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 computationSat, 13 Dec 2014 10:51:24 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/13/t141846800026f6gzbmtdjnfcw.htm/, Retrieved Thu, 16 May 2024 21:47:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=266962, Retrieved Thu, 16 May 2024 21:47:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-12-13 10:51:24] [a3e248f2ee98616f420122f2d0e2525c] [Current]
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Dataseries X:
1894
1757
3582
5321
5561
5907
4944
4966
3258
1964
1743
1262
2086
1793
3548
5672
6084
4914
4990
5139
3218
2179
2238
1442
2205
2025
3531
4977
7998
4880
5231
5202
3303
2683
2202
1376
2422
1997
3163
5964
5657
6415
6208
4500
2939
2702
2090
1504
2549
1931
3013
6204
5788
5611
5594
4647
3490
2487
1992
1507
2306
2002
3075
5331
5589
5813
4876
4665
3601
2192
2111
1580
2288
1993
3228
5000
5480
5770
4962
4685
3607
2222
2467
1594
2228
1910
3157
4809
6249
4607
4975
4784
3028
2461
2218
1351
2070
1887
3024
4596
6398
4459
5382
4359
2687
2249
2154
1169
2429
1762
2846
5627
5749
4502
5720
4403
2867
2635
2059
1511
2359
1741
2917
6249
5760
6250
5134
4831
3695
2462
2146
1579




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266962&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266962&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266962&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266962&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]0.999933893038648[/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=266962&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266962&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
217571894-137
335821757.009056653711824.99094334629
453213581.879355394241739.12064460576
555615320.88503201876240.114967981239
659075560.98412672909346.015873270908
749445906.97712594204-962.977125942038
849664944.0636594916521.9363405083523
932584965.99854985519-1707.99854985519
1019643258.11291059412-1294.11291059412
1117431964.08554987217-221.085549872166
1212621743.0146152939-481.014615293901
1320861262.03179841458823.968201585417
1417932085.94552996594-292.945529965943
1535481793.019365738831754.98063426117
1656723547.883983563042124.11601643696
1760845671.85958114459412.140418855405
1849146083.97275464926-1169.97275464926
1949904914.0773433436775.9226566563257
2051394989.99498098387149.005019016129
2132185138.99014973097-1920.99014973097
2221793218.12699082159-1039.12699082159
2322382179.0686935278258.9313064721782
2414422237.9961042304-795.9961042304
2522051442.0526208837762.947379116302
2620252204.9495638671-179.949563867095
2735312025.011895918861505.98810408114
2849773530.900443702611446.09955629739
2979984976.904402752523021.09559724748
3048807997.80028455011-3117.80028455011
3152314880.20610830291350.793891697086
3252025230.97681008176-28.9768100817591
3333035202.00191556886-1899.00191556886
3426833303.12553724624-620.12553724624
3522022683.04099461492-481.040994614924
3613762202.03180015844-826.03180015844
3724221376.054606452291045.94539354771
3819972421.93085572829-424.930855728292
3931631997.028090887661165.97190911234
4059643162.922921140072801.07707885993
4156575963.8148293058-306.814829305805
4264155657.02028259606757.979717403937
4362086414.94989226412-206.949892264116
4445006208.01368082853-1708.01368082853
4529394500.11291159439-1561.11291159439
4627022939.10320043091-237.103200430913
4720902702.01567417211-612.015674172107
4815042090.04045849652-586.040458496519
4925491504.038741353941044.96125864606
5019312548.93092078646-617.93092078646
5130131931.04084953551081.9591504645
5262043012.928474968263191.07152503174
5357886203.78904795802-415.789047958023
5456115788.02748655052-177.027486550524
5555945611.01170274921-17.0117027492115
5646475594.00112459198-947.001124591976
5734904647.06260336674-1157.06260336674
5824873490.0764898928-1003.0764898928
5919922487.06631033875-495.066310338751
6015071992.03272732944-485.032727329444
6123061507.03206403976798.96793596024
6220022305.94718265754-303.947182657536
6330752002.020093024661072.97990697534
6453313074.929068558762256.07093144124
6555895330.85085800613258.149141993872
6658135588.98293454465224.017065455352
6748765812.98519091251-936.985190912512
6846654876.0619412438-211.061941243803
6936014665.01395266359-1064.01395266359
7021923601.07033872925-1409.07033872925
7121112192.09314935842-81.0931493584244
7215802111.00536082169-531.00536082169
7322881580.03510315087707.964896849135
7419932287.95319859193-294.953198591926
7532281993.01949845971234.9805015403
7650003227.918359191711772.08164080829
7754804999.88285306746480.117146932542
7857705479.96826091432290.031739085677
7949625769.98082688303-807.980826883033
8046854962.0534131573-277.053413157296
8136074685.01831515928-1078.01831515928
8222223607.0712645151-1385.0712645151
8324672222.09156285255244.908437147447
8415942466.98380984741-872.983809847411
8522281594.05771030698633.942289693022
8619102227.95809200156-317.958092001556
8731571910.02101924331246.9789807567
8848093156.917566008711652.08243399129
8962494808.890785850391440.10921414961
9046076248.90479875584-1641.90479875584
9149754607.10854133707367.891458662925
9247844974.97567981356-190.97567981356
9330284784.01262482188-1756.01262482188
9424613028.11608465872-567.116084658723
9522182461.03749032109-243.037490321091
9613512218.01606646998-867.01606646998
9720701351.0573157976718.942684202402
9818872069.95247288376-182.952472883761
9930241887.012094432051136.98790556795
10045963023.924837184471572.07516281553
10163984595.896074887971802.10392511203
10244596397.88086838547-1938.88086838547
10353824459.12817352263922.871826477368
10443595381.93899174783-1022.93899174783
10526874359.06762338839-1672.06762338839
10622492687.11053530976-438.110535309757
10721542249.02896215623-95.0289621562256
10811692154.00628207593-985.006282075929
10924291169.065115772221259.93488422778
11017622428.9167095333-666.916709533302
11128461762.044087837141083.95591216286
11256272845.928342968412781.07165703159
11357495626.81615180345122.183848196548
11445025748.99192279707-1246.99192279707
11557204502.082434846851217.91756515315
11644035719.91948717059-1316.91948717059
11728674403.08705754564-1536.08705754564
11826352867.10154604775-232.101546047747
11920592635.01534352793-576.015343527934
12015112059.03807862405-548.038078624053
12123591511.03622913208847.963770867917
12217412358.94394369177-617.943943691771
12329171741.04085039641175.9591496036
12462492916.922260913953332.07773908605
12557606248.77972646568-488.779726465681
12662505760.03231174249489.967688257513
12751346249.96760972497-1115.96760972497
12848315134.07377322765-303.073773227647
12936954831.02003528621-1136.02003528621
13024623695.07509883257-1233.07509883257
13121462462.0815148479-316.081514847902
13215792146.02089518849-567.020895188486

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1757 & 1894 & -137 \tabularnewline
3 & 3582 & 1757.00905665371 & 1824.99094334629 \tabularnewline
4 & 5321 & 3581.87935539424 & 1739.12064460576 \tabularnewline
5 & 5561 & 5320.88503201876 & 240.114967981239 \tabularnewline
6 & 5907 & 5560.98412672909 & 346.015873270908 \tabularnewline
7 & 4944 & 5906.97712594204 & -962.977125942038 \tabularnewline
8 & 4966 & 4944.06365949165 & 21.9363405083523 \tabularnewline
9 & 3258 & 4965.99854985519 & -1707.99854985519 \tabularnewline
10 & 1964 & 3258.11291059412 & -1294.11291059412 \tabularnewline
11 & 1743 & 1964.08554987217 & -221.085549872166 \tabularnewline
12 & 1262 & 1743.0146152939 & -481.014615293901 \tabularnewline
13 & 2086 & 1262.03179841458 & 823.968201585417 \tabularnewline
14 & 1793 & 2085.94552996594 & -292.945529965943 \tabularnewline
15 & 3548 & 1793.01936573883 & 1754.98063426117 \tabularnewline
16 & 5672 & 3547.88398356304 & 2124.11601643696 \tabularnewline
17 & 6084 & 5671.85958114459 & 412.140418855405 \tabularnewline
18 & 4914 & 6083.97275464926 & -1169.97275464926 \tabularnewline
19 & 4990 & 4914.07734334367 & 75.9226566563257 \tabularnewline
20 & 5139 & 4989.99498098387 & 149.005019016129 \tabularnewline
21 & 3218 & 5138.99014973097 & -1920.99014973097 \tabularnewline
22 & 2179 & 3218.12699082159 & -1039.12699082159 \tabularnewline
23 & 2238 & 2179.06869352782 & 58.9313064721782 \tabularnewline
24 & 1442 & 2237.9961042304 & -795.9961042304 \tabularnewline
25 & 2205 & 1442.0526208837 & 762.947379116302 \tabularnewline
26 & 2025 & 2204.9495638671 & -179.949563867095 \tabularnewline
27 & 3531 & 2025.01189591886 & 1505.98810408114 \tabularnewline
28 & 4977 & 3530.90044370261 & 1446.09955629739 \tabularnewline
29 & 7998 & 4976.90440275252 & 3021.09559724748 \tabularnewline
30 & 4880 & 7997.80028455011 & -3117.80028455011 \tabularnewline
31 & 5231 & 4880.20610830291 & 350.793891697086 \tabularnewline
32 & 5202 & 5230.97681008176 & -28.9768100817591 \tabularnewline
33 & 3303 & 5202.00191556886 & -1899.00191556886 \tabularnewline
34 & 2683 & 3303.12553724624 & -620.12553724624 \tabularnewline
35 & 2202 & 2683.04099461492 & -481.040994614924 \tabularnewline
36 & 1376 & 2202.03180015844 & -826.03180015844 \tabularnewline
37 & 2422 & 1376.05460645229 & 1045.94539354771 \tabularnewline
38 & 1997 & 2421.93085572829 & -424.930855728292 \tabularnewline
39 & 3163 & 1997.02809088766 & 1165.97190911234 \tabularnewline
40 & 5964 & 3162.92292114007 & 2801.07707885993 \tabularnewline
41 & 5657 & 5963.8148293058 & -306.814829305805 \tabularnewline
42 & 6415 & 5657.02028259606 & 757.979717403937 \tabularnewline
43 & 6208 & 6414.94989226412 & -206.949892264116 \tabularnewline
44 & 4500 & 6208.01368082853 & -1708.01368082853 \tabularnewline
45 & 2939 & 4500.11291159439 & -1561.11291159439 \tabularnewline
46 & 2702 & 2939.10320043091 & -237.103200430913 \tabularnewline
47 & 2090 & 2702.01567417211 & -612.015674172107 \tabularnewline
48 & 1504 & 2090.04045849652 & -586.040458496519 \tabularnewline
49 & 2549 & 1504.03874135394 & 1044.96125864606 \tabularnewline
50 & 1931 & 2548.93092078646 & -617.93092078646 \tabularnewline
51 & 3013 & 1931.0408495355 & 1081.9591504645 \tabularnewline
52 & 6204 & 3012.92847496826 & 3191.07152503174 \tabularnewline
53 & 5788 & 6203.78904795802 & -415.789047958023 \tabularnewline
54 & 5611 & 5788.02748655052 & -177.027486550524 \tabularnewline
55 & 5594 & 5611.01170274921 & -17.0117027492115 \tabularnewline
56 & 4647 & 5594.00112459198 & -947.001124591976 \tabularnewline
57 & 3490 & 4647.06260336674 & -1157.06260336674 \tabularnewline
58 & 2487 & 3490.0764898928 & -1003.0764898928 \tabularnewline
59 & 1992 & 2487.06631033875 & -495.066310338751 \tabularnewline
60 & 1507 & 1992.03272732944 & -485.032727329444 \tabularnewline
61 & 2306 & 1507.03206403976 & 798.96793596024 \tabularnewline
62 & 2002 & 2305.94718265754 & -303.947182657536 \tabularnewline
63 & 3075 & 2002.02009302466 & 1072.97990697534 \tabularnewline
64 & 5331 & 3074.92906855876 & 2256.07093144124 \tabularnewline
65 & 5589 & 5330.85085800613 & 258.149141993872 \tabularnewline
66 & 5813 & 5588.98293454465 & 224.017065455352 \tabularnewline
67 & 4876 & 5812.98519091251 & -936.985190912512 \tabularnewline
68 & 4665 & 4876.0619412438 & -211.061941243803 \tabularnewline
69 & 3601 & 4665.01395266359 & -1064.01395266359 \tabularnewline
70 & 2192 & 3601.07033872925 & -1409.07033872925 \tabularnewline
71 & 2111 & 2192.09314935842 & -81.0931493584244 \tabularnewline
72 & 1580 & 2111.00536082169 & -531.00536082169 \tabularnewline
73 & 2288 & 1580.03510315087 & 707.964896849135 \tabularnewline
74 & 1993 & 2287.95319859193 & -294.953198591926 \tabularnewline
75 & 3228 & 1993.0194984597 & 1234.9805015403 \tabularnewline
76 & 5000 & 3227.91835919171 & 1772.08164080829 \tabularnewline
77 & 5480 & 4999.88285306746 & 480.117146932542 \tabularnewline
78 & 5770 & 5479.96826091432 & 290.031739085677 \tabularnewline
79 & 4962 & 5769.98082688303 & -807.980826883033 \tabularnewline
80 & 4685 & 4962.0534131573 & -277.053413157296 \tabularnewline
81 & 3607 & 4685.01831515928 & -1078.01831515928 \tabularnewline
82 & 2222 & 3607.0712645151 & -1385.0712645151 \tabularnewline
83 & 2467 & 2222.09156285255 & 244.908437147447 \tabularnewline
84 & 1594 & 2466.98380984741 & -872.983809847411 \tabularnewline
85 & 2228 & 1594.05771030698 & 633.942289693022 \tabularnewline
86 & 1910 & 2227.95809200156 & -317.958092001556 \tabularnewline
87 & 3157 & 1910.0210192433 & 1246.9789807567 \tabularnewline
88 & 4809 & 3156.91756600871 & 1652.08243399129 \tabularnewline
89 & 6249 & 4808.89078585039 & 1440.10921414961 \tabularnewline
90 & 4607 & 6248.90479875584 & -1641.90479875584 \tabularnewline
91 & 4975 & 4607.10854133707 & 367.891458662925 \tabularnewline
92 & 4784 & 4974.97567981356 & -190.97567981356 \tabularnewline
93 & 3028 & 4784.01262482188 & -1756.01262482188 \tabularnewline
94 & 2461 & 3028.11608465872 & -567.116084658723 \tabularnewline
95 & 2218 & 2461.03749032109 & -243.037490321091 \tabularnewline
96 & 1351 & 2218.01606646998 & -867.01606646998 \tabularnewline
97 & 2070 & 1351.0573157976 & 718.942684202402 \tabularnewline
98 & 1887 & 2069.95247288376 & -182.952472883761 \tabularnewline
99 & 3024 & 1887.01209443205 & 1136.98790556795 \tabularnewline
100 & 4596 & 3023.92483718447 & 1572.07516281553 \tabularnewline
101 & 6398 & 4595.89607488797 & 1802.10392511203 \tabularnewline
102 & 4459 & 6397.88086838547 & -1938.88086838547 \tabularnewline
103 & 5382 & 4459.12817352263 & 922.871826477368 \tabularnewline
104 & 4359 & 5381.93899174783 & -1022.93899174783 \tabularnewline
105 & 2687 & 4359.06762338839 & -1672.06762338839 \tabularnewline
106 & 2249 & 2687.11053530976 & -438.110535309757 \tabularnewline
107 & 2154 & 2249.02896215623 & -95.0289621562256 \tabularnewline
108 & 1169 & 2154.00628207593 & -985.006282075929 \tabularnewline
109 & 2429 & 1169.06511577222 & 1259.93488422778 \tabularnewline
110 & 1762 & 2428.9167095333 & -666.916709533302 \tabularnewline
111 & 2846 & 1762.04408783714 & 1083.95591216286 \tabularnewline
112 & 5627 & 2845.92834296841 & 2781.07165703159 \tabularnewline
113 & 5749 & 5626.81615180345 & 122.183848196548 \tabularnewline
114 & 4502 & 5748.99192279707 & -1246.99192279707 \tabularnewline
115 & 5720 & 4502.08243484685 & 1217.91756515315 \tabularnewline
116 & 4403 & 5719.91948717059 & -1316.91948717059 \tabularnewline
117 & 2867 & 4403.08705754564 & -1536.08705754564 \tabularnewline
118 & 2635 & 2867.10154604775 & -232.101546047747 \tabularnewline
119 & 2059 & 2635.01534352793 & -576.015343527934 \tabularnewline
120 & 1511 & 2059.03807862405 & -548.038078624053 \tabularnewline
121 & 2359 & 1511.03622913208 & 847.963770867917 \tabularnewline
122 & 1741 & 2358.94394369177 & -617.943943691771 \tabularnewline
123 & 2917 & 1741.0408503964 & 1175.9591496036 \tabularnewline
124 & 6249 & 2916.92226091395 & 3332.07773908605 \tabularnewline
125 & 5760 & 6248.77972646568 & -488.779726465681 \tabularnewline
126 & 6250 & 5760.03231174249 & 489.967688257513 \tabularnewline
127 & 5134 & 6249.96760972497 & -1115.96760972497 \tabularnewline
128 & 4831 & 5134.07377322765 & -303.073773227647 \tabularnewline
129 & 3695 & 4831.02003528621 & -1136.02003528621 \tabularnewline
130 & 2462 & 3695.07509883257 & -1233.07509883257 \tabularnewline
131 & 2146 & 2462.0815148479 & -316.081514847902 \tabularnewline
132 & 1579 & 2146.02089518849 & -567.020895188486 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266962&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]1757[/C][C]1894[/C][C]-137[/C][/ROW]
[ROW][C]3[/C][C]3582[/C][C]1757.00905665371[/C][C]1824.99094334629[/C][/ROW]
[ROW][C]4[/C][C]5321[/C][C]3581.87935539424[/C][C]1739.12064460576[/C][/ROW]
[ROW][C]5[/C][C]5561[/C][C]5320.88503201876[/C][C]240.114967981239[/C][/ROW]
[ROW][C]6[/C][C]5907[/C][C]5560.98412672909[/C][C]346.015873270908[/C][/ROW]
[ROW][C]7[/C][C]4944[/C][C]5906.97712594204[/C][C]-962.977125942038[/C][/ROW]
[ROW][C]8[/C][C]4966[/C][C]4944.06365949165[/C][C]21.9363405083523[/C][/ROW]
[ROW][C]9[/C][C]3258[/C][C]4965.99854985519[/C][C]-1707.99854985519[/C][/ROW]
[ROW][C]10[/C][C]1964[/C][C]3258.11291059412[/C][C]-1294.11291059412[/C][/ROW]
[ROW][C]11[/C][C]1743[/C][C]1964.08554987217[/C][C]-221.085549872166[/C][/ROW]
[ROW][C]12[/C][C]1262[/C][C]1743.0146152939[/C][C]-481.014615293901[/C][/ROW]
[ROW][C]13[/C][C]2086[/C][C]1262.03179841458[/C][C]823.968201585417[/C][/ROW]
[ROW][C]14[/C][C]1793[/C][C]2085.94552996594[/C][C]-292.945529965943[/C][/ROW]
[ROW][C]15[/C][C]3548[/C][C]1793.01936573883[/C][C]1754.98063426117[/C][/ROW]
[ROW][C]16[/C][C]5672[/C][C]3547.88398356304[/C][C]2124.11601643696[/C][/ROW]
[ROW][C]17[/C][C]6084[/C][C]5671.85958114459[/C][C]412.140418855405[/C][/ROW]
[ROW][C]18[/C][C]4914[/C][C]6083.97275464926[/C][C]-1169.97275464926[/C][/ROW]
[ROW][C]19[/C][C]4990[/C][C]4914.07734334367[/C][C]75.9226566563257[/C][/ROW]
[ROW][C]20[/C][C]5139[/C][C]4989.99498098387[/C][C]149.005019016129[/C][/ROW]
[ROW][C]21[/C][C]3218[/C][C]5138.99014973097[/C][C]-1920.99014973097[/C][/ROW]
[ROW][C]22[/C][C]2179[/C][C]3218.12699082159[/C][C]-1039.12699082159[/C][/ROW]
[ROW][C]23[/C][C]2238[/C][C]2179.06869352782[/C][C]58.9313064721782[/C][/ROW]
[ROW][C]24[/C][C]1442[/C][C]2237.9961042304[/C][C]-795.9961042304[/C][/ROW]
[ROW][C]25[/C][C]2205[/C][C]1442.0526208837[/C][C]762.947379116302[/C][/ROW]
[ROW][C]26[/C][C]2025[/C][C]2204.9495638671[/C][C]-179.949563867095[/C][/ROW]
[ROW][C]27[/C][C]3531[/C][C]2025.01189591886[/C][C]1505.98810408114[/C][/ROW]
[ROW][C]28[/C][C]4977[/C][C]3530.90044370261[/C][C]1446.09955629739[/C][/ROW]
[ROW][C]29[/C][C]7998[/C][C]4976.90440275252[/C][C]3021.09559724748[/C][/ROW]
[ROW][C]30[/C][C]4880[/C][C]7997.80028455011[/C][C]-3117.80028455011[/C][/ROW]
[ROW][C]31[/C][C]5231[/C][C]4880.20610830291[/C][C]350.793891697086[/C][/ROW]
[ROW][C]32[/C][C]5202[/C][C]5230.97681008176[/C][C]-28.9768100817591[/C][/ROW]
[ROW][C]33[/C][C]3303[/C][C]5202.00191556886[/C][C]-1899.00191556886[/C][/ROW]
[ROW][C]34[/C][C]2683[/C][C]3303.12553724624[/C][C]-620.12553724624[/C][/ROW]
[ROW][C]35[/C][C]2202[/C][C]2683.04099461492[/C][C]-481.040994614924[/C][/ROW]
[ROW][C]36[/C][C]1376[/C][C]2202.03180015844[/C][C]-826.03180015844[/C][/ROW]
[ROW][C]37[/C][C]2422[/C][C]1376.05460645229[/C][C]1045.94539354771[/C][/ROW]
[ROW][C]38[/C][C]1997[/C][C]2421.93085572829[/C][C]-424.930855728292[/C][/ROW]
[ROW][C]39[/C][C]3163[/C][C]1997.02809088766[/C][C]1165.97190911234[/C][/ROW]
[ROW][C]40[/C][C]5964[/C][C]3162.92292114007[/C][C]2801.07707885993[/C][/ROW]
[ROW][C]41[/C][C]5657[/C][C]5963.8148293058[/C][C]-306.814829305805[/C][/ROW]
[ROW][C]42[/C][C]6415[/C][C]5657.02028259606[/C][C]757.979717403937[/C][/ROW]
[ROW][C]43[/C][C]6208[/C][C]6414.94989226412[/C][C]-206.949892264116[/C][/ROW]
[ROW][C]44[/C][C]4500[/C][C]6208.01368082853[/C][C]-1708.01368082853[/C][/ROW]
[ROW][C]45[/C][C]2939[/C][C]4500.11291159439[/C][C]-1561.11291159439[/C][/ROW]
[ROW][C]46[/C][C]2702[/C][C]2939.10320043091[/C][C]-237.103200430913[/C][/ROW]
[ROW][C]47[/C][C]2090[/C][C]2702.01567417211[/C][C]-612.015674172107[/C][/ROW]
[ROW][C]48[/C][C]1504[/C][C]2090.04045849652[/C][C]-586.040458496519[/C][/ROW]
[ROW][C]49[/C][C]2549[/C][C]1504.03874135394[/C][C]1044.96125864606[/C][/ROW]
[ROW][C]50[/C][C]1931[/C][C]2548.93092078646[/C][C]-617.93092078646[/C][/ROW]
[ROW][C]51[/C][C]3013[/C][C]1931.0408495355[/C][C]1081.9591504645[/C][/ROW]
[ROW][C]52[/C][C]6204[/C][C]3012.92847496826[/C][C]3191.07152503174[/C][/ROW]
[ROW][C]53[/C][C]5788[/C][C]6203.78904795802[/C][C]-415.789047958023[/C][/ROW]
[ROW][C]54[/C][C]5611[/C][C]5788.02748655052[/C][C]-177.027486550524[/C][/ROW]
[ROW][C]55[/C][C]5594[/C][C]5611.01170274921[/C][C]-17.0117027492115[/C][/ROW]
[ROW][C]56[/C][C]4647[/C][C]5594.00112459198[/C][C]-947.001124591976[/C][/ROW]
[ROW][C]57[/C][C]3490[/C][C]4647.06260336674[/C][C]-1157.06260336674[/C][/ROW]
[ROW][C]58[/C][C]2487[/C][C]3490.0764898928[/C][C]-1003.0764898928[/C][/ROW]
[ROW][C]59[/C][C]1992[/C][C]2487.06631033875[/C][C]-495.066310338751[/C][/ROW]
[ROW][C]60[/C][C]1507[/C][C]1992.03272732944[/C][C]-485.032727329444[/C][/ROW]
[ROW][C]61[/C][C]2306[/C][C]1507.03206403976[/C][C]798.96793596024[/C][/ROW]
[ROW][C]62[/C][C]2002[/C][C]2305.94718265754[/C][C]-303.947182657536[/C][/ROW]
[ROW][C]63[/C][C]3075[/C][C]2002.02009302466[/C][C]1072.97990697534[/C][/ROW]
[ROW][C]64[/C][C]5331[/C][C]3074.92906855876[/C][C]2256.07093144124[/C][/ROW]
[ROW][C]65[/C][C]5589[/C][C]5330.85085800613[/C][C]258.149141993872[/C][/ROW]
[ROW][C]66[/C][C]5813[/C][C]5588.98293454465[/C][C]224.017065455352[/C][/ROW]
[ROW][C]67[/C][C]4876[/C][C]5812.98519091251[/C][C]-936.985190912512[/C][/ROW]
[ROW][C]68[/C][C]4665[/C][C]4876.0619412438[/C][C]-211.061941243803[/C][/ROW]
[ROW][C]69[/C][C]3601[/C][C]4665.01395266359[/C][C]-1064.01395266359[/C][/ROW]
[ROW][C]70[/C][C]2192[/C][C]3601.07033872925[/C][C]-1409.07033872925[/C][/ROW]
[ROW][C]71[/C][C]2111[/C][C]2192.09314935842[/C][C]-81.0931493584244[/C][/ROW]
[ROW][C]72[/C][C]1580[/C][C]2111.00536082169[/C][C]-531.00536082169[/C][/ROW]
[ROW][C]73[/C][C]2288[/C][C]1580.03510315087[/C][C]707.964896849135[/C][/ROW]
[ROW][C]74[/C][C]1993[/C][C]2287.95319859193[/C][C]-294.953198591926[/C][/ROW]
[ROW][C]75[/C][C]3228[/C][C]1993.0194984597[/C][C]1234.9805015403[/C][/ROW]
[ROW][C]76[/C][C]5000[/C][C]3227.91835919171[/C][C]1772.08164080829[/C][/ROW]
[ROW][C]77[/C][C]5480[/C][C]4999.88285306746[/C][C]480.117146932542[/C][/ROW]
[ROW][C]78[/C][C]5770[/C][C]5479.96826091432[/C][C]290.031739085677[/C][/ROW]
[ROW][C]79[/C][C]4962[/C][C]5769.98082688303[/C][C]-807.980826883033[/C][/ROW]
[ROW][C]80[/C][C]4685[/C][C]4962.0534131573[/C][C]-277.053413157296[/C][/ROW]
[ROW][C]81[/C][C]3607[/C][C]4685.01831515928[/C][C]-1078.01831515928[/C][/ROW]
[ROW][C]82[/C][C]2222[/C][C]3607.0712645151[/C][C]-1385.0712645151[/C][/ROW]
[ROW][C]83[/C][C]2467[/C][C]2222.09156285255[/C][C]244.908437147447[/C][/ROW]
[ROW][C]84[/C][C]1594[/C][C]2466.98380984741[/C][C]-872.983809847411[/C][/ROW]
[ROW][C]85[/C][C]2228[/C][C]1594.05771030698[/C][C]633.942289693022[/C][/ROW]
[ROW][C]86[/C][C]1910[/C][C]2227.95809200156[/C][C]-317.958092001556[/C][/ROW]
[ROW][C]87[/C][C]3157[/C][C]1910.0210192433[/C][C]1246.9789807567[/C][/ROW]
[ROW][C]88[/C][C]4809[/C][C]3156.91756600871[/C][C]1652.08243399129[/C][/ROW]
[ROW][C]89[/C][C]6249[/C][C]4808.89078585039[/C][C]1440.10921414961[/C][/ROW]
[ROW][C]90[/C][C]4607[/C][C]6248.90479875584[/C][C]-1641.90479875584[/C][/ROW]
[ROW][C]91[/C][C]4975[/C][C]4607.10854133707[/C][C]367.891458662925[/C][/ROW]
[ROW][C]92[/C][C]4784[/C][C]4974.97567981356[/C][C]-190.97567981356[/C][/ROW]
[ROW][C]93[/C][C]3028[/C][C]4784.01262482188[/C][C]-1756.01262482188[/C][/ROW]
[ROW][C]94[/C][C]2461[/C][C]3028.11608465872[/C][C]-567.116084658723[/C][/ROW]
[ROW][C]95[/C][C]2218[/C][C]2461.03749032109[/C][C]-243.037490321091[/C][/ROW]
[ROW][C]96[/C][C]1351[/C][C]2218.01606646998[/C][C]-867.01606646998[/C][/ROW]
[ROW][C]97[/C][C]2070[/C][C]1351.0573157976[/C][C]718.942684202402[/C][/ROW]
[ROW][C]98[/C][C]1887[/C][C]2069.95247288376[/C][C]-182.952472883761[/C][/ROW]
[ROW][C]99[/C][C]3024[/C][C]1887.01209443205[/C][C]1136.98790556795[/C][/ROW]
[ROW][C]100[/C][C]4596[/C][C]3023.92483718447[/C][C]1572.07516281553[/C][/ROW]
[ROW][C]101[/C][C]6398[/C][C]4595.89607488797[/C][C]1802.10392511203[/C][/ROW]
[ROW][C]102[/C][C]4459[/C][C]6397.88086838547[/C][C]-1938.88086838547[/C][/ROW]
[ROW][C]103[/C][C]5382[/C][C]4459.12817352263[/C][C]922.871826477368[/C][/ROW]
[ROW][C]104[/C][C]4359[/C][C]5381.93899174783[/C][C]-1022.93899174783[/C][/ROW]
[ROW][C]105[/C][C]2687[/C][C]4359.06762338839[/C][C]-1672.06762338839[/C][/ROW]
[ROW][C]106[/C][C]2249[/C][C]2687.11053530976[/C][C]-438.110535309757[/C][/ROW]
[ROW][C]107[/C][C]2154[/C][C]2249.02896215623[/C][C]-95.0289621562256[/C][/ROW]
[ROW][C]108[/C][C]1169[/C][C]2154.00628207593[/C][C]-985.006282075929[/C][/ROW]
[ROW][C]109[/C][C]2429[/C][C]1169.06511577222[/C][C]1259.93488422778[/C][/ROW]
[ROW][C]110[/C][C]1762[/C][C]2428.9167095333[/C][C]-666.916709533302[/C][/ROW]
[ROW][C]111[/C][C]2846[/C][C]1762.04408783714[/C][C]1083.95591216286[/C][/ROW]
[ROW][C]112[/C][C]5627[/C][C]2845.92834296841[/C][C]2781.07165703159[/C][/ROW]
[ROW][C]113[/C][C]5749[/C][C]5626.81615180345[/C][C]122.183848196548[/C][/ROW]
[ROW][C]114[/C][C]4502[/C][C]5748.99192279707[/C][C]-1246.99192279707[/C][/ROW]
[ROW][C]115[/C][C]5720[/C][C]4502.08243484685[/C][C]1217.91756515315[/C][/ROW]
[ROW][C]116[/C][C]4403[/C][C]5719.91948717059[/C][C]-1316.91948717059[/C][/ROW]
[ROW][C]117[/C][C]2867[/C][C]4403.08705754564[/C][C]-1536.08705754564[/C][/ROW]
[ROW][C]118[/C][C]2635[/C][C]2867.10154604775[/C][C]-232.101546047747[/C][/ROW]
[ROW][C]119[/C][C]2059[/C][C]2635.01534352793[/C][C]-576.015343527934[/C][/ROW]
[ROW][C]120[/C][C]1511[/C][C]2059.03807862405[/C][C]-548.038078624053[/C][/ROW]
[ROW][C]121[/C][C]2359[/C][C]1511.03622913208[/C][C]847.963770867917[/C][/ROW]
[ROW][C]122[/C][C]1741[/C][C]2358.94394369177[/C][C]-617.943943691771[/C][/ROW]
[ROW][C]123[/C][C]2917[/C][C]1741.0408503964[/C][C]1175.9591496036[/C][/ROW]
[ROW][C]124[/C][C]6249[/C][C]2916.92226091395[/C][C]3332.07773908605[/C][/ROW]
[ROW][C]125[/C][C]5760[/C][C]6248.77972646568[/C][C]-488.779726465681[/C][/ROW]
[ROW][C]126[/C][C]6250[/C][C]5760.03231174249[/C][C]489.967688257513[/C][/ROW]
[ROW][C]127[/C][C]5134[/C][C]6249.96760972497[/C][C]-1115.96760972497[/C][/ROW]
[ROW][C]128[/C][C]4831[/C][C]5134.07377322765[/C][C]-303.073773227647[/C][/ROW]
[ROW][C]129[/C][C]3695[/C][C]4831.02003528621[/C][C]-1136.02003528621[/C][/ROW]
[ROW][C]130[/C][C]2462[/C][C]3695.07509883257[/C][C]-1233.07509883257[/C][/ROW]
[ROW][C]131[/C][C]2146[/C][C]2462.0815148479[/C][C]-316.081514847902[/C][/ROW]
[ROW][C]132[/C][C]1579[/C][C]2146.02089518849[/C][C]-567.020895188486[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266962&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266962&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
217571894-137
335821757.009056653711824.99094334629
453213581.879355394241739.12064460576
555615320.88503201876240.114967981239
659075560.98412672909346.015873270908
749445906.97712594204-962.977125942038
849664944.0636594916521.9363405083523
932584965.99854985519-1707.99854985519
1019643258.11291059412-1294.11291059412
1117431964.08554987217-221.085549872166
1212621743.0146152939-481.014615293901
1320861262.03179841458823.968201585417
1417932085.94552996594-292.945529965943
1535481793.019365738831754.98063426117
1656723547.883983563042124.11601643696
1760845671.85958114459412.140418855405
1849146083.97275464926-1169.97275464926
1949904914.0773433436775.9226566563257
2051394989.99498098387149.005019016129
2132185138.99014973097-1920.99014973097
2221793218.12699082159-1039.12699082159
2322382179.0686935278258.9313064721782
2414422237.9961042304-795.9961042304
2522051442.0526208837762.947379116302
2620252204.9495638671-179.949563867095
2735312025.011895918861505.98810408114
2849773530.900443702611446.09955629739
2979984976.904402752523021.09559724748
3048807997.80028455011-3117.80028455011
3152314880.20610830291350.793891697086
3252025230.97681008176-28.9768100817591
3333035202.00191556886-1899.00191556886
3426833303.12553724624-620.12553724624
3522022683.04099461492-481.040994614924
3613762202.03180015844-826.03180015844
3724221376.054606452291045.94539354771
3819972421.93085572829-424.930855728292
3931631997.028090887661165.97190911234
4059643162.922921140072801.07707885993
4156575963.8148293058-306.814829305805
4264155657.02028259606757.979717403937
4362086414.94989226412-206.949892264116
4445006208.01368082853-1708.01368082853
4529394500.11291159439-1561.11291159439
4627022939.10320043091-237.103200430913
4720902702.01567417211-612.015674172107
4815042090.04045849652-586.040458496519
4925491504.038741353941044.96125864606
5019312548.93092078646-617.93092078646
5130131931.04084953551081.9591504645
5262043012.928474968263191.07152503174
5357886203.78904795802-415.789047958023
5456115788.02748655052-177.027486550524
5555945611.01170274921-17.0117027492115
5646475594.00112459198-947.001124591976
5734904647.06260336674-1157.06260336674
5824873490.0764898928-1003.0764898928
5919922487.06631033875-495.066310338751
6015071992.03272732944-485.032727329444
6123061507.03206403976798.96793596024
6220022305.94718265754-303.947182657536
6330752002.020093024661072.97990697534
6453313074.929068558762256.07093144124
6555895330.85085800613258.149141993872
6658135588.98293454465224.017065455352
6748765812.98519091251-936.985190912512
6846654876.0619412438-211.061941243803
6936014665.01395266359-1064.01395266359
7021923601.07033872925-1409.07033872925
7121112192.09314935842-81.0931493584244
7215802111.00536082169-531.00536082169
7322881580.03510315087707.964896849135
7419932287.95319859193-294.953198591926
7532281993.01949845971234.9805015403
7650003227.918359191711772.08164080829
7754804999.88285306746480.117146932542
7857705479.96826091432290.031739085677
7949625769.98082688303-807.980826883033
8046854962.0534131573-277.053413157296
8136074685.01831515928-1078.01831515928
8222223607.0712645151-1385.0712645151
8324672222.09156285255244.908437147447
8415942466.98380984741-872.983809847411
8522281594.05771030698633.942289693022
8619102227.95809200156-317.958092001556
8731571910.02101924331246.9789807567
8848093156.917566008711652.08243399129
8962494808.890785850391440.10921414961
9046076248.90479875584-1641.90479875584
9149754607.10854133707367.891458662925
9247844974.97567981356-190.97567981356
9330284784.01262482188-1756.01262482188
9424613028.11608465872-567.116084658723
9522182461.03749032109-243.037490321091
9613512218.01606646998-867.01606646998
9720701351.0573157976718.942684202402
9818872069.95247288376-182.952472883761
9930241887.012094432051136.98790556795
10045963023.924837184471572.07516281553
10163984595.896074887971802.10392511203
10244596397.88086838547-1938.88086838547
10353824459.12817352263922.871826477368
10443595381.93899174783-1022.93899174783
10526874359.06762338839-1672.06762338839
10622492687.11053530976-438.110535309757
10721542249.02896215623-95.0289621562256
10811692154.00628207593-985.006282075929
10924291169.065115772221259.93488422778
11017622428.9167095333-666.916709533302
11128461762.044087837141083.95591216286
11256272845.928342968412781.07165703159
11357495626.81615180345122.183848196548
11445025748.99192279707-1246.99192279707
11557204502.082434846851217.91756515315
11644035719.91948717059-1316.91948717059
11728674403.08705754564-1536.08705754564
11826352867.10154604775-232.101546047747
11920592635.01534352793-576.015343527934
12015112059.03807862405-548.038078624053
12123591511.03622913208847.963770867917
12217412358.94394369177-617.943943691771
12329171741.04085039641175.9591496036
12462492916.922260913953332.07773908605
12557606248.77972646568-488.779726465681
12662505760.03231174249489.967688257513
12751346249.96760972497-1115.96760972497
12848315134.07377322765-303.073773227647
12936954831.02003528621-1136.02003528621
13024623695.07509883257-1233.07509883257
13121462462.0815148479-316.081514847902
13215792146.02089518849-567.020895188486







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1331579.0374840284-732.1338407343673890.20880879118
1341579.0374840284-1689.344315238914847.41928329572
1351579.0374840284-2423.852257040915581.92722509772
1361579.0374840284-3043.075990620846201.15095867765
1371579.0374840284-3588.625398349886746.70036640669
1381579.0374840284-4081.841101428667239.91606948547
1391579.0374840284-4535.40059748517693.47556554191
1401579.0374840284-4957.564060049278115.63902810608
1411579.0374840284-5354.069066387138512.14403444394
1421579.0374840284-5729.093134179718887.16810223652
1431579.0374840284-6085.789965181869243.86493323866
1441579.0374840284-6426.609680288999584.6846483458

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
133 & 1579.0374840284 & -732.133840734367 & 3890.20880879118 \tabularnewline
134 & 1579.0374840284 & -1689.34431523891 & 4847.41928329572 \tabularnewline
135 & 1579.0374840284 & -2423.85225704091 & 5581.92722509772 \tabularnewline
136 & 1579.0374840284 & -3043.07599062084 & 6201.15095867765 \tabularnewline
137 & 1579.0374840284 & -3588.62539834988 & 6746.70036640669 \tabularnewline
138 & 1579.0374840284 & -4081.84110142866 & 7239.91606948547 \tabularnewline
139 & 1579.0374840284 & -4535.4005974851 & 7693.47556554191 \tabularnewline
140 & 1579.0374840284 & -4957.56406004927 & 8115.63902810608 \tabularnewline
141 & 1579.0374840284 & -5354.06906638713 & 8512.14403444394 \tabularnewline
142 & 1579.0374840284 & -5729.09313417971 & 8887.16810223652 \tabularnewline
143 & 1579.0374840284 & -6085.78996518186 & 9243.86493323866 \tabularnewline
144 & 1579.0374840284 & -6426.60968028899 & 9584.6846483458 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266962&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]133[/C][C]1579.0374840284[/C][C]-732.133840734367[/C][C]3890.20880879118[/C][/ROW]
[ROW][C]134[/C][C]1579.0374840284[/C][C]-1689.34431523891[/C][C]4847.41928329572[/C][/ROW]
[ROW][C]135[/C][C]1579.0374840284[/C][C]-2423.85225704091[/C][C]5581.92722509772[/C][/ROW]
[ROW][C]136[/C][C]1579.0374840284[/C][C]-3043.07599062084[/C][C]6201.15095867765[/C][/ROW]
[ROW][C]137[/C][C]1579.0374840284[/C][C]-3588.62539834988[/C][C]6746.70036640669[/C][/ROW]
[ROW][C]138[/C][C]1579.0374840284[/C][C]-4081.84110142866[/C][C]7239.91606948547[/C][/ROW]
[ROW][C]139[/C][C]1579.0374840284[/C][C]-4535.4005974851[/C][C]7693.47556554191[/C][/ROW]
[ROW][C]140[/C][C]1579.0374840284[/C][C]-4957.56406004927[/C][C]8115.63902810608[/C][/ROW]
[ROW][C]141[/C][C]1579.0374840284[/C][C]-5354.06906638713[/C][C]8512.14403444394[/C][/ROW]
[ROW][C]142[/C][C]1579.0374840284[/C][C]-5729.09313417971[/C][C]8887.16810223652[/C][/ROW]
[ROW][C]143[/C][C]1579.0374840284[/C][C]-6085.78996518186[/C][C]9243.86493323866[/C][/ROW]
[ROW][C]144[/C][C]1579.0374840284[/C][C]-6426.60968028899[/C][C]9584.6846483458[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266962&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266962&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
1331579.0374840284-732.1338407343673890.20880879118
1341579.0374840284-1689.344315238914847.41928329572
1351579.0374840284-2423.852257040915581.92722509772
1361579.0374840284-3043.075990620846201.15095867765
1371579.0374840284-3588.625398349886746.70036640669
1381579.0374840284-4081.841101428667239.91606948547
1391579.0374840284-4535.40059748517693.47556554191
1401579.0374840284-4957.564060049278115.63902810608
1411579.0374840284-5354.069066387138512.14403444394
1421579.0374840284-5729.093134179718887.16810223652
1431579.0374840284-6085.789965181869243.86493323866
1441579.0374840284-6426.609680288999584.6846483458



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
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')