Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 15 Aug 2011 08:06:55 -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/2011/Aug/15/t13134100937c3eqm849fxc9do.htm/, Retrieved Tue, 14 May 2024 07:08:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123757, Retrieved Tue, 14 May 2024 07:08:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsThiebaut Thomas
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks A - sta...] [2011-08-15 12:06:55] [5815de052410d7754c978b0de903e641] [Current]
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Dataseries X:
5740
5639
5538
5336
7380
7279
5740
4718
4819
4819
4920
5133
4516
3898
3392
3392
5336
5538
3999
2258
3179
3179
3898
4313
4212
3179
3696
3493
5234
4819
3179
1954
3078
3392
3696
4100
3280
2572
2876
2977
5639
5639
4100
3898
4516
4212
5032
6054
6257
4819
4414
3999
6773
6976
6459
6976
6874
6054
6976
7998
8413
7178
6358
6976
9638
10458
10256
10660
10559
9537
11278
11693
12300
10458
9739
10559
12513
14254
13839
13839
14042
13333
15176
15176
14862
13120
13434
13637
14973
16714
15479
16097
15580
15277
17636
17119
16400
15378
16400
16917
17534
18354
17534
18040
17423
17322
19883
20096
19276
17838
19063
19579
20197
21118
20197
20916
20602
19478
21837
21837




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123757&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123757&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123757&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 time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.653576516993629
beta0.0529349454904236
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.653576516993629 \tabularnewline
beta & 0.0529349454904236 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123757&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]0.653576516993629[/C][/ROW]
[ROW][C]beta[/C][C]0.0529349454904236[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123757&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123757&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
alpha0.653576516993629
beta0.0529349454904236
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1345165451.23530982906-935.235309829059
1438984212.20700582568-314.207005825676
1533923475.9892528732-83.9892528732007
1633923359.1639710643132.8360289356897
1753365238.0789793547797.9210206452253
1855385386.75312037245151.246879627548
1939993903.6791511722795.3208488277282
2022582881.97606051511-623.976060515112
2131792529.98634479155649.013655208454
2231792939.90509661066239.094903389342
2338983186.93255365647711.067446343529
2443133870.57267507416442.42732492584
2542123227.33012281279984.669877187208
2631793540.63582460749-361.635824607494
2736962933.92192127724762.078078722757
2834933520.55819923172-27.5581992317202
2952345490.47926539415-256.479265394153
3048195521.66916937277-702.669169372769
3131793527.24880501166-348.248805011661
3219542017.23864077446-63.2386407744557
3330782542.90809584263535.091904157367
3433922802.60425947207589.395740527934
3536963520.44133572436175.558664275644
3641003820.85407464962279.145925350385
3732803312.92296352864-32.922963528641
3825722513.7390488723358.2609511276678
3928762604.24496493967271.755035060335
4029772613.40960438869363.590395611312
4156394789.74569453835849.254305461647
4256395457.3746602733181.625339726696
4341004262.61015476468-162.610154764679
4438983078.00801059795819.991989402054
4545164524.11392289623-8.11392289623291
4642124564.70423283768-352.704232837679
4750324607.95873519795424.041264802048
4860545199.77041499697854.229585003029
4962575072.600167044041184.39983295596
5048195255.74153661338-436.741536613385
5144145234.68263699745-820.682636997451
5239994661.87230828697-662.872308286969
5367736400.27200947649372.727990523515
5469766573.37596233646402.624037663538
5564595459.64940526931999.35059473069
5669765470.924025385191505.07597461481
5768747197.6613318934-323.6613318934
5860547021.47800819968-967.478008199678
5969767019.57925544763-43.5792554476284
6079987526.17976302399471.82023697601
6184137321.611524568981091.38847543102
6271786937.30054991499240.699450085006
6363587304.37154323632-946.371543236322
6469766778.11122255686197.88877744314
6596389541.6483238971396.351676102875
66104589638.72200417705819.277995822953
67102569112.69187830911143.30812169091
68106609506.890505096961153.10949490304
691055910471.537841107387.4621588927293
70953710456.7102185331-919.710218533091
711127810923.4324766312354.567523368818
721169311999.9144368034-306.914436803441
731230011605.1901575067694.809842493338
741045810757.4392681345-299.439268134498
75973910432.0250338714-693.02503387141
761055910548.275749410610.7242505894283
771251313228.367398047-715.367398047047
781425413091.33185477771162.66814522234
791383912959.8380414103879.16195858974
801383913233.5066200139605.493379986057
811404213500.848021262541.151978737953
821333313479.0979316543-146.0979316543
831517614965.104124219210.895875780992
841517615785.7915482684-609.791548268397
851486215596.9148279934-734.914827993434
861312013477.6141033543-357.614103354301
871343412983.1340091485450.865990851487
881363714135.6787532482-498.67875324823
891497316258.5559667787-1285.55596677869
901671416406.9819474471307.018052552929
911547915595.9669365577-116.966936557652
921609715067.24554110031029.75445889975
931558015547.724526546732.2754734533155
941527714895.8394542142381.16054578582
951763616808.8962842472827.103715752834
961711917728.1120918596-609.11209185957
971640017476.4521188177-1076.4521188177
981537815232.9386068457145.061393154285
991640015332.76512036231067.23487963772
1001691716566.2272532533350.772746746698
1011753419008.0995345231-1474.09953452308
1021835419614.8861167869-1260.88611678694
1031753417607.8857754007-73.8857754007186
1041804017481.7012877423558.298712257656
1051742317269.3156046553153.684395344739
1061732216782.6608041877539.339195812332
1071988318924.0754538226958.924546177415
1082009619406.9587707084689.041229291597
1091927619861.8074152944-585.807415294428
1101783818399.0672295518-561.067229551838
1111906318369.355754578693.644245422027
1121957919110.031931515468.968068485017
1132019721000.6479127836-803.647912783552
1142111822146.3563303696-1028.35633036964
1152019720737.4498959515-540.449895951457
1162091620544.104977736371.895022264023
1172060220082.0446740226519.955325977422
1181947819993.370075713-515.370075713043
1192183721579.3101595299257.689840470081
1202183721474.632805768362.36719423196

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4516 & 5451.23530982906 & -935.235309829059 \tabularnewline
14 & 3898 & 4212.20700582568 & -314.207005825676 \tabularnewline
15 & 3392 & 3475.9892528732 & -83.9892528732007 \tabularnewline
16 & 3392 & 3359.16397106431 & 32.8360289356897 \tabularnewline
17 & 5336 & 5238.07897935477 & 97.9210206452253 \tabularnewline
18 & 5538 & 5386.75312037245 & 151.246879627548 \tabularnewline
19 & 3999 & 3903.67915117227 & 95.3208488277282 \tabularnewline
20 & 2258 & 2881.97606051511 & -623.976060515112 \tabularnewline
21 & 3179 & 2529.98634479155 & 649.013655208454 \tabularnewline
22 & 3179 & 2939.90509661066 & 239.094903389342 \tabularnewline
23 & 3898 & 3186.93255365647 & 711.067446343529 \tabularnewline
24 & 4313 & 3870.57267507416 & 442.42732492584 \tabularnewline
25 & 4212 & 3227.33012281279 & 984.669877187208 \tabularnewline
26 & 3179 & 3540.63582460749 & -361.635824607494 \tabularnewline
27 & 3696 & 2933.92192127724 & 762.078078722757 \tabularnewline
28 & 3493 & 3520.55819923172 & -27.5581992317202 \tabularnewline
29 & 5234 & 5490.47926539415 & -256.479265394153 \tabularnewline
30 & 4819 & 5521.66916937277 & -702.669169372769 \tabularnewline
31 & 3179 & 3527.24880501166 & -348.248805011661 \tabularnewline
32 & 1954 & 2017.23864077446 & -63.2386407744557 \tabularnewline
33 & 3078 & 2542.90809584263 & 535.091904157367 \tabularnewline
34 & 3392 & 2802.60425947207 & 589.395740527934 \tabularnewline
35 & 3696 & 3520.44133572436 & 175.558664275644 \tabularnewline
36 & 4100 & 3820.85407464962 & 279.145925350385 \tabularnewline
37 & 3280 & 3312.92296352864 & -32.922963528641 \tabularnewline
38 & 2572 & 2513.73904887233 & 58.2609511276678 \tabularnewline
39 & 2876 & 2604.24496493967 & 271.755035060335 \tabularnewline
40 & 2977 & 2613.40960438869 & 363.590395611312 \tabularnewline
41 & 5639 & 4789.74569453835 & 849.254305461647 \tabularnewline
42 & 5639 & 5457.3746602733 & 181.625339726696 \tabularnewline
43 & 4100 & 4262.61015476468 & -162.610154764679 \tabularnewline
44 & 3898 & 3078.00801059795 & 819.991989402054 \tabularnewline
45 & 4516 & 4524.11392289623 & -8.11392289623291 \tabularnewline
46 & 4212 & 4564.70423283768 & -352.704232837679 \tabularnewline
47 & 5032 & 4607.95873519795 & 424.041264802048 \tabularnewline
48 & 6054 & 5199.77041499697 & 854.229585003029 \tabularnewline
49 & 6257 & 5072.60016704404 & 1184.39983295596 \tabularnewline
50 & 4819 & 5255.74153661338 & -436.741536613385 \tabularnewline
51 & 4414 & 5234.68263699745 & -820.682636997451 \tabularnewline
52 & 3999 & 4661.87230828697 & -662.872308286969 \tabularnewline
53 & 6773 & 6400.27200947649 & 372.727990523515 \tabularnewline
54 & 6976 & 6573.37596233646 & 402.624037663538 \tabularnewline
55 & 6459 & 5459.64940526931 & 999.35059473069 \tabularnewline
56 & 6976 & 5470.92402538519 & 1505.07597461481 \tabularnewline
57 & 6874 & 7197.6613318934 & -323.6613318934 \tabularnewline
58 & 6054 & 7021.47800819968 & -967.478008199678 \tabularnewline
59 & 6976 & 7019.57925544763 & -43.5792554476284 \tabularnewline
60 & 7998 & 7526.17976302399 & 471.82023697601 \tabularnewline
61 & 8413 & 7321.61152456898 & 1091.38847543102 \tabularnewline
62 & 7178 & 6937.30054991499 & 240.699450085006 \tabularnewline
63 & 6358 & 7304.37154323632 & -946.371543236322 \tabularnewline
64 & 6976 & 6778.11122255686 & 197.88877744314 \tabularnewline
65 & 9638 & 9541.64832389713 & 96.351676102875 \tabularnewline
66 & 10458 & 9638.72200417705 & 819.277995822953 \tabularnewline
67 & 10256 & 9112.6918783091 & 1143.30812169091 \tabularnewline
68 & 10660 & 9506.89050509696 & 1153.10949490304 \tabularnewline
69 & 10559 & 10471.5378411073 & 87.4621588927293 \tabularnewline
70 & 9537 & 10456.7102185331 & -919.710218533091 \tabularnewline
71 & 11278 & 10923.4324766312 & 354.567523368818 \tabularnewline
72 & 11693 & 11999.9144368034 & -306.914436803441 \tabularnewline
73 & 12300 & 11605.1901575067 & 694.809842493338 \tabularnewline
74 & 10458 & 10757.4392681345 & -299.439268134498 \tabularnewline
75 & 9739 & 10432.0250338714 & -693.02503387141 \tabularnewline
76 & 10559 & 10548.2757494106 & 10.7242505894283 \tabularnewline
77 & 12513 & 13228.367398047 & -715.367398047047 \tabularnewline
78 & 14254 & 13091.3318547777 & 1162.66814522234 \tabularnewline
79 & 13839 & 12959.8380414103 & 879.16195858974 \tabularnewline
80 & 13839 & 13233.5066200139 & 605.493379986057 \tabularnewline
81 & 14042 & 13500.848021262 & 541.151978737953 \tabularnewline
82 & 13333 & 13479.0979316543 & -146.0979316543 \tabularnewline
83 & 15176 & 14965.104124219 & 210.895875780992 \tabularnewline
84 & 15176 & 15785.7915482684 & -609.791548268397 \tabularnewline
85 & 14862 & 15596.9148279934 & -734.914827993434 \tabularnewline
86 & 13120 & 13477.6141033543 & -357.614103354301 \tabularnewline
87 & 13434 & 12983.1340091485 & 450.865990851487 \tabularnewline
88 & 13637 & 14135.6787532482 & -498.67875324823 \tabularnewline
89 & 14973 & 16258.5559667787 & -1285.55596677869 \tabularnewline
90 & 16714 & 16406.9819474471 & 307.018052552929 \tabularnewline
91 & 15479 & 15595.9669365577 & -116.966936557652 \tabularnewline
92 & 16097 & 15067.2455411003 & 1029.75445889975 \tabularnewline
93 & 15580 & 15547.7245265467 & 32.2754734533155 \tabularnewline
94 & 15277 & 14895.8394542142 & 381.16054578582 \tabularnewline
95 & 17636 & 16808.8962842472 & 827.103715752834 \tabularnewline
96 & 17119 & 17728.1120918596 & -609.11209185957 \tabularnewline
97 & 16400 & 17476.4521188177 & -1076.4521188177 \tabularnewline
98 & 15378 & 15232.9386068457 & 145.061393154285 \tabularnewline
99 & 16400 & 15332.7651203623 & 1067.23487963772 \tabularnewline
100 & 16917 & 16566.2272532533 & 350.772746746698 \tabularnewline
101 & 17534 & 19008.0995345231 & -1474.09953452308 \tabularnewline
102 & 18354 & 19614.8861167869 & -1260.88611678694 \tabularnewline
103 & 17534 & 17607.8857754007 & -73.8857754007186 \tabularnewline
104 & 18040 & 17481.7012877423 & 558.298712257656 \tabularnewline
105 & 17423 & 17269.3156046553 & 153.684395344739 \tabularnewline
106 & 17322 & 16782.6608041877 & 539.339195812332 \tabularnewline
107 & 19883 & 18924.0754538226 & 958.924546177415 \tabularnewline
108 & 20096 & 19406.9587707084 & 689.041229291597 \tabularnewline
109 & 19276 & 19861.8074152944 & -585.807415294428 \tabularnewline
110 & 17838 & 18399.0672295518 & -561.067229551838 \tabularnewline
111 & 19063 & 18369.355754578 & 693.644245422027 \tabularnewline
112 & 19579 & 19110.031931515 & 468.968068485017 \tabularnewline
113 & 20197 & 21000.6479127836 & -803.647912783552 \tabularnewline
114 & 21118 & 22146.3563303696 & -1028.35633036964 \tabularnewline
115 & 20197 & 20737.4498959515 & -540.449895951457 \tabularnewline
116 & 20916 & 20544.104977736 & 371.895022264023 \tabularnewline
117 & 20602 & 20082.0446740226 & 519.955325977422 \tabularnewline
118 & 19478 & 19993.370075713 & -515.370075713043 \tabularnewline
119 & 21837 & 21579.3101595299 & 257.689840470081 \tabularnewline
120 & 21837 & 21474.632805768 & 362.36719423196 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123757&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]4516[/C][C]5451.23530982906[/C][C]-935.235309829059[/C][/ROW]
[ROW][C]14[/C][C]3898[/C][C]4212.20700582568[/C][C]-314.207005825676[/C][/ROW]
[ROW][C]15[/C][C]3392[/C][C]3475.9892528732[/C][C]-83.9892528732007[/C][/ROW]
[ROW][C]16[/C][C]3392[/C][C]3359.16397106431[/C][C]32.8360289356897[/C][/ROW]
[ROW][C]17[/C][C]5336[/C][C]5238.07897935477[/C][C]97.9210206452253[/C][/ROW]
[ROW][C]18[/C][C]5538[/C][C]5386.75312037245[/C][C]151.246879627548[/C][/ROW]
[ROW][C]19[/C][C]3999[/C][C]3903.67915117227[/C][C]95.3208488277282[/C][/ROW]
[ROW][C]20[/C][C]2258[/C][C]2881.97606051511[/C][C]-623.976060515112[/C][/ROW]
[ROW][C]21[/C][C]3179[/C][C]2529.98634479155[/C][C]649.013655208454[/C][/ROW]
[ROW][C]22[/C][C]3179[/C][C]2939.90509661066[/C][C]239.094903389342[/C][/ROW]
[ROW][C]23[/C][C]3898[/C][C]3186.93255365647[/C][C]711.067446343529[/C][/ROW]
[ROW][C]24[/C][C]4313[/C][C]3870.57267507416[/C][C]442.42732492584[/C][/ROW]
[ROW][C]25[/C][C]4212[/C][C]3227.33012281279[/C][C]984.669877187208[/C][/ROW]
[ROW][C]26[/C][C]3179[/C][C]3540.63582460749[/C][C]-361.635824607494[/C][/ROW]
[ROW][C]27[/C][C]3696[/C][C]2933.92192127724[/C][C]762.078078722757[/C][/ROW]
[ROW][C]28[/C][C]3493[/C][C]3520.55819923172[/C][C]-27.5581992317202[/C][/ROW]
[ROW][C]29[/C][C]5234[/C][C]5490.47926539415[/C][C]-256.479265394153[/C][/ROW]
[ROW][C]30[/C][C]4819[/C][C]5521.66916937277[/C][C]-702.669169372769[/C][/ROW]
[ROW][C]31[/C][C]3179[/C][C]3527.24880501166[/C][C]-348.248805011661[/C][/ROW]
[ROW][C]32[/C][C]1954[/C][C]2017.23864077446[/C][C]-63.2386407744557[/C][/ROW]
[ROW][C]33[/C][C]3078[/C][C]2542.90809584263[/C][C]535.091904157367[/C][/ROW]
[ROW][C]34[/C][C]3392[/C][C]2802.60425947207[/C][C]589.395740527934[/C][/ROW]
[ROW][C]35[/C][C]3696[/C][C]3520.44133572436[/C][C]175.558664275644[/C][/ROW]
[ROW][C]36[/C][C]4100[/C][C]3820.85407464962[/C][C]279.145925350385[/C][/ROW]
[ROW][C]37[/C][C]3280[/C][C]3312.92296352864[/C][C]-32.922963528641[/C][/ROW]
[ROW][C]38[/C][C]2572[/C][C]2513.73904887233[/C][C]58.2609511276678[/C][/ROW]
[ROW][C]39[/C][C]2876[/C][C]2604.24496493967[/C][C]271.755035060335[/C][/ROW]
[ROW][C]40[/C][C]2977[/C][C]2613.40960438869[/C][C]363.590395611312[/C][/ROW]
[ROW][C]41[/C][C]5639[/C][C]4789.74569453835[/C][C]849.254305461647[/C][/ROW]
[ROW][C]42[/C][C]5639[/C][C]5457.3746602733[/C][C]181.625339726696[/C][/ROW]
[ROW][C]43[/C][C]4100[/C][C]4262.61015476468[/C][C]-162.610154764679[/C][/ROW]
[ROW][C]44[/C][C]3898[/C][C]3078.00801059795[/C][C]819.991989402054[/C][/ROW]
[ROW][C]45[/C][C]4516[/C][C]4524.11392289623[/C][C]-8.11392289623291[/C][/ROW]
[ROW][C]46[/C][C]4212[/C][C]4564.70423283768[/C][C]-352.704232837679[/C][/ROW]
[ROW][C]47[/C][C]5032[/C][C]4607.95873519795[/C][C]424.041264802048[/C][/ROW]
[ROW][C]48[/C][C]6054[/C][C]5199.77041499697[/C][C]854.229585003029[/C][/ROW]
[ROW][C]49[/C][C]6257[/C][C]5072.60016704404[/C][C]1184.39983295596[/C][/ROW]
[ROW][C]50[/C][C]4819[/C][C]5255.74153661338[/C][C]-436.741536613385[/C][/ROW]
[ROW][C]51[/C][C]4414[/C][C]5234.68263699745[/C][C]-820.682636997451[/C][/ROW]
[ROW][C]52[/C][C]3999[/C][C]4661.87230828697[/C][C]-662.872308286969[/C][/ROW]
[ROW][C]53[/C][C]6773[/C][C]6400.27200947649[/C][C]372.727990523515[/C][/ROW]
[ROW][C]54[/C][C]6976[/C][C]6573.37596233646[/C][C]402.624037663538[/C][/ROW]
[ROW][C]55[/C][C]6459[/C][C]5459.64940526931[/C][C]999.35059473069[/C][/ROW]
[ROW][C]56[/C][C]6976[/C][C]5470.92402538519[/C][C]1505.07597461481[/C][/ROW]
[ROW][C]57[/C][C]6874[/C][C]7197.6613318934[/C][C]-323.6613318934[/C][/ROW]
[ROW][C]58[/C][C]6054[/C][C]7021.47800819968[/C][C]-967.478008199678[/C][/ROW]
[ROW][C]59[/C][C]6976[/C][C]7019.57925544763[/C][C]-43.5792554476284[/C][/ROW]
[ROW][C]60[/C][C]7998[/C][C]7526.17976302399[/C][C]471.82023697601[/C][/ROW]
[ROW][C]61[/C][C]8413[/C][C]7321.61152456898[/C][C]1091.38847543102[/C][/ROW]
[ROW][C]62[/C][C]7178[/C][C]6937.30054991499[/C][C]240.699450085006[/C][/ROW]
[ROW][C]63[/C][C]6358[/C][C]7304.37154323632[/C][C]-946.371543236322[/C][/ROW]
[ROW][C]64[/C][C]6976[/C][C]6778.11122255686[/C][C]197.88877744314[/C][/ROW]
[ROW][C]65[/C][C]9638[/C][C]9541.64832389713[/C][C]96.351676102875[/C][/ROW]
[ROW][C]66[/C][C]10458[/C][C]9638.72200417705[/C][C]819.277995822953[/C][/ROW]
[ROW][C]67[/C][C]10256[/C][C]9112.6918783091[/C][C]1143.30812169091[/C][/ROW]
[ROW][C]68[/C][C]10660[/C][C]9506.89050509696[/C][C]1153.10949490304[/C][/ROW]
[ROW][C]69[/C][C]10559[/C][C]10471.5378411073[/C][C]87.4621588927293[/C][/ROW]
[ROW][C]70[/C][C]9537[/C][C]10456.7102185331[/C][C]-919.710218533091[/C][/ROW]
[ROW][C]71[/C][C]11278[/C][C]10923.4324766312[/C][C]354.567523368818[/C][/ROW]
[ROW][C]72[/C][C]11693[/C][C]11999.9144368034[/C][C]-306.914436803441[/C][/ROW]
[ROW][C]73[/C][C]12300[/C][C]11605.1901575067[/C][C]694.809842493338[/C][/ROW]
[ROW][C]74[/C][C]10458[/C][C]10757.4392681345[/C][C]-299.439268134498[/C][/ROW]
[ROW][C]75[/C][C]9739[/C][C]10432.0250338714[/C][C]-693.02503387141[/C][/ROW]
[ROW][C]76[/C][C]10559[/C][C]10548.2757494106[/C][C]10.7242505894283[/C][/ROW]
[ROW][C]77[/C][C]12513[/C][C]13228.367398047[/C][C]-715.367398047047[/C][/ROW]
[ROW][C]78[/C][C]14254[/C][C]13091.3318547777[/C][C]1162.66814522234[/C][/ROW]
[ROW][C]79[/C][C]13839[/C][C]12959.8380414103[/C][C]879.16195858974[/C][/ROW]
[ROW][C]80[/C][C]13839[/C][C]13233.5066200139[/C][C]605.493379986057[/C][/ROW]
[ROW][C]81[/C][C]14042[/C][C]13500.848021262[/C][C]541.151978737953[/C][/ROW]
[ROW][C]82[/C][C]13333[/C][C]13479.0979316543[/C][C]-146.0979316543[/C][/ROW]
[ROW][C]83[/C][C]15176[/C][C]14965.104124219[/C][C]210.895875780992[/C][/ROW]
[ROW][C]84[/C][C]15176[/C][C]15785.7915482684[/C][C]-609.791548268397[/C][/ROW]
[ROW][C]85[/C][C]14862[/C][C]15596.9148279934[/C][C]-734.914827993434[/C][/ROW]
[ROW][C]86[/C][C]13120[/C][C]13477.6141033543[/C][C]-357.614103354301[/C][/ROW]
[ROW][C]87[/C][C]13434[/C][C]12983.1340091485[/C][C]450.865990851487[/C][/ROW]
[ROW][C]88[/C][C]13637[/C][C]14135.6787532482[/C][C]-498.67875324823[/C][/ROW]
[ROW][C]89[/C][C]14973[/C][C]16258.5559667787[/C][C]-1285.55596677869[/C][/ROW]
[ROW][C]90[/C][C]16714[/C][C]16406.9819474471[/C][C]307.018052552929[/C][/ROW]
[ROW][C]91[/C][C]15479[/C][C]15595.9669365577[/C][C]-116.966936557652[/C][/ROW]
[ROW][C]92[/C][C]16097[/C][C]15067.2455411003[/C][C]1029.75445889975[/C][/ROW]
[ROW][C]93[/C][C]15580[/C][C]15547.7245265467[/C][C]32.2754734533155[/C][/ROW]
[ROW][C]94[/C][C]15277[/C][C]14895.8394542142[/C][C]381.16054578582[/C][/ROW]
[ROW][C]95[/C][C]17636[/C][C]16808.8962842472[/C][C]827.103715752834[/C][/ROW]
[ROW][C]96[/C][C]17119[/C][C]17728.1120918596[/C][C]-609.11209185957[/C][/ROW]
[ROW][C]97[/C][C]16400[/C][C]17476.4521188177[/C][C]-1076.4521188177[/C][/ROW]
[ROW][C]98[/C][C]15378[/C][C]15232.9386068457[/C][C]145.061393154285[/C][/ROW]
[ROW][C]99[/C][C]16400[/C][C]15332.7651203623[/C][C]1067.23487963772[/C][/ROW]
[ROW][C]100[/C][C]16917[/C][C]16566.2272532533[/C][C]350.772746746698[/C][/ROW]
[ROW][C]101[/C][C]17534[/C][C]19008.0995345231[/C][C]-1474.09953452308[/C][/ROW]
[ROW][C]102[/C][C]18354[/C][C]19614.8861167869[/C][C]-1260.88611678694[/C][/ROW]
[ROW][C]103[/C][C]17534[/C][C]17607.8857754007[/C][C]-73.8857754007186[/C][/ROW]
[ROW][C]104[/C][C]18040[/C][C]17481.7012877423[/C][C]558.298712257656[/C][/ROW]
[ROW][C]105[/C][C]17423[/C][C]17269.3156046553[/C][C]153.684395344739[/C][/ROW]
[ROW][C]106[/C][C]17322[/C][C]16782.6608041877[/C][C]539.339195812332[/C][/ROW]
[ROW][C]107[/C][C]19883[/C][C]18924.0754538226[/C][C]958.924546177415[/C][/ROW]
[ROW][C]108[/C][C]20096[/C][C]19406.9587707084[/C][C]689.041229291597[/C][/ROW]
[ROW][C]109[/C][C]19276[/C][C]19861.8074152944[/C][C]-585.807415294428[/C][/ROW]
[ROW][C]110[/C][C]17838[/C][C]18399.0672295518[/C][C]-561.067229551838[/C][/ROW]
[ROW][C]111[/C][C]19063[/C][C]18369.355754578[/C][C]693.644245422027[/C][/ROW]
[ROW][C]112[/C][C]19579[/C][C]19110.031931515[/C][C]468.968068485017[/C][/ROW]
[ROW][C]113[/C][C]20197[/C][C]21000.6479127836[/C][C]-803.647912783552[/C][/ROW]
[ROW][C]114[/C][C]21118[/C][C]22146.3563303696[/C][C]-1028.35633036964[/C][/ROW]
[ROW][C]115[/C][C]20197[/C][C]20737.4498959515[/C][C]-540.449895951457[/C][/ROW]
[ROW][C]116[/C][C]20916[/C][C]20544.104977736[/C][C]371.895022264023[/C][/ROW]
[ROW][C]117[/C][C]20602[/C][C]20082.0446740226[/C][C]519.955325977422[/C][/ROW]
[ROW][C]118[/C][C]19478[/C][C]19993.370075713[/C][C]-515.370075713043[/C][/ROW]
[ROW][C]119[/C][C]21837[/C][C]21579.3101595299[/C][C]257.689840470081[/C][/ROW]
[ROW][C]120[/C][C]21837[/C][C]21474.632805768[/C][C]362.36719423196[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123757&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123757&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
1345165451.23530982906-935.235309829059
1438984212.20700582568-314.207005825676
1533923475.9892528732-83.9892528732007
1633923359.1639710643132.8360289356897
1753365238.0789793547797.9210206452253
1855385386.75312037245151.246879627548
1939993903.6791511722795.3208488277282
2022582881.97606051511-623.976060515112
2131792529.98634479155649.013655208454
2231792939.90509661066239.094903389342
2338983186.93255365647711.067446343529
2443133870.57267507416442.42732492584
2542123227.33012281279984.669877187208
2631793540.63582460749-361.635824607494
2736962933.92192127724762.078078722757
2834933520.55819923172-27.5581992317202
2952345490.47926539415-256.479265394153
3048195521.66916937277-702.669169372769
3131793527.24880501166-348.248805011661
3219542017.23864077446-63.2386407744557
3330782542.90809584263535.091904157367
3433922802.60425947207589.395740527934
3536963520.44133572436175.558664275644
3641003820.85407464962279.145925350385
3732803312.92296352864-32.922963528641
3825722513.7390488723358.2609511276678
3928762604.24496493967271.755035060335
4029772613.40960438869363.590395611312
4156394789.74569453835849.254305461647
4256395457.3746602733181.625339726696
4341004262.61015476468-162.610154764679
4438983078.00801059795819.991989402054
4545164524.11392289623-8.11392289623291
4642124564.70423283768-352.704232837679
4750324607.95873519795424.041264802048
4860545199.77041499697854.229585003029
4962575072.600167044041184.39983295596
5048195255.74153661338-436.741536613385
5144145234.68263699745-820.682636997451
5239994661.87230828697-662.872308286969
5367736400.27200947649372.727990523515
5469766573.37596233646402.624037663538
5564595459.64940526931999.35059473069
5669765470.924025385191505.07597461481
5768747197.6613318934-323.6613318934
5860547021.47800819968-967.478008199678
5969767019.57925544763-43.5792554476284
6079987526.17976302399471.82023697601
6184137321.611524568981091.38847543102
6271786937.30054991499240.699450085006
6363587304.37154323632-946.371543236322
6469766778.11122255686197.88877744314
6596389541.6483238971396.351676102875
66104589638.72200417705819.277995822953
67102569112.69187830911143.30812169091
68106609506.890505096961153.10949490304
691055910471.537841107387.4621588927293
70953710456.7102185331-919.710218533091
711127810923.4324766312354.567523368818
721169311999.9144368034-306.914436803441
731230011605.1901575067694.809842493338
741045810757.4392681345-299.439268134498
75973910432.0250338714-693.02503387141
761055910548.275749410610.7242505894283
771251313228.367398047-715.367398047047
781425413091.33185477771162.66814522234
791383912959.8380414103879.16195858974
801383913233.5066200139605.493379986057
811404213500.848021262541.151978737953
821333313479.0979316543-146.0979316543
831517614965.104124219210.895875780992
841517615785.7915482684-609.791548268397
851486215596.9148279934-734.914827993434
861312013477.6141033543-357.614103354301
871343412983.1340091485450.865990851487
881363714135.6787532482-498.67875324823
891497316258.5559667787-1285.55596677869
901671416406.9819474471307.018052552929
911547915595.9669365577-116.966936557652
921609715067.24554110031029.75445889975
931558015547.724526546732.2754734533155
941527714895.8394542142381.16054578582
951763616808.8962842472827.103715752834
961711917728.1120918596-609.11209185957
971640017476.4521188177-1076.4521188177
981537815232.9386068457145.061393154285
991640015332.76512036231067.23487963772
1001691716566.2272532533350.772746746698
1011753419008.0995345231-1474.09953452308
1021835419614.8861167869-1260.88611678694
1031753417607.8857754007-73.8857754007186
1041804017481.7012877423558.298712257656
1051742317269.3156046553153.684395344739
1061732216782.6608041877539.339195812332
1071988318924.0754538226958.924546177415
1082009619406.9587707084689.041229291597
1091927619861.8074152944-585.807415294428
1101783818399.0672295518-561.067229551838
1111906318369.355754578693.644245422027
1121957919110.031931515468.968068485017
1132019721000.6479127836-803.647912783552
1142111822146.3563303696-1028.35633036964
1152019720737.4498959515-540.449895951457
1162091620544.104977736371.895022264023
1172060220082.0446740226519.955325977422
1181947819993.370075713-515.370075713043
1192183721579.3101595299257.689840470081
1202183721474.632805768362.36719423196







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12121227.279295332419971.581026434422482.9775642303
12220129.188692788518604.881238695321653.4961468816
12320893.459398468319119.419403648522667.4993932881
12421071.575141489719058.699866343723084.4504166356
12522167.217899260719922.082092732224412.3537057891
12623740.528638752121267.090481542826213.9667959614
12723188.533272538120489.04700260225888.0195424742
12823698.948657589520774.500185348626623.3971298304
12923066.728839077619917.571933154126215.885745001
13022283.184476749918908.962812349925657.4061411499
13124495.216584709120895.116391816528095.3167776016
13224270.918727365720443.777162420128098.0602923112

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 21227.2792953324 & 19971.5810264344 & 22482.9775642303 \tabularnewline
122 & 20129.1886927885 & 18604.8812386953 & 21653.4961468816 \tabularnewline
123 & 20893.4593984683 & 19119.4194036485 & 22667.4993932881 \tabularnewline
124 & 21071.5751414897 & 19058.6998663437 & 23084.4504166356 \tabularnewline
125 & 22167.2178992607 & 19922.0820927322 & 24412.3537057891 \tabularnewline
126 & 23740.5286387521 & 21267.0904815428 & 26213.9667959614 \tabularnewline
127 & 23188.5332725381 & 20489.047002602 & 25888.0195424742 \tabularnewline
128 & 23698.9486575895 & 20774.5001853486 & 26623.3971298304 \tabularnewline
129 & 23066.7288390776 & 19917.5719331541 & 26215.885745001 \tabularnewline
130 & 22283.1844767499 & 18908.9628123499 & 25657.4061411499 \tabularnewline
131 & 24495.2165847091 & 20895.1163918165 & 28095.3167776016 \tabularnewline
132 & 24270.9187273657 & 20443.7771624201 & 28098.0602923112 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123757&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]21227.2792953324[/C][C]19971.5810264344[/C][C]22482.9775642303[/C][/ROW]
[ROW][C]122[/C][C]20129.1886927885[/C][C]18604.8812386953[/C][C]21653.4961468816[/C][/ROW]
[ROW][C]123[/C][C]20893.4593984683[/C][C]19119.4194036485[/C][C]22667.4993932881[/C][/ROW]
[ROW][C]124[/C][C]21071.5751414897[/C][C]19058.6998663437[/C][C]23084.4504166356[/C][/ROW]
[ROW][C]125[/C][C]22167.2178992607[/C][C]19922.0820927322[/C][C]24412.3537057891[/C][/ROW]
[ROW][C]126[/C][C]23740.5286387521[/C][C]21267.0904815428[/C][C]26213.9667959614[/C][/ROW]
[ROW][C]127[/C][C]23188.5332725381[/C][C]20489.047002602[/C][C]25888.0195424742[/C][/ROW]
[ROW][C]128[/C][C]23698.9486575895[/C][C]20774.5001853486[/C][C]26623.3971298304[/C][/ROW]
[ROW][C]129[/C][C]23066.7288390776[/C][C]19917.5719331541[/C][C]26215.885745001[/C][/ROW]
[ROW][C]130[/C][C]22283.1844767499[/C][C]18908.9628123499[/C][C]25657.4061411499[/C][/ROW]
[ROW][C]131[/C][C]24495.2165847091[/C][C]20895.1163918165[/C][C]28095.3167776016[/C][/ROW]
[ROW][C]132[/C][C]24270.9187273657[/C][C]20443.7771624201[/C][C]28098.0602923112[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123757&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123757&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
12121227.279295332419971.581026434422482.9775642303
12220129.188692788518604.881238695321653.4961468816
12320893.459398468319119.419403648522667.4993932881
12421071.575141489719058.699866343723084.4504166356
12522167.217899260719922.082092732224412.3537057891
12623740.528638752121267.090481542826213.9667959614
12723188.533272538120489.04700260225888.0195424742
12823698.948657589520774.500185348626623.3971298304
12923066.728839077619917.571933154126215.885745001
13022283.184476749918908.962812349925657.4061411499
13124495.216584709120895.116391816528095.3167776016
13224270.918727365720443.777162420128098.0602923112



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')