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 computationMon, 05 Dec 2016 15:27:35 +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/05/t14809481771pnva7muo2irq73.htm/, Retrieved Wed, 01 May 2024 16:52:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297738, Retrieved Wed, 01 May 2024 16:52:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [F1:N2774] [2016-12-03 13:43:19] [a4c5732063e280fade3b47e7f5057d96]
- RMP     [Exponential Smoothing] [F1:N2774] [2016-12-05 14:27:35] [8d7b5e4c30a3b8052caee801f90adcea] [Current]
- R P       [Exponential Smoothing] [F1:N1809] [2016-12-11 13:20:45] [a4c5732063e280fade3b47e7f5057d96]
Feedback Forum

Post a new message
Dataseries X:
5315.1
5327.75
5349.45
5346.8
5346.6
5325.25
5340.35
5354.75
5382.85
5392.35
5400.35
5410.8
5444.35
5424
5441.85
5447.6
5454.45
5478.8
5490.5
5500.75
5504.25
5513.65
5523.75
5536.4
5547.65
5562.85
5570.4
5589.7
5621.7
5612.3
5631.7
5652.85
5645.45
5664.1
5675.25
5689.65
5700.8
5711.35
5701.85
5732.5
5714.6
5746.35
5753
5764.1
5767.8
5781.9
5805
5805.2
5835.4
5838.8
5851.1
5854.85
5854.95
5870.9
5873.6
5882.75
5867.7
5879.05
5895.6
5891.5
5954.05
5952.95
5960.15
5942.6
5957.55
5949.15
5940.5
5940.1
5926.2
5926.8
5915.3
5912.05
5897
5887.75
5882.6
5905.45
5872
5881.95
5878.4
5874.2
5896.4
5890
5888.5
5873.3
5898.9
5887.65
5907.2
5921.3
5918.75
5920.95
5935.65
5941.3
5936
5931.4
5943.8
5949.85
5953.75
5963.75
5977.1
5973.7
6005.75
6014.5
6023.35
6042.8
6027.7
6041.15
6058.45
6073.2
6096.1
6103.3
6101.55
6115.15
6146.25
6134.3
6136.65
6168.05
6182.8
6204.3
6220.85
6229.75




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=297738&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=297738&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297738&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
alpha0.712774492128901
beta0.0879254927782068
gamma0.572121663469379

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.712774492128901 \tabularnewline
beta & 0.0879254927782068 \tabularnewline
gamma & 0.572121663469379 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297738&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]0.712774492128901[/C][/ROW]
[ROW][C]beta[/C][C]0.0879254927782068[/C][/ROW]
[ROW][C]gamma[/C][C]0.572121663469379[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297738&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297738&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
alpha0.712774492128901
beta0.0879254927782068
gamma0.572121663469379







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135444.355385.6026041666758.7473958333321
1454245408.8613246807915.1386753192137
155441.855441.383534899280.466465100717869
165447.65452.40616845448-4.80616845448003
175454.455460.38606235574-5.93606235573588
185478.85484.50941078714-5.70941078714168
195490.55467.7219125817922.7780874182135
205500.755504.4108530622-3.6608530621952
215504.255537.26077833625-33.0107783362537
225513.655528.33242210692-14.6824221069219
235523.755529.40413789313-5.65413789313425
245536.45536.80871695805-0.408716958054356
255547.655578.91782181042-31.2678218104156
265562.855526.6663707612636.1836292387452
275570.45568.91325311841.48674688159826
285589.75576.9960384537912.7039615462108
295621.75595.5677733852526.1322266147481
305612.35642.89231882127-30.5923188212691
315631.75611.7972657433719.9027342566296
325652.855640.658925435612.1910745644009
335645.455679.54499877771-34.094998777714
345664.15672.34806060746-8.24806060746141
355675.255679.38523442561-4.13523442561109
365689.655688.725219580670.924780419326453
375700.85726.78816729061-25.9881672906076
385711.355689.7893314111521.5606685888515
395701.855715.40049151434-13.5504915143365
405732.55713.1548372567419.345162743256
415714.65737.62951975615-23.0295197561545
425746.355736.473010449399.87698955061478
4357535740.9390613913712.0609386086262
445764.15760.87045998323.229540016805
455767.85783.12766838094-15.3276683809399
465781.95792.09593001981-10.1959300198141
4758055796.839440855658.16055914435401
485805.25814.96452250874-9.76452250874445
495835.45839.50541548819-4.10541548818946
505838.85825.8086208050412.9913791949648
515851.15838.8959910794712.2040089205329
525854.855861.38114979498-6.53114979498332
535854.955859.79480410266-4.84480410265678
545870.95877.49330161265-6.59330161264916
555873.65870.032369177743.56763082225825
565882.755881.380160827491.36983917251291
575867.75898.06725645549-30.3672564554881
585879.055895.02132685631-15.9713268563119
595895.65896.1651714788-0.56517147879913
605891.55902.07873794162-10.5787379416215
615954.055923.871755249430.1782447506002
625952.955936.4720799322916.4779200677067
635960.155951.184805726598.96519427341264
645942.65967.34935516851-24.7493551685111
655957.555950.979542209526.57045779048076
665949.155975.16751777345-26.0175177734527
675940.55952.95418612684-12.4541861268426
685940.15948.93973425615-8.83973425614477
695926.25948.91342778147-22.7134277814685
705926.85949.947291696-23.1472916960001
715915.35944.31691436826-29.0169143682642
725912.055922.33115602209-10.281156022088
7358975945.07830320099-48.0783032009913
745887.755888.7881009366-1.03810093659558
755882.65877.823645979074.77635402092983
765905.455873.2420785680832.2079214319183
7758725893.96607588406-21.96607588406
785881.955882.01980509824-0.0698050982391578
795878.45871.717327509146.68267249085511
805874.25874.3235747753-0.123574775298039
815896.45871.1628189296925.2371810703144
8258905902.2412025801-12.241202580105
835888.55900.0412052731-11.5412052731017
845873.35891.3070569648-18.0070569647996
855898.95899.56862342912-0.668623429119179
865887.655885.00443680562.64556319439998
875907.25878.055526052629.1444739473955
885921.35897.3123264033123.9876735966864
895918.755904.7212886849114.0287113150853
905920.955925.73163315768-4.78163315767688
915935.655916.5872903358519.0627096641538
925941.35931.0821105781910.2178894218077
9359365944.29093250273-8.29093250272854
945931.45948.04230982495-16.6423098249488
955943.85945.27424584504-1.47424584503551
965949.855945.737857469844.11214253015896
975953.755977.08565562741-23.3356556274057
985963.755949.9600749342913.7899250657056
995977.15959.0579960386718.0420039613255
1005973.75972.606932885781.09306711421777
1016005.755963.6789392137742.0710607862329
1026014.56004.961804725489.53819527451651
1036023.356014.215715336259.13428466375444
1046042.86023.8312850066418.9687149933634
1056027.76044.43530766876-16.7353076687577
1066041.156044.4655193105-3.3155193105049
1076058.456058.194326375080.255673624918927
1086073.26065.422734072937.77726592706676
1096096.16099.71594975674-3.61594975673597
1106103.36098.826148126554.47385187345299
1116101.556107.47800286598-5.92800286597867
1126115.156105.1497786398510.0002213601529
1136146.256113.855859270232.3941407297953
1146134.36146.84019452017-12.5401945201675
1156136.656142.85213256206-6.20213256205898
1166168.056144.7525318183223.2974681816813
1176182.86164.4462634623618.3537365376405
1186204.36195.762816525768.53718347424456
1196220.856223.34011551487-2.49011551486728
1206229.756234.48866195741-4.73866195741266

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5444.35 & 5385.60260416667 & 58.7473958333321 \tabularnewline
14 & 5424 & 5408.86132468079 & 15.1386753192137 \tabularnewline
15 & 5441.85 & 5441.38353489928 & 0.466465100717869 \tabularnewline
16 & 5447.6 & 5452.40616845448 & -4.80616845448003 \tabularnewline
17 & 5454.45 & 5460.38606235574 & -5.93606235573588 \tabularnewline
18 & 5478.8 & 5484.50941078714 & -5.70941078714168 \tabularnewline
19 & 5490.5 & 5467.72191258179 & 22.7780874182135 \tabularnewline
20 & 5500.75 & 5504.4108530622 & -3.6608530621952 \tabularnewline
21 & 5504.25 & 5537.26077833625 & -33.0107783362537 \tabularnewline
22 & 5513.65 & 5528.33242210692 & -14.6824221069219 \tabularnewline
23 & 5523.75 & 5529.40413789313 & -5.65413789313425 \tabularnewline
24 & 5536.4 & 5536.80871695805 & -0.408716958054356 \tabularnewline
25 & 5547.65 & 5578.91782181042 & -31.2678218104156 \tabularnewline
26 & 5562.85 & 5526.66637076126 & 36.1836292387452 \tabularnewline
27 & 5570.4 & 5568.9132531184 & 1.48674688159826 \tabularnewline
28 & 5589.7 & 5576.99603845379 & 12.7039615462108 \tabularnewline
29 & 5621.7 & 5595.56777338525 & 26.1322266147481 \tabularnewline
30 & 5612.3 & 5642.89231882127 & -30.5923188212691 \tabularnewline
31 & 5631.7 & 5611.79726574337 & 19.9027342566296 \tabularnewline
32 & 5652.85 & 5640.6589254356 & 12.1910745644009 \tabularnewline
33 & 5645.45 & 5679.54499877771 & -34.094998777714 \tabularnewline
34 & 5664.1 & 5672.34806060746 & -8.24806060746141 \tabularnewline
35 & 5675.25 & 5679.38523442561 & -4.13523442561109 \tabularnewline
36 & 5689.65 & 5688.72521958067 & 0.924780419326453 \tabularnewline
37 & 5700.8 & 5726.78816729061 & -25.9881672906076 \tabularnewline
38 & 5711.35 & 5689.78933141115 & 21.5606685888515 \tabularnewline
39 & 5701.85 & 5715.40049151434 & -13.5504915143365 \tabularnewline
40 & 5732.5 & 5713.15483725674 & 19.345162743256 \tabularnewline
41 & 5714.6 & 5737.62951975615 & -23.0295197561545 \tabularnewline
42 & 5746.35 & 5736.47301044939 & 9.87698955061478 \tabularnewline
43 & 5753 & 5740.93906139137 & 12.0609386086262 \tabularnewline
44 & 5764.1 & 5760.8704599832 & 3.229540016805 \tabularnewline
45 & 5767.8 & 5783.12766838094 & -15.3276683809399 \tabularnewline
46 & 5781.9 & 5792.09593001981 & -10.1959300198141 \tabularnewline
47 & 5805 & 5796.83944085565 & 8.16055914435401 \tabularnewline
48 & 5805.2 & 5814.96452250874 & -9.76452250874445 \tabularnewline
49 & 5835.4 & 5839.50541548819 & -4.10541548818946 \tabularnewline
50 & 5838.8 & 5825.80862080504 & 12.9913791949648 \tabularnewline
51 & 5851.1 & 5838.89599107947 & 12.2040089205329 \tabularnewline
52 & 5854.85 & 5861.38114979498 & -6.53114979498332 \tabularnewline
53 & 5854.95 & 5859.79480410266 & -4.84480410265678 \tabularnewline
54 & 5870.9 & 5877.49330161265 & -6.59330161264916 \tabularnewline
55 & 5873.6 & 5870.03236917774 & 3.56763082225825 \tabularnewline
56 & 5882.75 & 5881.38016082749 & 1.36983917251291 \tabularnewline
57 & 5867.7 & 5898.06725645549 & -30.3672564554881 \tabularnewline
58 & 5879.05 & 5895.02132685631 & -15.9713268563119 \tabularnewline
59 & 5895.6 & 5896.1651714788 & -0.56517147879913 \tabularnewline
60 & 5891.5 & 5902.07873794162 & -10.5787379416215 \tabularnewline
61 & 5954.05 & 5923.8717552494 & 30.1782447506002 \tabularnewline
62 & 5952.95 & 5936.47207993229 & 16.4779200677067 \tabularnewline
63 & 5960.15 & 5951.18480572659 & 8.96519427341264 \tabularnewline
64 & 5942.6 & 5967.34935516851 & -24.7493551685111 \tabularnewline
65 & 5957.55 & 5950.97954220952 & 6.57045779048076 \tabularnewline
66 & 5949.15 & 5975.16751777345 & -26.0175177734527 \tabularnewline
67 & 5940.5 & 5952.95418612684 & -12.4541861268426 \tabularnewline
68 & 5940.1 & 5948.93973425615 & -8.83973425614477 \tabularnewline
69 & 5926.2 & 5948.91342778147 & -22.7134277814685 \tabularnewline
70 & 5926.8 & 5949.947291696 & -23.1472916960001 \tabularnewline
71 & 5915.3 & 5944.31691436826 & -29.0169143682642 \tabularnewline
72 & 5912.05 & 5922.33115602209 & -10.281156022088 \tabularnewline
73 & 5897 & 5945.07830320099 & -48.0783032009913 \tabularnewline
74 & 5887.75 & 5888.7881009366 & -1.03810093659558 \tabularnewline
75 & 5882.6 & 5877.82364597907 & 4.77635402092983 \tabularnewline
76 & 5905.45 & 5873.24207856808 & 32.2079214319183 \tabularnewline
77 & 5872 & 5893.96607588406 & -21.96607588406 \tabularnewline
78 & 5881.95 & 5882.01980509824 & -0.0698050982391578 \tabularnewline
79 & 5878.4 & 5871.71732750914 & 6.68267249085511 \tabularnewline
80 & 5874.2 & 5874.3235747753 & -0.123574775298039 \tabularnewline
81 & 5896.4 & 5871.16281892969 & 25.2371810703144 \tabularnewline
82 & 5890 & 5902.2412025801 & -12.241202580105 \tabularnewline
83 & 5888.5 & 5900.0412052731 & -11.5412052731017 \tabularnewline
84 & 5873.3 & 5891.3070569648 & -18.0070569647996 \tabularnewline
85 & 5898.9 & 5899.56862342912 & -0.668623429119179 \tabularnewline
86 & 5887.65 & 5885.0044368056 & 2.64556319439998 \tabularnewline
87 & 5907.2 & 5878.0555260526 & 29.1444739473955 \tabularnewline
88 & 5921.3 & 5897.31232640331 & 23.9876735966864 \tabularnewline
89 & 5918.75 & 5904.72128868491 & 14.0287113150853 \tabularnewline
90 & 5920.95 & 5925.73163315768 & -4.78163315767688 \tabularnewline
91 & 5935.65 & 5916.58729033585 & 19.0627096641538 \tabularnewline
92 & 5941.3 & 5931.08211057819 & 10.2178894218077 \tabularnewline
93 & 5936 & 5944.29093250273 & -8.29093250272854 \tabularnewline
94 & 5931.4 & 5948.04230982495 & -16.6423098249488 \tabularnewline
95 & 5943.8 & 5945.27424584504 & -1.47424584503551 \tabularnewline
96 & 5949.85 & 5945.73785746984 & 4.11214253015896 \tabularnewline
97 & 5953.75 & 5977.08565562741 & -23.3356556274057 \tabularnewline
98 & 5963.75 & 5949.96007493429 & 13.7899250657056 \tabularnewline
99 & 5977.1 & 5959.05799603867 & 18.0420039613255 \tabularnewline
100 & 5973.7 & 5972.60693288578 & 1.09306711421777 \tabularnewline
101 & 6005.75 & 5963.67893921377 & 42.0710607862329 \tabularnewline
102 & 6014.5 & 6004.96180472548 & 9.53819527451651 \tabularnewline
103 & 6023.35 & 6014.21571533625 & 9.13428466375444 \tabularnewline
104 & 6042.8 & 6023.83128500664 & 18.9687149933634 \tabularnewline
105 & 6027.7 & 6044.43530766876 & -16.7353076687577 \tabularnewline
106 & 6041.15 & 6044.4655193105 & -3.3155193105049 \tabularnewline
107 & 6058.45 & 6058.19432637508 & 0.255673624918927 \tabularnewline
108 & 6073.2 & 6065.42273407293 & 7.77726592706676 \tabularnewline
109 & 6096.1 & 6099.71594975674 & -3.61594975673597 \tabularnewline
110 & 6103.3 & 6098.82614812655 & 4.47385187345299 \tabularnewline
111 & 6101.55 & 6107.47800286598 & -5.92800286597867 \tabularnewline
112 & 6115.15 & 6105.14977863985 & 10.0002213601529 \tabularnewline
113 & 6146.25 & 6113.8558592702 & 32.3941407297953 \tabularnewline
114 & 6134.3 & 6146.84019452017 & -12.5401945201675 \tabularnewline
115 & 6136.65 & 6142.85213256206 & -6.20213256205898 \tabularnewline
116 & 6168.05 & 6144.75253181832 & 23.2974681816813 \tabularnewline
117 & 6182.8 & 6164.44626346236 & 18.3537365376405 \tabularnewline
118 & 6204.3 & 6195.76281652576 & 8.53718347424456 \tabularnewline
119 & 6220.85 & 6223.34011551487 & -2.49011551486728 \tabularnewline
120 & 6229.75 & 6234.48866195741 & -4.73866195741266 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297738&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]5444.35[/C][C]5385.60260416667[/C][C]58.7473958333321[/C][/ROW]
[ROW][C]14[/C][C]5424[/C][C]5408.86132468079[/C][C]15.1386753192137[/C][/ROW]
[ROW][C]15[/C][C]5441.85[/C][C]5441.38353489928[/C][C]0.466465100717869[/C][/ROW]
[ROW][C]16[/C][C]5447.6[/C][C]5452.40616845448[/C][C]-4.80616845448003[/C][/ROW]
[ROW][C]17[/C][C]5454.45[/C][C]5460.38606235574[/C][C]-5.93606235573588[/C][/ROW]
[ROW][C]18[/C][C]5478.8[/C][C]5484.50941078714[/C][C]-5.70941078714168[/C][/ROW]
[ROW][C]19[/C][C]5490.5[/C][C]5467.72191258179[/C][C]22.7780874182135[/C][/ROW]
[ROW][C]20[/C][C]5500.75[/C][C]5504.4108530622[/C][C]-3.6608530621952[/C][/ROW]
[ROW][C]21[/C][C]5504.25[/C][C]5537.26077833625[/C][C]-33.0107783362537[/C][/ROW]
[ROW][C]22[/C][C]5513.65[/C][C]5528.33242210692[/C][C]-14.6824221069219[/C][/ROW]
[ROW][C]23[/C][C]5523.75[/C][C]5529.40413789313[/C][C]-5.65413789313425[/C][/ROW]
[ROW][C]24[/C][C]5536.4[/C][C]5536.80871695805[/C][C]-0.408716958054356[/C][/ROW]
[ROW][C]25[/C][C]5547.65[/C][C]5578.91782181042[/C][C]-31.2678218104156[/C][/ROW]
[ROW][C]26[/C][C]5562.85[/C][C]5526.66637076126[/C][C]36.1836292387452[/C][/ROW]
[ROW][C]27[/C][C]5570.4[/C][C]5568.9132531184[/C][C]1.48674688159826[/C][/ROW]
[ROW][C]28[/C][C]5589.7[/C][C]5576.99603845379[/C][C]12.7039615462108[/C][/ROW]
[ROW][C]29[/C][C]5621.7[/C][C]5595.56777338525[/C][C]26.1322266147481[/C][/ROW]
[ROW][C]30[/C][C]5612.3[/C][C]5642.89231882127[/C][C]-30.5923188212691[/C][/ROW]
[ROW][C]31[/C][C]5631.7[/C][C]5611.79726574337[/C][C]19.9027342566296[/C][/ROW]
[ROW][C]32[/C][C]5652.85[/C][C]5640.6589254356[/C][C]12.1910745644009[/C][/ROW]
[ROW][C]33[/C][C]5645.45[/C][C]5679.54499877771[/C][C]-34.094998777714[/C][/ROW]
[ROW][C]34[/C][C]5664.1[/C][C]5672.34806060746[/C][C]-8.24806060746141[/C][/ROW]
[ROW][C]35[/C][C]5675.25[/C][C]5679.38523442561[/C][C]-4.13523442561109[/C][/ROW]
[ROW][C]36[/C][C]5689.65[/C][C]5688.72521958067[/C][C]0.924780419326453[/C][/ROW]
[ROW][C]37[/C][C]5700.8[/C][C]5726.78816729061[/C][C]-25.9881672906076[/C][/ROW]
[ROW][C]38[/C][C]5711.35[/C][C]5689.78933141115[/C][C]21.5606685888515[/C][/ROW]
[ROW][C]39[/C][C]5701.85[/C][C]5715.40049151434[/C][C]-13.5504915143365[/C][/ROW]
[ROW][C]40[/C][C]5732.5[/C][C]5713.15483725674[/C][C]19.345162743256[/C][/ROW]
[ROW][C]41[/C][C]5714.6[/C][C]5737.62951975615[/C][C]-23.0295197561545[/C][/ROW]
[ROW][C]42[/C][C]5746.35[/C][C]5736.47301044939[/C][C]9.87698955061478[/C][/ROW]
[ROW][C]43[/C][C]5753[/C][C]5740.93906139137[/C][C]12.0609386086262[/C][/ROW]
[ROW][C]44[/C][C]5764.1[/C][C]5760.8704599832[/C][C]3.229540016805[/C][/ROW]
[ROW][C]45[/C][C]5767.8[/C][C]5783.12766838094[/C][C]-15.3276683809399[/C][/ROW]
[ROW][C]46[/C][C]5781.9[/C][C]5792.09593001981[/C][C]-10.1959300198141[/C][/ROW]
[ROW][C]47[/C][C]5805[/C][C]5796.83944085565[/C][C]8.16055914435401[/C][/ROW]
[ROW][C]48[/C][C]5805.2[/C][C]5814.96452250874[/C][C]-9.76452250874445[/C][/ROW]
[ROW][C]49[/C][C]5835.4[/C][C]5839.50541548819[/C][C]-4.10541548818946[/C][/ROW]
[ROW][C]50[/C][C]5838.8[/C][C]5825.80862080504[/C][C]12.9913791949648[/C][/ROW]
[ROW][C]51[/C][C]5851.1[/C][C]5838.89599107947[/C][C]12.2040089205329[/C][/ROW]
[ROW][C]52[/C][C]5854.85[/C][C]5861.38114979498[/C][C]-6.53114979498332[/C][/ROW]
[ROW][C]53[/C][C]5854.95[/C][C]5859.79480410266[/C][C]-4.84480410265678[/C][/ROW]
[ROW][C]54[/C][C]5870.9[/C][C]5877.49330161265[/C][C]-6.59330161264916[/C][/ROW]
[ROW][C]55[/C][C]5873.6[/C][C]5870.03236917774[/C][C]3.56763082225825[/C][/ROW]
[ROW][C]56[/C][C]5882.75[/C][C]5881.38016082749[/C][C]1.36983917251291[/C][/ROW]
[ROW][C]57[/C][C]5867.7[/C][C]5898.06725645549[/C][C]-30.3672564554881[/C][/ROW]
[ROW][C]58[/C][C]5879.05[/C][C]5895.02132685631[/C][C]-15.9713268563119[/C][/ROW]
[ROW][C]59[/C][C]5895.6[/C][C]5896.1651714788[/C][C]-0.56517147879913[/C][/ROW]
[ROW][C]60[/C][C]5891.5[/C][C]5902.07873794162[/C][C]-10.5787379416215[/C][/ROW]
[ROW][C]61[/C][C]5954.05[/C][C]5923.8717552494[/C][C]30.1782447506002[/C][/ROW]
[ROW][C]62[/C][C]5952.95[/C][C]5936.47207993229[/C][C]16.4779200677067[/C][/ROW]
[ROW][C]63[/C][C]5960.15[/C][C]5951.18480572659[/C][C]8.96519427341264[/C][/ROW]
[ROW][C]64[/C][C]5942.6[/C][C]5967.34935516851[/C][C]-24.7493551685111[/C][/ROW]
[ROW][C]65[/C][C]5957.55[/C][C]5950.97954220952[/C][C]6.57045779048076[/C][/ROW]
[ROW][C]66[/C][C]5949.15[/C][C]5975.16751777345[/C][C]-26.0175177734527[/C][/ROW]
[ROW][C]67[/C][C]5940.5[/C][C]5952.95418612684[/C][C]-12.4541861268426[/C][/ROW]
[ROW][C]68[/C][C]5940.1[/C][C]5948.93973425615[/C][C]-8.83973425614477[/C][/ROW]
[ROW][C]69[/C][C]5926.2[/C][C]5948.91342778147[/C][C]-22.7134277814685[/C][/ROW]
[ROW][C]70[/C][C]5926.8[/C][C]5949.947291696[/C][C]-23.1472916960001[/C][/ROW]
[ROW][C]71[/C][C]5915.3[/C][C]5944.31691436826[/C][C]-29.0169143682642[/C][/ROW]
[ROW][C]72[/C][C]5912.05[/C][C]5922.33115602209[/C][C]-10.281156022088[/C][/ROW]
[ROW][C]73[/C][C]5897[/C][C]5945.07830320099[/C][C]-48.0783032009913[/C][/ROW]
[ROW][C]74[/C][C]5887.75[/C][C]5888.7881009366[/C][C]-1.03810093659558[/C][/ROW]
[ROW][C]75[/C][C]5882.6[/C][C]5877.82364597907[/C][C]4.77635402092983[/C][/ROW]
[ROW][C]76[/C][C]5905.45[/C][C]5873.24207856808[/C][C]32.2079214319183[/C][/ROW]
[ROW][C]77[/C][C]5872[/C][C]5893.96607588406[/C][C]-21.96607588406[/C][/ROW]
[ROW][C]78[/C][C]5881.95[/C][C]5882.01980509824[/C][C]-0.0698050982391578[/C][/ROW]
[ROW][C]79[/C][C]5878.4[/C][C]5871.71732750914[/C][C]6.68267249085511[/C][/ROW]
[ROW][C]80[/C][C]5874.2[/C][C]5874.3235747753[/C][C]-0.123574775298039[/C][/ROW]
[ROW][C]81[/C][C]5896.4[/C][C]5871.16281892969[/C][C]25.2371810703144[/C][/ROW]
[ROW][C]82[/C][C]5890[/C][C]5902.2412025801[/C][C]-12.241202580105[/C][/ROW]
[ROW][C]83[/C][C]5888.5[/C][C]5900.0412052731[/C][C]-11.5412052731017[/C][/ROW]
[ROW][C]84[/C][C]5873.3[/C][C]5891.3070569648[/C][C]-18.0070569647996[/C][/ROW]
[ROW][C]85[/C][C]5898.9[/C][C]5899.56862342912[/C][C]-0.668623429119179[/C][/ROW]
[ROW][C]86[/C][C]5887.65[/C][C]5885.0044368056[/C][C]2.64556319439998[/C][/ROW]
[ROW][C]87[/C][C]5907.2[/C][C]5878.0555260526[/C][C]29.1444739473955[/C][/ROW]
[ROW][C]88[/C][C]5921.3[/C][C]5897.31232640331[/C][C]23.9876735966864[/C][/ROW]
[ROW][C]89[/C][C]5918.75[/C][C]5904.72128868491[/C][C]14.0287113150853[/C][/ROW]
[ROW][C]90[/C][C]5920.95[/C][C]5925.73163315768[/C][C]-4.78163315767688[/C][/ROW]
[ROW][C]91[/C][C]5935.65[/C][C]5916.58729033585[/C][C]19.0627096641538[/C][/ROW]
[ROW][C]92[/C][C]5941.3[/C][C]5931.08211057819[/C][C]10.2178894218077[/C][/ROW]
[ROW][C]93[/C][C]5936[/C][C]5944.29093250273[/C][C]-8.29093250272854[/C][/ROW]
[ROW][C]94[/C][C]5931.4[/C][C]5948.04230982495[/C][C]-16.6423098249488[/C][/ROW]
[ROW][C]95[/C][C]5943.8[/C][C]5945.27424584504[/C][C]-1.47424584503551[/C][/ROW]
[ROW][C]96[/C][C]5949.85[/C][C]5945.73785746984[/C][C]4.11214253015896[/C][/ROW]
[ROW][C]97[/C][C]5953.75[/C][C]5977.08565562741[/C][C]-23.3356556274057[/C][/ROW]
[ROW][C]98[/C][C]5963.75[/C][C]5949.96007493429[/C][C]13.7899250657056[/C][/ROW]
[ROW][C]99[/C][C]5977.1[/C][C]5959.05799603867[/C][C]18.0420039613255[/C][/ROW]
[ROW][C]100[/C][C]5973.7[/C][C]5972.60693288578[/C][C]1.09306711421777[/C][/ROW]
[ROW][C]101[/C][C]6005.75[/C][C]5963.67893921377[/C][C]42.0710607862329[/C][/ROW]
[ROW][C]102[/C][C]6014.5[/C][C]6004.96180472548[/C][C]9.53819527451651[/C][/ROW]
[ROW][C]103[/C][C]6023.35[/C][C]6014.21571533625[/C][C]9.13428466375444[/C][/ROW]
[ROW][C]104[/C][C]6042.8[/C][C]6023.83128500664[/C][C]18.9687149933634[/C][/ROW]
[ROW][C]105[/C][C]6027.7[/C][C]6044.43530766876[/C][C]-16.7353076687577[/C][/ROW]
[ROW][C]106[/C][C]6041.15[/C][C]6044.4655193105[/C][C]-3.3155193105049[/C][/ROW]
[ROW][C]107[/C][C]6058.45[/C][C]6058.19432637508[/C][C]0.255673624918927[/C][/ROW]
[ROW][C]108[/C][C]6073.2[/C][C]6065.42273407293[/C][C]7.77726592706676[/C][/ROW]
[ROW][C]109[/C][C]6096.1[/C][C]6099.71594975674[/C][C]-3.61594975673597[/C][/ROW]
[ROW][C]110[/C][C]6103.3[/C][C]6098.82614812655[/C][C]4.47385187345299[/C][/ROW]
[ROW][C]111[/C][C]6101.55[/C][C]6107.47800286598[/C][C]-5.92800286597867[/C][/ROW]
[ROW][C]112[/C][C]6115.15[/C][C]6105.14977863985[/C][C]10.0002213601529[/C][/ROW]
[ROW][C]113[/C][C]6146.25[/C][C]6113.8558592702[/C][C]32.3941407297953[/C][/ROW]
[ROW][C]114[/C][C]6134.3[/C][C]6146.84019452017[/C][C]-12.5401945201675[/C][/ROW]
[ROW][C]115[/C][C]6136.65[/C][C]6142.85213256206[/C][C]-6.20213256205898[/C][/ROW]
[ROW][C]116[/C][C]6168.05[/C][C]6144.75253181832[/C][C]23.2974681816813[/C][/ROW]
[ROW][C]117[/C][C]6182.8[/C][C]6164.44626346236[/C][C]18.3537365376405[/C][/ROW]
[ROW][C]118[/C][C]6204.3[/C][C]6195.76281652576[/C][C]8.53718347424456[/C][/ROW]
[ROW][C]119[/C][C]6220.85[/C][C]6223.34011551487[/C][C]-2.49011551486728[/C][/ROW]
[ROW][C]120[/C][C]6229.75[/C][C]6234.48866195741[/C][C]-4.73866195741266[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297738&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297738&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
135444.355385.6026041666758.7473958333321
1454245408.8613246807915.1386753192137
155441.855441.383534899280.466465100717869
165447.65452.40616845448-4.80616845448003
175454.455460.38606235574-5.93606235573588
185478.85484.50941078714-5.70941078714168
195490.55467.7219125817922.7780874182135
205500.755504.4108530622-3.6608530621952
215504.255537.26077833625-33.0107783362537
225513.655528.33242210692-14.6824221069219
235523.755529.40413789313-5.65413789313425
245536.45536.80871695805-0.408716958054356
255547.655578.91782181042-31.2678218104156
265562.855526.6663707612636.1836292387452
275570.45568.91325311841.48674688159826
285589.75576.9960384537912.7039615462108
295621.75595.5677733852526.1322266147481
305612.35642.89231882127-30.5923188212691
315631.75611.7972657433719.9027342566296
325652.855640.658925435612.1910745644009
335645.455679.54499877771-34.094998777714
345664.15672.34806060746-8.24806060746141
355675.255679.38523442561-4.13523442561109
365689.655688.725219580670.924780419326453
375700.85726.78816729061-25.9881672906076
385711.355689.7893314111521.5606685888515
395701.855715.40049151434-13.5504915143365
405732.55713.1548372567419.345162743256
415714.65737.62951975615-23.0295197561545
425746.355736.473010449399.87698955061478
4357535740.9390613913712.0609386086262
445764.15760.87045998323.229540016805
455767.85783.12766838094-15.3276683809399
465781.95792.09593001981-10.1959300198141
4758055796.839440855658.16055914435401
485805.25814.96452250874-9.76452250874445
495835.45839.50541548819-4.10541548818946
505838.85825.8086208050412.9913791949648
515851.15838.8959910794712.2040089205329
525854.855861.38114979498-6.53114979498332
535854.955859.79480410266-4.84480410265678
545870.95877.49330161265-6.59330161264916
555873.65870.032369177743.56763082225825
565882.755881.380160827491.36983917251291
575867.75898.06725645549-30.3672564554881
585879.055895.02132685631-15.9713268563119
595895.65896.1651714788-0.56517147879913
605891.55902.07873794162-10.5787379416215
615954.055923.871755249430.1782447506002
625952.955936.4720799322916.4779200677067
635960.155951.184805726598.96519427341264
645942.65967.34935516851-24.7493551685111
655957.555950.979542209526.57045779048076
665949.155975.16751777345-26.0175177734527
675940.55952.95418612684-12.4541861268426
685940.15948.93973425615-8.83973425614477
695926.25948.91342778147-22.7134277814685
705926.85949.947291696-23.1472916960001
715915.35944.31691436826-29.0169143682642
725912.055922.33115602209-10.281156022088
7358975945.07830320099-48.0783032009913
745887.755888.7881009366-1.03810093659558
755882.65877.823645979074.77635402092983
765905.455873.2420785680832.2079214319183
7758725893.96607588406-21.96607588406
785881.955882.01980509824-0.0698050982391578
795878.45871.717327509146.68267249085511
805874.25874.3235747753-0.123574775298039
815896.45871.1628189296925.2371810703144
8258905902.2412025801-12.241202580105
835888.55900.0412052731-11.5412052731017
845873.35891.3070569648-18.0070569647996
855898.95899.56862342912-0.668623429119179
865887.655885.00443680562.64556319439998
875907.25878.055526052629.1444739473955
885921.35897.3123264033123.9876735966864
895918.755904.7212886849114.0287113150853
905920.955925.73163315768-4.78163315767688
915935.655916.5872903358519.0627096641538
925941.35931.0821105781910.2178894218077
9359365944.29093250273-8.29093250272854
945931.45948.04230982495-16.6423098249488
955943.85945.27424584504-1.47424584503551
965949.855945.737857469844.11214253015896
975953.755977.08565562741-23.3356556274057
985963.755949.9600749342913.7899250657056
995977.15959.0579960386718.0420039613255
1005973.75972.606932885781.09306711421777
1016005.755963.6789392137742.0710607862329
1026014.56004.961804725489.53819527451651
1036023.356014.215715336259.13428466375444
1046042.86023.8312850066418.9687149933634
1056027.76044.43530766876-16.7353076687577
1066041.156044.4655193105-3.3155193105049
1076058.456058.194326375080.255673624918927
1086073.26065.422734072937.77726592706676
1096096.16099.71594975674-3.61594975673597
1106103.36098.826148126554.47385187345299
1116101.556107.47800286598-5.92800286597867
1126115.156105.1497786398510.0002213601529
1136146.256113.855859270232.3941407297953
1146134.36146.84019452017-12.5401945201675
1156136.656142.85213256206-6.20213256205898
1166168.056144.7525318183223.2974681816813
1176182.86164.4462634623618.3537365376405
1186204.36195.762816525768.53718347424456
1196220.856223.34011551487-2.49011551486728
1206229.756234.48866195741-4.73866195741266







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1216261.845493037216226.499850256736297.19113581769
1226268.945917067936224.218442595196313.67339154067
1236276.502716519836222.854653218846330.15077982081
1246285.191895404266222.807350852316347.57643995621
1256293.997917187986222.923935679896365.07189869606
1266298.026291249696218.233015799946377.81956669944
1276306.321710402616217.732698423716394.9107223815
1286320.182763875246222.691926755636417.67360099484
1296323.690508342116217.172287321796430.20872936243
1306340.393851444976224.709664668076456.07803822188
1316359.620935480336234.623431222616484.61843973806
1326371.877896836716237.413848941786506.34194473164

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 6261.84549303721 & 6226.49985025673 & 6297.19113581769 \tabularnewline
122 & 6268.94591706793 & 6224.21844259519 & 6313.67339154067 \tabularnewline
123 & 6276.50271651983 & 6222.85465321884 & 6330.15077982081 \tabularnewline
124 & 6285.19189540426 & 6222.80735085231 & 6347.57643995621 \tabularnewline
125 & 6293.99791718798 & 6222.92393567989 & 6365.07189869606 \tabularnewline
126 & 6298.02629124969 & 6218.23301579994 & 6377.81956669944 \tabularnewline
127 & 6306.32171040261 & 6217.73269842371 & 6394.9107223815 \tabularnewline
128 & 6320.18276387524 & 6222.69192675563 & 6417.67360099484 \tabularnewline
129 & 6323.69050834211 & 6217.17228732179 & 6430.20872936243 \tabularnewline
130 & 6340.39385144497 & 6224.70966466807 & 6456.07803822188 \tabularnewline
131 & 6359.62093548033 & 6234.62343122261 & 6484.61843973806 \tabularnewline
132 & 6371.87789683671 & 6237.41384894178 & 6506.34194473164 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297738&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]121[/C][C]6261.84549303721[/C][C]6226.49985025673[/C][C]6297.19113581769[/C][/ROW]
[ROW][C]122[/C][C]6268.94591706793[/C][C]6224.21844259519[/C][C]6313.67339154067[/C][/ROW]
[ROW][C]123[/C][C]6276.50271651983[/C][C]6222.85465321884[/C][C]6330.15077982081[/C][/ROW]
[ROW][C]124[/C][C]6285.19189540426[/C][C]6222.80735085231[/C][C]6347.57643995621[/C][/ROW]
[ROW][C]125[/C][C]6293.99791718798[/C][C]6222.92393567989[/C][C]6365.07189869606[/C][/ROW]
[ROW][C]126[/C][C]6298.02629124969[/C][C]6218.23301579994[/C][C]6377.81956669944[/C][/ROW]
[ROW][C]127[/C][C]6306.32171040261[/C][C]6217.73269842371[/C][C]6394.9107223815[/C][/ROW]
[ROW][C]128[/C][C]6320.18276387524[/C][C]6222.69192675563[/C][C]6417.67360099484[/C][/ROW]
[ROW][C]129[/C][C]6323.69050834211[/C][C]6217.17228732179[/C][C]6430.20872936243[/C][/ROW]
[ROW][C]130[/C][C]6340.39385144497[/C][C]6224.70966466807[/C][C]6456.07803822188[/C][/ROW]
[ROW][C]131[/C][C]6359.62093548033[/C][C]6234.62343122261[/C][C]6484.61843973806[/C][/ROW]
[ROW][C]132[/C][C]6371.87789683671[/C][C]6237.41384894178[/C][C]6506.34194473164[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297738&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297738&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
1216261.845493037216226.499850256736297.19113581769
1226268.945917067936224.218442595196313.67339154067
1236276.502716519836222.854653218846330.15077982081
1246285.191895404266222.807350852316347.57643995621
1256293.997917187986222.923935679896365.07189869606
1266298.026291249696218.233015799946377.81956669944
1276306.321710402616217.732698423716394.9107223815
1286320.182763875246222.691926755636417.67360099484
1296323.690508342116217.172287321796430.20872936243
1306340.393851444976224.709664668076456.07803822188
1316359.620935480336234.623431222616484.61843973806
1326371.877896836716237.413848941786506.34194473164



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
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 <- 'Double'
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')