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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 computationWed, 21 Dec 2016 12:46:18 +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/21/t1482320814s73kd6b2ch6l1j0.htm/, Retrieved Tue, 07 May 2024 00:07:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302185, Retrieved Tue, 07 May 2024 00:07:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact59
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-21 11:46:18] [2802fcbee976b89d2ab84425d3d65dcf] [Current]
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Dataseries X:
2312
1089
2742
3145
2966
2055
2450
2742
1697
2409
2233
2100
3434
1867
2365
3578
2845
2778
2056
2757
3325
3671
2147
3225
3556
4661
3344
5375
3907
3356
2184
3510
2834
3271
2834
2408
3261
1526
2938
2352
3915
3145
1566
2746
3572
2651
2805
3354
2523
1480
3278
5081
3332
2789
4111
2508
1833
2371
4268
2194
2935
3347
3034
5448
3427
3036
4196
3009
3369
4168
3403
1779
2761
2582
3153
3011
3419
4042
4379
4602
3249
4372
4328
3695
3614
2114
2839
2490
2610
2372
2833
4018
2734
3027
3862
3281
2746
2538
1805
2500
2601
3178
4193
2606
2491
4090
2786
2280
2403
2934
1601
1946
2554
2006
2830
3173
1960
3052
2151
2493
2752
2542
2027
1940
1877




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302185&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302185&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302185&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 time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.135300968994083
beta0.0293381382196797
gamma0.209233224772551

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.135300968994083 \tabularnewline
beta & 0.0293381382196797 \tabularnewline
gamma & 0.209233224772551 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302185&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]0.135300968994083[/C][/ROW]
[ROW][C]beta[/C][C]0.0293381382196797[/C][/ROW]
[ROW][C]gamma[/C][C]0.209233224772551[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302185&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302185&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
alpha0.135300968994083
beta0.0293381382196797
gamma0.209233224772551







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1334343289.82585470085144.174145299145
1418671791.5667657247375.4332342752748
1523652265.056395481499.9436045185962
1635783405.30069274138172.699307258617
1728452681.49109994084163.508900059161
1827782628.79541454228149.204585457724
1920562772.4232725825-716.423272582502
2027572921.54534917632-164.545349176321
2133251870.142217676071454.85778232393
2236712814.99592579042856.00407420958
2321472783.55537003836-636.55537003836
2432252578.55994899068646.440051009321
2535564054.18061095933-498.180610959325
2646612462.934077013592198.06592298641
2733443242.83886030346101.16113969654
2853754411.20234544633963.797654553667
2939073810.6978288244696.3021711755414
3033563763.9857080479-407.985708047903
3121843691.06546254646-1507.06546254646
3235103845.37521591631-335.375215916308
3328343075.48354534219-241.483545342187
3432713687.37656206419-416.376562064192
3528343213.59431154725-379.594311547246
3624083276.36245131767-868.362451317666
3732614334.79892561034-1073.79892561034
3815263146.05999064103-1620.05999064103
3929383007.40699320812-69.406993208117
4023524285.50509269006-1933.50509269006
4139153101.28257581353813.71742418647
4231453028.48795514399116.512044856013
4315662797.85328113185-1231.85328113185
4427463172.64873740525-426.64873740525
4535722378.295212585291193.70478741471
4626513129.32555428529-478.325554285291
4728052630.16767943435174.832320565652
4833542658.07264251054695.927357489457
4925233875.75225342519-1352.75225342519
5014802534.09330461024-1054.09330461024
5132782738.46697319488539.53302680512
5250813750.013615910121330.98638408988
5333323505.79415185065-173.794151850651
5427893170.60367562718-381.603675627181
5541112624.001309598291486.99869040171
5625083518.51231704646-1010.51231704646
5718332942.17591916526-1109.17591916526
5823713073.82697868805-702.826978688051
5942682656.287209351561611.71279064844
6021942972.40721823007-778.407218230069
6129353613.62600996023-678.626009960232
6233472413.56033627376933.439663726241
6330343179.41232862325-145.412328623247
6454484242.997356363211205.00264363679
6534273710.50095049118-283.50095049118
6630363323.45322051386-287.45322051386
6741963128.621673266171067.37832673383
6830093513.79045841488-504.790458414882
6933692989.32749796913379.672502030875
7041683403.14869477277764.851305227228
7134033615.97771243404-212.977712434036
7217793258.57798318093-1479.57798318093
7327613825.98937069052-1064.98937069052
7425822866.78458038385-284.78458038385
7531533269.25919748299-116.259197482991
7630114577.86606986704-1566.86606986704
7734193386.7798251117632.2201748882353
7840423028.740018975891013.25998102411
7943793247.186217424111131.81378257589
8046023349.055021175351252.94497882465
8132493221.8375695364727.1624304635297
8243723655.65436143874716.345638561262
8343283682.8180135462645.181986453803
8436953213.58648492452481.413515075481
8536144130.33142312145-516.331423121449
8621143397.69662755672-1283.69662755672
8728393702.72101718894-863.721017188937
8824904651.99258145509-2161.99258145509
8926103671.58176755-1061.58176755
9023723340.58501025073-968.58501025073
9128333302.01006468924-469.010064689245
9240183192.52213048802825.477869511978
9327342767.31871488974-33.31871488974
9430273299.02583854452-272.025838544519
9538623157.04722408219704.952775917812
9632812643.97093934829637.029060651711
9727463379.57055864647-633.570558646474
9825382470.0887324111167.9112675888914
9918053017.18586903544-1212.18586903544
10025003666.25371553521-1166.25371553521
10126013005.44246446415-404.442464464148
10231782768.57577563822409.424224361782
10341933000.69493415931192.3050658407
10426063350.645873137-744.645873136999
10524912551.85160153122-60.8516015312243
10640903030.761536494011059.23846350599
10727863245.0631775823-459.063177582296
10822802556.98511023186-276.985110231861
10924032930.18761602976-527.187616029764
11029342153.58808271093780.41191728907
11116012559.88935137206-958.889351372056
11219463246.94623491029-1300.94623491029
11325542700.61361198865-146.613611988648
11420062641.77558524523-635.775585245234
11528302865.86739082175-35.8673908217461
11631732686.07718565992486.92281434008
11719602169.39091075323-209.390910753228
11830522822.02554789602229.974452103981
11921512637.3096681105-486.309668110498
12024931966.25877494816526.741225051843
12127522393.9004283341358.099571665904
12225421968.13284616413573.867153835873
12320272025.463500099671.53649990033023
12419402778.04913084613-838.049130846131
12518772502.49901963065-625.499019630649

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3434 & 3289.82585470085 & 144.174145299145 \tabularnewline
14 & 1867 & 1791.56676572473 & 75.4332342752748 \tabularnewline
15 & 2365 & 2265.0563954814 & 99.9436045185962 \tabularnewline
16 & 3578 & 3405.30069274138 & 172.699307258617 \tabularnewline
17 & 2845 & 2681.49109994084 & 163.508900059161 \tabularnewline
18 & 2778 & 2628.79541454228 & 149.204585457724 \tabularnewline
19 & 2056 & 2772.4232725825 & -716.423272582502 \tabularnewline
20 & 2757 & 2921.54534917632 & -164.545349176321 \tabularnewline
21 & 3325 & 1870.14221767607 & 1454.85778232393 \tabularnewline
22 & 3671 & 2814.99592579042 & 856.00407420958 \tabularnewline
23 & 2147 & 2783.55537003836 & -636.55537003836 \tabularnewline
24 & 3225 & 2578.55994899068 & 646.440051009321 \tabularnewline
25 & 3556 & 4054.18061095933 & -498.180610959325 \tabularnewline
26 & 4661 & 2462.93407701359 & 2198.06592298641 \tabularnewline
27 & 3344 & 3242.83886030346 & 101.16113969654 \tabularnewline
28 & 5375 & 4411.20234544633 & 963.797654553667 \tabularnewline
29 & 3907 & 3810.69782882446 & 96.3021711755414 \tabularnewline
30 & 3356 & 3763.9857080479 & -407.985708047903 \tabularnewline
31 & 2184 & 3691.06546254646 & -1507.06546254646 \tabularnewline
32 & 3510 & 3845.37521591631 & -335.375215916308 \tabularnewline
33 & 2834 & 3075.48354534219 & -241.483545342187 \tabularnewline
34 & 3271 & 3687.37656206419 & -416.376562064192 \tabularnewline
35 & 2834 & 3213.59431154725 & -379.594311547246 \tabularnewline
36 & 2408 & 3276.36245131767 & -868.362451317666 \tabularnewline
37 & 3261 & 4334.79892561034 & -1073.79892561034 \tabularnewline
38 & 1526 & 3146.05999064103 & -1620.05999064103 \tabularnewline
39 & 2938 & 3007.40699320812 & -69.406993208117 \tabularnewline
40 & 2352 & 4285.50509269006 & -1933.50509269006 \tabularnewline
41 & 3915 & 3101.28257581353 & 813.71742418647 \tabularnewline
42 & 3145 & 3028.48795514399 & 116.512044856013 \tabularnewline
43 & 1566 & 2797.85328113185 & -1231.85328113185 \tabularnewline
44 & 2746 & 3172.64873740525 & -426.64873740525 \tabularnewline
45 & 3572 & 2378.29521258529 & 1193.70478741471 \tabularnewline
46 & 2651 & 3129.32555428529 & -478.325554285291 \tabularnewline
47 & 2805 & 2630.16767943435 & 174.832320565652 \tabularnewline
48 & 3354 & 2658.07264251054 & 695.927357489457 \tabularnewline
49 & 2523 & 3875.75225342519 & -1352.75225342519 \tabularnewline
50 & 1480 & 2534.09330461024 & -1054.09330461024 \tabularnewline
51 & 3278 & 2738.46697319488 & 539.53302680512 \tabularnewline
52 & 5081 & 3750.01361591012 & 1330.98638408988 \tabularnewline
53 & 3332 & 3505.79415185065 & -173.794151850651 \tabularnewline
54 & 2789 & 3170.60367562718 & -381.603675627181 \tabularnewline
55 & 4111 & 2624.00130959829 & 1486.99869040171 \tabularnewline
56 & 2508 & 3518.51231704646 & -1010.51231704646 \tabularnewline
57 & 1833 & 2942.17591916526 & -1109.17591916526 \tabularnewline
58 & 2371 & 3073.82697868805 & -702.826978688051 \tabularnewline
59 & 4268 & 2656.28720935156 & 1611.71279064844 \tabularnewline
60 & 2194 & 2972.40721823007 & -778.407218230069 \tabularnewline
61 & 2935 & 3613.62600996023 & -678.626009960232 \tabularnewline
62 & 3347 & 2413.56033627376 & 933.439663726241 \tabularnewline
63 & 3034 & 3179.41232862325 & -145.412328623247 \tabularnewline
64 & 5448 & 4242.99735636321 & 1205.00264363679 \tabularnewline
65 & 3427 & 3710.50095049118 & -283.50095049118 \tabularnewline
66 & 3036 & 3323.45322051386 & -287.45322051386 \tabularnewline
67 & 4196 & 3128.62167326617 & 1067.37832673383 \tabularnewline
68 & 3009 & 3513.79045841488 & -504.790458414882 \tabularnewline
69 & 3369 & 2989.32749796913 & 379.672502030875 \tabularnewline
70 & 4168 & 3403.14869477277 & 764.851305227228 \tabularnewline
71 & 3403 & 3615.97771243404 & -212.977712434036 \tabularnewline
72 & 1779 & 3258.57798318093 & -1479.57798318093 \tabularnewline
73 & 2761 & 3825.98937069052 & -1064.98937069052 \tabularnewline
74 & 2582 & 2866.78458038385 & -284.78458038385 \tabularnewline
75 & 3153 & 3269.25919748299 & -116.259197482991 \tabularnewline
76 & 3011 & 4577.86606986704 & -1566.86606986704 \tabularnewline
77 & 3419 & 3386.77982511176 & 32.2201748882353 \tabularnewline
78 & 4042 & 3028.74001897589 & 1013.25998102411 \tabularnewline
79 & 4379 & 3247.18621742411 & 1131.81378257589 \tabularnewline
80 & 4602 & 3349.05502117535 & 1252.94497882465 \tabularnewline
81 & 3249 & 3221.83756953647 & 27.1624304635297 \tabularnewline
82 & 4372 & 3655.65436143874 & 716.345638561262 \tabularnewline
83 & 4328 & 3682.8180135462 & 645.181986453803 \tabularnewline
84 & 3695 & 3213.58648492452 & 481.413515075481 \tabularnewline
85 & 3614 & 4130.33142312145 & -516.331423121449 \tabularnewline
86 & 2114 & 3397.69662755672 & -1283.69662755672 \tabularnewline
87 & 2839 & 3702.72101718894 & -863.721017188937 \tabularnewline
88 & 2490 & 4651.99258145509 & -2161.99258145509 \tabularnewline
89 & 2610 & 3671.58176755 & -1061.58176755 \tabularnewline
90 & 2372 & 3340.58501025073 & -968.58501025073 \tabularnewline
91 & 2833 & 3302.01006468924 & -469.010064689245 \tabularnewline
92 & 4018 & 3192.52213048802 & 825.477869511978 \tabularnewline
93 & 2734 & 2767.31871488974 & -33.31871488974 \tabularnewline
94 & 3027 & 3299.02583854452 & -272.025838544519 \tabularnewline
95 & 3862 & 3157.04722408219 & 704.952775917812 \tabularnewline
96 & 3281 & 2643.97093934829 & 637.029060651711 \tabularnewline
97 & 2746 & 3379.57055864647 & -633.570558646474 \tabularnewline
98 & 2538 & 2470.08873241111 & 67.9112675888914 \tabularnewline
99 & 1805 & 3017.18586903544 & -1212.18586903544 \tabularnewline
100 & 2500 & 3666.25371553521 & -1166.25371553521 \tabularnewline
101 & 2601 & 3005.44246446415 & -404.442464464148 \tabularnewline
102 & 3178 & 2768.57577563822 & 409.424224361782 \tabularnewline
103 & 4193 & 3000.6949341593 & 1192.3050658407 \tabularnewline
104 & 2606 & 3350.645873137 & -744.645873136999 \tabularnewline
105 & 2491 & 2551.85160153122 & -60.8516015312243 \tabularnewline
106 & 4090 & 3030.76153649401 & 1059.23846350599 \tabularnewline
107 & 2786 & 3245.0631775823 & -459.063177582296 \tabularnewline
108 & 2280 & 2556.98511023186 & -276.985110231861 \tabularnewline
109 & 2403 & 2930.18761602976 & -527.187616029764 \tabularnewline
110 & 2934 & 2153.58808271093 & 780.41191728907 \tabularnewline
111 & 1601 & 2559.88935137206 & -958.889351372056 \tabularnewline
112 & 1946 & 3246.94623491029 & -1300.94623491029 \tabularnewline
113 & 2554 & 2700.61361198865 & -146.613611988648 \tabularnewline
114 & 2006 & 2641.77558524523 & -635.775585245234 \tabularnewline
115 & 2830 & 2865.86739082175 & -35.8673908217461 \tabularnewline
116 & 3173 & 2686.07718565992 & 486.92281434008 \tabularnewline
117 & 1960 & 2169.39091075323 & -209.390910753228 \tabularnewline
118 & 3052 & 2822.02554789602 & 229.974452103981 \tabularnewline
119 & 2151 & 2637.3096681105 & -486.309668110498 \tabularnewline
120 & 2493 & 1966.25877494816 & 526.741225051843 \tabularnewline
121 & 2752 & 2393.9004283341 & 358.099571665904 \tabularnewline
122 & 2542 & 1968.13284616413 & 573.867153835873 \tabularnewline
123 & 2027 & 2025.46350009967 & 1.53649990033023 \tabularnewline
124 & 1940 & 2778.04913084613 & -838.049130846131 \tabularnewline
125 & 1877 & 2502.49901963065 & -625.499019630649 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302185&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]3434[/C][C]3289.82585470085[/C][C]144.174145299145[/C][/ROW]
[ROW][C]14[/C][C]1867[/C][C]1791.56676572473[/C][C]75.4332342752748[/C][/ROW]
[ROW][C]15[/C][C]2365[/C][C]2265.0563954814[/C][C]99.9436045185962[/C][/ROW]
[ROW][C]16[/C][C]3578[/C][C]3405.30069274138[/C][C]172.699307258617[/C][/ROW]
[ROW][C]17[/C][C]2845[/C][C]2681.49109994084[/C][C]163.508900059161[/C][/ROW]
[ROW][C]18[/C][C]2778[/C][C]2628.79541454228[/C][C]149.204585457724[/C][/ROW]
[ROW][C]19[/C][C]2056[/C][C]2772.4232725825[/C][C]-716.423272582502[/C][/ROW]
[ROW][C]20[/C][C]2757[/C][C]2921.54534917632[/C][C]-164.545349176321[/C][/ROW]
[ROW][C]21[/C][C]3325[/C][C]1870.14221767607[/C][C]1454.85778232393[/C][/ROW]
[ROW][C]22[/C][C]3671[/C][C]2814.99592579042[/C][C]856.00407420958[/C][/ROW]
[ROW][C]23[/C][C]2147[/C][C]2783.55537003836[/C][C]-636.55537003836[/C][/ROW]
[ROW][C]24[/C][C]3225[/C][C]2578.55994899068[/C][C]646.440051009321[/C][/ROW]
[ROW][C]25[/C][C]3556[/C][C]4054.18061095933[/C][C]-498.180610959325[/C][/ROW]
[ROW][C]26[/C][C]4661[/C][C]2462.93407701359[/C][C]2198.06592298641[/C][/ROW]
[ROW][C]27[/C][C]3344[/C][C]3242.83886030346[/C][C]101.16113969654[/C][/ROW]
[ROW][C]28[/C][C]5375[/C][C]4411.20234544633[/C][C]963.797654553667[/C][/ROW]
[ROW][C]29[/C][C]3907[/C][C]3810.69782882446[/C][C]96.3021711755414[/C][/ROW]
[ROW][C]30[/C][C]3356[/C][C]3763.9857080479[/C][C]-407.985708047903[/C][/ROW]
[ROW][C]31[/C][C]2184[/C][C]3691.06546254646[/C][C]-1507.06546254646[/C][/ROW]
[ROW][C]32[/C][C]3510[/C][C]3845.37521591631[/C][C]-335.375215916308[/C][/ROW]
[ROW][C]33[/C][C]2834[/C][C]3075.48354534219[/C][C]-241.483545342187[/C][/ROW]
[ROW][C]34[/C][C]3271[/C][C]3687.37656206419[/C][C]-416.376562064192[/C][/ROW]
[ROW][C]35[/C][C]2834[/C][C]3213.59431154725[/C][C]-379.594311547246[/C][/ROW]
[ROW][C]36[/C][C]2408[/C][C]3276.36245131767[/C][C]-868.362451317666[/C][/ROW]
[ROW][C]37[/C][C]3261[/C][C]4334.79892561034[/C][C]-1073.79892561034[/C][/ROW]
[ROW][C]38[/C][C]1526[/C][C]3146.05999064103[/C][C]-1620.05999064103[/C][/ROW]
[ROW][C]39[/C][C]2938[/C][C]3007.40699320812[/C][C]-69.406993208117[/C][/ROW]
[ROW][C]40[/C][C]2352[/C][C]4285.50509269006[/C][C]-1933.50509269006[/C][/ROW]
[ROW][C]41[/C][C]3915[/C][C]3101.28257581353[/C][C]813.71742418647[/C][/ROW]
[ROW][C]42[/C][C]3145[/C][C]3028.48795514399[/C][C]116.512044856013[/C][/ROW]
[ROW][C]43[/C][C]1566[/C][C]2797.85328113185[/C][C]-1231.85328113185[/C][/ROW]
[ROW][C]44[/C][C]2746[/C][C]3172.64873740525[/C][C]-426.64873740525[/C][/ROW]
[ROW][C]45[/C][C]3572[/C][C]2378.29521258529[/C][C]1193.70478741471[/C][/ROW]
[ROW][C]46[/C][C]2651[/C][C]3129.32555428529[/C][C]-478.325554285291[/C][/ROW]
[ROW][C]47[/C][C]2805[/C][C]2630.16767943435[/C][C]174.832320565652[/C][/ROW]
[ROW][C]48[/C][C]3354[/C][C]2658.07264251054[/C][C]695.927357489457[/C][/ROW]
[ROW][C]49[/C][C]2523[/C][C]3875.75225342519[/C][C]-1352.75225342519[/C][/ROW]
[ROW][C]50[/C][C]1480[/C][C]2534.09330461024[/C][C]-1054.09330461024[/C][/ROW]
[ROW][C]51[/C][C]3278[/C][C]2738.46697319488[/C][C]539.53302680512[/C][/ROW]
[ROW][C]52[/C][C]5081[/C][C]3750.01361591012[/C][C]1330.98638408988[/C][/ROW]
[ROW][C]53[/C][C]3332[/C][C]3505.79415185065[/C][C]-173.794151850651[/C][/ROW]
[ROW][C]54[/C][C]2789[/C][C]3170.60367562718[/C][C]-381.603675627181[/C][/ROW]
[ROW][C]55[/C][C]4111[/C][C]2624.00130959829[/C][C]1486.99869040171[/C][/ROW]
[ROW][C]56[/C][C]2508[/C][C]3518.51231704646[/C][C]-1010.51231704646[/C][/ROW]
[ROW][C]57[/C][C]1833[/C][C]2942.17591916526[/C][C]-1109.17591916526[/C][/ROW]
[ROW][C]58[/C][C]2371[/C][C]3073.82697868805[/C][C]-702.826978688051[/C][/ROW]
[ROW][C]59[/C][C]4268[/C][C]2656.28720935156[/C][C]1611.71279064844[/C][/ROW]
[ROW][C]60[/C][C]2194[/C][C]2972.40721823007[/C][C]-778.407218230069[/C][/ROW]
[ROW][C]61[/C][C]2935[/C][C]3613.62600996023[/C][C]-678.626009960232[/C][/ROW]
[ROW][C]62[/C][C]3347[/C][C]2413.56033627376[/C][C]933.439663726241[/C][/ROW]
[ROW][C]63[/C][C]3034[/C][C]3179.41232862325[/C][C]-145.412328623247[/C][/ROW]
[ROW][C]64[/C][C]5448[/C][C]4242.99735636321[/C][C]1205.00264363679[/C][/ROW]
[ROW][C]65[/C][C]3427[/C][C]3710.50095049118[/C][C]-283.50095049118[/C][/ROW]
[ROW][C]66[/C][C]3036[/C][C]3323.45322051386[/C][C]-287.45322051386[/C][/ROW]
[ROW][C]67[/C][C]4196[/C][C]3128.62167326617[/C][C]1067.37832673383[/C][/ROW]
[ROW][C]68[/C][C]3009[/C][C]3513.79045841488[/C][C]-504.790458414882[/C][/ROW]
[ROW][C]69[/C][C]3369[/C][C]2989.32749796913[/C][C]379.672502030875[/C][/ROW]
[ROW][C]70[/C][C]4168[/C][C]3403.14869477277[/C][C]764.851305227228[/C][/ROW]
[ROW][C]71[/C][C]3403[/C][C]3615.97771243404[/C][C]-212.977712434036[/C][/ROW]
[ROW][C]72[/C][C]1779[/C][C]3258.57798318093[/C][C]-1479.57798318093[/C][/ROW]
[ROW][C]73[/C][C]2761[/C][C]3825.98937069052[/C][C]-1064.98937069052[/C][/ROW]
[ROW][C]74[/C][C]2582[/C][C]2866.78458038385[/C][C]-284.78458038385[/C][/ROW]
[ROW][C]75[/C][C]3153[/C][C]3269.25919748299[/C][C]-116.259197482991[/C][/ROW]
[ROW][C]76[/C][C]3011[/C][C]4577.86606986704[/C][C]-1566.86606986704[/C][/ROW]
[ROW][C]77[/C][C]3419[/C][C]3386.77982511176[/C][C]32.2201748882353[/C][/ROW]
[ROW][C]78[/C][C]4042[/C][C]3028.74001897589[/C][C]1013.25998102411[/C][/ROW]
[ROW][C]79[/C][C]4379[/C][C]3247.18621742411[/C][C]1131.81378257589[/C][/ROW]
[ROW][C]80[/C][C]4602[/C][C]3349.05502117535[/C][C]1252.94497882465[/C][/ROW]
[ROW][C]81[/C][C]3249[/C][C]3221.83756953647[/C][C]27.1624304635297[/C][/ROW]
[ROW][C]82[/C][C]4372[/C][C]3655.65436143874[/C][C]716.345638561262[/C][/ROW]
[ROW][C]83[/C][C]4328[/C][C]3682.8180135462[/C][C]645.181986453803[/C][/ROW]
[ROW][C]84[/C][C]3695[/C][C]3213.58648492452[/C][C]481.413515075481[/C][/ROW]
[ROW][C]85[/C][C]3614[/C][C]4130.33142312145[/C][C]-516.331423121449[/C][/ROW]
[ROW][C]86[/C][C]2114[/C][C]3397.69662755672[/C][C]-1283.69662755672[/C][/ROW]
[ROW][C]87[/C][C]2839[/C][C]3702.72101718894[/C][C]-863.721017188937[/C][/ROW]
[ROW][C]88[/C][C]2490[/C][C]4651.99258145509[/C][C]-2161.99258145509[/C][/ROW]
[ROW][C]89[/C][C]2610[/C][C]3671.58176755[/C][C]-1061.58176755[/C][/ROW]
[ROW][C]90[/C][C]2372[/C][C]3340.58501025073[/C][C]-968.58501025073[/C][/ROW]
[ROW][C]91[/C][C]2833[/C][C]3302.01006468924[/C][C]-469.010064689245[/C][/ROW]
[ROW][C]92[/C][C]4018[/C][C]3192.52213048802[/C][C]825.477869511978[/C][/ROW]
[ROW][C]93[/C][C]2734[/C][C]2767.31871488974[/C][C]-33.31871488974[/C][/ROW]
[ROW][C]94[/C][C]3027[/C][C]3299.02583854452[/C][C]-272.025838544519[/C][/ROW]
[ROW][C]95[/C][C]3862[/C][C]3157.04722408219[/C][C]704.952775917812[/C][/ROW]
[ROW][C]96[/C][C]3281[/C][C]2643.97093934829[/C][C]637.029060651711[/C][/ROW]
[ROW][C]97[/C][C]2746[/C][C]3379.57055864647[/C][C]-633.570558646474[/C][/ROW]
[ROW][C]98[/C][C]2538[/C][C]2470.08873241111[/C][C]67.9112675888914[/C][/ROW]
[ROW][C]99[/C][C]1805[/C][C]3017.18586903544[/C][C]-1212.18586903544[/C][/ROW]
[ROW][C]100[/C][C]2500[/C][C]3666.25371553521[/C][C]-1166.25371553521[/C][/ROW]
[ROW][C]101[/C][C]2601[/C][C]3005.44246446415[/C][C]-404.442464464148[/C][/ROW]
[ROW][C]102[/C][C]3178[/C][C]2768.57577563822[/C][C]409.424224361782[/C][/ROW]
[ROW][C]103[/C][C]4193[/C][C]3000.6949341593[/C][C]1192.3050658407[/C][/ROW]
[ROW][C]104[/C][C]2606[/C][C]3350.645873137[/C][C]-744.645873136999[/C][/ROW]
[ROW][C]105[/C][C]2491[/C][C]2551.85160153122[/C][C]-60.8516015312243[/C][/ROW]
[ROW][C]106[/C][C]4090[/C][C]3030.76153649401[/C][C]1059.23846350599[/C][/ROW]
[ROW][C]107[/C][C]2786[/C][C]3245.0631775823[/C][C]-459.063177582296[/C][/ROW]
[ROW][C]108[/C][C]2280[/C][C]2556.98511023186[/C][C]-276.985110231861[/C][/ROW]
[ROW][C]109[/C][C]2403[/C][C]2930.18761602976[/C][C]-527.187616029764[/C][/ROW]
[ROW][C]110[/C][C]2934[/C][C]2153.58808271093[/C][C]780.41191728907[/C][/ROW]
[ROW][C]111[/C][C]1601[/C][C]2559.88935137206[/C][C]-958.889351372056[/C][/ROW]
[ROW][C]112[/C][C]1946[/C][C]3246.94623491029[/C][C]-1300.94623491029[/C][/ROW]
[ROW][C]113[/C][C]2554[/C][C]2700.61361198865[/C][C]-146.613611988648[/C][/ROW]
[ROW][C]114[/C][C]2006[/C][C]2641.77558524523[/C][C]-635.775585245234[/C][/ROW]
[ROW][C]115[/C][C]2830[/C][C]2865.86739082175[/C][C]-35.8673908217461[/C][/ROW]
[ROW][C]116[/C][C]3173[/C][C]2686.07718565992[/C][C]486.92281434008[/C][/ROW]
[ROW][C]117[/C][C]1960[/C][C]2169.39091075323[/C][C]-209.390910753228[/C][/ROW]
[ROW][C]118[/C][C]3052[/C][C]2822.02554789602[/C][C]229.974452103981[/C][/ROW]
[ROW][C]119[/C][C]2151[/C][C]2637.3096681105[/C][C]-486.309668110498[/C][/ROW]
[ROW][C]120[/C][C]2493[/C][C]1966.25877494816[/C][C]526.741225051843[/C][/ROW]
[ROW][C]121[/C][C]2752[/C][C]2393.9004283341[/C][C]358.099571665904[/C][/ROW]
[ROW][C]122[/C][C]2542[/C][C]1968.13284616413[/C][C]573.867153835873[/C][/ROW]
[ROW][C]123[/C][C]2027[/C][C]2025.46350009967[/C][C]1.53649990033023[/C][/ROW]
[ROW][C]124[/C][C]1940[/C][C]2778.04913084613[/C][C]-838.049130846131[/C][/ROW]
[ROW][C]125[/C][C]1877[/C][C]2502.49901963065[/C][C]-625.499019630649[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302185&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302185&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
1334343289.82585470085144.174145299145
1418671791.5667657247375.4332342752748
1523652265.056395481499.9436045185962
1635783405.30069274138172.699307258617
1728452681.49109994084163.508900059161
1827782628.79541454228149.204585457724
1920562772.4232725825-716.423272582502
2027572921.54534917632-164.545349176321
2133251870.142217676071454.85778232393
2236712814.99592579042856.00407420958
2321472783.55537003836-636.55537003836
2432252578.55994899068646.440051009321
2535564054.18061095933-498.180610959325
2646612462.934077013592198.06592298641
2733443242.83886030346101.16113969654
2853754411.20234544633963.797654553667
2939073810.6978288244696.3021711755414
3033563763.9857080479-407.985708047903
3121843691.06546254646-1507.06546254646
3235103845.37521591631-335.375215916308
3328343075.48354534219-241.483545342187
3432713687.37656206419-416.376562064192
3528343213.59431154725-379.594311547246
3624083276.36245131767-868.362451317666
3732614334.79892561034-1073.79892561034
3815263146.05999064103-1620.05999064103
3929383007.40699320812-69.406993208117
4023524285.50509269006-1933.50509269006
4139153101.28257581353813.71742418647
4231453028.48795514399116.512044856013
4315662797.85328113185-1231.85328113185
4427463172.64873740525-426.64873740525
4535722378.295212585291193.70478741471
4626513129.32555428529-478.325554285291
4728052630.16767943435174.832320565652
4833542658.07264251054695.927357489457
4925233875.75225342519-1352.75225342519
5014802534.09330461024-1054.09330461024
5132782738.46697319488539.53302680512
5250813750.013615910121330.98638408988
5333323505.79415185065-173.794151850651
5427893170.60367562718-381.603675627181
5541112624.001309598291486.99869040171
5625083518.51231704646-1010.51231704646
5718332942.17591916526-1109.17591916526
5823713073.82697868805-702.826978688051
5942682656.287209351561611.71279064844
6021942972.40721823007-778.407218230069
6129353613.62600996023-678.626009960232
6233472413.56033627376933.439663726241
6330343179.41232862325-145.412328623247
6454484242.997356363211205.00264363679
6534273710.50095049118-283.50095049118
6630363323.45322051386-287.45322051386
6741963128.621673266171067.37832673383
6830093513.79045841488-504.790458414882
6933692989.32749796913379.672502030875
7041683403.14869477277764.851305227228
7134033615.97771243404-212.977712434036
7217793258.57798318093-1479.57798318093
7327613825.98937069052-1064.98937069052
7425822866.78458038385-284.78458038385
7531533269.25919748299-116.259197482991
7630114577.86606986704-1566.86606986704
7734193386.7798251117632.2201748882353
7840423028.740018975891013.25998102411
7943793247.186217424111131.81378257589
8046023349.055021175351252.94497882465
8132493221.8375695364727.1624304635297
8243723655.65436143874716.345638561262
8343283682.8180135462645.181986453803
8436953213.58648492452481.413515075481
8536144130.33142312145-516.331423121449
8621143397.69662755672-1283.69662755672
8728393702.72101718894-863.721017188937
8824904651.99258145509-2161.99258145509
8926103671.58176755-1061.58176755
9023723340.58501025073-968.58501025073
9128333302.01006468924-469.010064689245
9240183192.52213048802825.477869511978
9327342767.31871488974-33.31871488974
9430273299.02583854452-272.025838544519
9538623157.04722408219704.952775917812
9632812643.97093934829637.029060651711
9727463379.57055864647-633.570558646474
9825382470.0887324111167.9112675888914
9918053017.18586903544-1212.18586903544
10025003666.25371553521-1166.25371553521
10126013005.44246446415-404.442464464148
10231782768.57577563822409.424224361782
10341933000.69493415931192.3050658407
10426063350.645873137-744.645873136999
10524912551.85160153122-60.8516015312243
10640903030.761536494011059.23846350599
10727863245.0631775823-459.063177582296
10822802556.98511023186-276.985110231861
10924032930.18761602976-527.187616029764
11029342153.58808271093780.41191728907
11116012559.88935137206-958.889351372056
11219463246.94623491029-1300.94623491029
11325542700.61361198865-146.613611988648
11420062641.77558524523-635.775585245234
11528302865.86739082175-35.8673908217461
11631732686.07718565992486.92281434008
11719602169.39091075323-209.390910753228
11830522822.02554789602229.974452103981
11921512637.3096681105-486.309668110498
12024931966.25877494816526.741225051843
12127522393.9004283341358.099571665904
12225421968.13284616413573.867153835873
12320272025.463500099671.53649990033023
12419402778.04913084613-838.049130846131
12518772502.49901963065-625.499019630649







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1262287.77125991767643.9223886432793931.62013119206
1272706.350419451141046.635854422114366.06498448016
1282626.06930597234949.7351790575774302.40343288711
1291915.66039667367221.9498925661753609.37090078117
1302675.08683224956963.2413093037454386.93235519538
1312327.71885543048596.9789182241574058.45879263681
1321905.73800109337155.3445206943943656.13148149234
1332229.49577121521458.6908498752974000.30069255513
1341790.78898319268-1.18313906855863582.76110545391
1351661.12321356684-152.7688851666383475.01531230031
1362255.79043663307419.2293559265894092.35151733955
1372129.60164669381269.6270726792473989.57622070838

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
126 & 2287.77125991767 & 643.922388643279 & 3931.62013119206 \tabularnewline
127 & 2706.35041945114 & 1046.63585442211 & 4366.06498448016 \tabularnewline
128 & 2626.06930597234 & 949.735179057577 & 4302.40343288711 \tabularnewline
129 & 1915.66039667367 & 221.949892566175 & 3609.37090078117 \tabularnewline
130 & 2675.08683224956 & 963.241309303745 & 4386.93235519538 \tabularnewline
131 & 2327.71885543048 & 596.978918224157 & 4058.45879263681 \tabularnewline
132 & 1905.73800109337 & 155.344520694394 & 3656.13148149234 \tabularnewline
133 & 2229.49577121521 & 458.690849875297 & 4000.30069255513 \tabularnewline
134 & 1790.78898319268 & -1.1831390685586 & 3582.76110545391 \tabularnewline
135 & 1661.12321356684 & -152.768885166638 & 3475.01531230031 \tabularnewline
136 & 2255.79043663307 & 419.229355926589 & 4092.35151733955 \tabularnewline
137 & 2129.60164669381 & 269.627072679247 & 3989.57622070838 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302185&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]126[/C][C]2287.77125991767[/C][C]643.922388643279[/C][C]3931.62013119206[/C][/ROW]
[ROW][C]127[/C][C]2706.35041945114[/C][C]1046.63585442211[/C][C]4366.06498448016[/C][/ROW]
[ROW][C]128[/C][C]2626.06930597234[/C][C]949.735179057577[/C][C]4302.40343288711[/C][/ROW]
[ROW][C]129[/C][C]1915.66039667367[/C][C]221.949892566175[/C][C]3609.37090078117[/C][/ROW]
[ROW][C]130[/C][C]2675.08683224956[/C][C]963.241309303745[/C][C]4386.93235519538[/C][/ROW]
[ROW][C]131[/C][C]2327.71885543048[/C][C]596.978918224157[/C][C]4058.45879263681[/C][/ROW]
[ROW][C]132[/C][C]1905.73800109337[/C][C]155.344520694394[/C][C]3656.13148149234[/C][/ROW]
[ROW][C]133[/C][C]2229.49577121521[/C][C]458.690849875297[/C][C]4000.30069255513[/C][/ROW]
[ROW][C]134[/C][C]1790.78898319268[/C][C]-1.1831390685586[/C][C]3582.76110545391[/C][/ROW]
[ROW][C]135[/C][C]1661.12321356684[/C][C]-152.768885166638[/C][C]3475.01531230031[/C][/ROW]
[ROW][C]136[/C][C]2255.79043663307[/C][C]419.229355926589[/C][C]4092.35151733955[/C][/ROW]
[ROW][C]137[/C][C]2129.60164669381[/C][C]269.627072679247[/C][C]3989.57622070838[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302185&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302185&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
1262287.77125991767643.9223886432793931.62013119206
1272706.350419451141046.635854422114366.06498448016
1282626.06930597234949.7351790575774302.40343288711
1291915.66039667367221.9498925661753609.37090078117
1302675.08683224956963.2413093037454386.93235519538
1312327.71885543048596.9789182241574058.45879263681
1321905.73800109337155.3445206943943656.13148149234
1332229.49577121521458.6908498752974000.30069255513
1341790.78898319268-1.18313906855863582.76110545391
1351661.12321356684-152.7688851666383475.01531230031
1362255.79043663307419.2293559265894092.35151733955
1372129.60164669381269.6270726792473989.57622070838



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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 <- 'Single'
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')