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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 01 Dec 2011 03:50:09 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/01/t1322729427vp7zf8jxl9csm7m.htm/, Retrieved Fri, 19 Apr 2024 10:20:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=149180, Retrieved Fri, 19 Apr 2024 10:20:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMPD        [Exponential Smoothing] [single - WS8] [2011-12-01 08:44:41] [6d29560f77ba0d0db0a9caaa1b5e377d]
-   P             [Exponential Smoothing] [triple - WS8] [2011-12-01 08:50:09] [d21839ec896caba47931721a9c4efa75] [Current]
- RM                [Exponential Smoothing] [] [2012-08-16 15:43:30] [74be16979710d4c4e7c6647856088456]
- R                 [Exponential Smoothing] [] [2012-08-16 15:56:33] [74be16979710d4c4e7c6647856088456]
- R                 [Exponential Smoothing] [] [2012-11-12 20:32:20] [c0a25563b5321cce5982f113c9f242b0]
-  M                  [Exponential Smoothing] [] [2012-11-12 20:32:48] [c0a25563b5321cce5982f113c9f242b0]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9700
9081
9084
9743
8587
9731
9563
9998
9437
10038
9918
9252
9737
9035
9133
9487
8700
9627
8947
9283
8829
9947
9628
9318
9605
8640
9214
9567
8547
9185
9470
9123
9278
10170
9434
9655
9429
8739
9552
9687
9019
9672
9206
9069
9788
10312
10105
9863
9656
9295
9946
9701
9049
10190
9706
9765
9893
9994
10433
10073
10112
9266
9820
10097
9115
10411
9678
10408
10153
10368
10581
10597
10680
9738
9556

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'AstonUniversity' @ aston.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149180&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149180&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149180&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'AstonUniversity' @ aston.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.118633222491809
beta0.177842898062907
gamma0.593783465793253

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.118633222491809 \tabularnewline
beta & 0.177842898062907 \tabularnewline
gamma & 0.593783465793253 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149180&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]0.118633222491809[/C][/ROW]
[ROW][C]beta[/C][C]0.177842898062907[/C][/ROW]
[ROW][C]gamma[/C][C]0.593783465793253[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149180&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149180&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.118633222491809
beta0.177842898062907
gamma0.593783465793253






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1397379768.09802350428-31.0980235042771
1490359094.8206924271-59.8206924270944
1591339216.54046372284-83.5404637228421
1694879563.68373905242-76.6837390524197
1787008755.77257036365-55.7725703636497
1896279656.62380040231-29.6238004023144
1989479350.24380475726-403.24380475726
2092839699.78239553077-416.782395530772
2188299042.42155295708-213.421552957079
2299479575.43327830206371.566721697942
2396289462.01672409119165.983275908815
2493188775.37973766758542.620262332422
2596059309.97278290412295.027217095883
2686408661.11902781626-21.1190278162594
2792148776.59914227257437.400857727431
2895679201.70519948799365.294800512012
2985478479.0693673379467.9306326620626
3091859432.78885628384-247.788856283843
3194708924.90192534563545.098074654368
3291239419.77362094319-296.773620943191
3392788925.52238256834352.477617431659
34101709886.2017998858283.798200114197
3594349707.31587557335-273.315875573349
3696559208.93777542572446.062224574276
3794299643.72781956288-214.727819562881
3887398799.42061989147-60.420619891469
3995529179.84407265206372.155927347936
4096879587.740861833399.2591381667062
4190198700.5756600874318.424339912604
4296729546.72216590022125.277834099783
4392069533.85368355153-327.853683551533
4490699501.9707945651-432.970794565092
4597889345.86084071632442.139159283677
461031210297.64501435314.3549856469581
47101059805.95946625441299.040533745587
4898639774.763480507488.2365194925878
4996569836.53709925205-180.537099252051
5092959093.01482721878201.985172781224
5199469752.46311858526193.536881414742
52970110014.0928950339-313.09289503392
5390499201.74857262777-152.74857262777
54101909890.01737584943299.982624150571
5597069663.5188578340742.4811421659306
5697659631.15772153098133.842278469023
57989310022.8300650853-129.830065085269
58999410693.3737308994-699.37373089942
591043310261.436617568171.563382432012
601007310097.5384434705-24.5384434705411
61101129995.63683516516116.363164834836
6292669484.1543084668-218.154308466797
63982010077.1025414236-257.102541423639
64100979998.3875218314398.6124781685721
6591159305.7422417942-190.7422417942
661041110212.5772925192198.422707480755
6796789823.26733998655-145.267339986553
68104089796.48292855706611.517071442942
691015310096.947740158956.0522598411408
701036810485.514342959-117.514342959017
711058110584.7149952119-3.71499521191436
721059710300.0096105402296.990389459754
731068010319.389992721360.610007278996
7497389676.3680764116361.6319235883657
75955610302.5795309453-746.579530945288

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 9737 & 9768.09802350428 & -31.0980235042771 \tabularnewline
14 & 9035 & 9094.8206924271 & -59.8206924270944 \tabularnewline
15 & 9133 & 9216.54046372284 & -83.5404637228421 \tabularnewline
16 & 9487 & 9563.68373905242 & -76.6837390524197 \tabularnewline
17 & 8700 & 8755.77257036365 & -55.7725703636497 \tabularnewline
18 & 9627 & 9656.62380040231 & -29.6238004023144 \tabularnewline
19 & 8947 & 9350.24380475726 & -403.24380475726 \tabularnewline
20 & 9283 & 9699.78239553077 & -416.782395530772 \tabularnewline
21 & 8829 & 9042.42155295708 & -213.421552957079 \tabularnewline
22 & 9947 & 9575.43327830206 & 371.566721697942 \tabularnewline
23 & 9628 & 9462.01672409119 & 165.983275908815 \tabularnewline
24 & 9318 & 8775.37973766758 & 542.620262332422 \tabularnewline
25 & 9605 & 9309.97278290412 & 295.027217095883 \tabularnewline
26 & 8640 & 8661.11902781626 & -21.1190278162594 \tabularnewline
27 & 9214 & 8776.59914227257 & 437.400857727431 \tabularnewline
28 & 9567 & 9201.70519948799 & 365.294800512012 \tabularnewline
29 & 8547 & 8479.06936733794 & 67.9306326620626 \tabularnewline
30 & 9185 & 9432.78885628384 & -247.788856283843 \tabularnewline
31 & 9470 & 8924.90192534563 & 545.098074654368 \tabularnewline
32 & 9123 & 9419.77362094319 & -296.773620943191 \tabularnewline
33 & 9278 & 8925.52238256834 & 352.477617431659 \tabularnewline
34 & 10170 & 9886.2017998858 & 283.798200114197 \tabularnewline
35 & 9434 & 9707.31587557335 & -273.315875573349 \tabularnewline
36 & 9655 & 9208.93777542572 & 446.062224574276 \tabularnewline
37 & 9429 & 9643.72781956288 & -214.727819562881 \tabularnewline
38 & 8739 & 8799.42061989147 & -60.420619891469 \tabularnewline
39 & 9552 & 9179.84407265206 & 372.155927347936 \tabularnewline
40 & 9687 & 9587.7408618333 & 99.2591381667062 \tabularnewline
41 & 9019 & 8700.5756600874 & 318.424339912604 \tabularnewline
42 & 9672 & 9546.72216590022 & 125.277834099783 \tabularnewline
43 & 9206 & 9533.85368355153 & -327.853683551533 \tabularnewline
44 & 9069 & 9501.9707945651 & -432.970794565092 \tabularnewline
45 & 9788 & 9345.86084071632 & 442.139159283677 \tabularnewline
46 & 10312 & 10297.645014353 & 14.3549856469581 \tabularnewline
47 & 10105 & 9805.95946625441 & 299.040533745587 \tabularnewline
48 & 9863 & 9774.7634805074 & 88.2365194925878 \tabularnewline
49 & 9656 & 9836.53709925205 & -180.537099252051 \tabularnewline
50 & 9295 & 9093.01482721878 & 201.985172781224 \tabularnewline
51 & 9946 & 9752.46311858526 & 193.536881414742 \tabularnewline
52 & 9701 & 10014.0928950339 & -313.09289503392 \tabularnewline
53 & 9049 & 9201.74857262777 & -152.74857262777 \tabularnewline
54 & 10190 & 9890.01737584943 & 299.982624150571 \tabularnewline
55 & 9706 & 9663.51885783407 & 42.4811421659306 \tabularnewline
56 & 9765 & 9631.15772153098 & 133.842278469023 \tabularnewline
57 & 9893 & 10022.8300650853 & -129.830065085269 \tabularnewline
58 & 9994 & 10693.3737308994 & -699.37373089942 \tabularnewline
59 & 10433 & 10261.436617568 & 171.563382432012 \tabularnewline
60 & 10073 & 10097.5384434705 & -24.5384434705411 \tabularnewline
61 & 10112 & 9995.63683516516 & 116.363164834836 \tabularnewline
62 & 9266 & 9484.1543084668 & -218.154308466797 \tabularnewline
63 & 9820 & 10077.1025414236 & -257.102541423639 \tabularnewline
64 & 10097 & 9998.38752183143 & 98.6124781685721 \tabularnewline
65 & 9115 & 9305.7422417942 & -190.7422417942 \tabularnewline
66 & 10411 & 10212.5772925192 & 198.422707480755 \tabularnewline
67 & 9678 & 9823.26733998655 & -145.267339986553 \tabularnewline
68 & 10408 & 9796.48292855706 & 611.517071442942 \tabularnewline
69 & 10153 & 10096.9477401589 & 56.0522598411408 \tabularnewline
70 & 10368 & 10485.514342959 & -117.514342959017 \tabularnewline
71 & 10581 & 10584.7149952119 & -3.71499521191436 \tabularnewline
72 & 10597 & 10300.0096105402 & 296.990389459754 \tabularnewline
73 & 10680 & 10319.389992721 & 360.610007278996 \tabularnewline
74 & 9738 & 9676.36807641163 & 61.6319235883657 \tabularnewline
75 & 9556 & 10302.5795309453 & -746.579530945288 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149180&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]9737[/C][C]9768.09802350428[/C][C]-31.0980235042771[/C][/ROW]
[ROW][C]14[/C][C]9035[/C][C]9094.8206924271[/C][C]-59.8206924270944[/C][/ROW]
[ROW][C]15[/C][C]9133[/C][C]9216.54046372284[/C][C]-83.5404637228421[/C][/ROW]
[ROW][C]16[/C][C]9487[/C][C]9563.68373905242[/C][C]-76.6837390524197[/C][/ROW]
[ROW][C]17[/C][C]8700[/C][C]8755.77257036365[/C][C]-55.7725703636497[/C][/ROW]
[ROW][C]18[/C][C]9627[/C][C]9656.62380040231[/C][C]-29.6238004023144[/C][/ROW]
[ROW][C]19[/C][C]8947[/C][C]9350.24380475726[/C][C]-403.24380475726[/C][/ROW]
[ROW][C]20[/C][C]9283[/C][C]9699.78239553077[/C][C]-416.782395530772[/C][/ROW]
[ROW][C]21[/C][C]8829[/C][C]9042.42155295708[/C][C]-213.421552957079[/C][/ROW]
[ROW][C]22[/C][C]9947[/C][C]9575.43327830206[/C][C]371.566721697942[/C][/ROW]
[ROW][C]23[/C][C]9628[/C][C]9462.01672409119[/C][C]165.983275908815[/C][/ROW]
[ROW][C]24[/C][C]9318[/C][C]8775.37973766758[/C][C]542.620262332422[/C][/ROW]
[ROW][C]25[/C][C]9605[/C][C]9309.97278290412[/C][C]295.027217095883[/C][/ROW]
[ROW][C]26[/C][C]8640[/C][C]8661.11902781626[/C][C]-21.1190278162594[/C][/ROW]
[ROW][C]27[/C][C]9214[/C][C]8776.59914227257[/C][C]437.400857727431[/C][/ROW]
[ROW][C]28[/C][C]9567[/C][C]9201.70519948799[/C][C]365.294800512012[/C][/ROW]
[ROW][C]29[/C][C]8547[/C][C]8479.06936733794[/C][C]67.9306326620626[/C][/ROW]
[ROW][C]30[/C][C]9185[/C][C]9432.78885628384[/C][C]-247.788856283843[/C][/ROW]
[ROW][C]31[/C][C]9470[/C][C]8924.90192534563[/C][C]545.098074654368[/C][/ROW]
[ROW][C]32[/C][C]9123[/C][C]9419.77362094319[/C][C]-296.773620943191[/C][/ROW]
[ROW][C]33[/C][C]9278[/C][C]8925.52238256834[/C][C]352.477617431659[/C][/ROW]
[ROW][C]34[/C][C]10170[/C][C]9886.2017998858[/C][C]283.798200114197[/C][/ROW]
[ROW][C]35[/C][C]9434[/C][C]9707.31587557335[/C][C]-273.315875573349[/C][/ROW]
[ROW][C]36[/C][C]9655[/C][C]9208.93777542572[/C][C]446.062224574276[/C][/ROW]
[ROW][C]37[/C][C]9429[/C][C]9643.72781956288[/C][C]-214.727819562881[/C][/ROW]
[ROW][C]38[/C][C]8739[/C][C]8799.42061989147[/C][C]-60.420619891469[/C][/ROW]
[ROW][C]39[/C][C]9552[/C][C]9179.84407265206[/C][C]372.155927347936[/C][/ROW]
[ROW][C]40[/C][C]9687[/C][C]9587.7408618333[/C][C]99.2591381667062[/C][/ROW]
[ROW][C]41[/C][C]9019[/C][C]8700.5756600874[/C][C]318.424339912604[/C][/ROW]
[ROW][C]42[/C][C]9672[/C][C]9546.72216590022[/C][C]125.277834099783[/C][/ROW]
[ROW][C]43[/C][C]9206[/C][C]9533.85368355153[/C][C]-327.853683551533[/C][/ROW]
[ROW][C]44[/C][C]9069[/C][C]9501.9707945651[/C][C]-432.970794565092[/C][/ROW]
[ROW][C]45[/C][C]9788[/C][C]9345.86084071632[/C][C]442.139159283677[/C][/ROW]
[ROW][C]46[/C][C]10312[/C][C]10297.645014353[/C][C]14.3549856469581[/C][/ROW]
[ROW][C]47[/C][C]10105[/C][C]9805.95946625441[/C][C]299.040533745587[/C][/ROW]
[ROW][C]48[/C][C]9863[/C][C]9774.7634805074[/C][C]88.2365194925878[/C][/ROW]
[ROW][C]49[/C][C]9656[/C][C]9836.53709925205[/C][C]-180.537099252051[/C][/ROW]
[ROW][C]50[/C][C]9295[/C][C]9093.01482721878[/C][C]201.985172781224[/C][/ROW]
[ROW][C]51[/C][C]9946[/C][C]9752.46311858526[/C][C]193.536881414742[/C][/ROW]
[ROW][C]52[/C][C]9701[/C][C]10014.0928950339[/C][C]-313.09289503392[/C][/ROW]
[ROW][C]53[/C][C]9049[/C][C]9201.74857262777[/C][C]-152.74857262777[/C][/ROW]
[ROW][C]54[/C][C]10190[/C][C]9890.01737584943[/C][C]299.982624150571[/C][/ROW]
[ROW][C]55[/C][C]9706[/C][C]9663.51885783407[/C][C]42.4811421659306[/C][/ROW]
[ROW][C]56[/C][C]9765[/C][C]9631.15772153098[/C][C]133.842278469023[/C][/ROW]
[ROW][C]57[/C][C]9893[/C][C]10022.8300650853[/C][C]-129.830065085269[/C][/ROW]
[ROW][C]58[/C][C]9994[/C][C]10693.3737308994[/C][C]-699.37373089942[/C][/ROW]
[ROW][C]59[/C][C]10433[/C][C]10261.436617568[/C][C]171.563382432012[/C][/ROW]
[ROW][C]60[/C][C]10073[/C][C]10097.5384434705[/C][C]-24.5384434705411[/C][/ROW]
[ROW][C]61[/C][C]10112[/C][C]9995.63683516516[/C][C]116.363164834836[/C][/ROW]
[ROW][C]62[/C][C]9266[/C][C]9484.1543084668[/C][C]-218.154308466797[/C][/ROW]
[ROW][C]63[/C][C]9820[/C][C]10077.1025414236[/C][C]-257.102541423639[/C][/ROW]
[ROW][C]64[/C][C]10097[/C][C]9998.38752183143[/C][C]98.6124781685721[/C][/ROW]
[ROW][C]65[/C][C]9115[/C][C]9305.7422417942[/C][C]-190.7422417942[/C][/ROW]
[ROW][C]66[/C][C]10411[/C][C]10212.5772925192[/C][C]198.422707480755[/C][/ROW]
[ROW][C]67[/C][C]9678[/C][C]9823.26733998655[/C][C]-145.267339986553[/C][/ROW]
[ROW][C]68[/C][C]10408[/C][C]9796.48292855706[/C][C]611.517071442942[/C][/ROW]
[ROW][C]69[/C][C]10153[/C][C]10096.9477401589[/C][C]56.0522598411408[/C][/ROW]
[ROW][C]70[/C][C]10368[/C][C]10485.514342959[/C][C]-117.514342959017[/C][/ROW]
[ROW][C]71[/C][C]10581[/C][C]10584.7149952119[/C][C]-3.71499521191436[/C][/ROW]
[ROW][C]72[/C][C]10597[/C][C]10300.0096105402[/C][C]296.990389459754[/C][/ROW]
[ROW][C]73[/C][C]10680[/C][C]10319.389992721[/C][C]360.610007278996[/C][/ROW]
[ROW][C]74[/C][C]9738[/C][C]9676.36807641163[/C][C]61.6319235883657[/C][/ROW]
[ROW][C]75[/C][C]9556[/C][C]10302.5795309453[/C][C]-746.579530945288[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149180&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149180&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1397379768.09802350428-31.0980235042771
1490359094.8206924271-59.8206924270944
1591339216.54046372284-83.5404637228421
1694879563.68373905242-76.6837390524197
1787008755.77257036365-55.7725703636497
1896279656.62380040231-29.6238004023144
1989479350.24380475726-403.24380475726
2092839699.78239553077-416.782395530772
2188299042.42155295708-213.421552957079
2299479575.43327830206371.566721697942
2396289462.01672409119165.983275908815
2493188775.37973766758542.620262332422
2596059309.97278290412295.027217095883
2686408661.11902781626-21.1190278162594
2792148776.59914227257437.400857727431
2895679201.70519948799365.294800512012
2985478479.0693673379467.9306326620626
3091859432.78885628384-247.788856283843
3194708924.90192534563545.098074654368
3291239419.77362094319-296.773620943191
3392788925.52238256834352.477617431659
34101709886.2017998858283.798200114197
3594349707.31587557335-273.315875573349
3696559208.93777542572446.062224574276
3794299643.72781956288-214.727819562881
3887398799.42061989147-60.420619891469
3995529179.84407265206372.155927347936
4096879587.740861833399.2591381667062
4190198700.5756600874318.424339912604
4296729546.72216590022125.277834099783
4392069533.85368355153-327.853683551533
4490699501.9707945651-432.970794565092
4597889345.86084071632442.139159283677
461031210297.64501435314.3549856469581
47101059805.95946625441299.040533745587
4898639774.763480507488.2365194925878
4996569836.53709925205-180.537099252051
5092959093.01482721878201.985172781224
5199469752.46311858526193.536881414742
52970110014.0928950339-313.09289503392
5390499201.74857262777-152.74857262777
54101909890.01737584943299.982624150571
5597069663.5188578340742.4811421659306
5697659631.15772153098133.842278469023
57989310022.8300650853-129.830065085269
58999410693.3737308994-699.37373089942
591043310261.436617568171.563382432012
601007310097.5384434705-24.5384434705411
61101129995.63683516516116.363164834836
6292669484.1543084668-218.154308466797
63982010077.1025414236-257.102541423639
64100979998.3875218314398.6124781685721
6591159305.7422417942-190.7422417942
661041110212.5772925192198.422707480755
6796789823.26733998655-145.267339986553
68104089796.48292855706611.517071442942
691015310096.947740158956.0522598411408
701036810485.514342959-117.514342959017
711058110584.7149952119-3.71499521191436
721059710300.0096105402296.990389459754
731068010319.389992721360.610007278996
7497389676.3680764116361.6319235883657
75955610302.5795309453-746.579530945288






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7610362.08400429869787.7649000431310936.4031085541
779514.355744847738934.4570012135210094.2544884819
7810659.556369005610072.347474147211246.765263864
7910074.72467916239478.2925554024410671.1568029222
8010472.17987524989864.456933633111079.9028168666
8110407.44884061119786.243868409811028.6538128123
8210695.396580956310058.426994432211332.3661674803
8310867.438852321810212.36272810611522.5149765376
8410739.968678641710064.415064697211415.5222925861
8510750.567990172710052.164260738811448.9717196067
869893.847174684659170.242569128510617.4517802408
8710074.02543694359322.9103340858210825.1405398013

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
76 & 10362.0840042986 & 9787.76490004313 & 10936.4031085541 \tabularnewline
77 & 9514.35574484773 & 8934.45700121352 & 10094.2544884819 \tabularnewline
78 & 10659.5563690056 & 10072.3474741472 & 11246.765263864 \tabularnewline
79 & 10074.7246791623 & 9478.29255540244 & 10671.1568029222 \tabularnewline
80 & 10472.1798752498 & 9864.4569336331 & 11079.9028168666 \tabularnewline
81 & 10407.4488406111 & 9786.2438684098 & 11028.6538128123 \tabularnewline
82 & 10695.3965809563 & 10058.4269944322 & 11332.3661674803 \tabularnewline
83 & 10867.4388523218 & 10212.362728106 & 11522.5149765376 \tabularnewline
84 & 10739.9686786417 & 10064.4150646972 & 11415.5222925861 \tabularnewline
85 & 10750.5679901727 & 10052.1642607388 & 11448.9717196067 \tabularnewline
86 & 9893.84717468465 & 9170.2425691285 & 10617.4517802408 \tabularnewline
87 & 10074.0254369435 & 9322.91033408582 & 10825.1405398013 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149180&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]76[/C][C]10362.0840042986[/C][C]9787.76490004313[/C][C]10936.4031085541[/C][/ROW]
[ROW][C]77[/C][C]9514.35574484773[/C][C]8934.45700121352[/C][C]10094.2544884819[/C][/ROW]
[ROW][C]78[/C][C]10659.5563690056[/C][C]10072.3474741472[/C][C]11246.765263864[/C][/ROW]
[ROW][C]79[/C][C]10074.7246791623[/C][C]9478.29255540244[/C][C]10671.1568029222[/C][/ROW]
[ROW][C]80[/C][C]10472.1798752498[/C][C]9864.4569336331[/C][C]11079.9028168666[/C][/ROW]
[ROW][C]81[/C][C]10407.4488406111[/C][C]9786.2438684098[/C][C]11028.6538128123[/C][/ROW]
[ROW][C]82[/C][C]10695.3965809563[/C][C]10058.4269944322[/C][C]11332.3661674803[/C][/ROW]
[ROW][C]83[/C][C]10867.4388523218[/C][C]10212.362728106[/C][C]11522.5149765376[/C][/ROW]
[ROW][C]84[/C][C]10739.9686786417[/C][C]10064.4150646972[/C][C]11415.5222925861[/C][/ROW]
[ROW][C]85[/C][C]10750.5679901727[/C][C]10052.1642607388[/C][C]11448.9717196067[/C][/ROW]
[ROW][C]86[/C][C]9893.84717468465[/C][C]9170.2425691285[/C][C]10617.4517802408[/C][/ROW]
[ROW][C]87[/C][C]10074.0254369435[/C][C]9322.91033408582[/C][C]10825.1405398013[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149180&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149180&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7610362.08400429869787.7649000431310936.4031085541
779514.355744847738934.4570012135210094.2544884819
7810659.556369005610072.347474147211246.765263864
7910074.72467916239478.2925554024410671.1568029222
8010472.17987524989864.456933633111079.9028168666
8110407.44884061119786.243868409811028.6538128123
8210695.396580956310058.426994432211332.3661674803
8310867.438852321810212.36272810611522.5149765376
8410739.968678641710064.415064697211415.5222925861
8510750.567990172710052.164260738811448.9717196067
869893.847174684659170.242569128510617.4517802408
8710074.02543694359322.9103340858210825.1405398013


Figures (Output of Computation)

Input Parameters & R Code

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