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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 22:15:54 +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/t14816638226gdtbw33mdbb6yt.htm/, Retrieved Fri, 01 Nov 2024 03:39:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299233, Retrieved Fri, 01 Nov 2024 03:39:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-13 21:15:54] [130d73899007e5ff8a4f636b9bcfb397] [Current]
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Dataseries X:
5290
5135
5075
5115
5115
5115
5230
5305
5360
5415
5370
5355
5595
5485
5510
5565
5665
5690
5750
5690
5720
5530
5495
5475
5455
5500
5495
5485
5495
5500
5430
5420
5455
5405
5300
5470
5440
5350
5250
5100
5065
4980
4970
4910
4840
4850
4910
4895
4955
4960
4940
4905
4925
4960
4925
5025
5045
5090
5120
5145
5095
5075
5125
5075
5100
5085
5065
5090
5020
5030
5000
5030
5015
4955
4940
5060
5070
5005
4945
5015
5035
4985
5020
4920
5125
5080
5060
5095
5105
5105
5115
5070
5115
5150
5115
5060
5075
5155
5120
5030
4995
5035
4970
4970
4975
4965
4915
4910
4895
4880
4910
4935
4975
4895
4940
4880




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=299233&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=299233&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299233&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
alpha0.927422535157376
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.927422535157376 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299233&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]0.927422535157376[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299233&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299233&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
alpha0.927422535157376
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
251355290-155
350755146.24950705061-71.2495070506066
451155080.1711085930234.8288914069799
551155112.47220735842.52779264159744
651155114.816539218420.183460781575377
752305114.98668488157115.013315118425
853055221.6526251655683.3473748344413
953605298.9508588332361.0491411667717
1054155355.569208103359.4307918967033
1153705410.68666379055-40.6866637905478
1253555372.95293491082-17.9529349108216
1355955356.30297850231238.697021497687
1454855577.67597531421-92.6759753142123
1555105491.7261873401218.273812659877
1655655508.6737330041456.3262669958622
1756655560.91198233739104.088017662609
1856905657.4455555575532.5544444424468
1957505687.6372809530162.3627190469933
2056905745.47387195088-55.4738719508769
2157205694.026152991225.9738470088014
2255305718.11488403189-188.114884031891
2354955543.6529013822-48.6529013821983
2454755498.53110423956-23.5311042395579
2554555476.70782789065-21.7078278906538
2655005456.5754991155443.4245008844564
2754955496.84835981375-1.84835981374999
2854855495.1341492694-10.1341492693991
2954955485.735510862319.26448913769036
3055005494.327606865325.67239313467599
3154305499.58831208669-69.5883120866947
3254205435.05054327393-15.0505432739301
3354555421.0923302753333.9076697246737
3454055452.53906729266-47.5390672926624
3553005408.45026498508-108.450264985084
3654705307.87104529413162.128954705871
3754405458.23309148986-18.233091489863
3853505441.32331155658-91.3233115565772
3952505356.62801443381-106.62801443381
4051005257.73879096881-157.738790968809
4150655111.44828155586-46.4482815558567
4249805068.37109852162-88.3710985216212
4349704986.41375029606-16.4137502960566
4449104971.19126838505-61.1912683850478
4548404914.44110712989-74.4411071298919
4648504845.402746835574.59725316443382
4749104849.6663430200960.3336569799139
4848954905.62113613171-10.6211361317137
4949554895.7708551341959.2291448658125
5049604950.701298820849.29870117915743
5149404959.32512384209-19.3251238420871
5249054941.40256849623-36.4025684962289
5349254907.6420061352217.3579938647836
5449604923.7402008105436.25979918946
5549254957.36835569913-32.3683556991264
5650254927.3492131977797.6507868022336
5750455017.9127534540127.0872465459943
5850905043.0340763161246.9659236838752
5951205086.5913323250333.4086676749685
6051455117.5752835963827.4247164036196
6150955143.0095836094-48.0095836093969
6250755098.48441386652-23.4844138665203
6351255076.7044392217548.2955607782533
6450755121.49483063556-46.4948306355618
6551005078.3744769358221.6255230641837
6650855098.43047436011-13.430474360106
6750655085.97474978069-20.9747497806902
6850905066.5222941647923.4777058352092
6950205088.29604763016-68.2960476301596
7050305024.956753995775.04324600423206
7150005029.63397399044-29.6339739904352
7250305002.1507587054427.8492412945616
7350155027.97877266905-12.9787726690502
7449555015.94196641709-60.9419664170882
7549404959.42301342508-19.4230134250765
7650604941.409673074118.590326926003
7750705051.3930147168518.606985283147
7850055068.64955217979-63.6495521797851
7949455009.61952313558-64.6195231355778
8050154949.6899211685265.3100788314805
8150355010.2599600497424.7400399502612
8249855033.20443062031-48.2044306203052
8350204988.498555368631.5014446313962
8449205017.71370500977-97.7137050097726
8551254927.09181298999197.908187010011
8650805110.63632551521-30.6363255152137
8750605082.22350683799-22.2235068379878
8850955061.6129257862133.387074213786
8951055092.5768507950512.4231492049485
9051055104.098359325340.901640674656846
9151155104.9345612056310.065438794365
9250705114.26947596978-44.2694759697761
9351155073.212966335841.7870336642018
9451505111.9672030333638.0327969666414
9551155147.23967601529-32.2396760152869
9650605117.33987395254-57.3398739525364
9750755064.1615826858710.8384173141285
9851555074.2133751484380.7866248515656
9951205149.13671157508-29.1367115750809
10050305122.11466865997-92.1146686599695
10149955036.68544912616-41.6854491261593
10250354998.025424218436.9745757815981
10349705032.31647902614-62.3164790261408
10449704974.52277206564-4.52277206563576
10549754970.328251330584.67174866941514
10649654974.66093632519-9.66093632519187
10749154965.70116626649-50.7011662664891
10849104918.67976211219-8.67976211218593
10948954910.62995512954-15.6299551295397
11048804896.13438251891-16.134382518906
11149104881.1709925800228.8290074199767
11249354907.9076637275327.0923362724707
11349754933.0337069166841.9662930833192
11448954971.95419283917-76.95419283917
11549404900.5851402252839.4148597747226
11648804937.13936940042-57.1393694004237

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 5135 & 5290 & -155 \tabularnewline
3 & 5075 & 5146.24950705061 & -71.2495070506066 \tabularnewline
4 & 5115 & 5080.17110859302 & 34.8288914069799 \tabularnewline
5 & 5115 & 5112.4722073584 & 2.52779264159744 \tabularnewline
6 & 5115 & 5114.81653921842 & 0.183460781575377 \tabularnewline
7 & 5230 & 5114.98668488157 & 115.013315118425 \tabularnewline
8 & 5305 & 5221.65262516556 & 83.3473748344413 \tabularnewline
9 & 5360 & 5298.95085883323 & 61.0491411667717 \tabularnewline
10 & 5415 & 5355.5692081033 & 59.4307918967033 \tabularnewline
11 & 5370 & 5410.68666379055 & -40.6866637905478 \tabularnewline
12 & 5355 & 5372.95293491082 & -17.9529349108216 \tabularnewline
13 & 5595 & 5356.30297850231 & 238.697021497687 \tabularnewline
14 & 5485 & 5577.67597531421 & -92.6759753142123 \tabularnewline
15 & 5510 & 5491.72618734012 & 18.273812659877 \tabularnewline
16 & 5565 & 5508.67373300414 & 56.3262669958622 \tabularnewline
17 & 5665 & 5560.91198233739 & 104.088017662609 \tabularnewline
18 & 5690 & 5657.44555555755 & 32.5544444424468 \tabularnewline
19 & 5750 & 5687.63728095301 & 62.3627190469933 \tabularnewline
20 & 5690 & 5745.47387195088 & -55.4738719508769 \tabularnewline
21 & 5720 & 5694.0261529912 & 25.9738470088014 \tabularnewline
22 & 5530 & 5718.11488403189 & -188.114884031891 \tabularnewline
23 & 5495 & 5543.6529013822 & -48.6529013821983 \tabularnewline
24 & 5475 & 5498.53110423956 & -23.5311042395579 \tabularnewline
25 & 5455 & 5476.70782789065 & -21.7078278906538 \tabularnewline
26 & 5500 & 5456.57549911554 & 43.4245008844564 \tabularnewline
27 & 5495 & 5496.84835981375 & -1.84835981374999 \tabularnewline
28 & 5485 & 5495.1341492694 & -10.1341492693991 \tabularnewline
29 & 5495 & 5485.73551086231 & 9.26448913769036 \tabularnewline
30 & 5500 & 5494.32760686532 & 5.67239313467599 \tabularnewline
31 & 5430 & 5499.58831208669 & -69.5883120866947 \tabularnewline
32 & 5420 & 5435.05054327393 & -15.0505432739301 \tabularnewline
33 & 5455 & 5421.09233027533 & 33.9076697246737 \tabularnewline
34 & 5405 & 5452.53906729266 & -47.5390672926624 \tabularnewline
35 & 5300 & 5408.45026498508 & -108.450264985084 \tabularnewline
36 & 5470 & 5307.87104529413 & 162.128954705871 \tabularnewline
37 & 5440 & 5458.23309148986 & -18.233091489863 \tabularnewline
38 & 5350 & 5441.32331155658 & -91.3233115565772 \tabularnewline
39 & 5250 & 5356.62801443381 & -106.62801443381 \tabularnewline
40 & 5100 & 5257.73879096881 & -157.738790968809 \tabularnewline
41 & 5065 & 5111.44828155586 & -46.4482815558567 \tabularnewline
42 & 4980 & 5068.37109852162 & -88.3710985216212 \tabularnewline
43 & 4970 & 4986.41375029606 & -16.4137502960566 \tabularnewline
44 & 4910 & 4971.19126838505 & -61.1912683850478 \tabularnewline
45 & 4840 & 4914.44110712989 & -74.4411071298919 \tabularnewline
46 & 4850 & 4845.40274683557 & 4.59725316443382 \tabularnewline
47 & 4910 & 4849.66634302009 & 60.3336569799139 \tabularnewline
48 & 4895 & 4905.62113613171 & -10.6211361317137 \tabularnewline
49 & 4955 & 4895.77085513419 & 59.2291448658125 \tabularnewline
50 & 4960 & 4950.70129882084 & 9.29870117915743 \tabularnewline
51 & 4940 & 4959.32512384209 & -19.3251238420871 \tabularnewline
52 & 4905 & 4941.40256849623 & -36.4025684962289 \tabularnewline
53 & 4925 & 4907.64200613522 & 17.3579938647836 \tabularnewline
54 & 4960 & 4923.74020081054 & 36.25979918946 \tabularnewline
55 & 4925 & 4957.36835569913 & -32.3683556991264 \tabularnewline
56 & 5025 & 4927.34921319777 & 97.6507868022336 \tabularnewline
57 & 5045 & 5017.91275345401 & 27.0872465459943 \tabularnewline
58 & 5090 & 5043.03407631612 & 46.9659236838752 \tabularnewline
59 & 5120 & 5086.59133232503 & 33.4086676749685 \tabularnewline
60 & 5145 & 5117.57528359638 & 27.4247164036196 \tabularnewline
61 & 5095 & 5143.0095836094 & -48.0095836093969 \tabularnewline
62 & 5075 & 5098.48441386652 & -23.4844138665203 \tabularnewline
63 & 5125 & 5076.70443922175 & 48.2955607782533 \tabularnewline
64 & 5075 & 5121.49483063556 & -46.4948306355618 \tabularnewline
65 & 5100 & 5078.37447693582 & 21.6255230641837 \tabularnewline
66 & 5085 & 5098.43047436011 & -13.430474360106 \tabularnewline
67 & 5065 & 5085.97474978069 & -20.9747497806902 \tabularnewline
68 & 5090 & 5066.52229416479 & 23.4777058352092 \tabularnewline
69 & 5020 & 5088.29604763016 & -68.2960476301596 \tabularnewline
70 & 5030 & 5024.95675399577 & 5.04324600423206 \tabularnewline
71 & 5000 & 5029.63397399044 & -29.6339739904352 \tabularnewline
72 & 5030 & 5002.15075870544 & 27.8492412945616 \tabularnewline
73 & 5015 & 5027.97877266905 & -12.9787726690502 \tabularnewline
74 & 4955 & 5015.94196641709 & -60.9419664170882 \tabularnewline
75 & 4940 & 4959.42301342508 & -19.4230134250765 \tabularnewline
76 & 5060 & 4941.409673074 & 118.590326926003 \tabularnewline
77 & 5070 & 5051.39301471685 & 18.606985283147 \tabularnewline
78 & 5005 & 5068.64955217979 & -63.6495521797851 \tabularnewline
79 & 4945 & 5009.61952313558 & -64.6195231355778 \tabularnewline
80 & 5015 & 4949.68992116852 & 65.3100788314805 \tabularnewline
81 & 5035 & 5010.25996004974 & 24.7400399502612 \tabularnewline
82 & 4985 & 5033.20443062031 & -48.2044306203052 \tabularnewline
83 & 5020 & 4988.4985553686 & 31.5014446313962 \tabularnewline
84 & 4920 & 5017.71370500977 & -97.7137050097726 \tabularnewline
85 & 5125 & 4927.09181298999 & 197.908187010011 \tabularnewline
86 & 5080 & 5110.63632551521 & -30.6363255152137 \tabularnewline
87 & 5060 & 5082.22350683799 & -22.2235068379878 \tabularnewline
88 & 5095 & 5061.61292578621 & 33.387074213786 \tabularnewline
89 & 5105 & 5092.57685079505 & 12.4231492049485 \tabularnewline
90 & 5105 & 5104.09835932534 & 0.901640674656846 \tabularnewline
91 & 5115 & 5104.93456120563 & 10.065438794365 \tabularnewline
92 & 5070 & 5114.26947596978 & -44.2694759697761 \tabularnewline
93 & 5115 & 5073.2129663358 & 41.7870336642018 \tabularnewline
94 & 5150 & 5111.96720303336 & 38.0327969666414 \tabularnewline
95 & 5115 & 5147.23967601529 & -32.2396760152869 \tabularnewline
96 & 5060 & 5117.33987395254 & -57.3398739525364 \tabularnewline
97 & 5075 & 5064.16158268587 & 10.8384173141285 \tabularnewline
98 & 5155 & 5074.21337514843 & 80.7866248515656 \tabularnewline
99 & 5120 & 5149.13671157508 & -29.1367115750809 \tabularnewline
100 & 5030 & 5122.11466865997 & -92.1146686599695 \tabularnewline
101 & 4995 & 5036.68544912616 & -41.6854491261593 \tabularnewline
102 & 5035 & 4998.0254242184 & 36.9745757815981 \tabularnewline
103 & 4970 & 5032.31647902614 & -62.3164790261408 \tabularnewline
104 & 4970 & 4974.52277206564 & -4.52277206563576 \tabularnewline
105 & 4975 & 4970.32825133058 & 4.67174866941514 \tabularnewline
106 & 4965 & 4974.66093632519 & -9.66093632519187 \tabularnewline
107 & 4915 & 4965.70116626649 & -50.7011662664891 \tabularnewline
108 & 4910 & 4918.67976211219 & -8.67976211218593 \tabularnewline
109 & 4895 & 4910.62995512954 & -15.6299551295397 \tabularnewline
110 & 4880 & 4896.13438251891 & -16.134382518906 \tabularnewline
111 & 4910 & 4881.17099258002 & 28.8290074199767 \tabularnewline
112 & 4935 & 4907.90766372753 & 27.0923362724707 \tabularnewline
113 & 4975 & 4933.03370691668 & 41.9662930833192 \tabularnewline
114 & 4895 & 4971.95419283917 & -76.95419283917 \tabularnewline
115 & 4940 & 4900.58514022528 & 39.4148597747226 \tabularnewline
116 & 4880 & 4937.13936940042 & -57.1393694004237 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299233&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]2[/C][C]5135[/C][C]5290[/C][C]-155[/C][/ROW]
[ROW][C]3[/C][C]5075[/C][C]5146.24950705061[/C][C]-71.2495070506066[/C][/ROW]
[ROW][C]4[/C][C]5115[/C][C]5080.17110859302[/C][C]34.8288914069799[/C][/ROW]
[ROW][C]5[/C][C]5115[/C][C]5112.4722073584[/C][C]2.52779264159744[/C][/ROW]
[ROW][C]6[/C][C]5115[/C][C]5114.81653921842[/C][C]0.183460781575377[/C][/ROW]
[ROW][C]7[/C][C]5230[/C][C]5114.98668488157[/C][C]115.013315118425[/C][/ROW]
[ROW][C]8[/C][C]5305[/C][C]5221.65262516556[/C][C]83.3473748344413[/C][/ROW]
[ROW][C]9[/C][C]5360[/C][C]5298.95085883323[/C][C]61.0491411667717[/C][/ROW]
[ROW][C]10[/C][C]5415[/C][C]5355.5692081033[/C][C]59.4307918967033[/C][/ROW]
[ROW][C]11[/C][C]5370[/C][C]5410.68666379055[/C][C]-40.6866637905478[/C][/ROW]
[ROW][C]12[/C][C]5355[/C][C]5372.95293491082[/C][C]-17.9529349108216[/C][/ROW]
[ROW][C]13[/C][C]5595[/C][C]5356.30297850231[/C][C]238.697021497687[/C][/ROW]
[ROW][C]14[/C][C]5485[/C][C]5577.67597531421[/C][C]-92.6759753142123[/C][/ROW]
[ROW][C]15[/C][C]5510[/C][C]5491.72618734012[/C][C]18.273812659877[/C][/ROW]
[ROW][C]16[/C][C]5565[/C][C]5508.67373300414[/C][C]56.3262669958622[/C][/ROW]
[ROW][C]17[/C][C]5665[/C][C]5560.91198233739[/C][C]104.088017662609[/C][/ROW]
[ROW][C]18[/C][C]5690[/C][C]5657.44555555755[/C][C]32.5544444424468[/C][/ROW]
[ROW][C]19[/C][C]5750[/C][C]5687.63728095301[/C][C]62.3627190469933[/C][/ROW]
[ROW][C]20[/C][C]5690[/C][C]5745.47387195088[/C][C]-55.4738719508769[/C][/ROW]
[ROW][C]21[/C][C]5720[/C][C]5694.0261529912[/C][C]25.9738470088014[/C][/ROW]
[ROW][C]22[/C][C]5530[/C][C]5718.11488403189[/C][C]-188.114884031891[/C][/ROW]
[ROW][C]23[/C][C]5495[/C][C]5543.6529013822[/C][C]-48.6529013821983[/C][/ROW]
[ROW][C]24[/C][C]5475[/C][C]5498.53110423956[/C][C]-23.5311042395579[/C][/ROW]
[ROW][C]25[/C][C]5455[/C][C]5476.70782789065[/C][C]-21.7078278906538[/C][/ROW]
[ROW][C]26[/C][C]5500[/C][C]5456.57549911554[/C][C]43.4245008844564[/C][/ROW]
[ROW][C]27[/C][C]5495[/C][C]5496.84835981375[/C][C]-1.84835981374999[/C][/ROW]
[ROW][C]28[/C][C]5485[/C][C]5495.1341492694[/C][C]-10.1341492693991[/C][/ROW]
[ROW][C]29[/C][C]5495[/C][C]5485.73551086231[/C][C]9.26448913769036[/C][/ROW]
[ROW][C]30[/C][C]5500[/C][C]5494.32760686532[/C][C]5.67239313467599[/C][/ROW]
[ROW][C]31[/C][C]5430[/C][C]5499.58831208669[/C][C]-69.5883120866947[/C][/ROW]
[ROW][C]32[/C][C]5420[/C][C]5435.05054327393[/C][C]-15.0505432739301[/C][/ROW]
[ROW][C]33[/C][C]5455[/C][C]5421.09233027533[/C][C]33.9076697246737[/C][/ROW]
[ROW][C]34[/C][C]5405[/C][C]5452.53906729266[/C][C]-47.5390672926624[/C][/ROW]
[ROW][C]35[/C][C]5300[/C][C]5408.45026498508[/C][C]-108.450264985084[/C][/ROW]
[ROW][C]36[/C][C]5470[/C][C]5307.87104529413[/C][C]162.128954705871[/C][/ROW]
[ROW][C]37[/C][C]5440[/C][C]5458.23309148986[/C][C]-18.233091489863[/C][/ROW]
[ROW][C]38[/C][C]5350[/C][C]5441.32331155658[/C][C]-91.3233115565772[/C][/ROW]
[ROW][C]39[/C][C]5250[/C][C]5356.62801443381[/C][C]-106.62801443381[/C][/ROW]
[ROW][C]40[/C][C]5100[/C][C]5257.73879096881[/C][C]-157.738790968809[/C][/ROW]
[ROW][C]41[/C][C]5065[/C][C]5111.44828155586[/C][C]-46.4482815558567[/C][/ROW]
[ROW][C]42[/C][C]4980[/C][C]5068.37109852162[/C][C]-88.3710985216212[/C][/ROW]
[ROW][C]43[/C][C]4970[/C][C]4986.41375029606[/C][C]-16.4137502960566[/C][/ROW]
[ROW][C]44[/C][C]4910[/C][C]4971.19126838505[/C][C]-61.1912683850478[/C][/ROW]
[ROW][C]45[/C][C]4840[/C][C]4914.44110712989[/C][C]-74.4411071298919[/C][/ROW]
[ROW][C]46[/C][C]4850[/C][C]4845.40274683557[/C][C]4.59725316443382[/C][/ROW]
[ROW][C]47[/C][C]4910[/C][C]4849.66634302009[/C][C]60.3336569799139[/C][/ROW]
[ROW][C]48[/C][C]4895[/C][C]4905.62113613171[/C][C]-10.6211361317137[/C][/ROW]
[ROW][C]49[/C][C]4955[/C][C]4895.77085513419[/C][C]59.2291448658125[/C][/ROW]
[ROW][C]50[/C][C]4960[/C][C]4950.70129882084[/C][C]9.29870117915743[/C][/ROW]
[ROW][C]51[/C][C]4940[/C][C]4959.32512384209[/C][C]-19.3251238420871[/C][/ROW]
[ROW][C]52[/C][C]4905[/C][C]4941.40256849623[/C][C]-36.4025684962289[/C][/ROW]
[ROW][C]53[/C][C]4925[/C][C]4907.64200613522[/C][C]17.3579938647836[/C][/ROW]
[ROW][C]54[/C][C]4960[/C][C]4923.74020081054[/C][C]36.25979918946[/C][/ROW]
[ROW][C]55[/C][C]4925[/C][C]4957.36835569913[/C][C]-32.3683556991264[/C][/ROW]
[ROW][C]56[/C][C]5025[/C][C]4927.34921319777[/C][C]97.6507868022336[/C][/ROW]
[ROW][C]57[/C][C]5045[/C][C]5017.91275345401[/C][C]27.0872465459943[/C][/ROW]
[ROW][C]58[/C][C]5090[/C][C]5043.03407631612[/C][C]46.9659236838752[/C][/ROW]
[ROW][C]59[/C][C]5120[/C][C]5086.59133232503[/C][C]33.4086676749685[/C][/ROW]
[ROW][C]60[/C][C]5145[/C][C]5117.57528359638[/C][C]27.4247164036196[/C][/ROW]
[ROW][C]61[/C][C]5095[/C][C]5143.0095836094[/C][C]-48.0095836093969[/C][/ROW]
[ROW][C]62[/C][C]5075[/C][C]5098.48441386652[/C][C]-23.4844138665203[/C][/ROW]
[ROW][C]63[/C][C]5125[/C][C]5076.70443922175[/C][C]48.2955607782533[/C][/ROW]
[ROW][C]64[/C][C]5075[/C][C]5121.49483063556[/C][C]-46.4948306355618[/C][/ROW]
[ROW][C]65[/C][C]5100[/C][C]5078.37447693582[/C][C]21.6255230641837[/C][/ROW]
[ROW][C]66[/C][C]5085[/C][C]5098.43047436011[/C][C]-13.430474360106[/C][/ROW]
[ROW][C]67[/C][C]5065[/C][C]5085.97474978069[/C][C]-20.9747497806902[/C][/ROW]
[ROW][C]68[/C][C]5090[/C][C]5066.52229416479[/C][C]23.4777058352092[/C][/ROW]
[ROW][C]69[/C][C]5020[/C][C]5088.29604763016[/C][C]-68.2960476301596[/C][/ROW]
[ROW][C]70[/C][C]5030[/C][C]5024.95675399577[/C][C]5.04324600423206[/C][/ROW]
[ROW][C]71[/C][C]5000[/C][C]5029.63397399044[/C][C]-29.6339739904352[/C][/ROW]
[ROW][C]72[/C][C]5030[/C][C]5002.15075870544[/C][C]27.8492412945616[/C][/ROW]
[ROW][C]73[/C][C]5015[/C][C]5027.97877266905[/C][C]-12.9787726690502[/C][/ROW]
[ROW][C]74[/C][C]4955[/C][C]5015.94196641709[/C][C]-60.9419664170882[/C][/ROW]
[ROW][C]75[/C][C]4940[/C][C]4959.42301342508[/C][C]-19.4230134250765[/C][/ROW]
[ROW][C]76[/C][C]5060[/C][C]4941.409673074[/C][C]118.590326926003[/C][/ROW]
[ROW][C]77[/C][C]5070[/C][C]5051.39301471685[/C][C]18.606985283147[/C][/ROW]
[ROW][C]78[/C][C]5005[/C][C]5068.64955217979[/C][C]-63.6495521797851[/C][/ROW]
[ROW][C]79[/C][C]4945[/C][C]5009.61952313558[/C][C]-64.6195231355778[/C][/ROW]
[ROW][C]80[/C][C]5015[/C][C]4949.68992116852[/C][C]65.3100788314805[/C][/ROW]
[ROW][C]81[/C][C]5035[/C][C]5010.25996004974[/C][C]24.7400399502612[/C][/ROW]
[ROW][C]82[/C][C]4985[/C][C]5033.20443062031[/C][C]-48.2044306203052[/C][/ROW]
[ROW][C]83[/C][C]5020[/C][C]4988.4985553686[/C][C]31.5014446313962[/C][/ROW]
[ROW][C]84[/C][C]4920[/C][C]5017.71370500977[/C][C]-97.7137050097726[/C][/ROW]
[ROW][C]85[/C][C]5125[/C][C]4927.09181298999[/C][C]197.908187010011[/C][/ROW]
[ROW][C]86[/C][C]5080[/C][C]5110.63632551521[/C][C]-30.6363255152137[/C][/ROW]
[ROW][C]87[/C][C]5060[/C][C]5082.22350683799[/C][C]-22.2235068379878[/C][/ROW]
[ROW][C]88[/C][C]5095[/C][C]5061.61292578621[/C][C]33.387074213786[/C][/ROW]
[ROW][C]89[/C][C]5105[/C][C]5092.57685079505[/C][C]12.4231492049485[/C][/ROW]
[ROW][C]90[/C][C]5105[/C][C]5104.09835932534[/C][C]0.901640674656846[/C][/ROW]
[ROW][C]91[/C][C]5115[/C][C]5104.93456120563[/C][C]10.065438794365[/C][/ROW]
[ROW][C]92[/C][C]5070[/C][C]5114.26947596978[/C][C]-44.2694759697761[/C][/ROW]
[ROW][C]93[/C][C]5115[/C][C]5073.2129663358[/C][C]41.7870336642018[/C][/ROW]
[ROW][C]94[/C][C]5150[/C][C]5111.96720303336[/C][C]38.0327969666414[/C][/ROW]
[ROW][C]95[/C][C]5115[/C][C]5147.23967601529[/C][C]-32.2396760152869[/C][/ROW]
[ROW][C]96[/C][C]5060[/C][C]5117.33987395254[/C][C]-57.3398739525364[/C][/ROW]
[ROW][C]97[/C][C]5075[/C][C]5064.16158268587[/C][C]10.8384173141285[/C][/ROW]
[ROW][C]98[/C][C]5155[/C][C]5074.21337514843[/C][C]80.7866248515656[/C][/ROW]
[ROW][C]99[/C][C]5120[/C][C]5149.13671157508[/C][C]-29.1367115750809[/C][/ROW]
[ROW][C]100[/C][C]5030[/C][C]5122.11466865997[/C][C]-92.1146686599695[/C][/ROW]
[ROW][C]101[/C][C]4995[/C][C]5036.68544912616[/C][C]-41.6854491261593[/C][/ROW]
[ROW][C]102[/C][C]5035[/C][C]4998.0254242184[/C][C]36.9745757815981[/C][/ROW]
[ROW][C]103[/C][C]4970[/C][C]5032.31647902614[/C][C]-62.3164790261408[/C][/ROW]
[ROW][C]104[/C][C]4970[/C][C]4974.52277206564[/C][C]-4.52277206563576[/C][/ROW]
[ROW][C]105[/C][C]4975[/C][C]4970.32825133058[/C][C]4.67174866941514[/C][/ROW]
[ROW][C]106[/C][C]4965[/C][C]4974.66093632519[/C][C]-9.66093632519187[/C][/ROW]
[ROW][C]107[/C][C]4915[/C][C]4965.70116626649[/C][C]-50.7011662664891[/C][/ROW]
[ROW][C]108[/C][C]4910[/C][C]4918.67976211219[/C][C]-8.67976211218593[/C][/ROW]
[ROW][C]109[/C][C]4895[/C][C]4910.62995512954[/C][C]-15.6299551295397[/C][/ROW]
[ROW][C]110[/C][C]4880[/C][C]4896.13438251891[/C][C]-16.134382518906[/C][/ROW]
[ROW][C]111[/C][C]4910[/C][C]4881.17099258002[/C][C]28.8290074199767[/C][/ROW]
[ROW][C]112[/C][C]4935[/C][C]4907.90766372753[/C][C]27.0923362724707[/C][/ROW]
[ROW][C]113[/C][C]4975[/C][C]4933.03370691668[/C][C]41.9662930833192[/C][/ROW]
[ROW][C]114[/C][C]4895[/C][C]4971.95419283917[/C][C]-76.95419283917[/C][/ROW]
[ROW][C]115[/C][C]4940[/C][C]4900.58514022528[/C][C]39.4148597747226[/C][/ROW]
[ROW][C]116[/C][C]4880[/C][C]4937.13936940042[/C][C]-57.1393694004237[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299233&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299233&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
251355290-155
350755146.24950705061-71.2495070506066
451155080.1711085930234.8288914069799
551155112.47220735842.52779264159744
651155114.816539218420.183460781575377
752305114.98668488157115.013315118425
853055221.6526251655683.3473748344413
953605298.9508588332361.0491411667717
1054155355.569208103359.4307918967033
1153705410.68666379055-40.6866637905478
1253555372.95293491082-17.9529349108216
1355955356.30297850231238.697021497687
1454855577.67597531421-92.6759753142123
1555105491.7261873401218.273812659877
1655655508.6737330041456.3262669958622
1756655560.91198233739104.088017662609
1856905657.4455555575532.5544444424468
1957505687.6372809530162.3627190469933
2056905745.47387195088-55.4738719508769
2157205694.026152991225.9738470088014
2255305718.11488403189-188.114884031891
2354955543.6529013822-48.6529013821983
2454755498.53110423956-23.5311042395579
2554555476.70782789065-21.7078278906538
2655005456.5754991155443.4245008844564
2754955496.84835981375-1.84835981374999
2854855495.1341492694-10.1341492693991
2954955485.735510862319.26448913769036
3055005494.327606865325.67239313467599
3154305499.58831208669-69.5883120866947
3254205435.05054327393-15.0505432739301
3354555421.0923302753333.9076697246737
3454055452.53906729266-47.5390672926624
3553005408.45026498508-108.450264985084
3654705307.87104529413162.128954705871
3754405458.23309148986-18.233091489863
3853505441.32331155658-91.3233115565772
3952505356.62801443381-106.62801443381
4051005257.73879096881-157.738790968809
4150655111.44828155586-46.4482815558567
4249805068.37109852162-88.3710985216212
4349704986.41375029606-16.4137502960566
4449104971.19126838505-61.1912683850478
4548404914.44110712989-74.4411071298919
4648504845.402746835574.59725316443382
4749104849.6663430200960.3336569799139
4848954905.62113613171-10.6211361317137
4949554895.7708551341959.2291448658125
5049604950.701298820849.29870117915743
5149404959.32512384209-19.3251238420871
5249054941.40256849623-36.4025684962289
5349254907.6420061352217.3579938647836
5449604923.7402008105436.25979918946
5549254957.36835569913-32.3683556991264
5650254927.3492131977797.6507868022336
5750455017.9127534540127.0872465459943
5850905043.0340763161246.9659236838752
5951205086.5913323250333.4086676749685
6051455117.5752835963827.4247164036196
6150955143.0095836094-48.0095836093969
6250755098.48441386652-23.4844138665203
6351255076.7044392217548.2955607782533
6450755121.49483063556-46.4948306355618
6551005078.3744769358221.6255230641837
6650855098.43047436011-13.430474360106
6750655085.97474978069-20.9747497806902
6850905066.5222941647923.4777058352092
6950205088.29604763016-68.2960476301596
7050305024.956753995775.04324600423206
7150005029.63397399044-29.6339739904352
7250305002.1507587054427.8492412945616
7350155027.97877266905-12.9787726690502
7449555015.94196641709-60.9419664170882
7549404959.42301342508-19.4230134250765
7650604941.409673074118.590326926003
7750705051.3930147168518.606985283147
7850055068.64955217979-63.6495521797851
7949455009.61952313558-64.6195231355778
8050154949.6899211685265.3100788314805
8150355010.2599600497424.7400399502612
8249855033.20443062031-48.2044306203052
8350204988.498555368631.5014446313962
8449205017.71370500977-97.7137050097726
8551254927.09181298999197.908187010011
8650805110.63632551521-30.6363255152137
8750605082.22350683799-22.2235068379878
8850955061.6129257862133.387074213786
8951055092.5768507950512.4231492049485
9051055104.098359325340.901640674656846
9151155104.9345612056310.065438794365
9250705114.26947596978-44.2694759697761
9351155073.212966335841.7870336642018
9451505111.9672030333638.0327969666414
9551155147.23967601529-32.2396760152869
9650605117.33987395254-57.3398739525364
9750755064.1615826858710.8384173141285
9851555074.2133751484380.7866248515656
9951205149.13671157508-29.1367115750809
10050305122.11466865997-92.1146686599695
10149955036.68544912616-41.6854491261593
10250354998.025424218436.9745757815981
10349705032.31647902614-62.3164790261408
10449704974.52277206564-4.52277206563576
10549754970.328251330584.67174866941514
10649654974.66093632519-9.66093632519187
10749154965.70116626649-50.7011662664891
10849104918.67976211219-8.67976211218593
10948954910.62995512954-15.6299551295397
11048804896.13438251891-16.134382518906
11149104881.1709925800228.8290074199767
11249354907.9076637275327.0923362724707
11349754933.0337069166841.9662930833192
11448954971.95419283917-76.95419283917
11549404900.5851402252839.4148597747226
11648804937.13936940042-57.1393694004237







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1174884.147030573794757.452163357745010.84189778984
1184884.147030573794711.353040542145056.94102060544
1194884.147030573794675.187856084555093.10620506303
1204884.147030573794644.417787018925123.87627412866
1214884.147030573794617.170844692815151.12321645477
1224884.147030573794592.458056768265175.83600437932
1234884.147030573794569.681402798845198.61265834873
1244884.147030573794548.446561905585219.847499242
1254884.147030573794528.477270436355239.81679071123
1264884.147030573794509.571067799365258.72299334822
1274884.147030573794491.574329662795276.71973148479
1284884.147030573794474.367212729235293.92684841835

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 4884.14703057379 & 4757.45216335774 & 5010.84189778984 \tabularnewline
118 & 4884.14703057379 & 4711.35304054214 & 5056.94102060544 \tabularnewline
119 & 4884.14703057379 & 4675.18785608455 & 5093.10620506303 \tabularnewline
120 & 4884.14703057379 & 4644.41778701892 & 5123.87627412866 \tabularnewline
121 & 4884.14703057379 & 4617.17084469281 & 5151.12321645477 \tabularnewline
122 & 4884.14703057379 & 4592.45805676826 & 5175.83600437932 \tabularnewline
123 & 4884.14703057379 & 4569.68140279884 & 5198.61265834873 \tabularnewline
124 & 4884.14703057379 & 4548.44656190558 & 5219.847499242 \tabularnewline
125 & 4884.14703057379 & 4528.47727043635 & 5239.81679071123 \tabularnewline
126 & 4884.14703057379 & 4509.57106779936 & 5258.72299334822 \tabularnewline
127 & 4884.14703057379 & 4491.57432966279 & 5276.71973148479 \tabularnewline
128 & 4884.14703057379 & 4474.36721272923 & 5293.92684841835 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299233&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]4884.14703057379[/C][C]4757.45216335774[/C][C]5010.84189778984[/C][/ROW]
[ROW][C]118[/C][C]4884.14703057379[/C][C]4711.35304054214[/C][C]5056.94102060544[/C][/ROW]
[ROW][C]119[/C][C]4884.14703057379[/C][C]4675.18785608455[/C][C]5093.10620506303[/C][/ROW]
[ROW][C]120[/C][C]4884.14703057379[/C][C]4644.41778701892[/C][C]5123.87627412866[/C][/ROW]
[ROW][C]121[/C][C]4884.14703057379[/C][C]4617.17084469281[/C][C]5151.12321645477[/C][/ROW]
[ROW][C]122[/C][C]4884.14703057379[/C][C]4592.45805676826[/C][C]5175.83600437932[/C][/ROW]
[ROW][C]123[/C][C]4884.14703057379[/C][C]4569.68140279884[/C][C]5198.61265834873[/C][/ROW]
[ROW][C]124[/C][C]4884.14703057379[/C][C]4548.44656190558[/C][C]5219.847499242[/C][/ROW]
[ROW][C]125[/C][C]4884.14703057379[/C][C]4528.47727043635[/C][C]5239.81679071123[/C][/ROW]
[ROW][C]126[/C][C]4884.14703057379[/C][C]4509.57106779936[/C][C]5258.72299334822[/C][/ROW]
[ROW][C]127[/C][C]4884.14703057379[/C][C]4491.57432966279[/C][C]5276.71973148479[/C][/ROW]
[ROW][C]128[/C][C]4884.14703057379[/C][C]4474.36721272923[/C][C]5293.92684841835[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299233&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299233&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
1174884.147030573794757.452163357745010.84189778984
1184884.147030573794711.353040542145056.94102060544
1194884.147030573794675.187856084555093.10620506303
1204884.147030573794644.417787018925123.87627412866
1214884.147030573794617.170844692815151.12321645477
1224884.147030573794592.458056768265175.83600437932
1234884.147030573794569.681402798845198.61265834873
1244884.147030573794548.446561905585219.847499242
1254884.147030573794528.477270436355239.81679071123
1264884.147030573794509.571067799365258.72299334822
1274884.147030573794491.574329662795276.71973148479
1284884.147030573794474.367212729235293.92684841835



Parameters (Session):
par1 = 12 ; par2 = 12 ; par3 = BFGS ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
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')