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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 13 Dec 2016 16:53:17 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/13/t1481644541411t5kacvd9ugti.htm/, Retrieved Fri, 01 Nov 2024 03:27:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299166, Retrieved Fri, 01 Nov 2024 03:27:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-13 15:53:17] [9b171b8beffcb53bb49a1e7c02b89c12] [Current]
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Dataseries X:
6600
6160
6320
5820
6080
6240
5740
6980
6540
6780
6580
6020
6440
6440
7040
6620
6460
6320
6560
6080
6040
6260
5780
5120
6040
5860
5900
5160
5800
5300
5600
5620
6300
5800
5460
5420
5800
5260
5900
5840
5640
5560
5540
5540
5480
5440
5260
5420
5600
5200
5480
5300
4660
4940
4880
4980
5160
5180
4860
5220
4900
4740
4920
4780
4300
4540
4420
4660
4760
4560
4600
4800
4980
4300
4800
3980
4120
4580
4240
4540
4200
4780
4820
4320
4300
3700
3920
3740
4120
4160
4160
3960
3960
4160
3920
3460
4040
3720
4060
4140
3700
3900
3720
3760
3520
3800
3520
3640
4200
3860
4160
3920
3860
3860
3780




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299166&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299166&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299166&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.365404739676724
beta0.0160956204114789
gamma0.737418595755599

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.365404739676724 \tabularnewline
beta & 0.0160956204114789 \tabularnewline
gamma & 0.737418595755599 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299166&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]0.365404739676724[/C][/ROW]
[ROW][C]beta[/C][C]0.0160956204114789[/C][/ROW]
[ROW][C]gamma[/C][C]0.737418595755599[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299166&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299166&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
alpha0.365404739676724
beta0.0160956204114789
gamma0.737418595755599







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1364406225.73183760684214.268162393159
1464406312.75458862075127.245411379255
1570407023.7271971511416.2728028488573
1666206658.41226233973-38.412262339727
1764606545.38922702508-85.3892270250753
1863206450.53170992721-130.531709927212
1965605813.41120433064746.588795669362
2060807330.35235469147-1250.35235469147
2160406393.5812348608-353.5812348608
2262606440.74830762759-180.74830762759
2357806124.17296185827-344.172961858271
2451205415.85724849307-295.857248493075
2560405785.39236479914254.607635200865
2658605837.4079427934822.5920572065243
2759006448.5691706927-548.569170692695
2851605838.30613279269-678.306132792693
2958005452.75429428972347.245705710281
3053005480.6780565365-180.678056536503
3156005221.21768254797378.782317452027
3256205652.62858959468-32.6285895946821
3363005570.99781413431729.00218586569
3458006091.51561757499-291.515617574985
3554605654.22763417219-194.227634172185
3654205020.43332661391399.566673386085
3758005902.88729346752-102.887293467516
3852605714.80621478788-454.80621478788
3959005880.5423643526719.4576356473308
4058405416.76826354835423.231736451654
4156405919.76309276823-279.763092768228
4255605473.9585918506786.0414081493254
4355405577.76601727854-37.7660172785418
4455405665.99433524585-125.994335245848
4554805907.66363514532-427.663635145316
4654405522.16536441904-82.1653644190446
4752605202.3323488440157.6676511559863
4854204935.36693060388484.63306939612
4956005611.18711675714-11.187116757138
5052005289.88033219622-89.8803321962241
5154805810.99745261133-330.997452611329
5253005406.15300448753-106.153004487533
5346605381.65602666435-721.656026664351
5449404937.888525171722.11147482828437
5548804944.92075465672-64.9207546567168
5649804973.609776654846.39022334516085
5751605114.9324615740145.0675384259857
5851805059.08222523305120.917774766949
5948604875.31739541785-15.3173954178537
6052204777.48143665661442.51856334339
6149005201.63471513467-301.634715134668
6247404731.410406483338.58959351667454
6349205170.2931804723-250.293180472298
6447804895.24985593786-115.249855937856
6543004574.43576970945-274.435769709455
6645404630.45005822494-90.4500582249375
6744204569.41636325823-149.416363258231
6846604597.2292458988262.770754101175
6947604774.21287239333-14.2128723933329
7045604728.80739605566-168.80739605566
7146004370.32974011837229.670259881627
7248004572.61134961678227.388650383221
7349804565.00208458101414.99791541899
7443004501.10950564829-201.109505648287
7548004740.2839917995659.7160082004402
7639804641.6021251643-661.602125164296
7741204043.3294317286176.6705682713928
7845804312.47714294966267.522857050344
7942404355.49894265173-115.498942651735
8045404496.0449803491543.9550196508544
8142004631.06113432974-431.061134329735
8247804359.47457786388420.525422136125
8348204404.76224343789415.237756562111
8443204676.82256596118-356.822565961175
8543004543.13701360328-243.137013603285
8637003946.17616132892-246.176161328925
8739204286.40696449446-366.406964494459
8837403687.4291790845352.5708209154736
8941203692.76399554178427.236004458215
9041604178.54499365-18.5449936499963
9141603935.33731113898224.662688861022
9239604274.339949702-314.339949701999
9339604053.57794645453-93.5779464545335
9441604303.23886443815-143.238864438151
9539204136.15330243795-216.153302437951
9634603808.59504954969-348.595049549687
9740403723.55468760704316.445312392961
9837203325.37505839459394.624941605408
9940603842.99234653596217.007653464036
10041403656.1923725124483.8076274876
10137003999.89816073427-299.898160734265
10239004012.56138899753-112.561388997529
10337203849.44798015728-129.447980157282
10437603805.37756316685-45.3775631668514
10535203786.33947570245-266.339475702446
10638003948.75247003212-148.752470032115
10735203744.61796880063-224.617968800627
10836403351.02612165739288.973878342611
10942003812.95730931523387.042690684772
11038603480.36162565512379.638374344884
11141603912.49861228935247.501387710648
11239203864.9869453177555.0130546822465
11338603686.03585634678173.964143653222
11438603963.07564414996-103.075644149957
11537803799.14034465425-19.1403446542531

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 6440 & 6225.73183760684 & 214.268162393159 \tabularnewline
14 & 6440 & 6312.75458862075 & 127.245411379255 \tabularnewline
15 & 7040 & 7023.72719715114 & 16.2728028488573 \tabularnewline
16 & 6620 & 6658.41226233973 & -38.412262339727 \tabularnewline
17 & 6460 & 6545.38922702508 & -85.3892270250753 \tabularnewline
18 & 6320 & 6450.53170992721 & -130.531709927212 \tabularnewline
19 & 6560 & 5813.41120433064 & 746.588795669362 \tabularnewline
20 & 6080 & 7330.35235469147 & -1250.35235469147 \tabularnewline
21 & 6040 & 6393.5812348608 & -353.5812348608 \tabularnewline
22 & 6260 & 6440.74830762759 & -180.74830762759 \tabularnewline
23 & 5780 & 6124.17296185827 & -344.172961858271 \tabularnewline
24 & 5120 & 5415.85724849307 & -295.857248493075 \tabularnewline
25 & 6040 & 5785.39236479914 & 254.607635200865 \tabularnewline
26 & 5860 & 5837.40794279348 & 22.5920572065243 \tabularnewline
27 & 5900 & 6448.5691706927 & -548.569170692695 \tabularnewline
28 & 5160 & 5838.30613279269 & -678.306132792693 \tabularnewline
29 & 5800 & 5452.75429428972 & 347.245705710281 \tabularnewline
30 & 5300 & 5480.6780565365 & -180.678056536503 \tabularnewline
31 & 5600 & 5221.21768254797 & 378.782317452027 \tabularnewline
32 & 5620 & 5652.62858959468 & -32.6285895946821 \tabularnewline
33 & 6300 & 5570.99781413431 & 729.00218586569 \tabularnewline
34 & 5800 & 6091.51561757499 & -291.515617574985 \tabularnewline
35 & 5460 & 5654.22763417219 & -194.227634172185 \tabularnewline
36 & 5420 & 5020.43332661391 & 399.566673386085 \tabularnewline
37 & 5800 & 5902.88729346752 & -102.887293467516 \tabularnewline
38 & 5260 & 5714.80621478788 & -454.80621478788 \tabularnewline
39 & 5900 & 5880.54236435267 & 19.4576356473308 \tabularnewline
40 & 5840 & 5416.76826354835 & 423.231736451654 \tabularnewline
41 & 5640 & 5919.76309276823 & -279.763092768228 \tabularnewline
42 & 5560 & 5473.95859185067 & 86.0414081493254 \tabularnewline
43 & 5540 & 5577.76601727854 & -37.7660172785418 \tabularnewline
44 & 5540 & 5665.99433524585 & -125.994335245848 \tabularnewline
45 & 5480 & 5907.66363514532 & -427.663635145316 \tabularnewline
46 & 5440 & 5522.16536441904 & -82.1653644190446 \tabularnewline
47 & 5260 & 5202.33234884401 & 57.6676511559863 \tabularnewline
48 & 5420 & 4935.36693060388 & 484.63306939612 \tabularnewline
49 & 5600 & 5611.18711675714 & -11.187116757138 \tabularnewline
50 & 5200 & 5289.88033219622 & -89.8803321962241 \tabularnewline
51 & 5480 & 5810.99745261133 & -330.997452611329 \tabularnewline
52 & 5300 & 5406.15300448753 & -106.153004487533 \tabularnewline
53 & 4660 & 5381.65602666435 & -721.656026664351 \tabularnewline
54 & 4940 & 4937.88852517172 & 2.11147482828437 \tabularnewline
55 & 4880 & 4944.92075465672 & -64.9207546567168 \tabularnewline
56 & 4980 & 4973.60977665484 & 6.39022334516085 \tabularnewline
57 & 5160 & 5114.93246157401 & 45.0675384259857 \tabularnewline
58 & 5180 & 5059.08222523305 & 120.917774766949 \tabularnewline
59 & 4860 & 4875.31739541785 & -15.3173954178537 \tabularnewline
60 & 5220 & 4777.48143665661 & 442.51856334339 \tabularnewline
61 & 4900 & 5201.63471513467 & -301.634715134668 \tabularnewline
62 & 4740 & 4731.41040648333 & 8.58959351667454 \tabularnewline
63 & 4920 & 5170.2931804723 & -250.293180472298 \tabularnewline
64 & 4780 & 4895.24985593786 & -115.249855937856 \tabularnewline
65 & 4300 & 4574.43576970945 & -274.435769709455 \tabularnewline
66 & 4540 & 4630.45005822494 & -90.4500582249375 \tabularnewline
67 & 4420 & 4569.41636325823 & -149.416363258231 \tabularnewline
68 & 4660 & 4597.22924589882 & 62.770754101175 \tabularnewline
69 & 4760 & 4774.21287239333 & -14.2128723933329 \tabularnewline
70 & 4560 & 4728.80739605566 & -168.80739605566 \tabularnewline
71 & 4600 & 4370.32974011837 & 229.670259881627 \tabularnewline
72 & 4800 & 4572.61134961678 & 227.388650383221 \tabularnewline
73 & 4980 & 4565.00208458101 & 414.99791541899 \tabularnewline
74 & 4300 & 4501.10950564829 & -201.109505648287 \tabularnewline
75 & 4800 & 4740.28399179956 & 59.7160082004402 \tabularnewline
76 & 3980 & 4641.6021251643 & -661.602125164296 \tabularnewline
77 & 4120 & 4043.32943172861 & 76.6705682713928 \tabularnewline
78 & 4580 & 4312.47714294966 & 267.522857050344 \tabularnewline
79 & 4240 & 4355.49894265173 & -115.498942651735 \tabularnewline
80 & 4540 & 4496.04498034915 & 43.9550196508544 \tabularnewline
81 & 4200 & 4631.06113432974 & -431.061134329735 \tabularnewline
82 & 4780 & 4359.47457786388 & 420.525422136125 \tabularnewline
83 & 4820 & 4404.76224343789 & 415.237756562111 \tabularnewline
84 & 4320 & 4676.82256596118 & -356.822565961175 \tabularnewline
85 & 4300 & 4543.13701360328 & -243.137013603285 \tabularnewline
86 & 3700 & 3946.17616132892 & -246.176161328925 \tabularnewline
87 & 3920 & 4286.40696449446 & -366.406964494459 \tabularnewline
88 & 3740 & 3687.42917908453 & 52.5708209154736 \tabularnewline
89 & 4120 & 3692.76399554178 & 427.236004458215 \tabularnewline
90 & 4160 & 4178.54499365 & -18.5449936499963 \tabularnewline
91 & 4160 & 3935.33731113898 & 224.662688861022 \tabularnewline
92 & 3960 & 4274.339949702 & -314.339949701999 \tabularnewline
93 & 3960 & 4053.57794645453 & -93.5779464545335 \tabularnewline
94 & 4160 & 4303.23886443815 & -143.238864438151 \tabularnewline
95 & 3920 & 4136.15330243795 & -216.153302437951 \tabularnewline
96 & 3460 & 3808.59504954969 & -348.595049549687 \tabularnewline
97 & 4040 & 3723.55468760704 & 316.445312392961 \tabularnewline
98 & 3720 & 3325.37505839459 & 394.624941605408 \tabularnewline
99 & 4060 & 3842.99234653596 & 217.007653464036 \tabularnewline
100 & 4140 & 3656.1923725124 & 483.8076274876 \tabularnewline
101 & 3700 & 3999.89816073427 & -299.898160734265 \tabularnewline
102 & 3900 & 4012.56138899753 & -112.561388997529 \tabularnewline
103 & 3720 & 3849.44798015728 & -129.447980157282 \tabularnewline
104 & 3760 & 3805.37756316685 & -45.3775631668514 \tabularnewline
105 & 3520 & 3786.33947570245 & -266.339475702446 \tabularnewline
106 & 3800 & 3948.75247003212 & -148.752470032115 \tabularnewline
107 & 3520 & 3744.61796880063 & -224.617968800627 \tabularnewline
108 & 3640 & 3351.02612165739 & 288.973878342611 \tabularnewline
109 & 4200 & 3812.95730931523 & 387.042690684772 \tabularnewline
110 & 3860 & 3480.36162565512 & 379.638374344884 \tabularnewline
111 & 4160 & 3912.49861228935 & 247.501387710648 \tabularnewline
112 & 3920 & 3864.98694531775 & 55.0130546822465 \tabularnewline
113 & 3860 & 3686.03585634678 & 173.964143653222 \tabularnewline
114 & 3860 & 3963.07564414996 & -103.075644149957 \tabularnewline
115 & 3780 & 3799.14034465425 & -19.1403446542531 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299166&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]6440[/C][C]6225.73183760684[/C][C]214.268162393159[/C][/ROW]
[ROW][C]14[/C][C]6440[/C][C]6312.75458862075[/C][C]127.245411379255[/C][/ROW]
[ROW][C]15[/C][C]7040[/C][C]7023.72719715114[/C][C]16.2728028488573[/C][/ROW]
[ROW][C]16[/C][C]6620[/C][C]6658.41226233973[/C][C]-38.412262339727[/C][/ROW]
[ROW][C]17[/C][C]6460[/C][C]6545.38922702508[/C][C]-85.3892270250753[/C][/ROW]
[ROW][C]18[/C][C]6320[/C][C]6450.53170992721[/C][C]-130.531709927212[/C][/ROW]
[ROW][C]19[/C][C]6560[/C][C]5813.41120433064[/C][C]746.588795669362[/C][/ROW]
[ROW][C]20[/C][C]6080[/C][C]7330.35235469147[/C][C]-1250.35235469147[/C][/ROW]
[ROW][C]21[/C][C]6040[/C][C]6393.5812348608[/C][C]-353.5812348608[/C][/ROW]
[ROW][C]22[/C][C]6260[/C][C]6440.74830762759[/C][C]-180.74830762759[/C][/ROW]
[ROW][C]23[/C][C]5780[/C][C]6124.17296185827[/C][C]-344.172961858271[/C][/ROW]
[ROW][C]24[/C][C]5120[/C][C]5415.85724849307[/C][C]-295.857248493075[/C][/ROW]
[ROW][C]25[/C][C]6040[/C][C]5785.39236479914[/C][C]254.607635200865[/C][/ROW]
[ROW][C]26[/C][C]5860[/C][C]5837.40794279348[/C][C]22.5920572065243[/C][/ROW]
[ROW][C]27[/C][C]5900[/C][C]6448.5691706927[/C][C]-548.569170692695[/C][/ROW]
[ROW][C]28[/C][C]5160[/C][C]5838.30613279269[/C][C]-678.306132792693[/C][/ROW]
[ROW][C]29[/C][C]5800[/C][C]5452.75429428972[/C][C]347.245705710281[/C][/ROW]
[ROW][C]30[/C][C]5300[/C][C]5480.6780565365[/C][C]-180.678056536503[/C][/ROW]
[ROW][C]31[/C][C]5600[/C][C]5221.21768254797[/C][C]378.782317452027[/C][/ROW]
[ROW][C]32[/C][C]5620[/C][C]5652.62858959468[/C][C]-32.6285895946821[/C][/ROW]
[ROW][C]33[/C][C]6300[/C][C]5570.99781413431[/C][C]729.00218586569[/C][/ROW]
[ROW][C]34[/C][C]5800[/C][C]6091.51561757499[/C][C]-291.515617574985[/C][/ROW]
[ROW][C]35[/C][C]5460[/C][C]5654.22763417219[/C][C]-194.227634172185[/C][/ROW]
[ROW][C]36[/C][C]5420[/C][C]5020.43332661391[/C][C]399.566673386085[/C][/ROW]
[ROW][C]37[/C][C]5800[/C][C]5902.88729346752[/C][C]-102.887293467516[/C][/ROW]
[ROW][C]38[/C][C]5260[/C][C]5714.80621478788[/C][C]-454.80621478788[/C][/ROW]
[ROW][C]39[/C][C]5900[/C][C]5880.54236435267[/C][C]19.4576356473308[/C][/ROW]
[ROW][C]40[/C][C]5840[/C][C]5416.76826354835[/C][C]423.231736451654[/C][/ROW]
[ROW][C]41[/C][C]5640[/C][C]5919.76309276823[/C][C]-279.763092768228[/C][/ROW]
[ROW][C]42[/C][C]5560[/C][C]5473.95859185067[/C][C]86.0414081493254[/C][/ROW]
[ROW][C]43[/C][C]5540[/C][C]5577.76601727854[/C][C]-37.7660172785418[/C][/ROW]
[ROW][C]44[/C][C]5540[/C][C]5665.99433524585[/C][C]-125.994335245848[/C][/ROW]
[ROW][C]45[/C][C]5480[/C][C]5907.66363514532[/C][C]-427.663635145316[/C][/ROW]
[ROW][C]46[/C][C]5440[/C][C]5522.16536441904[/C][C]-82.1653644190446[/C][/ROW]
[ROW][C]47[/C][C]5260[/C][C]5202.33234884401[/C][C]57.6676511559863[/C][/ROW]
[ROW][C]48[/C][C]5420[/C][C]4935.36693060388[/C][C]484.63306939612[/C][/ROW]
[ROW][C]49[/C][C]5600[/C][C]5611.18711675714[/C][C]-11.187116757138[/C][/ROW]
[ROW][C]50[/C][C]5200[/C][C]5289.88033219622[/C][C]-89.8803321962241[/C][/ROW]
[ROW][C]51[/C][C]5480[/C][C]5810.99745261133[/C][C]-330.997452611329[/C][/ROW]
[ROW][C]52[/C][C]5300[/C][C]5406.15300448753[/C][C]-106.153004487533[/C][/ROW]
[ROW][C]53[/C][C]4660[/C][C]5381.65602666435[/C][C]-721.656026664351[/C][/ROW]
[ROW][C]54[/C][C]4940[/C][C]4937.88852517172[/C][C]2.11147482828437[/C][/ROW]
[ROW][C]55[/C][C]4880[/C][C]4944.92075465672[/C][C]-64.9207546567168[/C][/ROW]
[ROW][C]56[/C][C]4980[/C][C]4973.60977665484[/C][C]6.39022334516085[/C][/ROW]
[ROW][C]57[/C][C]5160[/C][C]5114.93246157401[/C][C]45.0675384259857[/C][/ROW]
[ROW][C]58[/C][C]5180[/C][C]5059.08222523305[/C][C]120.917774766949[/C][/ROW]
[ROW][C]59[/C][C]4860[/C][C]4875.31739541785[/C][C]-15.3173954178537[/C][/ROW]
[ROW][C]60[/C][C]5220[/C][C]4777.48143665661[/C][C]442.51856334339[/C][/ROW]
[ROW][C]61[/C][C]4900[/C][C]5201.63471513467[/C][C]-301.634715134668[/C][/ROW]
[ROW][C]62[/C][C]4740[/C][C]4731.41040648333[/C][C]8.58959351667454[/C][/ROW]
[ROW][C]63[/C][C]4920[/C][C]5170.2931804723[/C][C]-250.293180472298[/C][/ROW]
[ROW][C]64[/C][C]4780[/C][C]4895.24985593786[/C][C]-115.249855937856[/C][/ROW]
[ROW][C]65[/C][C]4300[/C][C]4574.43576970945[/C][C]-274.435769709455[/C][/ROW]
[ROW][C]66[/C][C]4540[/C][C]4630.45005822494[/C][C]-90.4500582249375[/C][/ROW]
[ROW][C]67[/C][C]4420[/C][C]4569.41636325823[/C][C]-149.416363258231[/C][/ROW]
[ROW][C]68[/C][C]4660[/C][C]4597.22924589882[/C][C]62.770754101175[/C][/ROW]
[ROW][C]69[/C][C]4760[/C][C]4774.21287239333[/C][C]-14.2128723933329[/C][/ROW]
[ROW][C]70[/C][C]4560[/C][C]4728.80739605566[/C][C]-168.80739605566[/C][/ROW]
[ROW][C]71[/C][C]4600[/C][C]4370.32974011837[/C][C]229.670259881627[/C][/ROW]
[ROW][C]72[/C][C]4800[/C][C]4572.61134961678[/C][C]227.388650383221[/C][/ROW]
[ROW][C]73[/C][C]4980[/C][C]4565.00208458101[/C][C]414.99791541899[/C][/ROW]
[ROW][C]74[/C][C]4300[/C][C]4501.10950564829[/C][C]-201.109505648287[/C][/ROW]
[ROW][C]75[/C][C]4800[/C][C]4740.28399179956[/C][C]59.7160082004402[/C][/ROW]
[ROW][C]76[/C][C]3980[/C][C]4641.6021251643[/C][C]-661.602125164296[/C][/ROW]
[ROW][C]77[/C][C]4120[/C][C]4043.32943172861[/C][C]76.6705682713928[/C][/ROW]
[ROW][C]78[/C][C]4580[/C][C]4312.47714294966[/C][C]267.522857050344[/C][/ROW]
[ROW][C]79[/C][C]4240[/C][C]4355.49894265173[/C][C]-115.498942651735[/C][/ROW]
[ROW][C]80[/C][C]4540[/C][C]4496.04498034915[/C][C]43.9550196508544[/C][/ROW]
[ROW][C]81[/C][C]4200[/C][C]4631.06113432974[/C][C]-431.061134329735[/C][/ROW]
[ROW][C]82[/C][C]4780[/C][C]4359.47457786388[/C][C]420.525422136125[/C][/ROW]
[ROW][C]83[/C][C]4820[/C][C]4404.76224343789[/C][C]415.237756562111[/C][/ROW]
[ROW][C]84[/C][C]4320[/C][C]4676.82256596118[/C][C]-356.822565961175[/C][/ROW]
[ROW][C]85[/C][C]4300[/C][C]4543.13701360328[/C][C]-243.137013603285[/C][/ROW]
[ROW][C]86[/C][C]3700[/C][C]3946.17616132892[/C][C]-246.176161328925[/C][/ROW]
[ROW][C]87[/C][C]3920[/C][C]4286.40696449446[/C][C]-366.406964494459[/C][/ROW]
[ROW][C]88[/C][C]3740[/C][C]3687.42917908453[/C][C]52.5708209154736[/C][/ROW]
[ROW][C]89[/C][C]4120[/C][C]3692.76399554178[/C][C]427.236004458215[/C][/ROW]
[ROW][C]90[/C][C]4160[/C][C]4178.54499365[/C][C]-18.5449936499963[/C][/ROW]
[ROW][C]91[/C][C]4160[/C][C]3935.33731113898[/C][C]224.662688861022[/C][/ROW]
[ROW][C]92[/C][C]3960[/C][C]4274.339949702[/C][C]-314.339949701999[/C][/ROW]
[ROW][C]93[/C][C]3960[/C][C]4053.57794645453[/C][C]-93.5779464545335[/C][/ROW]
[ROW][C]94[/C][C]4160[/C][C]4303.23886443815[/C][C]-143.238864438151[/C][/ROW]
[ROW][C]95[/C][C]3920[/C][C]4136.15330243795[/C][C]-216.153302437951[/C][/ROW]
[ROW][C]96[/C][C]3460[/C][C]3808.59504954969[/C][C]-348.595049549687[/C][/ROW]
[ROW][C]97[/C][C]4040[/C][C]3723.55468760704[/C][C]316.445312392961[/C][/ROW]
[ROW][C]98[/C][C]3720[/C][C]3325.37505839459[/C][C]394.624941605408[/C][/ROW]
[ROW][C]99[/C][C]4060[/C][C]3842.99234653596[/C][C]217.007653464036[/C][/ROW]
[ROW][C]100[/C][C]4140[/C][C]3656.1923725124[/C][C]483.8076274876[/C][/ROW]
[ROW][C]101[/C][C]3700[/C][C]3999.89816073427[/C][C]-299.898160734265[/C][/ROW]
[ROW][C]102[/C][C]3900[/C][C]4012.56138899753[/C][C]-112.561388997529[/C][/ROW]
[ROW][C]103[/C][C]3720[/C][C]3849.44798015728[/C][C]-129.447980157282[/C][/ROW]
[ROW][C]104[/C][C]3760[/C][C]3805.37756316685[/C][C]-45.3775631668514[/C][/ROW]
[ROW][C]105[/C][C]3520[/C][C]3786.33947570245[/C][C]-266.339475702446[/C][/ROW]
[ROW][C]106[/C][C]3800[/C][C]3948.75247003212[/C][C]-148.752470032115[/C][/ROW]
[ROW][C]107[/C][C]3520[/C][C]3744.61796880063[/C][C]-224.617968800627[/C][/ROW]
[ROW][C]108[/C][C]3640[/C][C]3351.02612165739[/C][C]288.973878342611[/C][/ROW]
[ROW][C]109[/C][C]4200[/C][C]3812.95730931523[/C][C]387.042690684772[/C][/ROW]
[ROW][C]110[/C][C]3860[/C][C]3480.36162565512[/C][C]379.638374344884[/C][/ROW]
[ROW][C]111[/C][C]4160[/C][C]3912.49861228935[/C][C]247.501387710648[/C][/ROW]
[ROW][C]112[/C][C]3920[/C][C]3864.98694531775[/C][C]55.0130546822465[/C][/ROW]
[ROW][C]113[/C][C]3860[/C][C]3686.03585634678[/C][C]173.964143653222[/C][/ROW]
[ROW][C]114[/C][C]3860[/C][C]3963.07564414996[/C][C]-103.075644149957[/C][/ROW]
[ROW][C]115[/C][C]3780[/C][C]3799.14034465425[/C][C]-19.1403446542531[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299166&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299166&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
1364406225.73183760684214.268162393159
1464406312.75458862075127.245411379255
1570407023.7271971511416.2728028488573
1666206658.41226233973-38.412262339727
1764606545.38922702508-85.3892270250753
1863206450.53170992721-130.531709927212
1965605813.41120433064746.588795669362
2060807330.35235469147-1250.35235469147
2160406393.5812348608-353.5812348608
2262606440.74830762759-180.74830762759
2357806124.17296185827-344.172961858271
2451205415.85724849307-295.857248493075
2560405785.39236479914254.607635200865
2658605837.4079427934822.5920572065243
2759006448.5691706927-548.569170692695
2851605838.30613279269-678.306132792693
2958005452.75429428972347.245705710281
3053005480.6780565365-180.678056536503
3156005221.21768254797378.782317452027
3256205652.62858959468-32.6285895946821
3363005570.99781413431729.00218586569
3458006091.51561757499-291.515617574985
3554605654.22763417219-194.227634172185
3654205020.43332661391399.566673386085
3758005902.88729346752-102.887293467516
3852605714.80621478788-454.80621478788
3959005880.5423643526719.4576356473308
4058405416.76826354835423.231736451654
4156405919.76309276823-279.763092768228
4255605473.9585918506786.0414081493254
4355405577.76601727854-37.7660172785418
4455405665.99433524585-125.994335245848
4554805907.66363514532-427.663635145316
4654405522.16536441904-82.1653644190446
4752605202.3323488440157.6676511559863
4854204935.36693060388484.63306939612
4956005611.18711675714-11.187116757138
5052005289.88033219622-89.8803321962241
5154805810.99745261133-330.997452611329
5253005406.15300448753-106.153004487533
5346605381.65602666435-721.656026664351
5449404937.888525171722.11147482828437
5548804944.92075465672-64.9207546567168
5649804973.609776654846.39022334516085
5751605114.9324615740145.0675384259857
5851805059.08222523305120.917774766949
5948604875.31739541785-15.3173954178537
6052204777.48143665661442.51856334339
6149005201.63471513467-301.634715134668
6247404731.410406483338.58959351667454
6349205170.2931804723-250.293180472298
6447804895.24985593786-115.249855937856
6543004574.43576970945-274.435769709455
6645404630.45005822494-90.4500582249375
6744204569.41636325823-149.416363258231
6846604597.2292458988262.770754101175
6947604774.21287239333-14.2128723933329
7045604728.80739605566-168.80739605566
7146004370.32974011837229.670259881627
7248004572.61134961678227.388650383221
7349804565.00208458101414.99791541899
7443004501.10950564829-201.109505648287
7548004740.2839917995659.7160082004402
7639804641.6021251643-661.602125164296
7741204043.3294317286176.6705682713928
7845804312.47714294966267.522857050344
7942404355.49894265173-115.498942651735
8045404496.0449803491543.9550196508544
8142004631.06113432974-431.061134329735
8247804359.47457786388420.525422136125
8348204404.76224343789415.237756562111
8443204676.82256596118-356.822565961175
8543004543.13701360328-243.137013603285
8637003946.17616132892-246.176161328925
8739204286.40696449446-366.406964494459
8837403687.4291790845352.5708209154736
8941203692.76399554178427.236004458215
9041604178.54499365-18.5449936499963
9141603935.33731113898224.662688861022
9239604274.339949702-314.339949701999
9339604053.57794645453-93.5779464545335
9441604303.23886443815-143.238864438151
9539204136.15330243795-216.153302437951
9634603808.59504954969-348.595049549687
9740403723.55468760704316.445312392961
9837203325.37505839459394.624941605408
9940603842.99234653596217.007653464036
10041403656.1923725124483.8076274876
10137003999.89816073427-299.898160734265
10239004012.56138899753-112.561388997529
10337203849.44798015728-129.447980157282
10437603805.37756316685-45.3775631668514
10535203786.33947570245-266.339475702446
10638003948.75247003212-148.752470032115
10735203744.61796880063-224.617968800627
10836403351.02612165739288.973878342611
10942003812.95730931523387.042690684772
11038603480.36162565512379.638374344884
11141603912.49861228935247.501387710648
11239203864.9869453177555.0130546822465
11338603686.03585634678173.964143653222
11438603963.07564414996-103.075644149957
11537803799.14034465425-19.1403446542531







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1163838.981677160833222.216404956764455.74694936491
1173737.652822887923079.748000475744395.5576453001
1184058.510179699463360.690277724634756.33008167428
1193880.199579142153143.472154278474616.92700400583
1203817.318159520563042.521979194414592.1143398467
1214226.142169832013413.981840876115038.30249878792
1223752.970688202152904.042274244874601.89910215944
1233986.634444965933101.444864049364871.8240258825
1243759.235213081062838.217220216724680.25320594541
1253616.151076233572659.675035808974572.62711665817
1263699.260549377822707.643824440674690.87727431496
1273612.155566113172585.670106002534638.6410262238

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
116 & 3838.98167716083 & 3222.21640495676 & 4455.74694936491 \tabularnewline
117 & 3737.65282288792 & 3079.74800047574 & 4395.5576453001 \tabularnewline
118 & 4058.51017969946 & 3360.69027772463 & 4756.33008167428 \tabularnewline
119 & 3880.19957914215 & 3143.47215427847 & 4616.92700400583 \tabularnewline
120 & 3817.31815952056 & 3042.52197919441 & 4592.1143398467 \tabularnewline
121 & 4226.14216983201 & 3413.98184087611 & 5038.30249878792 \tabularnewline
122 & 3752.97068820215 & 2904.04227424487 & 4601.89910215944 \tabularnewline
123 & 3986.63444496593 & 3101.44486404936 & 4871.8240258825 \tabularnewline
124 & 3759.23521308106 & 2838.21722021672 & 4680.25320594541 \tabularnewline
125 & 3616.15107623357 & 2659.67503580897 & 4572.62711665817 \tabularnewline
126 & 3699.26054937782 & 2707.64382444067 & 4690.87727431496 \tabularnewline
127 & 3612.15556611317 & 2585.67010600253 & 4638.6410262238 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299166&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]116[/C][C]3838.98167716083[/C][C]3222.21640495676[/C][C]4455.74694936491[/C][/ROW]
[ROW][C]117[/C][C]3737.65282288792[/C][C]3079.74800047574[/C][C]4395.5576453001[/C][/ROW]
[ROW][C]118[/C][C]4058.51017969946[/C][C]3360.69027772463[/C][C]4756.33008167428[/C][/ROW]
[ROW][C]119[/C][C]3880.19957914215[/C][C]3143.47215427847[/C][C]4616.92700400583[/C][/ROW]
[ROW][C]120[/C][C]3817.31815952056[/C][C]3042.52197919441[/C][C]4592.1143398467[/C][/ROW]
[ROW][C]121[/C][C]4226.14216983201[/C][C]3413.98184087611[/C][C]5038.30249878792[/C][/ROW]
[ROW][C]122[/C][C]3752.97068820215[/C][C]2904.04227424487[/C][C]4601.89910215944[/C][/ROW]
[ROW][C]123[/C][C]3986.63444496593[/C][C]3101.44486404936[/C][C]4871.8240258825[/C][/ROW]
[ROW][C]124[/C][C]3759.23521308106[/C][C]2838.21722021672[/C][C]4680.25320594541[/C][/ROW]
[ROW][C]125[/C][C]3616.15107623357[/C][C]2659.67503580897[/C][C]4572.62711665817[/C][/ROW]
[ROW][C]126[/C][C]3699.26054937782[/C][C]2707.64382444067[/C][C]4690.87727431496[/C][/ROW]
[ROW][C]127[/C][C]3612.15556611317[/C][C]2585.67010600253[/C][C]4638.6410262238[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299166&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299166&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
1163838.981677160833222.216404956764455.74694936491
1173737.652822887923079.748000475744395.5576453001
1184058.510179699463360.690277724634756.33008167428
1193880.199579142153143.472154278474616.92700400583
1203817.318159520563042.521979194414592.1143398467
1214226.142169832013413.981840876115038.30249878792
1223752.970688202152904.042274244874601.89910215944
1233986.634444965933101.444864049364871.8240258825
1243759.235213081062838.217220216724680.25320594541
1253616.151076233572659.675035808974572.62711665817
1263699.260549377822707.643824440674690.87727431496
1273612.155566113172585.670106002534638.6410262238



Parameters (Session):
par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')