298607-44.2581629860703
150276279.064679163095-3.06467916309509
151371279.61999122321491.3800087767864







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
152330.81387598269185.963305475878475.664446489502
153323.389971374643155.307723965391491.472218783896
154285.42262598538396.9508880188077473.894363951959
155292.44355259997185.5823669460701499.304738253873
156253.60401810440829.8597349413868477.348301267429
157217.926938231469-21.5129464288157457.366822891754
158207.405756884298-46.7623223155234461.57383608412
159224.084821081785-44.0035348796836492.173177043253
160233.26377297372-48.0568994272244514.584445374664
161260.530572944769-33.4273744526703554.488520342208
162288.493223788444-17.5806708123725594.567118389261
163316.311348820605-1.41681026213672634.039507903347

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
152 & 330.81387598269 & 185.963305475878 & 475.664446489502 \tabularnewline
153 & 323.389971374643 & 155.307723965391 & 491.472218783896 \tabularnewline
154 & 285.422625985383 & 96.9508880188077 & 473.894363951959 \tabularnewline
155 & 292.443552599971 & 85.5823669460701 & 499.304738253873 \tabularnewline
156 & 253.604018104408 & 29.8597349413868 & 477.348301267429 \tabularnewline
157 & 217.926938231469 & -21.5129464288157 & 457.366822891754 \tabularnewline
158 & 207.405756884298 & -46.7623223155234 & 461.57383608412 \tabularnewline
159 & 224.084821081785 & -44.0035348796836 & 492.173177043253 \tabularnewline
160 & 233.26377297372 & -48.0568994272244 & 514.584445374664 \tabularnewline
161 & 260.530572944769 & -33.4273744526703 & 554.488520342208 \tabularnewline
162 & 288.493223788444 & -17.5806708123725 & 594.567118389261 \tabularnewline
163 & 316.311348820605 & -1.41681026213672 & 634.039507903347 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286269&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]152[/C][C]330.81387598269[/C][C]185.963305475878[/C][C]475.664446489502[/C][/ROW]
[ROW][C]153[/C][C]323.389971374643[/C][C]155.307723965391[/C][C]491.472218783896[/C][/ROW]
[ROW][C]154[/C][C]285.422625985383[/C][C]96.9508880188077[/C][C]473.894363951959[/C][/ROW]
[ROW][C]155[/C][C]292.443552599971[/C][C]85.5823669460701[/C][C]499.304738253873[/C][/ROW]
[ROW][C]156[/C][C]253.604018104408[/C][C]29.8597349413868[/C][C]477.348301267429[/C][/ROW]
[ROW][C]157[/C][C]217.926938231469[/C][C]-21.5129464288157[/C][C]457.366822891754[/C][/ROW]
[ROW][C]158[/C][C]207.405756884298[/C][C]-46.7623223155234[/C][C]461.57383608412[/C][/ROW]
[ROW][C]159[/C][C]224.084821081785[/C][C]-44.0035348796836[/C][C]492.173177043253[/C][/ROW]
[ROW][C]160[/C][C]233.26377297372[/C][C]-48.0568994272244[/C][C]514.584445374664[/C][/ROW]
[ROW][C]161[/C][C]260.530572944769[/C][C]-33.4273744526703[/C][C]554.488520342208[/C][/ROW]
[ROW][C]162[/C][C]288.493223788444[/C][C]-17.5806708123725[/C][C]594.567118389261[/C][/ROW]
[ROW][C]163[/C][C]316.311348820605[/C][C]-1.41681026213672[/C][C]634.039507903347[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286269&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286269&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
152330.81387598269185.963305475878475.664446489502
153323.389971374643155.307723965391491.472218783896
154285.42262598538396.9508880188077473.894363951959
155292.44355259997185.5823669460701499.304738253873
156253.60401810440829.8597349413868477.348301267429
157217.926938231469-21.5129464288157457.366822891754
158207.405756884298-46.7623223155234461.57383608412
159224.084821081785-44.0035348796836492.173177043253
160233.26377297372-48.0568994272244514.584445374664
161260.530572944769-33.4273744526703554.488520342208
162288.493223788444-17.5806708123725594.567118389261
163316.311348820605-1.41681026213672634.039507903347



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
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')