Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 07 Dec 2016 13:54:53 +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/07/t1481115347u3cea9z797ouo6i.htm/, Retrieved Tue, 07 May 2024 08:36:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298076, Retrieved Tue, 07 May 2024 08:36:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsF1 competition
Estimated Impact47
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2016-12-07 12:54:53] [00d6a26c230b6c589ee3bbc701d55499] [Current]
Feedback Forum

Post a new message
Dataseries X:
3840
3140
4580
4740
3920
4900
3400
3440
2600
2220
2190
2550
2720
3720
4710
5070
6030
5280
4420
3940
2750
2980
2690
2650
4000
4150
6050
6280
5520
4800
4610
3530
2790
2750
2470
2610
3680
3820
4460
4760
3290
3610
3650
3130
2850
2720
2740
2760
3330
3850
5430
5180
4770
5360
4950
3720
3330
3000
2760
3040
3260
3780
4670
4320
4080
4210
3350
3390
2630
2350
2330
2230
2830
3230
4240
3750
4160
3960
3000
2890
2300
2320
2270
1970
2920
3310
4370
3990
3970
3850
3510
2840
2130
2280
1960
1740
2370
1980
2680
3510
3350
3290
3150
2490
2490
2930
3590
2040
2480
2760
3400
3470
3130
3670
3080
2430




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=298076&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=298076&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298076&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
alpha0.47532948343221
beta0.0247383914198423
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.47532948343221 \tabularnewline
beta & 0.0247383914198423 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298076&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]0.47532948343221[/C][/ROW]
[ROW][C]beta[/C][C]0.0247383914198423[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298076&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298076&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
alpha0.47532948343221
beta0.0247383914198423
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1327202351.88034188034368.119658119656
1437203521.27455879705198.725441202951
1547104638.7375000606171.262499939392
1650705055.6181816341914.381818365815
1760306031.04757905914-1.04757905913812
1852805316.63061061283-36.6306106128322
1944203975.70257628835444.297423711652
2039404315.26492587147-375.264925871469
2127503328.76909606464-578.769096064636
2229802709.15272053788270.847279462124
2326902764.06892040902-74.0689204090168
2426503042.08197978311-392.081979783111
2540003212.88180614899787.118193851005
2641504496.42819318503-346.428193185029
2760505285.34305576903764.656944230966
2862806007.58005454808272.419945451917
2955207106.21058360918-1586.21058360918
3048005609.6531350546-809.653135054603
3146104134.52717888339475.472821116615
3235304040.18821584167-510.188215841674
3327902862.48048566214-72.4804856621358
3427502914.93382233365-164.933822333654
3524702562.26590070373-92.2659007037346
3626102645.08619172959-35.0861917295897
3736803588.7749479532491.2250520467587
3838203923.12825233958-103.128252339581
3944605389.82911299785-929.829112997852
4047605007.62416920657-247.624169206567
4132904837.0380983296-1547.0380983296
4236103720.14224970173-110.142249701732
4336503213.61257498225436.387425017754
4431302544.91871901536585.08128098464
4528502091.72719755883758.272802441173
4627202474.57324317834245.426756821664
4727402343.93262080627396.067379193734
4827602683.4589818868276.5410181131801
4933303742.37819628205-412.378196282053
5038503725.35973523949124.640264760513
5154304859.23557914570.764420860001
5251805558.54057369796-378.540573697962
5347704652.72323608516117.276763914839
5453605109.1540260513250.845973948702
5549505093.53735132378-143.537351323779
5637204252.96081076799-532.960810767985
5733303371.80985155861-41.8098515586125
5830003108.48018865138-108.48018865138
5927602887.69466792287-127.69466792287
6030402803.49738021342236.502619786575
6132603676.69248912564-416.692489125639
6237803934.09326537601-154.093265376009
6346705160.9816343033-490.981634303298
6443204836.48472984847-516.484729848466
6540804102.5667834791-22.5667834791002
6642104538.28881136199-328.28881136199
6733504009.34418754267-659.344187542673
6833902682.07832038467707.921679615328
6926302625.847096603714.15290339628973
7023502327.3246716905922.6753283094108
7123302138.28195282892191.718047171085
7222302380.23245153131-150.232451531308
7328302705.57911609496124.420883905044
7432303343.01834624719-113.018346247188
7542404398.2116794861-158.211679486097
7637504207.95866644736-457.958666447357
7741603751.14151198555408.858488014454
7839604226.73988230809-266.739882308091
7930003549.2905560953-549.290556095299
8028902988.92889391282-98.9288939128228
8123002167.67179225877132.328207741232
8223201929.04095350431390.959046495691
8322701997.32459605794272.67540394206
8419702092.87565820074-122.875658200743
8529202570.18049568463349.819504315367
8633103187.68358406857122.31641593143
8743704331.2967455467538.7032544532467
8839904079.96018706432-89.9601870643191
8939704259.76960359521-289.769603595207
9038504047.52044909994-197.520449099939
9135103254.23864685312255.761353146876
9228403321.81138755525-481.811387555246
9321302444.36846785049-314.368467850488
9422802128.32858603986151.671413960135
9519602017.22114703549-57.2211470354864
9617401740.95878075618-0.958780756177475
9723702518.18723532005-148.187235320051
9819802767.71658522608-787.716585226076
9926803412.30160539699-732.301605396986
10035102695.31836761718814.681632382818
10133503179.27476063663170.725239363365
10232903218.7058577930271.2941422069839
10331502778.57717834303371.42282165697
10424902503.05862900783-13.0586290078309
10524901930.70616444298559.293835557017
10629302279.16050106094650.839498939059
10735902306.291644688321283.70835531168
10820402723.26869163979-683.268691639789
10924803117.24237518065-637.242375180652
11027602811.3301354432-51.3301354432037
11134003856.23796913495-456.237969134955
11234704106.6006291606-636.600629160603
11331303570.25759496317-440.257594963171
11436703267.32024784029402.679752159713
11530803146.29259020429-66.292590204288
11624302459.95687467713-29.9568746771261

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2720 & 2351.88034188034 & 368.119658119656 \tabularnewline
14 & 3720 & 3521.27455879705 & 198.725441202951 \tabularnewline
15 & 4710 & 4638.73750006061 & 71.262499939392 \tabularnewline
16 & 5070 & 5055.61818163419 & 14.381818365815 \tabularnewline
17 & 6030 & 6031.04757905914 & -1.04757905913812 \tabularnewline
18 & 5280 & 5316.63061061283 & -36.6306106128322 \tabularnewline
19 & 4420 & 3975.70257628835 & 444.297423711652 \tabularnewline
20 & 3940 & 4315.26492587147 & -375.264925871469 \tabularnewline
21 & 2750 & 3328.76909606464 & -578.769096064636 \tabularnewline
22 & 2980 & 2709.15272053788 & 270.847279462124 \tabularnewline
23 & 2690 & 2764.06892040902 & -74.0689204090168 \tabularnewline
24 & 2650 & 3042.08197978311 & -392.081979783111 \tabularnewline
25 & 4000 & 3212.88180614899 & 787.118193851005 \tabularnewline
26 & 4150 & 4496.42819318503 & -346.428193185029 \tabularnewline
27 & 6050 & 5285.34305576903 & 764.656944230966 \tabularnewline
28 & 6280 & 6007.58005454808 & 272.419945451917 \tabularnewline
29 & 5520 & 7106.21058360918 & -1586.21058360918 \tabularnewline
30 & 4800 & 5609.6531350546 & -809.653135054603 \tabularnewline
31 & 4610 & 4134.52717888339 & 475.472821116615 \tabularnewline
32 & 3530 & 4040.18821584167 & -510.188215841674 \tabularnewline
33 & 2790 & 2862.48048566214 & -72.4804856621358 \tabularnewline
34 & 2750 & 2914.93382233365 & -164.933822333654 \tabularnewline
35 & 2470 & 2562.26590070373 & -92.2659007037346 \tabularnewline
36 & 2610 & 2645.08619172959 & -35.0861917295897 \tabularnewline
37 & 3680 & 3588.77494795324 & 91.2250520467587 \tabularnewline
38 & 3820 & 3923.12825233958 & -103.128252339581 \tabularnewline
39 & 4460 & 5389.82911299785 & -929.829112997852 \tabularnewline
40 & 4760 & 5007.62416920657 & -247.624169206567 \tabularnewline
41 & 3290 & 4837.0380983296 & -1547.0380983296 \tabularnewline
42 & 3610 & 3720.14224970173 & -110.142249701732 \tabularnewline
43 & 3650 & 3213.61257498225 & 436.387425017754 \tabularnewline
44 & 3130 & 2544.91871901536 & 585.08128098464 \tabularnewline
45 & 2850 & 2091.72719755883 & 758.272802441173 \tabularnewline
46 & 2720 & 2474.57324317834 & 245.426756821664 \tabularnewline
47 & 2740 & 2343.93262080627 & 396.067379193734 \tabularnewline
48 & 2760 & 2683.45898188682 & 76.5410181131801 \tabularnewline
49 & 3330 & 3742.37819628205 & -412.378196282053 \tabularnewline
50 & 3850 & 3725.35973523949 & 124.640264760513 \tabularnewline
51 & 5430 & 4859.23557914 & 570.764420860001 \tabularnewline
52 & 5180 & 5558.54057369796 & -378.540573697962 \tabularnewline
53 & 4770 & 4652.72323608516 & 117.276763914839 \tabularnewline
54 & 5360 & 5109.1540260513 & 250.845973948702 \tabularnewline
55 & 4950 & 5093.53735132378 & -143.537351323779 \tabularnewline
56 & 3720 & 4252.96081076799 & -532.960810767985 \tabularnewline
57 & 3330 & 3371.80985155861 & -41.8098515586125 \tabularnewline
58 & 3000 & 3108.48018865138 & -108.48018865138 \tabularnewline
59 & 2760 & 2887.69466792287 & -127.69466792287 \tabularnewline
60 & 3040 & 2803.49738021342 & 236.502619786575 \tabularnewline
61 & 3260 & 3676.69248912564 & -416.692489125639 \tabularnewline
62 & 3780 & 3934.09326537601 & -154.093265376009 \tabularnewline
63 & 4670 & 5160.9816343033 & -490.981634303298 \tabularnewline
64 & 4320 & 4836.48472984847 & -516.484729848466 \tabularnewline
65 & 4080 & 4102.5667834791 & -22.5667834791002 \tabularnewline
66 & 4210 & 4538.28881136199 & -328.28881136199 \tabularnewline
67 & 3350 & 4009.34418754267 & -659.344187542673 \tabularnewline
68 & 3390 & 2682.07832038467 & 707.921679615328 \tabularnewline
69 & 2630 & 2625.84709660371 & 4.15290339628973 \tabularnewline
70 & 2350 & 2327.32467169059 & 22.6753283094108 \tabularnewline
71 & 2330 & 2138.28195282892 & 191.718047171085 \tabularnewline
72 & 2230 & 2380.23245153131 & -150.232451531308 \tabularnewline
73 & 2830 & 2705.57911609496 & 124.420883905044 \tabularnewline
74 & 3230 & 3343.01834624719 & -113.018346247188 \tabularnewline
75 & 4240 & 4398.2116794861 & -158.211679486097 \tabularnewline
76 & 3750 & 4207.95866644736 & -457.958666447357 \tabularnewline
77 & 4160 & 3751.14151198555 & 408.858488014454 \tabularnewline
78 & 3960 & 4226.73988230809 & -266.739882308091 \tabularnewline
79 & 3000 & 3549.2905560953 & -549.290556095299 \tabularnewline
80 & 2890 & 2988.92889391282 & -98.9288939128228 \tabularnewline
81 & 2300 & 2167.67179225877 & 132.328207741232 \tabularnewline
82 & 2320 & 1929.04095350431 & 390.959046495691 \tabularnewline
83 & 2270 & 1997.32459605794 & 272.67540394206 \tabularnewline
84 & 1970 & 2092.87565820074 & -122.875658200743 \tabularnewline
85 & 2920 & 2570.18049568463 & 349.819504315367 \tabularnewline
86 & 3310 & 3187.68358406857 & 122.31641593143 \tabularnewline
87 & 4370 & 4331.29674554675 & 38.7032544532467 \tabularnewline
88 & 3990 & 4079.96018706432 & -89.9601870643191 \tabularnewline
89 & 3970 & 4259.76960359521 & -289.769603595207 \tabularnewline
90 & 3850 & 4047.52044909994 & -197.520449099939 \tabularnewline
91 & 3510 & 3254.23864685312 & 255.761353146876 \tabularnewline
92 & 2840 & 3321.81138755525 & -481.811387555246 \tabularnewline
93 & 2130 & 2444.36846785049 & -314.368467850488 \tabularnewline
94 & 2280 & 2128.32858603986 & 151.671413960135 \tabularnewline
95 & 1960 & 2017.22114703549 & -57.2211470354864 \tabularnewline
96 & 1740 & 1740.95878075618 & -0.958780756177475 \tabularnewline
97 & 2370 & 2518.18723532005 & -148.187235320051 \tabularnewline
98 & 1980 & 2767.71658522608 & -787.716585226076 \tabularnewline
99 & 2680 & 3412.30160539699 & -732.301605396986 \tabularnewline
100 & 3510 & 2695.31836761718 & 814.681632382818 \tabularnewline
101 & 3350 & 3179.27476063663 & 170.725239363365 \tabularnewline
102 & 3290 & 3218.70585779302 & 71.2941422069839 \tabularnewline
103 & 3150 & 2778.57717834303 & 371.42282165697 \tabularnewline
104 & 2490 & 2503.05862900783 & -13.0586290078309 \tabularnewline
105 & 2490 & 1930.70616444298 & 559.293835557017 \tabularnewline
106 & 2930 & 2279.16050106094 & 650.839498939059 \tabularnewline
107 & 3590 & 2306.29164468832 & 1283.70835531168 \tabularnewline
108 & 2040 & 2723.26869163979 & -683.268691639789 \tabularnewline
109 & 2480 & 3117.24237518065 & -637.242375180652 \tabularnewline
110 & 2760 & 2811.3301354432 & -51.3301354432037 \tabularnewline
111 & 3400 & 3856.23796913495 & -456.237969134955 \tabularnewline
112 & 3470 & 4106.6006291606 & -636.600629160603 \tabularnewline
113 & 3130 & 3570.25759496317 & -440.257594963171 \tabularnewline
114 & 3670 & 3267.32024784029 & 402.679752159713 \tabularnewline
115 & 3080 & 3146.29259020429 & -66.292590204288 \tabularnewline
116 & 2430 & 2459.95687467713 & -29.9568746771261 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298076&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]2720[/C][C]2351.88034188034[/C][C]368.119658119656[/C][/ROW]
[ROW][C]14[/C][C]3720[/C][C]3521.27455879705[/C][C]198.725441202951[/C][/ROW]
[ROW][C]15[/C][C]4710[/C][C]4638.73750006061[/C][C]71.262499939392[/C][/ROW]
[ROW][C]16[/C][C]5070[/C][C]5055.61818163419[/C][C]14.381818365815[/C][/ROW]
[ROW][C]17[/C][C]6030[/C][C]6031.04757905914[/C][C]-1.04757905913812[/C][/ROW]
[ROW][C]18[/C][C]5280[/C][C]5316.63061061283[/C][C]-36.6306106128322[/C][/ROW]
[ROW][C]19[/C][C]4420[/C][C]3975.70257628835[/C][C]444.297423711652[/C][/ROW]
[ROW][C]20[/C][C]3940[/C][C]4315.26492587147[/C][C]-375.264925871469[/C][/ROW]
[ROW][C]21[/C][C]2750[/C][C]3328.76909606464[/C][C]-578.769096064636[/C][/ROW]
[ROW][C]22[/C][C]2980[/C][C]2709.15272053788[/C][C]270.847279462124[/C][/ROW]
[ROW][C]23[/C][C]2690[/C][C]2764.06892040902[/C][C]-74.0689204090168[/C][/ROW]
[ROW][C]24[/C][C]2650[/C][C]3042.08197978311[/C][C]-392.081979783111[/C][/ROW]
[ROW][C]25[/C][C]4000[/C][C]3212.88180614899[/C][C]787.118193851005[/C][/ROW]
[ROW][C]26[/C][C]4150[/C][C]4496.42819318503[/C][C]-346.428193185029[/C][/ROW]
[ROW][C]27[/C][C]6050[/C][C]5285.34305576903[/C][C]764.656944230966[/C][/ROW]
[ROW][C]28[/C][C]6280[/C][C]6007.58005454808[/C][C]272.419945451917[/C][/ROW]
[ROW][C]29[/C][C]5520[/C][C]7106.21058360918[/C][C]-1586.21058360918[/C][/ROW]
[ROW][C]30[/C][C]4800[/C][C]5609.6531350546[/C][C]-809.653135054603[/C][/ROW]
[ROW][C]31[/C][C]4610[/C][C]4134.52717888339[/C][C]475.472821116615[/C][/ROW]
[ROW][C]32[/C][C]3530[/C][C]4040.18821584167[/C][C]-510.188215841674[/C][/ROW]
[ROW][C]33[/C][C]2790[/C][C]2862.48048566214[/C][C]-72.4804856621358[/C][/ROW]
[ROW][C]34[/C][C]2750[/C][C]2914.93382233365[/C][C]-164.933822333654[/C][/ROW]
[ROW][C]35[/C][C]2470[/C][C]2562.26590070373[/C][C]-92.2659007037346[/C][/ROW]
[ROW][C]36[/C][C]2610[/C][C]2645.08619172959[/C][C]-35.0861917295897[/C][/ROW]
[ROW][C]37[/C][C]3680[/C][C]3588.77494795324[/C][C]91.2250520467587[/C][/ROW]
[ROW][C]38[/C][C]3820[/C][C]3923.12825233958[/C][C]-103.128252339581[/C][/ROW]
[ROW][C]39[/C][C]4460[/C][C]5389.82911299785[/C][C]-929.829112997852[/C][/ROW]
[ROW][C]40[/C][C]4760[/C][C]5007.62416920657[/C][C]-247.624169206567[/C][/ROW]
[ROW][C]41[/C][C]3290[/C][C]4837.0380983296[/C][C]-1547.0380983296[/C][/ROW]
[ROW][C]42[/C][C]3610[/C][C]3720.14224970173[/C][C]-110.142249701732[/C][/ROW]
[ROW][C]43[/C][C]3650[/C][C]3213.61257498225[/C][C]436.387425017754[/C][/ROW]
[ROW][C]44[/C][C]3130[/C][C]2544.91871901536[/C][C]585.08128098464[/C][/ROW]
[ROW][C]45[/C][C]2850[/C][C]2091.72719755883[/C][C]758.272802441173[/C][/ROW]
[ROW][C]46[/C][C]2720[/C][C]2474.57324317834[/C][C]245.426756821664[/C][/ROW]
[ROW][C]47[/C][C]2740[/C][C]2343.93262080627[/C][C]396.067379193734[/C][/ROW]
[ROW][C]48[/C][C]2760[/C][C]2683.45898188682[/C][C]76.5410181131801[/C][/ROW]
[ROW][C]49[/C][C]3330[/C][C]3742.37819628205[/C][C]-412.378196282053[/C][/ROW]
[ROW][C]50[/C][C]3850[/C][C]3725.35973523949[/C][C]124.640264760513[/C][/ROW]
[ROW][C]51[/C][C]5430[/C][C]4859.23557914[/C][C]570.764420860001[/C][/ROW]
[ROW][C]52[/C][C]5180[/C][C]5558.54057369796[/C][C]-378.540573697962[/C][/ROW]
[ROW][C]53[/C][C]4770[/C][C]4652.72323608516[/C][C]117.276763914839[/C][/ROW]
[ROW][C]54[/C][C]5360[/C][C]5109.1540260513[/C][C]250.845973948702[/C][/ROW]
[ROW][C]55[/C][C]4950[/C][C]5093.53735132378[/C][C]-143.537351323779[/C][/ROW]
[ROW][C]56[/C][C]3720[/C][C]4252.96081076799[/C][C]-532.960810767985[/C][/ROW]
[ROW][C]57[/C][C]3330[/C][C]3371.80985155861[/C][C]-41.8098515586125[/C][/ROW]
[ROW][C]58[/C][C]3000[/C][C]3108.48018865138[/C][C]-108.48018865138[/C][/ROW]
[ROW][C]59[/C][C]2760[/C][C]2887.69466792287[/C][C]-127.69466792287[/C][/ROW]
[ROW][C]60[/C][C]3040[/C][C]2803.49738021342[/C][C]236.502619786575[/C][/ROW]
[ROW][C]61[/C][C]3260[/C][C]3676.69248912564[/C][C]-416.692489125639[/C][/ROW]
[ROW][C]62[/C][C]3780[/C][C]3934.09326537601[/C][C]-154.093265376009[/C][/ROW]
[ROW][C]63[/C][C]4670[/C][C]5160.9816343033[/C][C]-490.981634303298[/C][/ROW]
[ROW][C]64[/C][C]4320[/C][C]4836.48472984847[/C][C]-516.484729848466[/C][/ROW]
[ROW][C]65[/C][C]4080[/C][C]4102.5667834791[/C][C]-22.5667834791002[/C][/ROW]
[ROW][C]66[/C][C]4210[/C][C]4538.28881136199[/C][C]-328.28881136199[/C][/ROW]
[ROW][C]67[/C][C]3350[/C][C]4009.34418754267[/C][C]-659.344187542673[/C][/ROW]
[ROW][C]68[/C][C]3390[/C][C]2682.07832038467[/C][C]707.921679615328[/C][/ROW]
[ROW][C]69[/C][C]2630[/C][C]2625.84709660371[/C][C]4.15290339628973[/C][/ROW]
[ROW][C]70[/C][C]2350[/C][C]2327.32467169059[/C][C]22.6753283094108[/C][/ROW]
[ROW][C]71[/C][C]2330[/C][C]2138.28195282892[/C][C]191.718047171085[/C][/ROW]
[ROW][C]72[/C][C]2230[/C][C]2380.23245153131[/C][C]-150.232451531308[/C][/ROW]
[ROW][C]73[/C][C]2830[/C][C]2705.57911609496[/C][C]124.420883905044[/C][/ROW]
[ROW][C]74[/C][C]3230[/C][C]3343.01834624719[/C][C]-113.018346247188[/C][/ROW]
[ROW][C]75[/C][C]4240[/C][C]4398.2116794861[/C][C]-158.211679486097[/C][/ROW]
[ROW][C]76[/C][C]3750[/C][C]4207.95866644736[/C][C]-457.958666447357[/C][/ROW]
[ROW][C]77[/C][C]4160[/C][C]3751.14151198555[/C][C]408.858488014454[/C][/ROW]
[ROW][C]78[/C][C]3960[/C][C]4226.73988230809[/C][C]-266.739882308091[/C][/ROW]
[ROW][C]79[/C][C]3000[/C][C]3549.2905560953[/C][C]-549.290556095299[/C][/ROW]
[ROW][C]80[/C][C]2890[/C][C]2988.92889391282[/C][C]-98.9288939128228[/C][/ROW]
[ROW][C]81[/C][C]2300[/C][C]2167.67179225877[/C][C]132.328207741232[/C][/ROW]
[ROW][C]82[/C][C]2320[/C][C]1929.04095350431[/C][C]390.959046495691[/C][/ROW]
[ROW][C]83[/C][C]2270[/C][C]1997.32459605794[/C][C]272.67540394206[/C][/ROW]
[ROW][C]84[/C][C]1970[/C][C]2092.87565820074[/C][C]-122.875658200743[/C][/ROW]
[ROW][C]85[/C][C]2920[/C][C]2570.18049568463[/C][C]349.819504315367[/C][/ROW]
[ROW][C]86[/C][C]3310[/C][C]3187.68358406857[/C][C]122.31641593143[/C][/ROW]
[ROW][C]87[/C][C]4370[/C][C]4331.29674554675[/C][C]38.7032544532467[/C][/ROW]
[ROW][C]88[/C][C]3990[/C][C]4079.96018706432[/C][C]-89.9601870643191[/C][/ROW]
[ROW][C]89[/C][C]3970[/C][C]4259.76960359521[/C][C]-289.769603595207[/C][/ROW]
[ROW][C]90[/C][C]3850[/C][C]4047.52044909994[/C][C]-197.520449099939[/C][/ROW]
[ROW][C]91[/C][C]3510[/C][C]3254.23864685312[/C][C]255.761353146876[/C][/ROW]
[ROW][C]92[/C][C]2840[/C][C]3321.81138755525[/C][C]-481.811387555246[/C][/ROW]
[ROW][C]93[/C][C]2130[/C][C]2444.36846785049[/C][C]-314.368467850488[/C][/ROW]
[ROW][C]94[/C][C]2280[/C][C]2128.32858603986[/C][C]151.671413960135[/C][/ROW]
[ROW][C]95[/C][C]1960[/C][C]2017.22114703549[/C][C]-57.2211470354864[/C][/ROW]
[ROW][C]96[/C][C]1740[/C][C]1740.95878075618[/C][C]-0.958780756177475[/C][/ROW]
[ROW][C]97[/C][C]2370[/C][C]2518.18723532005[/C][C]-148.187235320051[/C][/ROW]
[ROW][C]98[/C][C]1980[/C][C]2767.71658522608[/C][C]-787.716585226076[/C][/ROW]
[ROW][C]99[/C][C]2680[/C][C]3412.30160539699[/C][C]-732.301605396986[/C][/ROW]
[ROW][C]100[/C][C]3510[/C][C]2695.31836761718[/C][C]814.681632382818[/C][/ROW]
[ROW][C]101[/C][C]3350[/C][C]3179.27476063663[/C][C]170.725239363365[/C][/ROW]
[ROW][C]102[/C][C]3290[/C][C]3218.70585779302[/C][C]71.2941422069839[/C][/ROW]
[ROW][C]103[/C][C]3150[/C][C]2778.57717834303[/C][C]371.42282165697[/C][/ROW]
[ROW][C]104[/C][C]2490[/C][C]2503.05862900783[/C][C]-13.0586290078309[/C][/ROW]
[ROW][C]105[/C][C]2490[/C][C]1930.70616444298[/C][C]559.293835557017[/C][/ROW]
[ROW][C]106[/C][C]2930[/C][C]2279.16050106094[/C][C]650.839498939059[/C][/ROW]
[ROW][C]107[/C][C]3590[/C][C]2306.29164468832[/C][C]1283.70835531168[/C][/ROW]
[ROW][C]108[/C][C]2040[/C][C]2723.26869163979[/C][C]-683.268691639789[/C][/ROW]
[ROW][C]109[/C][C]2480[/C][C]3117.24237518065[/C][C]-637.242375180652[/C][/ROW]
[ROW][C]110[/C][C]2760[/C][C]2811.3301354432[/C][C]-51.3301354432037[/C][/ROW]
[ROW][C]111[/C][C]3400[/C][C]3856.23796913495[/C][C]-456.237969134955[/C][/ROW]
[ROW][C]112[/C][C]3470[/C][C]4106.6006291606[/C][C]-636.600629160603[/C][/ROW]
[ROW][C]113[/C][C]3130[/C][C]3570.25759496317[/C][C]-440.257594963171[/C][/ROW]
[ROW][C]114[/C][C]3670[/C][C]3267.32024784029[/C][C]402.679752159713[/C][/ROW]
[ROW][C]115[/C][C]3080[/C][C]3146.29259020429[/C][C]-66.292590204288[/C][/ROW]
[ROW][C]116[/C][C]2430[/C][C]2459.95687467713[/C][C]-29.9568746771261[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298076&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298076&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
1327202351.88034188034368.119658119656
1437203521.27455879705198.725441202951
1547104638.7375000606171.262499939392
1650705055.6181816341914.381818365815
1760306031.04757905914-1.04757905913812
1852805316.63061061283-36.6306106128322
1944203975.70257628835444.297423711652
2039404315.26492587147-375.264925871469
2127503328.76909606464-578.769096064636
2229802709.15272053788270.847279462124
2326902764.06892040902-74.0689204090168
2426503042.08197978311-392.081979783111
2540003212.88180614899787.118193851005
2641504496.42819318503-346.428193185029
2760505285.34305576903764.656944230966
2862806007.58005454808272.419945451917
2955207106.21058360918-1586.21058360918
3048005609.6531350546-809.653135054603
3146104134.52717888339475.472821116615
3235304040.18821584167-510.188215841674
3327902862.48048566214-72.4804856621358
3427502914.93382233365-164.933822333654
3524702562.26590070373-92.2659007037346
3626102645.08619172959-35.0861917295897
3736803588.7749479532491.2250520467587
3838203923.12825233958-103.128252339581
3944605389.82911299785-929.829112997852
4047605007.62416920657-247.624169206567
4132904837.0380983296-1547.0380983296
4236103720.14224970173-110.142249701732
4336503213.61257498225436.387425017754
4431302544.91871901536585.08128098464
4528502091.72719755883758.272802441173
4627202474.57324317834245.426756821664
4727402343.93262080627396.067379193734
4827602683.4589818868276.5410181131801
4933303742.37819628205-412.378196282053
5038503725.35973523949124.640264760513
5154304859.23557914570.764420860001
5251805558.54057369796-378.540573697962
5347704652.72323608516117.276763914839
5453605109.1540260513250.845973948702
5549505093.53735132378-143.537351323779
5637204252.96081076799-532.960810767985
5733303371.80985155861-41.8098515586125
5830003108.48018865138-108.48018865138
5927602887.69466792287-127.69466792287
6030402803.49738021342236.502619786575
6132603676.69248912564-416.692489125639
6237803934.09326537601-154.093265376009
6346705160.9816343033-490.981634303298
6443204836.48472984847-516.484729848466
6540804102.5667834791-22.5667834791002
6642104538.28881136199-328.28881136199
6733504009.34418754267-659.344187542673
6833902682.07832038467707.921679615328
6926302625.847096603714.15290339628973
7023502327.3246716905922.6753283094108
7123302138.28195282892191.718047171085
7222302380.23245153131-150.232451531308
7328302705.57911609496124.420883905044
7432303343.01834624719-113.018346247188
7542404398.2116794861-158.211679486097
7637504207.95866644736-457.958666447357
7741603751.14151198555408.858488014454
7839604226.73988230809-266.739882308091
7930003549.2905560953-549.290556095299
8028902988.92889391282-98.9288939128228
8123002167.67179225877132.328207741232
8223201929.04095350431390.959046495691
8322701997.32459605794272.67540394206
8419702092.87565820074-122.875658200743
8529202570.18049568463349.819504315367
8633103187.68358406857122.31641593143
8743704331.2967455467538.7032544532467
8839904079.96018706432-89.9601870643191
8939704259.76960359521-289.769603595207
9038504047.52044909994-197.520449099939
9135103254.23864685312255.761353146876
9228403321.81138755525-481.811387555246
9321302444.36846785049-314.368467850488
9422802128.32858603986151.671413960135
9519602017.22114703549-57.2211470354864
9617401740.95878075618-0.958780756177475
9723702518.18723532005-148.187235320051
9819802767.71658522608-787.716585226076
9926803412.30160539699-732.301605396986
10035102695.31836761718814.681632382818
10133503179.27476063663170.725239363365
10232903218.7058577930271.2941422069839
10331502778.57717834303371.42282165697
10424902503.05862900783-13.0586290078309
10524901930.70616444298559.293835557017
10629302279.16050106094650.839498939059
10735902306.291644688321283.70835531168
10820402723.26869163979-683.268691639789
10924803117.24237518065-637.242375180652
11027602811.3301354432-51.3301354432037
11134003856.23796913495-456.237969134955
11234704106.6006291606-636.600629160603
11331303570.25759496317-440.257594963171
11436703267.32024784029402.679752159713
11530803146.29259020429-66.292590204288
11624302459.95687467713-29.9568746771261







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1172178.637890160681282.337410340483074.93836998088
1182301.467265615521304.494598723623298.43993250743
1192335.822266487991243.179533346593428.46499962939
1201080.04446975792-104.5726174667982264.66155698263
1211800.42348700995526.6396891654583074.20728485443
1222089.79440297414729.0178360267243450.57096992156
1232932.233535617541486.16890711774378.29816411738
1243295.769208920951765.76350320154825.7749146404
1253163.462963948141550.583961571444776.34196632484
1263515.66068443011820.753984323415210.5673845368
1272956.039720523791179.771227655054732.30821339254
1282319.92684679067462.8151246990944177.03856888224
1292068.56473695135-51.56060936986844188.69008327256
1302191.39411240619-2.223553753478434385.01177856587
1312225.74911327865-41.62052689567554493.11875345298
132969.971316548584-1371.432857392873311.37549049003
1331690.35033380061-725.3909373072264106.09160490846
1341979.72124976481-510.6771915857934470.11969111541

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 2178.63789016068 & 1282.33741034048 & 3074.93836998088 \tabularnewline
118 & 2301.46726561552 & 1304.49459872362 & 3298.43993250743 \tabularnewline
119 & 2335.82226648799 & 1243.17953334659 & 3428.46499962939 \tabularnewline
120 & 1080.04446975792 & -104.572617466798 & 2264.66155698263 \tabularnewline
121 & 1800.42348700995 & 526.639689165458 & 3074.20728485443 \tabularnewline
122 & 2089.79440297414 & 729.017836026724 & 3450.57096992156 \tabularnewline
123 & 2932.23353561754 & 1486.1689071177 & 4378.29816411738 \tabularnewline
124 & 3295.76920892095 & 1765.7635032015 & 4825.7749146404 \tabularnewline
125 & 3163.46296394814 & 1550.58396157144 & 4776.34196632484 \tabularnewline
126 & 3515.6606844301 & 1820.75398432341 & 5210.5673845368 \tabularnewline
127 & 2956.03972052379 & 1179.77122765505 & 4732.30821339254 \tabularnewline
128 & 2319.92684679067 & 462.815124699094 & 4177.03856888224 \tabularnewline
129 & 2068.56473695135 & -51.5606093698684 & 4188.69008327256 \tabularnewline
130 & 2191.39411240619 & -2.22355375347843 & 4385.01177856587 \tabularnewline
131 & 2225.74911327865 & -41.6205268956755 & 4493.11875345298 \tabularnewline
132 & 969.971316548584 & -1371.43285739287 & 3311.37549049003 \tabularnewline
133 & 1690.35033380061 & -725.390937307226 & 4106.09160490846 \tabularnewline
134 & 1979.72124976481 & -510.677191585793 & 4470.11969111541 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298076&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]117[/C][C]2178.63789016068[/C][C]1282.33741034048[/C][C]3074.93836998088[/C][/ROW]
[ROW][C]118[/C][C]2301.46726561552[/C][C]1304.49459872362[/C][C]3298.43993250743[/C][/ROW]
[ROW][C]119[/C][C]2335.82226648799[/C][C]1243.17953334659[/C][C]3428.46499962939[/C][/ROW]
[ROW][C]120[/C][C]1080.04446975792[/C][C]-104.572617466798[/C][C]2264.66155698263[/C][/ROW]
[ROW][C]121[/C][C]1800.42348700995[/C][C]526.639689165458[/C][C]3074.20728485443[/C][/ROW]
[ROW][C]122[/C][C]2089.79440297414[/C][C]729.017836026724[/C][C]3450.57096992156[/C][/ROW]
[ROW][C]123[/C][C]2932.23353561754[/C][C]1486.1689071177[/C][C]4378.29816411738[/C][/ROW]
[ROW][C]124[/C][C]3295.76920892095[/C][C]1765.7635032015[/C][C]4825.7749146404[/C][/ROW]
[ROW][C]125[/C][C]3163.46296394814[/C][C]1550.58396157144[/C][C]4776.34196632484[/C][/ROW]
[ROW][C]126[/C][C]3515.6606844301[/C][C]1820.75398432341[/C][C]5210.5673845368[/C][/ROW]
[ROW][C]127[/C][C]2956.03972052379[/C][C]1179.77122765505[/C][C]4732.30821339254[/C][/ROW]
[ROW][C]128[/C][C]2319.92684679067[/C][C]462.815124699094[/C][C]4177.03856888224[/C][/ROW]
[ROW][C]129[/C][C]2068.56473695135[/C][C]-51.5606093698684[/C][C]4188.69008327256[/C][/ROW]
[ROW][C]130[/C][C]2191.39411240619[/C][C]-2.22355375347843[/C][C]4385.01177856587[/C][/ROW]
[ROW][C]131[/C][C]2225.74911327865[/C][C]-41.6205268956755[/C][C]4493.11875345298[/C][/ROW]
[ROW][C]132[/C][C]969.971316548584[/C][C]-1371.43285739287[/C][C]3311.37549049003[/C][/ROW]
[ROW][C]133[/C][C]1690.35033380061[/C][C]-725.390937307226[/C][C]4106.09160490846[/C][/ROW]
[ROW][C]134[/C][C]1979.72124976481[/C][C]-510.677191585793[/C][C]4470.11969111541[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298076&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298076&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
1172178.637890160681282.337410340483074.93836998088
1182301.467265615521304.494598723623298.43993250743
1192335.822266487991243.179533346593428.46499962939
1201080.04446975792-104.5726174667982264.66155698263
1211800.42348700995526.6396891654583074.20728485443
1222089.79440297414729.0178360267243450.57096992156
1232932.233535617541486.16890711774378.29816411738
1243295.769208920951765.76350320154825.7749146404
1253163.462963948141550.583961571444776.34196632484
1263515.66068443011820.753984323415210.5673845368
1272956.039720523791179.771227655054732.30821339254
1282319.92684679067462.8151246990944177.03856888224
1292068.56473695135-51.56060936986844188.69008327256
1302191.39411240619-2.223553753478434385.01177856587
1312225.74911327865-41.62052689567554493.11875345298
132969.971316548584-1371.432857392873311.37549049003
1331690.35033380061-725.3909373072264106.09160490846
1341979.72124976481-510.6771915857934470.11969111541



Parameters (Session):
par4 = No season ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 18 ;
R code (references can be found in the software module):
par4 <- '18'
par3 <- 'multiplicative'
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')