Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 09 Aug 2012 05:08:52 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Aug/09/t1344503364qqgssnv3fzcf93p.htm/, Retrieved Wed, 01 May 2024 21:04:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169164, Retrieved Wed, 01 May 2024 21:04:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan der Smissen Britt
Estimated Impact145
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks A-Stap 32] [2012-08-09 09:08:52] [b3616d670e39c9c081ac68ec1f5d1a32] [Current]
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Dataseries X:
95870
95523
95208
94541
101097
100781
95870
92581
92928
92928
93244
93910
93559
96190
97172
96190
99799
97488
92261
90964
90964
91599
89004
90964
89319
90964
93559
94541
96852
95870
89981
87670
86692
87670
86057
86692
84728
88021
89635
89981
96190
96190
88021
86057
86057
87039
82764
80799
78524
79186
82133
79821
86057
87039
80799
78524
77221
78524
74910
73613
68390
69688
70004
70355
76559
75893
68390
65097
63799
65444
59208
54964
47115
47777
47777
47115
52684
53004
46448
45151
42524
46133
39577
35653
28146
29764
27800
28462
33373
34355
31093
30742
30742
35017
27484
22573
14058
20929
19946
20293
28146
27164
23555
25204
25204
31093
24222
20293
14058
22258
21595
21911
28782
28146
25835
26186
27800
31409
25835
21275




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169164&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169164&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169164&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.791744723389592
beta0.0130855858701509
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.791744723389592 \tabularnewline
beta & 0.0130855858701509 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169164&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]0.791744723389592[/C][/ROW]
[ROW][C]beta[/C][C]0.0130855858701509[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169164&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169164&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
alpha0.791744723389592
beta0.0130855858701509
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
139355993943.9094551282-384.909455128218
149619096361.153964155-171.153964155004
159717297228.3233576022-56.3233576021594
169619096209.8257429033-19.825742903311
179979999905.8528519014-106.852851901407
189748897679.2446636165-191.244663616526
199226194469.2133241644-2208.21332416438
209096489345.08795428981618.91204571021
219096490725.7165486504238.283451349635
229159990627.7917940488971.208205951247
238900491572.135161019-2568.135161019
249096490243.5317401899720.46825981015
258931990525.2593374884-1206.25933748837
269096492305.8549450396-1341.85494503964
279355992227.04793753141331.95206246855
289454192286.69987486842254.30012513162
299685297760.0802310043-908.080231004336
309587094868.17832739741001.82167260257
318998192181.7161688398-2200.71616883985
328767087859.6329293707-189.632929370709
338669287501.1823094449-809.182309444936
348767086696.0652199675973.93478003249
358605786875.0063608492-818.006360849191
368669287604.5852637165-912.585263716537
378472886162.8390689955-1434.83906899553
388802187702.5900990598318.409900940154
398963589480.6952405422154.30475945778
408998188773.40584201031207.59415798975
419619092722.00638918783467.99361081218
429619093700.44958759282489.55041240717
438802191548.2215135908-3527.22151359079
448605786604.2382884311-547.238288431123
458605785839.461059993217.538940006954
468703986235.0559075219803.944092478137
478276485920.932704281-3156.93270428099
488079984769.4562301148-3970.45623011484
497852480756.6875920393-2232.68759203931
507918681980.3964183007-2794.39641830066
518213381178.0545709383954.945429061743
527982181250.5930163923-1429.59301639233
538605783481.20396152272575.79603847729
548703983439.4942328453599.505767155
558079980814.5483341907-15.5483341906802
567852479209.3989235128-685.398923512781
577722178430.9591026326-1209.95910263264
587852477740.1288296864783.871170313607
597491076506.6984941328-1596.6984941328
607361376358.7323655074-2745.73236550736
616839073627.8442650391-5237.84426503912
626968872274.4349611789-2586.43496117892
637000472338.8979323034-2334.89793230339
647035569197.37551420141157.62448579859
657655974224.59836355832334.40163644169
667589374116.51058349991776.48941650007
676839069188.0114986772-798.011498677224
686509766708.4089029989-1611.40890299894
696379964962.5270842153-1163.52708421534
706544464599.1297905226844.870209477376
715920862794.3059041706-3586.30590417059
725496460687.250000796-5723.250000796
734711554904.5479278657-7789.54792786574
744777751881.1892665561-4104.18926655606
754777750578.8161559605-2801.81615596052
764711547572.5664078057-457.566407805651
775268451326.92283433251357.07716566748
785300450079.61227621862924.38772378137
794644845286.45183298861161.54816701137
804515143971.8774827231179.12251727703
814252444340.5206081196-1816.52060811964
824613343683.47583352122449.52416647877
833957742048.0347321087-2471.03473210875
843565340212.2360033316-4559.2360033316
852814634766.1551187264-6620.1551187264
862976433293.6045534891-3529.60455348914
872780032580.7870049418-4780.78700494183
882846228338.8019682522123.198031747754
893337332779.8037110136593.196288986393
903435531095.10008493313259.89991506686
913109326044.93995602415048.06004397589
923074227695.89776163123046.1022383688
933074228822.94341392911919.05658607094
943501731954.74041467263062.25958532745
952748429728.8371126523-2244.83711265225
962257327588.7338490253-5015.73384902529
971405821298.7800300962-7240.7800300962
982092919918.80058624131010.19941375866
991994622527.1420665894-2581.14206658941
1002029321058.1429008484-765.142900848419
1012814624894.6292459933251.37075400702
1022716425898.36042552971265.63957447034
1032355519649.47165324563905.52834675437
1042520419974.90328062055229.09671937953
1052520422614.21242241622589.78757758381
1063109326540.68660596174552.31339403829
1072422224430.2836747389-208.283674738865
1082029323387.6456011695-3094.64560116946
1091405818237.3176020927-4179.31760209266
1102225821113.25494092061144.74505907943
1112159523195.3104182481-1600.31041824808
1122191123006.3367997741-1095.33679977405
1132878227539.69893126841242.30106873163
1142814626640.25084072341505.74915927664
1152583521234.7560217664600.24397823405
1162618622496.5804342973689.41956570305
1172780023461.97177242364338.02822757643
1183140929294.18868503212114.81131496792
1192583524350.10934479041484.89065520957
1202127524152.0975081664-2877.09750816645

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 93559 & 93943.9094551282 & -384.909455128218 \tabularnewline
14 & 96190 & 96361.153964155 & -171.153964155004 \tabularnewline
15 & 97172 & 97228.3233576022 & -56.3233576021594 \tabularnewline
16 & 96190 & 96209.8257429033 & -19.825742903311 \tabularnewline
17 & 99799 & 99905.8528519014 & -106.852851901407 \tabularnewline
18 & 97488 & 97679.2446636165 & -191.244663616526 \tabularnewline
19 & 92261 & 94469.2133241644 & -2208.21332416438 \tabularnewline
20 & 90964 & 89345.0879542898 & 1618.91204571021 \tabularnewline
21 & 90964 & 90725.7165486504 & 238.283451349635 \tabularnewline
22 & 91599 & 90627.7917940488 & 971.208205951247 \tabularnewline
23 & 89004 & 91572.135161019 & -2568.135161019 \tabularnewline
24 & 90964 & 90243.5317401899 & 720.46825981015 \tabularnewline
25 & 89319 & 90525.2593374884 & -1206.25933748837 \tabularnewline
26 & 90964 & 92305.8549450396 & -1341.85494503964 \tabularnewline
27 & 93559 & 92227.0479375314 & 1331.95206246855 \tabularnewline
28 & 94541 & 92286.6998748684 & 2254.30012513162 \tabularnewline
29 & 96852 & 97760.0802310043 & -908.080231004336 \tabularnewline
30 & 95870 & 94868.1783273974 & 1001.82167260257 \tabularnewline
31 & 89981 & 92181.7161688398 & -2200.71616883985 \tabularnewline
32 & 87670 & 87859.6329293707 & -189.632929370709 \tabularnewline
33 & 86692 & 87501.1823094449 & -809.182309444936 \tabularnewline
34 & 87670 & 86696.0652199675 & 973.93478003249 \tabularnewline
35 & 86057 & 86875.0063608492 & -818.006360849191 \tabularnewline
36 & 86692 & 87604.5852637165 & -912.585263716537 \tabularnewline
37 & 84728 & 86162.8390689955 & -1434.83906899553 \tabularnewline
38 & 88021 & 87702.5900990598 & 318.409900940154 \tabularnewline
39 & 89635 & 89480.6952405422 & 154.30475945778 \tabularnewline
40 & 89981 & 88773.4058420103 & 1207.59415798975 \tabularnewline
41 & 96190 & 92722.0063891878 & 3467.99361081218 \tabularnewline
42 & 96190 & 93700.4495875928 & 2489.55041240717 \tabularnewline
43 & 88021 & 91548.2215135908 & -3527.22151359079 \tabularnewline
44 & 86057 & 86604.2382884311 & -547.238288431123 \tabularnewline
45 & 86057 & 85839.461059993 & 217.538940006954 \tabularnewline
46 & 87039 & 86235.0559075219 & 803.944092478137 \tabularnewline
47 & 82764 & 85920.932704281 & -3156.93270428099 \tabularnewline
48 & 80799 & 84769.4562301148 & -3970.45623011484 \tabularnewline
49 & 78524 & 80756.6875920393 & -2232.68759203931 \tabularnewline
50 & 79186 & 81980.3964183007 & -2794.39641830066 \tabularnewline
51 & 82133 & 81178.0545709383 & 954.945429061743 \tabularnewline
52 & 79821 & 81250.5930163923 & -1429.59301639233 \tabularnewline
53 & 86057 & 83481.2039615227 & 2575.79603847729 \tabularnewline
54 & 87039 & 83439.494232845 & 3599.505767155 \tabularnewline
55 & 80799 & 80814.5483341907 & -15.5483341906802 \tabularnewline
56 & 78524 & 79209.3989235128 & -685.398923512781 \tabularnewline
57 & 77221 & 78430.9591026326 & -1209.95910263264 \tabularnewline
58 & 78524 & 77740.1288296864 & 783.871170313607 \tabularnewline
59 & 74910 & 76506.6984941328 & -1596.6984941328 \tabularnewline
60 & 73613 & 76358.7323655074 & -2745.73236550736 \tabularnewline
61 & 68390 & 73627.8442650391 & -5237.84426503912 \tabularnewline
62 & 69688 & 72274.4349611789 & -2586.43496117892 \tabularnewline
63 & 70004 & 72338.8979323034 & -2334.89793230339 \tabularnewline
64 & 70355 & 69197.3755142014 & 1157.62448579859 \tabularnewline
65 & 76559 & 74224.5983635583 & 2334.40163644169 \tabularnewline
66 & 75893 & 74116.5105834999 & 1776.48941650007 \tabularnewline
67 & 68390 & 69188.0114986772 & -798.011498677224 \tabularnewline
68 & 65097 & 66708.4089029989 & -1611.40890299894 \tabularnewline
69 & 63799 & 64962.5270842153 & -1163.52708421534 \tabularnewline
70 & 65444 & 64599.1297905226 & 844.870209477376 \tabularnewline
71 & 59208 & 62794.3059041706 & -3586.30590417059 \tabularnewline
72 & 54964 & 60687.250000796 & -5723.250000796 \tabularnewline
73 & 47115 & 54904.5479278657 & -7789.54792786574 \tabularnewline
74 & 47777 & 51881.1892665561 & -4104.18926655606 \tabularnewline
75 & 47777 & 50578.8161559605 & -2801.81615596052 \tabularnewline
76 & 47115 & 47572.5664078057 & -457.566407805651 \tabularnewline
77 & 52684 & 51326.9228343325 & 1357.07716566748 \tabularnewline
78 & 53004 & 50079.6122762186 & 2924.38772378137 \tabularnewline
79 & 46448 & 45286.4518329886 & 1161.54816701137 \tabularnewline
80 & 45151 & 43971.877482723 & 1179.12251727703 \tabularnewline
81 & 42524 & 44340.5206081196 & -1816.52060811964 \tabularnewline
82 & 46133 & 43683.4758335212 & 2449.52416647877 \tabularnewline
83 & 39577 & 42048.0347321087 & -2471.03473210875 \tabularnewline
84 & 35653 & 40212.2360033316 & -4559.2360033316 \tabularnewline
85 & 28146 & 34766.1551187264 & -6620.1551187264 \tabularnewline
86 & 29764 & 33293.6045534891 & -3529.60455348914 \tabularnewline
87 & 27800 & 32580.7870049418 & -4780.78700494183 \tabularnewline
88 & 28462 & 28338.8019682522 & 123.198031747754 \tabularnewline
89 & 33373 & 32779.8037110136 & 593.196288986393 \tabularnewline
90 & 34355 & 31095.1000849331 & 3259.89991506686 \tabularnewline
91 & 31093 & 26044.9399560241 & 5048.06004397589 \tabularnewline
92 & 30742 & 27695.8977616312 & 3046.1022383688 \tabularnewline
93 & 30742 & 28822.9434139291 & 1919.05658607094 \tabularnewline
94 & 35017 & 31954.7404146726 & 3062.25958532745 \tabularnewline
95 & 27484 & 29728.8371126523 & -2244.83711265225 \tabularnewline
96 & 22573 & 27588.7338490253 & -5015.73384902529 \tabularnewline
97 & 14058 & 21298.7800300962 & -7240.7800300962 \tabularnewline
98 & 20929 & 19918.8005862413 & 1010.19941375866 \tabularnewline
99 & 19946 & 22527.1420665894 & -2581.14206658941 \tabularnewline
100 & 20293 & 21058.1429008484 & -765.142900848419 \tabularnewline
101 & 28146 & 24894.629245993 & 3251.37075400702 \tabularnewline
102 & 27164 & 25898.3604255297 & 1265.63957447034 \tabularnewline
103 & 23555 & 19649.4716532456 & 3905.52834675437 \tabularnewline
104 & 25204 & 19974.9032806205 & 5229.09671937953 \tabularnewline
105 & 25204 & 22614.2124224162 & 2589.78757758381 \tabularnewline
106 & 31093 & 26540.6866059617 & 4552.31339403829 \tabularnewline
107 & 24222 & 24430.2836747389 & -208.283674738865 \tabularnewline
108 & 20293 & 23387.6456011695 & -3094.64560116946 \tabularnewline
109 & 14058 & 18237.3176020927 & -4179.31760209266 \tabularnewline
110 & 22258 & 21113.2549409206 & 1144.74505907943 \tabularnewline
111 & 21595 & 23195.3104182481 & -1600.31041824808 \tabularnewline
112 & 21911 & 23006.3367997741 & -1095.33679977405 \tabularnewline
113 & 28782 & 27539.6989312684 & 1242.30106873163 \tabularnewline
114 & 28146 & 26640.2508407234 & 1505.74915927664 \tabularnewline
115 & 25835 & 21234.756021766 & 4600.24397823405 \tabularnewline
116 & 26186 & 22496.580434297 & 3689.41956570305 \tabularnewline
117 & 27800 & 23461.9717724236 & 4338.02822757643 \tabularnewline
118 & 31409 & 29294.1886850321 & 2114.81131496792 \tabularnewline
119 & 25835 & 24350.1093447904 & 1484.89065520957 \tabularnewline
120 & 21275 & 24152.0975081664 & -2877.09750816645 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169164&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]93559[/C][C]93943.9094551282[/C][C]-384.909455128218[/C][/ROW]
[ROW][C]14[/C][C]96190[/C][C]96361.153964155[/C][C]-171.153964155004[/C][/ROW]
[ROW][C]15[/C][C]97172[/C][C]97228.3233576022[/C][C]-56.3233576021594[/C][/ROW]
[ROW][C]16[/C][C]96190[/C][C]96209.8257429033[/C][C]-19.825742903311[/C][/ROW]
[ROW][C]17[/C][C]99799[/C][C]99905.8528519014[/C][C]-106.852851901407[/C][/ROW]
[ROW][C]18[/C][C]97488[/C][C]97679.2446636165[/C][C]-191.244663616526[/C][/ROW]
[ROW][C]19[/C][C]92261[/C][C]94469.2133241644[/C][C]-2208.21332416438[/C][/ROW]
[ROW][C]20[/C][C]90964[/C][C]89345.0879542898[/C][C]1618.91204571021[/C][/ROW]
[ROW][C]21[/C][C]90964[/C][C]90725.7165486504[/C][C]238.283451349635[/C][/ROW]
[ROW][C]22[/C][C]91599[/C][C]90627.7917940488[/C][C]971.208205951247[/C][/ROW]
[ROW][C]23[/C][C]89004[/C][C]91572.135161019[/C][C]-2568.135161019[/C][/ROW]
[ROW][C]24[/C][C]90964[/C][C]90243.5317401899[/C][C]720.46825981015[/C][/ROW]
[ROW][C]25[/C][C]89319[/C][C]90525.2593374884[/C][C]-1206.25933748837[/C][/ROW]
[ROW][C]26[/C][C]90964[/C][C]92305.8549450396[/C][C]-1341.85494503964[/C][/ROW]
[ROW][C]27[/C][C]93559[/C][C]92227.0479375314[/C][C]1331.95206246855[/C][/ROW]
[ROW][C]28[/C][C]94541[/C][C]92286.6998748684[/C][C]2254.30012513162[/C][/ROW]
[ROW][C]29[/C][C]96852[/C][C]97760.0802310043[/C][C]-908.080231004336[/C][/ROW]
[ROW][C]30[/C][C]95870[/C][C]94868.1783273974[/C][C]1001.82167260257[/C][/ROW]
[ROW][C]31[/C][C]89981[/C][C]92181.7161688398[/C][C]-2200.71616883985[/C][/ROW]
[ROW][C]32[/C][C]87670[/C][C]87859.6329293707[/C][C]-189.632929370709[/C][/ROW]
[ROW][C]33[/C][C]86692[/C][C]87501.1823094449[/C][C]-809.182309444936[/C][/ROW]
[ROW][C]34[/C][C]87670[/C][C]86696.0652199675[/C][C]973.93478003249[/C][/ROW]
[ROW][C]35[/C][C]86057[/C][C]86875.0063608492[/C][C]-818.006360849191[/C][/ROW]
[ROW][C]36[/C][C]86692[/C][C]87604.5852637165[/C][C]-912.585263716537[/C][/ROW]
[ROW][C]37[/C][C]84728[/C][C]86162.8390689955[/C][C]-1434.83906899553[/C][/ROW]
[ROW][C]38[/C][C]88021[/C][C]87702.5900990598[/C][C]318.409900940154[/C][/ROW]
[ROW][C]39[/C][C]89635[/C][C]89480.6952405422[/C][C]154.30475945778[/C][/ROW]
[ROW][C]40[/C][C]89981[/C][C]88773.4058420103[/C][C]1207.59415798975[/C][/ROW]
[ROW][C]41[/C][C]96190[/C][C]92722.0063891878[/C][C]3467.99361081218[/C][/ROW]
[ROW][C]42[/C][C]96190[/C][C]93700.4495875928[/C][C]2489.55041240717[/C][/ROW]
[ROW][C]43[/C][C]88021[/C][C]91548.2215135908[/C][C]-3527.22151359079[/C][/ROW]
[ROW][C]44[/C][C]86057[/C][C]86604.2382884311[/C][C]-547.238288431123[/C][/ROW]
[ROW][C]45[/C][C]86057[/C][C]85839.461059993[/C][C]217.538940006954[/C][/ROW]
[ROW][C]46[/C][C]87039[/C][C]86235.0559075219[/C][C]803.944092478137[/C][/ROW]
[ROW][C]47[/C][C]82764[/C][C]85920.932704281[/C][C]-3156.93270428099[/C][/ROW]
[ROW][C]48[/C][C]80799[/C][C]84769.4562301148[/C][C]-3970.45623011484[/C][/ROW]
[ROW][C]49[/C][C]78524[/C][C]80756.6875920393[/C][C]-2232.68759203931[/C][/ROW]
[ROW][C]50[/C][C]79186[/C][C]81980.3964183007[/C][C]-2794.39641830066[/C][/ROW]
[ROW][C]51[/C][C]82133[/C][C]81178.0545709383[/C][C]954.945429061743[/C][/ROW]
[ROW][C]52[/C][C]79821[/C][C]81250.5930163923[/C][C]-1429.59301639233[/C][/ROW]
[ROW][C]53[/C][C]86057[/C][C]83481.2039615227[/C][C]2575.79603847729[/C][/ROW]
[ROW][C]54[/C][C]87039[/C][C]83439.494232845[/C][C]3599.505767155[/C][/ROW]
[ROW][C]55[/C][C]80799[/C][C]80814.5483341907[/C][C]-15.5483341906802[/C][/ROW]
[ROW][C]56[/C][C]78524[/C][C]79209.3989235128[/C][C]-685.398923512781[/C][/ROW]
[ROW][C]57[/C][C]77221[/C][C]78430.9591026326[/C][C]-1209.95910263264[/C][/ROW]
[ROW][C]58[/C][C]78524[/C][C]77740.1288296864[/C][C]783.871170313607[/C][/ROW]
[ROW][C]59[/C][C]74910[/C][C]76506.6984941328[/C][C]-1596.6984941328[/C][/ROW]
[ROW][C]60[/C][C]73613[/C][C]76358.7323655074[/C][C]-2745.73236550736[/C][/ROW]
[ROW][C]61[/C][C]68390[/C][C]73627.8442650391[/C][C]-5237.84426503912[/C][/ROW]
[ROW][C]62[/C][C]69688[/C][C]72274.4349611789[/C][C]-2586.43496117892[/C][/ROW]
[ROW][C]63[/C][C]70004[/C][C]72338.8979323034[/C][C]-2334.89793230339[/C][/ROW]
[ROW][C]64[/C][C]70355[/C][C]69197.3755142014[/C][C]1157.62448579859[/C][/ROW]
[ROW][C]65[/C][C]76559[/C][C]74224.5983635583[/C][C]2334.40163644169[/C][/ROW]
[ROW][C]66[/C][C]75893[/C][C]74116.5105834999[/C][C]1776.48941650007[/C][/ROW]
[ROW][C]67[/C][C]68390[/C][C]69188.0114986772[/C][C]-798.011498677224[/C][/ROW]
[ROW][C]68[/C][C]65097[/C][C]66708.4089029989[/C][C]-1611.40890299894[/C][/ROW]
[ROW][C]69[/C][C]63799[/C][C]64962.5270842153[/C][C]-1163.52708421534[/C][/ROW]
[ROW][C]70[/C][C]65444[/C][C]64599.1297905226[/C][C]844.870209477376[/C][/ROW]
[ROW][C]71[/C][C]59208[/C][C]62794.3059041706[/C][C]-3586.30590417059[/C][/ROW]
[ROW][C]72[/C][C]54964[/C][C]60687.250000796[/C][C]-5723.250000796[/C][/ROW]
[ROW][C]73[/C][C]47115[/C][C]54904.5479278657[/C][C]-7789.54792786574[/C][/ROW]
[ROW][C]74[/C][C]47777[/C][C]51881.1892665561[/C][C]-4104.18926655606[/C][/ROW]
[ROW][C]75[/C][C]47777[/C][C]50578.8161559605[/C][C]-2801.81615596052[/C][/ROW]
[ROW][C]76[/C][C]47115[/C][C]47572.5664078057[/C][C]-457.566407805651[/C][/ROW]
[ROW][C]77[/C][C]52684[/C][C]51326.9228343325[/C][C]1357.07716566748[/C][/ROW]
[ROW][C]78[/C][C]53004[/C][C]50079.6122762186[/C][C]2924.38772378137[/C][/ROW]
[ROW][C]79[/C][C]46448[/C][C]45286.4518329886[/C][C]1161.54816701137[/C][/ROW]
[ROW][C]80[/C][C]45151[/C][C]43971.877482723[/C][C]1179.12251727703[/C][/ROW]
[ROW][C]81[/C][C]42524[/C][C]44340.5206081196[/C][C]-1816.52060811964[/C][/ROW]
[ROW][C]82[/C][C]46133[/C][C]43683.4758335212[/C][C]2449.52416647877[/C][/ROW]
[ROW][C]83[/C][C]39577[/C][C]42048.0347321087[/C][C]-2471.03473210875[/C][/ROW]
[ROW][C]84[/C][C]35653[/C][C]40212.2360033316[/C][C]-4559.2360033316[/C][/ROW]
[ROW][C]85[/C][C]28146[/C][C]34766.1551187264[/C][C]-6620.1551187264[/C][/ROW]
[ROW][C]86[/C][C]29764[/C][C]33293.6045534891[/C][C]-3529.60455348914[/C][/ROW]
[ROW][C]87[/C][C]27800[/C][C]32580.7870049418[/C][C]-4780.78700494183[/C][/ROW]
[ROW][C]88[/C][C]28462[/C][C]28338.8019682522[/C][C]123.198031747754[/C][/ROW]
[ROW][C]89[/C][C]33373[/C][C]32779.8037110136[/C][C]593.196288986393[/C][/ROW]
[ROW][C]90[/C][C]34355[/C][C]31095.1000849331[/C][C]3259.89991506686[/C][/ROW]
[ROW][C]91[/C][C]31093[/C][C]26044.9399560241[/C][C]5048.06004397589[/C][/ROW]
[ROW][C]92[/C][C]30742[/C][C]27695.8977616312[/C][C]3046.1022383688[/C][/ROW]
[ROW][C]93[/C][C]30742[/C][C]28822.9434139291[/C][C]1919.05658607094[/C][/ROW]
[ROW][C]94[/C][C]35017[/C][C]31954.7404146726[/C][C]3062.25958532745[/C][/ROW]
[ROW][C]95[/C][C]27484[/C][C]29728.8371126523[/C][C]-2244.83711265225[/C][/ROW]
[ROW][C]96[/C][C]22573[/C][C]27588.7338490253[/C][C]-5015.73384902529[/C][/ROW]
[ROW][C]97[/C][C]14058[/C][C]21298.7800300962[/C][C]-7240.7800300962[/C][/ROW]
[ROW][C]98[/C][C]20929[/C][C]19918.8005862413[/C][C]1010.19941375866[/C][/ROW]
[ROW][C]99[/C][C]19946[/C][C]22527.1420665894[/C][C]-2581.14206658941[/C][/ROW]
[ROW][C]100[/C][C]20293[/C][C]21058.1429008484[/C][C]-765.142900848419[/C][/ROW]
[ROW][C]101[/C][C]28146[/C][C]24894.629245993[/C][C]3251.37075400702[/C][/ROW]
[ROW][C]102[/C][C]27164[/C][C]25898.3604255297[/C][C]1265.63957447034[/C][/ROW]
[ROW][C]103[/C][C]23555[/C][C]19649.4716532456[/C][C]3905.52834675437[/C][/ROW]
[ROW][C]104[/C][C]25204[/C][C]19974.9032806205[/C][C]5229.09671937953[/C][/ROW]
[ROW][C]105[/C][C]25204[/C][C]22614.2124224162[/C][C]2589.78757758381[/C][/ROW]
[ROW][C]106[/C][C]31093[/C][C]26540.6866059617[/C][C]4552.31339403829[/C][/ROW]
[ROW][C]107[/C][C]24222[/C][C]24430.2836747389[/C][C]-208.283674738865[/C][/ROW]
[ROW][C]108[/C][C]20293[/C][C]23387.6456011695[/C][C]-3094.64560116946[/C][/ROW]
[ROW][C]109[/C][C]14058[/C][C]18237.3176020927[/C][C]-4179.31760209266[/C][/ROW]
[ROW][C]110[/C][C]22258[/C][C]21113.2549409206[/C][C]1144.74505907943[/C][/ROW]
[ROW][C]111[/C][C]21595[/C][C]23195.3104182481[/C][C]-1600.31041824808[/C][/ROW]
[ROW][C]112[/C][C]21911[/C][C]23006.3367997741[/C][C]-1095.33679977405[/C][/ROW]
[ROW][C]113[/C][C]28782[/C][C]27539.6989312684[/C][C]1242.30106873163[/C][/ROW]
[ROW][C]114[/C][C]28146[/C][C]26640.2508407234[/C][C]1505.74915927664[/C][/ROW]
[ROW][C]115[/C][C]25835[/C][C]21234.756021766[/C][C]4600.24397823405[/C][/ROW]
[ROW][C]116[/C][C]26186[/C][C]22496.580434297[/C][C]3689.41956570305[/C][/ROW]
[ROW][C]117[/C][C]27800[/C][C]23461.9717724236[/C][C]4338.02822757643[/C][/ROW]
[ROW][C]118[/C][C]31409[/C][C]29294.1886850321[/C][C]2114.81131496792[/C][/ROW]
[ROW][C]119[/C][C]25835[/C][C]24350.1093447904[/C][C]1484.89065520957[/C][/ROW]
[ROW][C]120[/C][C]21275[/C][C]24152.0975081664[/C][C]-2877.09750816645[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169164&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169164&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
139355993943.9094551282-384.909455128218
149619096361.153964155-171.153964155004
159717297228.3233576022-56.3233576021594
169619096209.8257429033-19.825742903311
179979999905.8528519014-106.852851901407
189748897679.2446636165-191.244663616526
199226194469.2133241644-2208.21332416438
209096489345.08795428981618.91204571021
219096490725.7165486504238.283451349635
229159990627.7917940488971.208205951247
238900491572.135161019-2568.135161019
249096490243.5317401899720.46825981015
258931990525.2593374884-1206.25933748837
269096492305.8549450396-1341.85494503964
279355992227.04793753141331.95206246855
289454192286.69987486842254.30012513162
299685297760.0802310043-908.080231004336
309587094868.17832739741001.82167260257
318998192181.7161688398-2200.71616883985
328767087859.6329293707-189.632929370709
338669287501.1823094449-809.182309444936
348767086696.0652199675973.93478003249
358605786875.0063608492-818.006360849191
368669287604.5852637165-912.585263716537
378472886162.8390689955-1434.83906899553
388802187702.5900990598318.409900940154
398963589480.6952405422154.30475945778
408998188773.40584201031207.59415798975
419619092722.00638918783467.99361081218
429619093700.44958759282489.55041240717
438802191548.2215135908-3527.22151359079
448605786604.2382884311-547.238288431123
458605785839.461059993217.538940006954
468703986235.0559075219803.944092478137
478276485920.932704281-3156.93270428099
488079984769.4562301148-3970.45623011484
497852480756.6875920393-2232.68759203931
507918681980.3964183007-2794.39641830066
518213381178.0545709383954.945429061743
527982181250.5930163923-1429.59301639233
538605783481.20396152272575.79603847729
548703983439.4942328453599.505767155
558079980814.5483341907-15.5483341906802
567852479209.3989235128-685.398923512781
577722178430.9591026326-1209.95910263264
587852477740.1288296864783.871170313607
597491076506.6984941328-1596.6984941328
607361376358.7323655074-2745.73236550736
616839073627.8442650391-5237.84426503912
626968872274.4349611789-2586.43496117892
637000472338.8979323034-2334.89793230339
647035569197.37551420141157.62448579859
657655974224.59836355832334.40163644169
667589374116.51058349991776.48941650007
676839069188.0114986772-798.011498677224
686509766708.4089029989-1611.40890299894
696379964962.5270842153-1163.52708421534
706544464599.1297905226844.870209477376
715920862794.3059041706-3586.30590417059
725496460687.250000796-5723.250000796
734711554904.5479278657-7789.54792786574
744777751881.1892665561-4104.18926655606
754777750578.8161559605-2801.81615596052
764711547572.5664078057-457.566407805651
775268451326.92283433251357.07716566748
785300450079.61227621862924.38772378137
794644845286.45183298861161.54816701137
804515143971.8774827231179.12251727703
814252444340.5206081196-1816.52060811964
824613343683.47583352122449.52416647877
833957742048.0347321087-2471.03473210875
843565340212.2360033316-4559.2360033316
852814634766.1551187264-6620.1551187264
862976433293.6045534891-3529.60455348914
872780032580.7870049418-4780.78700494183
882846228338.8019682522123.198031747754
893337332779.8037110136593.196288986393
903435531095.10008493313259.89991506686
913109326044.93995602415048.06004397589
923074227695.89776163123046.1022383688
933074228822.94341392911919.05658607094
943501731954.74041467263062.25958532745
952748429728.8371126523-2244.83711265225
962257327588.7338490253-5015.73384902529
971405821298.7800300962-7240.7800300962
982092919918.80058624131010.19941375866
991994622527.1420665894-2581.14206658941
1002029321058.1429008484-765.142900848419
1012814624894.6292459933251.37075400702
1022716425898.36042552971265.63957447034
1032355519649.47165324563905.52834675437
1042520419974.90328062055229.09671937953
1052520422614.21242241622589.78757758381
1063109326540.68660596174552.31339403829
1072422224430.2836747389-208.283674738865
1082029323387.6456011695-3094.64560116946
1091405818237.3176020927-4179.31760209266
1102225821113.25494092061144.74505907943
1112159523195.3104182481-1600.31041824808
1122191123006.3367997741-1095.33679977405
1132878227539.69893126841242.30106873163
1142814626640.25084072341505.74915927664
1152583521234.7560217664600.24397823405
1162618622496.5804342973689.41956570305
1172780023461.97177242364338.02822757643
1183140929294.18868503212114.81131496792
1192583524350.10934479041484.89065520957
1202127524152.0975081664-2877.09750816645







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12119055.541787781313743.67450431724367.4090712456
12226499.91390334319690.41350541833309.4143012681
12327242.809141909519180.883558120635304.7347256983
12428581.474108373119410.97593688637751.9722798602
12534635.674802350624453.065569844244818.2840348569
12632961.421070638521836.530794637544086.3113466394
12727146.517165272415132.481512955439160.5528175895
12824667.093114339811805.786994172237528.3992345074
12922898.91255462559224.2034766927636573.6216325582
13024841.008357783610380.837897794839301.1788177725
13118076.93013617992854.7149050559233299.1453673038
13215765.0489005832-199.33790651853131729.4357076849

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 19055.5417877813 & 13743.674504317 & 24367.4090712456 \tabularnewline
122 & 26499.913903343 & 19690.413505418 & 33309.4143012681 \tabularnewline
123 & 27242.8091419095 & 19180.8835581206 & 35304.7347256983 \tabularnewline
124 & 28581.4741083731 & 19410.975936886 & 37751.9722798602 \tabularnewline
125 & 34635.6748023506 & 24453.0655698442 & 44818.2840348569 \tabularnewline
126 & 32961.4210706385 & 21836.5307946375 & 44086.3113466394 \tabularnewline
127 & 27146.5171652724 & 15132.4815129554 & 39160.5528175895 \tabularnewline
128 & 24667.0931143398 & 11805.7869941722 & 37528.3992345074 \tabularnewline
129 & 22898.9125546255 & 9224.20347669276 & 36573.6216325582 \tabularnewline
130 & 24841.0083577836 & 10380.8378977948 & 39301.1788177725 \tabularnewline
131 & 18076.9301361799 & 2854.71490505592 & 33299.1453673038 \tabularnewline
132 & 15765.0489005832 & -199.337906518531 & 31729.4357076849 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169164&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]121[/C][C]19055.5417877813[/C][C]13743.674504317[/C][C]24367.4090712456[/C][/ROW]
[ROW][C]122[/C][C]26499.913903343[/C][C]19690.413505418[/C][C]33309.4143012681[/C][/ROW]
[ROW][C]123[/C][C]27242.8091419095[/C][C]19180.8835581206[/C][C]35304.7347256983[/C][/ROW]
[ROW][C]124[/C][C]28581.4741083731[/C][C]19410.975936886[/C][C]37751.9722798602[/C][/ROW]
[ROW][C]125[/C][C]34635.6748023506[/C][C]24453.0655698442[/C][C]44818.2840348569[/C][/ROW]
[ROW][C]126[/C][C]32961.4210706385[/C][C]21836.5307946375[/C][C]44086.3113466394[/C][/ROW]
[ROW][C]127[/C][C]27146.5171652724[/C][C]15132.4815129554[/C][C]39160.5528175895[/C][/ROW]
[ROW][C]128[/C][C]24667.0931143398[/C][C]11805.7869941722[/C][C]37528.3992345074[/C][/ROW]
[ROW][C]129[/C][C]22898.9125546255[/C][C]9224.20347669276[/C][C]36573.6216325582[/C][/ROW]
[ROW][C]130[/C][C]24841.0083577836[/C][C]10380.8378977948[/C][C]39301.1788177725[/C][/ROW]
[ROW][C]131[/C][C]18076.9301361799[/C][C]2854.71490505592[/C][C]33299.1453673038[/C][/ROW]
[ROW][C]132[/C][C]15765.0489005832[/C][C]-199.337906518531[/C][C]31729.4357076849[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169164&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169164&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
12119055.541787781313743.67450431724367.4090712456
12226499.91390334319690.41350541833309.4143012681
12327242.809141909519180.883558120635304.7347256983
12428581.474108373119410.97593688637751.9722798602
12534635.674802350624453.065569844244818.2840348569
12632961.421070638521836.530794637544086.3113466394
12727146.517165272415132.481512955439160.5528175895
12824667.093114339811805.786994172237528.3992345074
12922898.91255462559224.2034766927636573.6216325582
13024841.008357783610380.837897794839301.1788177725
13118076.93013617992854.7149050559233299.1453673038
13215765.0489005832-199.33790651853131729.4357076849



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')