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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 computationWed, 02 Dec 2009 14:26:47 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/02/t1259789261b0qm9choeh99l61.htm/, Retrieved Sun, 28 Apr 2024 03:33:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62597, Retrieved Sun, 28 Apr 2024 03:33:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact131

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-   PD      [Exponential Smoothing] [Exponential Smoot...] [2009-12-02 21:26:47] [2622964eb3e61db9b0dfd11950e3a18c] [Current]
-   PD        [Exponential Smoothing] [Exponential Smoot...] [2009-12-03 18:09:40] [e2a6b1b31bd881219e1879835b4c60d0]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0.0314796223103059
-3.00870920563557
-2.07677512619799
-1.25010391965540
0.817975239137125
0.0252076485413113
0.554937772830776
0.230027371950115
2.35672227418686
1.41350455171120
2.73311719024401
1.31551925971717
-2.70076272244080
-0.721411049152714
-0.149388576811997
-0.118199629770334
-0.676562489695275
1.79699928690761
1.79845572032988
0.245100010770855
1.80710848932636
-1.75934771184948
-0.0186697168761931
0.189651523600062
-1.84149562719087
-1.07019530156943
-0.507291477584104
0.866365633831705
-1.76077926699189
-0.580719393339347
-0.435702079860853
-0.994868534845203
1.63136048315789
-1.1949403709466
-1.00525975426991
1.32302234837564
-0.628357549594746
0.632048410440518
-2.16903155809288
2.53779364144266
-0.632933703679292
-1.41749196342200
-0.455343045381255
0.812255211942954
0.627897309219833
0.650904313655623
-1.29800419154382
0.74391671726854
-1.50461634127457
-1.42734677658523
0.263353807408564
-0.430830854870631
0.379576092518008
1.70309353400146
-3.12314448117342
-1.32526207118689
-0.60032490743804
1.23607137604666
0.738007075905376
0.899100896289585

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62597&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62597&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62597&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00511311737670761
beta0.260114412291294
gamma0.525051146760498

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00511311737670761 \tabularnewline
beta & 0.260114412291294 \tabularnewline
gamma & 0.525051146760498 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62597&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]0.00511311737670761[/C][/ROW]
[ROW][C]beta[/C][C]0.260114412291294[/C][/ROW]
[ROW][C]gamma[/C][C]0.525051146760498[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62597&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62597&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
alpha0.00511311737670761
beta0.260114412291294
gamma0.525051146760498






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13-2.7007627224408-3.078434892766690.377672170325891
14-0.721411049152714-1.144146076167180.422735027014468
15-0.149388576811997-0.5416799909651370.39229141415314
16-0.118199629770334-0.3468511427382690.228651512967935
17-0.676562489695275-0.650349492584578-0.0262129971106967
181.796999286907611.99144775679617-0.194448469888564
191.798455720329880.6281944066849961.17026131364488
200.2451000107708550.335905416592872-0.090805405822017
211.807108489326362.29450177275622-0.487393283429857
22-1.759347711849481.22865088406288-2.98799859591236
23-0.01866971687619312.551450621411-2.57012033828719
240.1896515236000621.10909622888707-0.919444705287008
25-1.84149562719087-2.841527338287571.00003171109670
26-1.07019530156943-0.885920041691832-0.184275259877598
27-0.507291477584104-0.308670759806620-0.198620717777484
280.866365633831705-0.2093395923904411.07570522622215
29-1.76077926699189-0.64750923678777-1.11327003020412
30-0.5807193933393471.89353370868427-2.47425310202362
31-0.4357020798608531.22115451235218-1.65685659221303
32-0.9948685348452030.241563466848861-1.23643200169406
331.631360483157891.97150653754671-0.340146054388816
34-1.1949403709466-0.415259403324323-0.779680967622277
35-1.005259754269911.12461887306691-2.12987862733682
361.323022348375640.5348602078742240.788162140501416
37-0.628357549594746-2.414003811776431.78564626218169
380.632048410440518-1.081618819169411.71366722960993
39-2.16903155809288-0.508231423848648-1.66080013424423
402.537793641442660.2412712353023122.29652240614035
41-0.632933703679292-1.340497281187010.707563577507715
42-1.4174919634220.494951825516196-1.91244378893820
43-0.4553430453812550.249200970004793-0.704544015386047
440.812255211942954-0.5078633057223321.32011851766529
450.6278973092198331.70478342316529-1.07688611394546
460.650904313655623-0.9148857674821611.56579008113778
47-1.29800419154382-0.0647312780017505-1.23327291354207
480.743916717268540.87915529562683-0.135238578358290
49-1.50461634127457-1.549831961191360.0452156199167872
50-1.42734677658523-0.262714263898025-1.16463251268720
510.263353807408564-1.469349614265201.73270342167377
52-0.4308308548706311.36659353103896-1.79742438590959
530.379576092518008-1.069655221762571.44923131428058
541.70309353400146-0.6015600865319922.30465362053345
55-3.12314448117342-0.191715463240113-2.93142901793331
56-1.325262071186890.0975546571912894-1.42281672837818
57-0.600324907438041.04051827031719-1.64084317775523
581.23607137604666-0.205882297659981.44195367370664
590.738007075905376-0.8229557457513131.56096282165669
600.8991008962895850.708052743673830.191048152615755

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & -2.7007627224408 & -3.07843489276669 & 0.377672170325891 \tabularnewline
14 & -0.721411049152714 & -1.14414607616718 & 0.422735027014468 \tabularnewline
15 & -0.149388576811997 & -0.541679990965137 & 0.39229141415314 \tabularnewline
16 & -0.118199629770334 & -0.346851142738269 & 0.228651512967935 \tabularnewline
17 & -0.676562489695275 & -0.650349492584578 & -0.0262129971106967 \tabularnewline
18 & 1.79699928690761 & 1.99144775679617 & -0.194448469888564 \tabularnewline
19 & 1.79845572032988 & 0.628194406684996 & 1.17026131364488 \tabularnewline
20 & 0.245100010770855 & 0.335905416592872 & -0.090805405822017 \tabularnewline
21 & 1.80710848932636 & 2.29450177275622 & -0.487393283429857 \tabularnewline
22 & -1.75934771184948 & 1.22865088406288 & -2.98799859591236 \tabularnewline
23 & -0.0186697168761931 & 2.551450621411 & -2.57012033828719 \tabularnewline
24 & 0.189651523600062 & 1.10909622888707 & -0.919444705287008 \tabularnewline
25 & -1.84149562719087 & -2.84152733828757 & 1.00003171109670 \tabularnewline
26 & -1.07019530156943 & -0.885920041691832 & -0.184275259877598 \tabularnewline
27 & -0.507291477584104 & -0.308670759806620 & -0.198620717777484 \tabularnewline
28 & 0.866365633831705 & -0.209339592390441 & 1.07570522622215 \tabularnewline
29 & -1.76077926699189 & -0.64750923678777 & -1.11327003020412 \tabularnewline
30 & -0.580719393339347 & 1.89353370868427 & -2.47425310202362 \tabularnewline
31 & -0.435702079860853 & 1.22115451235218 & -1.65685659221303 \tabularnewline
32 & -0.994868534845203 & 0.241563466848861 & -1.23643200169406 \tabularnewline
33 & 1.63136048315789 & 1.97150653754671 & -0.340146054388816 \tabularnewline
34 & -1.1949403709466 & -0.415259403324323 & -0.779680967622277 \tabularnewline
35 & -1.00525975426991 & 1.12461887306691 & -2.12987862733682 \tabularnewline
36 & 1.32302234837564 & 0.534860207874224 & 0.788162140501416 \tabularnewline
37 & -0.628357549594746 & -2.41400381177643 & 1.78564626218169 \tabularnewline
38 & 0.632048410440518 & -1.08161881916941 & 1.71366722960993 \tabularnewline
39 & -2.16903155809288 & -0.508231423848648 & -1.66080013424423 \tabularnewline
40 & 2.53779364144266 & 0.241271235302312 & 2.29652240614035 \tabularnewline
41 & -0.632933703679292 & -1.34049728118701 & 0.707563577507715 \tabularnewline
42 & -1.417491963422 & 0.494951825516196 & -1.91244378893820 \tabularnewline
43 & -0.455343045381255 & 0.249200970004793 & -0.704544015386047 \tabularnewline
44 & 0.812255211942954 & -0.507863305722332 & 1.32011851766529 \tabularnewline
45 & 0.627897309219833 & 1.70478342316529 & -1.07688611394546 \tabularnewline
46 & 0.650904313655623 & -0.914885767482161 & 1.56579008113778 \tabularnewline
47 & -1.29800419154382 & -0.0647312780017505 & -1.23327291354207 \tabularnewline
48 & 0.74391671726854 & 0.87915529562683 & -0.135238578358290 \tabularnewline
49 & -1.50461634127457 & -1.54983196119136 & 0.0452156199167872 \tabularnewline
50 & -1.42734677658523 & -0.262714263898025 & -1.16463251268720 \tabularnewline
51 & 0.263353807408564 & -1.46934961426520 & 1.73270342167377 \tabularnewline
52 & -0.430830854870631 & 1.36659353103896 & -1.79742438590959 \tabularnewline
53 & 0.379576092518008 & -1.06965522176257 & 1.44923131428058 \tabularnewline
54 & 1.70309353400146 & -0.601560086531992 & 2.30465362053345 \tabularnewline
55 & -3.12314448117342 & -0.191715463240113 & -2.93142901793331 \tabularnewline
56 & -1.32526207118689 & 0.0975546571912894 & -1.42281672837818 \tabularnewline
57 & -0.60032490743804 & 1.04051827031719 & -1.64084317775523 \tabularnewline
58 & 1.23607137604666 & -0.20588229765998 & 1.44195367370664 \tabularnewline
59 & 0.738007075905376 & -0.822955745751313 & 1.56096282165669 \tabularnewline
60 & 0.899100896289585 & 0.70805274367383 & 0.191048152615755 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62597&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]-2.7007627224408[/C][C]-3.07843489276669[/C][C]0.377672170325891[/C][/ROW]
[ROW][C]14[/C][C]-0.721411049152714[/C][C]-1.14414607616718[/C][C]0.422735027014468[/C][/ROW]
[ROW][C]15[/C][C]-0.149388576811997[/C][C]-0.541679990965137[/C][C]0.39229141415314[/C][/ROW]
[ROW][C]16[/C][C]-0.118199629770334[/C][C]-0.346851142738269[/C][C]0.228651512967935[/C][/ROW]
[ROW][C]17[/C][C]-0.676562489695275[/C][C]-0.650349492584578[/C][C]-0.0262129971106967[/C][/ROW]
[ROW][C]18[/C][C]1.79699928690761[/C][C]1.99144775679617[/C][C]-0.194448469888564[/C][/ROW]
[ROW][C]19[/C][C]1.79845572032988[/C][C]0.628194406684996[/C][C]1.17026131364488[/C][/ROW]
[ROW][C]20[/C][C]0.245100010770855[/C][C]0.335905416592872[/C][C]-0.090805405822017[/C][/ROW]
[ROW][C]21[/C][C]1.80710848932636[/C][C]2.29450177275622[/C][C]-0.487393283429857[/C][/ROW]
[ROW][C]22[/C][C]-1.75934771184948[/C][C]1.22865088406288[/C][C]-2.98799859591236[/C][/ROW]
[ROW][C]23[/C][C]-0.0186697168761931[/C][C]2.551450621411[/C][C]-2.57012033828719[/C][/ROW]
[ROW][C]24[/C][C]0.189651523600062[/C][C]1.10909622888707[/C][C]-0.919444705287008[/C][/ROW]
[ROW][C]25[/C][C]-1.84149562719087[/C][C]-2.84152733828757[/C][C]1.00003171109670[/C][/ROW]
[ROW][C]26[/C][C]-1.07019530156943[/C][C]-0.885920041691832[/C][C]-0.184275259877598[/C][/ROW]
[ROW][C]27[/C][C]-0.507291477584104[/C][C]-0.308670759806620[/C][C]-0.198620717777484[/C][/ROW]
[ROW][C]28[/C][C]0.866365633831705[/C][C]-0.209339592390441[/C][C]1.07570522622215[/C][/ROW]
[ROW][C]29[/C][C]-1.76077926699189[/C][C]-0.64750923678777[/C][C]-1.11327003020412[/C][/ROW]
[ROW][C]30[/C][C]-0.580719393339347[/C][C]1.89353370868427[/C][C]-2.47425310202362[/C][/ROW]
[ROW][C]31[/C][C]-0.435702079860853[/C][C]1.22115451235218[/C][C]-1.65685659221303[/C][/ROW]
[ROW][C]32[/C][C]-0.994868534845203[/C][C]0.241563466848861[/C][C]-1.23643200169406[/C][/ROW]
[ROW][C]33[/C][C]1.63136048315789[/C][C]1.97150653754671[/C][C]-0.340146054388816[/C][/ROW]
[ROW][C]34[/C][C]-1.1949403709466[/C][C]-0.415259403324323[/C][C]-0.779680967622277[/C][/ROW]
[ROW][C]35[/C][C]-1.00525975426991[/C][C]1.12461887306691[/C][C]-2.12987862733682[/C][/ROW]
[ROW][C]36[/C][C]1.32302234837564[/C][C]0.534860207874224[/C][C]0.788162140501416[/C][/ROW]
[ROW][C]37[/C][C]-0.628357549594746[/C][C]-2.41400381177643[/C][C]1.78564626218169[/C][/ROW]
[ROW][C]38[/C][C]0.632048410440518[/C][C]-1.08161881916941[/C][C]1.71366722960993[/C][/ROW]
[ROW][C]39[/C][C]-2.16903155809288[/C][C]-0.508231423848648[/C][C]-1.66080013424423[/C][/ROW]
[ROW][C]40[/C][C]2.53779364144266[/C][C]0.241271235302312[/C][C]2.29652240614035[/C][/ROW]
[ROW][C]41[/C][C]-0.632933703679292[/C][C]-1.34049728118701[/C][C]0.707563577507715[/C][/ROW]
[ROW][C]42[/C][C]-1.417491963422[/C][C]0.494951825516196[/C][C]-1.91244378893820[/C][/ROW]
[ROW][C]43[/C][C]-0.455343045381255[/C][C]0.249200970004793[/C][C]-0.704544015386047[/C][/ROW]
[ROW][C]44[/C][C]0.812255211942954[/C][C]-0.507863305722332[/C][C]1.32011851766529[/C][/ROW]
[ROW][C]45[/C][C]0.627897309219833[/C][C]1.70478342316529[/C][C]-1.07688611394546[/C][/ROW]
[ROW][C]46[/C][C]0.650904313655623[/C][C]-0.914885767482161[/C][C]1.56579008113778[/C][/ROW]
[ROW][C]47[/C][C]-1.29800419154382[/C][C]-0.0647312780017505[/C][C]-1.23327291354207[/C][/ROW]
[ROW][C]48[/C][C]0.74391671726854[/C][C]0.87915529562683[/C][C]-0.135238578358290[/C][/ROW]
[ROW][C]49[/C][C]-1.50461634127457[/C][C]-1.54983196119136[/C][C]0.0452156199167872[/C][/ROW]
[ROW][C]50[/C][C]-1.42734677658523[/C][C]-0.262714263898025[/C][C]-1.16463251268720[/C][/ROW]
[ROW][C]51[/C][C]0.263353807408564[/C][C]-1.46934961426520[/C][C]1.73270342167377[/C][/ROW]
[ROW][C]52[/C][C]-0.430830854870631[/C][C]1.36659353103896[/C][C]-1.79742438590959[/C][/ROW]
[ROW][C]53[/C][C]0.379576092518008[/C][C]-1.06965522176257[/C][C]1.44923131428058[/C][/ROW]
[ROW][C]54[/C][C]1.70309353400146[/C][C]-0.601560086531992[/C][C]2.30465362053345[/C][/ROW]
[ROW][C]55[/C][C]-3.12314448117342[/C][C]-0.191715463240113[/C][C]-2.93142901793331[/C][/ROW]
[ROW][C]56[/C][C]-1.32526207118689[/C][C]0.0975546571912894[/C][C]-1.42281672837818[/C][/ROW]
[ROW][C]57[/C][C]-0.60032490743804[/C][C]1.04051827031719[/C][C]-1.64084317775523[/C][/ROW]
[ROW][C]58[/C][C]1.23607137604666[/C][C]-0.20588229765998[/C][C]1.44195367370664[/C][/ROW]
[ROW][C]59[/C][C]0.738007075905376[/C][C]-0.822955745751313[/C][C]1.56096282165669[/C][/ROW]
[ROW][C]60[/C][C]0.899100896289585[/C][C]0.70805274367383[/C][C]0.191048152615755[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62597&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62597&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
13-2.7007627224408-3.078434892766690.377672170325891
14-0.721411049152714-1.144146076167180.422735027014468
15-0.149388576811997-0.5416799909651370.39229141415314
16-0.118199629770334-0.3468511427382690.228651512967935
17-0.676562489695275-0.650349492584578-0.0262129971106967
181.796999286907611.99144775679617-0.194448469888564
191.798455720329880.6281944066849961.17026131364488
200.2451000107708550.335905416592872-0.090805405822017
211.807108489326362.29450177275622-0.487393283429857
22-1.759347711849481.22865088406288-2.98799859591236
23-0.01866971687619312.551450621411-2.57012033828719
240.1896515236000621.10909622888707-0.919444705287008
25-1.84149562719087-2.841527338287571.00003171109670
26-1.07019530156943-0.885920041691832-0.184275259877598
27-0.507291477584104-0.308670759806620-0.198620717777484
280.866365633831705-0.2093395923904411.07570522622215
29-1.76077926699189-0.64750923678777-1.11327003020412
30-0.5807193933393471.89353370868427-2.47425310202362
31-0.4357020798608531.22115451235218-1.65685659221303
32-0.9948685348452030.241563466848861-1.23643200169406
331.631360483157891.97150653754671-0.340146054388816
34-1.1949403709466-0.415259403324323-0.779680967622277
35-1.005259754269911.12461887306691-2.12987862733682
361.323022348375640.5348602078742240.788162140501416
37-0.628357549594746-2.414003811776431.78564626218169
380.632048410440518-1.081618819169411.71366722960993
39-2.16903155809288-0.508231423848648-1.66080013424423
402.537793641442660.2412712353023122.29652240614035
41-0.632933703679292-1.340497281187010.707563577507715
42-1.4174919634220.494951825516196-1.91244378893820
43-0.4553430453812550.249200970004793-0.704544015386047
440.812255211942954-0.5078633057223321.32011851766529
450.6278973092198331.70478342316529-1.07688611394546
460.650904313655623-0.9148857674821611.56579008113778
47-1.29800419154382-0.0647312780017505-1.23327291354207
480.743916717268540.87915529562683-0.135238578358290
49-1.50461634127457-1.549831961191360.0452156199167872
50-1.42734677658523-0.262714263898025-1.16463251268720
510.263353807408564-1.469349614265201.73270342167377
52-0.4308308548706311.36659353103896-1.79742438590959
530.379576092518008-1.069655221762571.44923131428058
541.70309353400146-0.6015600865319922.30465362053345
55-3.12314448117342-0.191715463240113-2.93142901793331
56-1.325262071186890.0975546571912894-1.42281672837818
57-0.600324907438041.04051827031719-1.64084317775523
581.23607137604666-0.205882297659981.44195367370664
590.738007075905376-0.8229557457513131.56096282165669
600.8991008962895850.708052743673830.191048152615755






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61-1.62531067371396-4.411795335679491.16117398825156
62-0.970776169290266-3.757318669305001.81576633072447
63-0.656804300749603-3.443430979139322.12982237764011
640.325135427083718-2.461606696148283.11187755031571
65-0.404711546120209-3.191605305036552.38218221279613
660.502157150503387-2.284929356951823.28924365795859
67-1.83866182775345-4.625987115570290.948663460063385
68-0.746181142481291-3.533796157638812.04143387267623
690.0922334312146882-2.695727168753652.88019403118303
700.468820442929303-2.319546504207943.25718739006654
71-0.0911293248799895-2.879968279806962.69770963004698
720.71655434253189-2.072827171338103.50593585640188

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & -1.62531067371396 & -4.41179533567949 & 1.16117398825156 \tabularnewline
62 & -0.970776169290266 & -3.75731866930500 & 1.81576633072447 \tabularnewline
63 & -0.656804300749603 & -3.44343097913932 & 2.12982237764011 \tabularnewline
64 & 0.325135427083718 & -2.46160669614828 & 3.11187755031571 \tabularnewline
65 & -0.404711546120209 & -3.19160530503655 & 2.38218221279613 \tabularnewline
66 & 0.502157150503387 & -2.28492935695182 & 3.28924365795859 \tabularnewline
67 & -1.83866182775345 & -4.62598711557029 & 0.948663460063385 \tabularnewline
68 & -0.746181142481291 & -3.53379615763881 & 2.04143387267623 \tabularnewline
69 & 0.0922334312146882 & -2.69572716875365 & 2.88019403118303 \tabularnewline
70 & 0.468820442929303 & -2.31954650420794 & 3.25718739006654 \tabularnewline
71 & -0.0911293248799895 & -2.87996827980696 & 2.69770963004698 \tabularnewline
72 & 0.71655434253189 & -2.07282717133810 & 3.50593585640188 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62597&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]61[/C][C]-1.62531067371396[/C][C]-4.41179533567949[/C][C]1.16117398825156[/C][/ROW]
[ROW][C]62[/C][C]-0.970776169290266[/C][C]-3.75731866930500[/C][C]1.81576633072447[/C][/ROW]
[ROW][C]63[/C][C]-0.656804300749603[/C][C]-3.44343097913932[/C][C]2.12982237764011[/C][/ROW]
[ROW][C]64[/C][C]0.325135427083718[/C][C]-2.46160669614828[/C][C]3.11187755031571[/C][/ROW]
[ROW][C]65[/C][C]-0.404711546120209[/C][C]-3.19160530503655[/C][C]2.38218221279613[/C][/ROW]
[ROW][C]66[/C][C]0.502157150503387[/C][C]-2.28492935695182[/C][C]3.28924365795859[/C][/ROW]
[ROW][C]67[/C][C]-1.83866182775345[/C][C]-4.62598711557029[/C][C]0.948663460063385[/C][/ROW]
[ROW][C]68[/C][C]-0.746181142481291[/C][C]-3.53379615763881[/C][C]2.04143387267623[/C][/ROW]
[ROW][C]69[/C][C]0.0922334312146882[/C][C]-2.69572716875365[/C][C]2.88019403118303[/C][/ROW]
[ROW][C]70[/C][C]0.468820442929303[/C][C]-2.31954650420794[/C][C]3.25718739006654[/C][/ROW]
[ROW][C]71[/C][C]-0.0911293248799895[/C][C]-2.87996827980696[/C][C]2.69770963004698[/C][/ROW]
[ROW][C]72[/C][C]0.71655434253189[/C][C]-2.07282717133810[/C][C]3.50593585640188[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62597&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62597&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
61-1.62531067371396-4.411795335679491.16117398825156
62-0.970776169290266-3.757318669305001.81576633072447
63-0.656804300749603-3.443430979139322.12982237764011
640.325135427083718-2.461606696148283.11187755031571
65-0.404711546120209-3.191605305036552.38218221279613
660.502157150503387-2.284929356951823.28924365795859
67-1.83866182775345-4.625987115570290.948663460063385
68-0.746181142481291-3.533796157638812.04143387267623
690.0922334312146882-2.695727168753652.88019403118303
700.468820442929303-2.319546504207943.25718739006654
71-0.0911293248799895-2.879968279806962.69770963004698
720.71655434253189-2.072827171338103.50593585640188


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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')