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, 17 Dec 2016 12:53:30 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/17/t14819756420l56bgjl2c6vkcj.htm/, Retrieved Thu, 02 May 2024 00:17:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300733, Retrieved Thu, 02 May 2024 00:17:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-17 11:53:30] [349958aef20b862f8399a5ba04d6f6e3] [Current]
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Dataseries X:
990
1384
1350
716
2068
1392
734
758
558
1620
3132
1392
918
776
1348
502
1274
1638
912
1250
1614
2840
1150
1652
1526
1412
882
848
820
1226
1212
2110
1178
2548
1568
2088
2178
3016
5514
1358
3604
1962
2036
2246
3434
4316
3032
5296
3850
2098
3992
4860
7336
9614
2988
2756
3540
2710
3730
3508
2640
2788
3502
3700
3250
4866
2836
3498
3468
3924
5738
7028
5608
6030
11976
7774
7906
10940
7626
5930
6286
6788
6932
6660
4910
4182
3550
3184
3872
3226
2504
3648
4448
2954
3842
3982
4864
6796
5844
5656
6118
7068
7696
7016
5820
4904
3860
7222
7738
7142
13804
7964
9716
8462
6884
8072
7320
11700
10792
10930
7112
8196
16818
10524
14878
13696




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300733&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300733&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300733&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.430444482025788
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.430444482025788 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300733&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]0.430444482025788[/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=300733&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300733&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
alpha0.430444482025788
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21384990394
313501159.59512591816190.40487408184
47161241.5538533175-525.553853317503
520681015.332097149591052.66790285041
613921468.44718733721-76.447187337209
77341435.54091738152-701.540917381516
87581133.56650057933-375.566500579333
9558971.905972771224-413.905972771224
101620793.742430714335826.257569285665
1131321149.400442145391982.59955785461
1213922002.79948189067-610.799481890673
139181739.88421528662-821.884215286623
147761386.1086899524-610.108689952401
1513481123.49077092641224.509229073592
165021220.129529745-718.129529744999
171274911.014636286491362.985363713509
1816381067.25968315309570.740316846906
199121312.93170320949-400.931703209495
2012501140.35286389377109.647136106233
2116141187.54986860063426.450131399375
2228401371.112974520661468.88702547934
2311502003.38728935751-853.387289357514
2416521636.0514396226315.9485603773724
2515261642.91640943332-116.916409433323
2614121592.59038613448-180.590386134481
278821514.85625091599-632.856250915987
288481242.44676979367-394.446769793673
298201072.65933428309-252.65933428309
301226963.903518008625262.096481991375
3112121076.72150244018135.278497559816
3221101134.95138525155975.048614748454
3311781554.65568117691-376.655681176906
3425481392.526321590641155.47367840936
3515681889.89359058799-321.89359058799
3620881751.33627071992336.663729280078
3721781896.25131528676281.748684713245
3830162017.52848193959998.471518060405
3955142447.315037348613066.68496265139
4013583767.35265763336-2409.35265763336
4136042730.26010090091873.739899099088
4219623106.35661919388-1144.35661919388
4320362613.77462699219-577.77462699219
4422462365.07472694889-119.074726948894
4534342313.819667785021120.18033221498
4643162795.995110660771520.00488933923
4730323450.27282792906-418.27282792906
4852963270.229597165672025.77040283433
4938504142.21128891687-292.211288916867
5020984016.43055201696-1918.43055201696
5139923190.65270675157801.347293248427
5248603535.588227316661324.41177268334
5373364105.673966798193230.32603320181
5496145496.149982934164117.85001706584
5529887268.65580058995-4280.65580058995
5627565426.07113177432-2670.07113177432
5735404276.75374648572-736.753746485717
5827103959.62216169911-1249.62216169911
5937303421.72919757859308.270802421406
6035083554.42266345055-46.4226634505499
6126403534.44028412732-894.44028412732
6227883149.43339932314-361.433399323138
6335022993.85638696467508.14361303533
6437003212.58400127237487.415998727625
6532503422.38952837577-172.389528375769
6648663348.185407127391517.81459287261
6728364001.52032336762-1165.52032336762
6834983499.82853148512-1.82853148511776
6934683499.04145019714-31.0414501971381
7039243485.6798292457438.320170754298
7157383674.352328107492063.64767189251
7270284562.638081318982465.36191868102
7356085623.83951541174-15.8395154117361
7460305617.02148340479412.978516595208
75119765794.785807068396181.21419293161
7677748455.45534863529-681.455348635287
7779068162.12665406827-256.126654068268
78109408051.878349124852888.12165087515
7976269295.05437716327-1669.05437716327
8059308576.61913031235-2646.61913031235
8162867437.39652964551-1151.39652964551
8267886941.78424683596-153.78424683596
8369326875.5886663629356.4113336370701
8466606899.87061365072-239.870613650723
8549106796.61963160463-1886.61963160463
8641825984.53462149889-1802.53462149889
8735505208.64354001425-1658.64354001425
8831844494.6895805674-1310.6895805674
8938723930.51048296347-58.5104829634683
9032263905.32496843118-679.32496843118
9125043612.91328426764-1108.91328426764
9236483135.58768000954512.412319990462
9344483356.152735671471091.84726432853
9429543826.13236581663-872.132365816635
9538423450.72780135477391.272198645232
9639823619.14876023171362.851239768294
9748643775.336074186181088.66392581382
9867964243.945453833272552.05454616673
9958445342.46325105957501.536748940434
10056565558.3469771741397.6530228258716
10161185600.38118200266517.618817997337
10270685823.187346002331244.81265399767
10376966359.01008407151336.9899159285
10470166934.5100159070581.4899840929547
10558206969.58692990023-1149.58692990023
10649046474.75357931571-1570.75357931571
10738605798.63136847701-1938.63136847701
10872224964.158193233982257.84180676602
10977385936.033740243551801.96625975645
11071426711.68017355236430.31982644764
111138046896.908968353046907.09103164696
11279649870.02818977528-1906.02818977528
11397169049.58887290091666.411127099091
11484629336.4418653213-874.4418653213
11568848960.04318954141-2076.04318954141
11680728066.421854156095.5781458439069
11773208068.82293625454-748.822936254537
118117007746.496235329423953.50376467058
119107929448.260115500051343.73988449995
1201093010026.665534061903.334465938977
121711210415.5008703482-3303.50087034817
12281968993.52714933941-797.527149339412
123168188650.235988640518167.76401135949
1241052412166.004937819-1642.00493781901
1251487811459.21297287573418.78702712428
1261369612930.8109839227765.189016077285

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1384 & 990 & 394 \tabularnewline
3 & 1350 & 1159.59512591816 & 190.40487408184 \tabularnewline
4 & 716 & 1241.5538533175 & -525.553853317503 \tabularnewline
5 & 2068 & 1015.33209714959 & 1052.66790285041 \tabularnewline
6 & 1392 & 1468.44718733721 & -76.447187337209 \tabularnewline
7 & 734 & 1435.54091738152 & -701.540917381516 \tabularnewline
8 & 758 & 1133.56650057933 & -375.566500579333 \tabularnewline
9 & 558 & 971.905972771224 & -413.905972771224 \tabularnewline
10 & 1620 & 793.742430714335 & 826.257569285665 \tabularnewline
11 & 3132 & 1149.40044214539 & 1982.59955785461 \tabularnewline
12 & 1392 & 2002.79948189067 & -610.799481890673 \tabularnewline
13 & 918 & 1739.88421528662 & -821.884215286623 \tabularnewline
14 & 776 & 1386.1086899524 & -610.108689952401 \tabularnewline
15 & 1348 & 1123.49077092641 & 224.509229073592 \tabularnewline
16 & 502 & 1220.129529745 & -718.129529744999 \tabularnewline
17 & 1274 & 911.014636286491 & 362.985363713509 \tabularnewline
18 & 1638 & 1067.25968315309 & 570.740316846906 \tabularnewline
19 & 912 & 1312.93170320949 & -400.931703209495 \tabularnewline
20 & 1250 & 1140.35286389377 & 109.647136106233 \tabularnewline
21 & 1614 & 1187.54986860063 & 426.450131399375 \tabularnewline
22 & 2840 & 1371.11297452066 & 1468.88702547934 \tabularnewline
23 & 1150 & 2003.38728935751 & -853.387289357514 \tabularnewline
24 & 1652 & 1636.05143962263 & 15.9485603773724 \tabularnewline
25 & 1526 & 1642.91640943332 & -116.916409433323 \tabularnewline
26 & 1412 & 1592.59038613448 & -180.590386134481 \tabularnewline
27 & 882 & 1514.85625091599 & -632.856250915987 \tabularnewline
28 & 848 & 1242.44676979367 & -394.446769793673 \tabularnewline
29 & 820 & 1072.65933428309 & -252.65933428309 \tabularnewline
30 & 1226 & 963.903518008625 & 262.096481991375 \tabularnewline
31 & 1212 & 1076.72150244018 & 135.278497559816 \tabularnewline
32 & 2110 & 1134.95138525155 & 975.048614748454 \tabularnewline
33 & 1178 & 1554.65568117691 & -376.655681176906 \tabularnewline
34 & 2548 & 1392.52632159064 & 1155.47367840936 \tabularnewline
35 & 1568 & 1889.89359058799 & -321.89359058799 \tabularnewline
36 & 2088 & 1751.33627071992 & 336.663729280078 \tabularnewline
37 & 2178 & 1896.25131528676 & 281.748684713245 \tabularnewline
38 & 3016 & 2017.52848193959 & 998.471518060405 \tabularnewline
39 & 5514 & 2447.31503734861 & 3066.68496265139 \tabularnewline
40 & 1358 & 3767.35265763336 & -2409.35265763336 \tabularnewline
41 & 3604 & 2730.26010090091 & 873.739899099088 \tabularnewline
42 & 1962 & 3106.35661919388 & -1144.35661919388 \tabularnewline
43 & 2036 & 2613.77462699219 & -577.77462699219 \tabularnewline
44 & 2246 & 2365.07472694889 & -119.074726948894 \tabularnewline
45 & 3434 & 2313.81966778502 & 1120.18033221498 \tabularnewline
46 & 4316 & 2795.99511066077 & 1520.00488933923 \tabularnewline
47 & 3032 & 3450.27282792906 & -418.27282792906 \tabularnewline
48 & 5296 & 3270.22959716567 & 2025.77040283433 \tabularnewline
49 & 3850 & 4142.21128891687 & -292.211288916867 \tabularnewline
50 & 2098 & 4016.43055201696 & -1918.43055201696 \tabularnewline
51 & 3992 & 3190.65270675157 & 801.347293248427 \tabularnewline
52 & 4860 & 3535.58822731666 & 1324.41177268334 \tabularnewline
53 & 7336 & 4105.67396679819 & 3230.32603320181 \tabularnewline
54 & 9614 & 5496.14998293416 & 4117.85001706584 \tabularnewline
55 & 2988 & 7268.65580058995 & -4280.65580058995 \tabularnewline
56 & 2756 & 5426.07113177432 & -2670.07113177432 \tabularnewline
57 & 3540 & 4276.75374648572 & -736.753746485717 \tabularnewline
58 & 2710 & 3959.62216169911 & -1249.62216169911 \tabularnewline
59 & 3730 & 3421.72919757859 & 308.270802421406 \tabularnewline
60 & 3508 & 3554.42266345055 & -46.4226634505499 \tabularnewline
61 & 2640 & 3534.44028412732 & -894.44028412732 \tabularnewline
62 & 2788 & 3149.43339932314 & -361.433399323138 \tabularnewline
63 & 3502 & 2993.85638696467 & 508.14361303533 \tabularnewline
64 & 3700 & 3212.58400127237 & 487.415998727625 \tabularnewline
65 & 3250 & 3422.38952837577 & -172.389528375769 \tabularnewline
66 & 4866 & 3348.18540712739 & 1517.81459287261 \tabularnewline
67 & 2836 & 4001.52032336762 & -1165.52032336762 \tabularnewline
68 & 3498 & 3499.82853148512 & -1.82853148511776 \tabularnewline
69 & 3468 & 3499.04145019714 & -31.0414501971381 \tabularnewline
70 & 3924 & 3485.6798292457 & 438.320170754298 \tabularnewline
71 & 5738 & 3674.35232810749 & 2063.64767189251 \tabularnewline
72 & 7028 & 4562.63808131898 & 2465.36191868102 \tabularnewline
73 & 5608 & 5623.83951541174 & -15.8395154117361 \tabularnewline
74 & 6030 & 5617.02148340479 & 412.978516595208 \tabularnewline
75 & 11976 & 5794.78580706839 & 6181.21419293161 \tabularnewline
76 & 7774 & 8455.45534863529 & -681.455348635287 \tabularnewline
77 & 7906 & 8162.12665406827 & -256.126654068268 \tabularnewline
78 & 10940 & 8051.87834912485 & 2888.12165087515 \tabularnewline
79 & 7626 & 9295.05437716327 & -1669.05437716327 \tabularnewline
80 & 5930 & 8576.61913031235 & -2646.61913031235 \tabularnewline
81 & 6286 & 7437.39652964551 & -1151.39652964551 \tabularnewline
82 & 6788 & 6941.78424683596 & -153.78424683596 \tabularnewline
83 & 6932 & 6875.58866636293 & 56.4113336370701 \tabularnewline
84 & 6660 & 6899.87061365072 & -239.870613650723 \tabularnewline
85 & 4910 & 6796.61963160463 & -1886.61963160463 \tabularnewline
86 & 4182 & 5984.53462149889 & -1802.53462149889 \tabularnewline
87 & 3550 & 5208.64354001425 & -1658.64354001425 \tabularnewline
88 & 3184 & 4494.6895805674 & -1310.6895805674 \tabularnewline
89 & 3872 & 3930.51048296347 & -58.5104829634683 \tabularnewline
90 & 3226 & 3905.32496843118 & -679.32496843118 \tabularnewline
91 & 2504 & 3612.91328426764 & -1108.91328426764 \tabularnewline
92 & 3648 & 3135.58768000954 & 512.412319990462 \tabularnewline
93 & 4448 & 3356.15273567147 & 1091.84726432853 \tabularnewline
94 & 2954 & 3826.13236581663 & -872.132365816635 \tabularnewline
95 & 3842 & 3450.72780135477 & 391.272198645232 \tabularnewline
96 & 3982 & 3619.14876023171 & 362.851239768294 \tabularnewline
97 & 4864 & 3775.33607418618 & 1088.66392581382 \tabularnewline
98 & 6796 & 4243.94545383327 & 2552.05454616673 \tabularnewline
99 & 5844 & 5342.46325105957 & 501.536748940434 \tabularnewline
100 & 5656 & 5558.34697717413 & 97.6530228258716 \tabularnewline
101 & 6118 & 5600.38118200266 & 517.618817997337 \tabularnewline
102 & 7068 & 5823.18734600233 & 1244.81265399767 \tabularnewline
103 & 7696 & 6359.0100840715 & 1336.9899159285 \tabularnewline
104 & 7016 & 6934.51001590705 & 81.4899840929547 \tabularnewline
105 & 5820 & 6969.58692990023 & -1149.58692990023 \tabularnewline
106 & 4904 & 6474.75357931571 & -1570.75357931571 \tabularnewline
107 & 3860 & 5798.63136847701 & -1938.63136847701 \tabularnewline
108 & 7222 & 4964.15819323398 & 2257.84180676602 \tabularnewline
109 & 7738 & 5936.03374024355 & 1801.96625975645 \tabularnewline
110 & 7142 & 6711.68017355236 & 430.31982644764 \tabularnewline
111 & 13804 & 6896.90896835304 & 6907.09103164696 \tabularnewline
112 & 7964 & 9870.02818977528 & -1906.02818977528 \tabularnewline
113 & 9716 & 9049.58887290091 & 666.411127099091 \tabularnewline
114 & 8462 & 9336.4418653213 & -874.4418653213 \tabularnewline
115 & 6884 & 8960.04318954141 & -2076.04318954141 \tabularnewline
116 & 8072 & 8066.42185415609 & 5.5781458439069 \tabularnewline
117 & 7320 & 8068.82293625454 & -748.822936254537 \tabularnewline
118 & 11700 & 7746.49623532942 & 3953.50376467058 \tabularnewline
119 & 10792 & 9448.26011550005 & 1343.73988449995 \tabularnewline
120 & 10930 & 10026.665534061 & 903.334465938977 \tabularnewline
121 & 7112 & 10415.5008703482 & -3303.50087034817 \tabularnewline
122 & 8196 & 8993.52714933941 & -797.527149339412 \tabularnewline
123 & 16818 & 8650.23598864051 & 8167.76401135949 \tabularnewline
124 & 10524 & 12166.004937819 & -1642.00493781901 \tabularnewline
125 & 14878 & 11459.2129728757 & 3418.78702712428 \tabularnewline
126 & 13696 & 12930.8109839227 & 765.189016077285 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300733&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]1384[/C][C]990[/C][C]394[/C][/ROW]
[ROW][C]3[/C][C]1350[/C][C]1159.59512591816[/C][C]190.40487408184[/C][/ROW]
[ROW][C]4[/C][C]716[/C][C]1241.5538533175[/C][C]-525.553853317503[/C][/ROW]
[ROW][C]5[/C][C]2068[/C][C]1015.33209714959[/C][C]1052.66790285041[/C][/ROW]
[ROW][C]6[/C][C]1392[/C][C]1468.44718733721[/C][C]-76.447187337209[/C][/ROW]
[ROW][C]7[/C][C]734[/C][C]1435.54091738152[/C][C]-701.540917381516[/C][/ROW]
[ROW][C]8[/C][C]758[/C][C]1133.56650057933[/C][C]-375.566500579333[/C][/ROW]
[ROW][C]9[/C][C]558[/C][C]971.905972771224[/C][C]-413.905972771224[/C][/ROW]
[ROW][C]10[/C][C]1620[/C][C]793.742430714335[/C][C]826.257569285665[/C][/ROW]
[ROW][C]11[/C][C]3132[/C][C]1149.40044214539[/C][C]1982.59955785461[/C][/ROW]
[ROW][C]12[/C][C]1392[/C][C]2002.79948189067[/C][C]-610.799481890673[/C][/ROW]
[ROW][C]13[/C][C]918[/C][C]1739.88421528662[/C][C]-821.884215286623[/C][/ROW]
[ROW][C]14[/C][C]776[/C][C]1386.1086899524[/C][C]-610.108689952401[/C][/ROW]
[ROW][C]15[/C][C]1348[/C][C]1123.49077092641[/C][C]224.509229073592[/C][/ROW]
[ROW][C]16[/C][C]502[/C][C]1220.129529745[/C][C]-718.129529744999[/C][/ROW]
[ROW][C]17[/C][C]1274[/C][C]911.014636286491[/C][C]362.985363713509[/C][/ROW]
[ROW][C]18[/C][C]1638[/C][C]1067.25968315309[/C][C]570.740316846906[/C][/ROW]
[ROW][C]19[/C][C]912[/C][C]1312.93170320949[/C][C]-400.931703209495[/C][/ROW]
[ROW][C]20[/C][C]1250[/C][C]1140.35286389377[/C][C]109.647136106233[/C][/ROW]
[ROW][C]21[/C][C]1614[/C][C]1187.54986860063[/C][C]426.450131399375[/C][/ROW]
[ROW][C]22[/C][C]2840[/C][C]1371.11297452066[/C][C]1468.88702547934[/C][/ROW]
[ROW][C]23[/C][C]1150[/C][C]2003.38728935751[/C][C]-853.387289357514[/C][/ROW]
[ROW][C]24[/C][C]1652[/C][C]1636.05143962263[/C][C]15.9485603773724[/C][/ROW]
[ROW][C]25[/C][C]1526[/C][C]1642.91640943332[/C][C]-116.916409433323[/C][/ROW]
[ROW][C]26[/C][C]1412[/C][C]1592.59038613448[/C][C]-180.590386134481[/C][/ROW]
[ROW][C]27[/C][C]882[/C][C]1514.85625091599[/C][C]-632.856250915987[/C][/ROW]
[ROW][C]28[/C][C]848[/C][C]1242.44676979367[/C][C]-394.446769793673[/C][/ROW]
[ROW][C]29[/C][C]820[/C][C]1072.65933428309[/C][C]-252.65933428309[/C][/ROW]
[ROW][C]30[/C][C]1226[/C][C]963.903518008625[/C][C]262.096481991375[/C][/ROW]
[ROW][C]31[/C][C]1212[/C][C]1076.72150244018[/C][C]135.278497559816[/C][/ROW]
[ROW][C]32[/C][C]2110[/C][C]1134.95138525155[/C][C]975.048614748454[/C][/ROW]
[ROW][C]33[/C][C]1178[/C][C]1554.65568117691[/C][C]-376.655681176906[/C][/ROW]
[ROW][C]34[/C][C]2548[/C][C]1392.52632159064[/C][C]1155.47367840936[/C][/ROW]
[ROW][C]35[/C][C]1568[/C][C]1889.89359058799[/C][C]-321.89359058799[/C][/ROW]
[ROW][C]36[/C][C]2088[/C][C]1751.33627071992[/C][C]336.663729280078[/C][/ROW]
[ROW][C]37[/C][C]2178[/C][C]1896.25131528676[/C][C]281.748684713245[/C][/ROW]
[ROW][C]38[/C][C]3016[/C][C]2017.52848193959[/C][C]998.471518060405[/C][/ROW]
[ROW][C]39[/C][C]5514[/C][C]2447.31503734861[/C][C]3066.68496265139[/C][/ROW]
[ROW][C]40[/C][C]1358[/C][C]3767.35265763336[/C][C]-2409.35265763336[/C][/ROW]
[ROW][C]41[/C][C]3604[/C][C]2730.26010090091[/C][C]873.739899099088[/C][/ROW]
[ROW][C]42[/C][C]1962[/C][C]3106.35661919388[/C][C]-1144.35661919388[/C][/ROW]
[ROW][C]43[/C][C]2036[/C][C]2613.77462699219[/C][C]-577.77462699219[/C][/ROW]
[ROW][C]44[/C][C]2246[/C][C]2365.07472694889[/C][C]-119.074726948894[/C][/ROW]
[ROW][C]45[/C][C]3434[/C][C]2313.81966778502[/C][C]1120.18033221498[/C][/ROW]
[ROW][C]46[/C][C]4316[/C][C]2795.99511066077[/C][C]1520.00488933923[/C][/ROW]
[ROW][C]47[/C][C]3032[/C][C]3450.27282792906[/C][C]-418.27282792906[/C][/ROW]
[ROW][C]48[/C][C]5296[/C][C]3270.22959716567[/C][C]2025.77040283433[/C][/ROW]
[ROW][C]49[/C][C]3850[/C][C]4142.21128891687[/C][C]-292.211288916867[/C][/ROW]
[ROW][C]50[/C][C]2098[/C][C]4016.43055201696[/C][C]-1918.43055201696[/C][/ROW]
[ROW][C]51[/C][C]3992[/C][C]3190.65270675157[/C][C]801.347293248427[/C][/ROW]
[ROW][C]52[/C][C]4860[/C][C]3535.58822731666[/C][C]1324.41177268334[/C][/ROW]
[ROW][C]53[/C][C]7336[/C][C]4105.67396679819[/C][C]3230.32603320181[/C][/ROW]
[ROW][C]54[/C][C]9614[/C][C]5496.14998293416[/C][C]4117.85001706584[/C][/ROW]
[ROW][C]55[/C][C]2988[/C][C]7268.65580058995[/C][C]-4280.65580058995[/C][/ROW]
[ROW][C]56[/C][C]2756[/C][C]5426.07113177432[/C][C]-2670.07113177432[/C][/ROW]
[ROW][C]57[/C][C]3540[/C][C]4276.75374648572[/C][C]-736.753746485717[/C][/ROW]
[ROW][C]58[/C][C]2710[/C][C]3959.62216169911[/C][C]-1249.62216169911[/C][/ROW]
[ROW][C]59[/C][C]3730[/C][C]3421.72919757859[/C][C]308.270802421406[/C][/ROW]
[ROW][C]60[/C][C]3508[/C][C]3554.42266345055[/C][C]-46.4226634505499[/C][/ROW]
[ROW][C]61[/C][C]2640[/C][C]3534.44028412732[/C][C]-894.44028412732[/C][/ROW]
[ROW][C]62[/C][C]2788[/C][C]3149.43339932314[/C][C]-361.433399323138[/C][/ROW]
[ROW][C]63[/C][C]3502[/C][C]2993.85638696467[/C][C]508.14361303533[/C][/ROW]
[ROW][C]64[/C][C]3700[/C][C]3212.58400127237[/C][C]487.415998727625[/C][/ROW]
[ROW][C]65[/C][C]3250[/C][C]3422.38952837577[/C][C]-172.389528375769[/C][/ROW]
[ROW][C]66[/C][C]4866[/C][C]3348.18540712739[/C][C]1517.81459287261[/C][/ROW]
[ROW][C]67[/C][C]2836[/C][C]4001.52032336762[/C][C]-1165.52032336762[/C][/ROW]
[ROW][C]68[/C][C]3498[/C][C]3499.82853148512[/C][C]-1.82853148511776[/C][/ROW]
[ROW][C]69[/C][C]3468[/C][C]3499.04145019714[/C][C]-31.0414501971381[/C][/ROW]
[ROW][C]70[/C][C]3924[/C][C]3485.6798292457[/C][C]438.320170754298[/C][/ROW]
[ROW][C]71[/C][C]5738[/C][C]3674.35232810749[/C][C]2063.64767189251[/C][/ROW]
[ROW][C]72[/C][C]7028[/C][C]4562.63808131898[/C][C]2465.36191868102[/C][/ROW]
[ROW][C]73[/C][C]5608[/C][C]5623.83951541174[/C][C]-15.8395154117361[/C][/ROW]
[ROW][C]74[/C][C]6030[/C][C]5617.02148340479[/C][C]412.978516595208[/C][/ROW]
[ROW][C]75[/C][C]11976[/C][C]5794.78580706839[/C][C]6181.21419293161[/C][/ROW]
[ROW][C]76[/C][C]7774[/C][C]8455.45534863529[/C][C]-681.455348635287[/C][/ROW]
[ROW][C]77[/C][C]7906[/C][C]8162.12665406827[/C][C]-256.126654068268[/C][/ROW]
[ROW][C]78[/C][C]10940[/C][C]8051.87834912485[/C][C]2888.12165087515[/C][/ROW]
[ROW][C]79[/C][C]7626[/C][C]9295.05437716327[/C][C]-1669.05437716327[/C][/ROW]
[ROW][C]80[/C][C]5930[/C][C]8576.61913031235[/C][C]-2646.61913031235[/C][/ROW]
[ROW][C]81[/C][C]6286[/C][C]7437.39652964551[/C][C]-1151.39652964551[/C][/ROW]
[ROW][C]82[/C][C]6788[/C][C]6941.78424683596[/C][C]-153.78424683596[/C][/ROW]
[ROW][C]83[/C][C]6932[/C][C]6875.58866636293[/C][C]56.4113336370701[/C][/ROW]
[ROW][C]84[/C][C]6660[/C][C]6899.87061365072[/C][C]-239.870613650723[/C][/ROW]
[ROW][C]85[/C][C]4910[/C][C]6796.61963160463[/C][C]-1886.61963160463[/C][/ROW]
[ROW][C]86[/C][C]4182[/C][C]5984.53462149889[/C][C]-1802.53462149889[/C][/ROW]
[ROW][C]87[/C][C]3550[/C][C]5208.64354001425[/C][C]-1658.64354001425[/C][/ROW]
[ROW][C]88[/C][C]3184[/C][C]4494.6895805674[/C][C]-1310.6895805674[/C][/ROW]
[ROW][C]89[/C][C]3872[/C][C]3930.51048296347[/C][C]-58.5104829634683[/C][/ROW]
[ROW][C]90[/C][C]3226[/C][C]3905.32496843118[/C][C]-679.32496843118[/C][/ROW]
[ROW][C]91[/C][C]2504[/C][C]3612.91328426764[/C][C]-1108.91328426764[/C][/ROW]
[ROW][C]92[/C][C]3648[/C][C]3135.58768000954[/C][C]512.412319990462[/C][/ROW]
[ROW][C]93[/C][C]4448[/C][C]3356.15273567147[/C][C]1091.84726432853[/C][/ROW]
[ROW][C]94[/C][C]2954[/C][C]3826.13236581663[/C][C]-872.132365816635[/C][/ROW]
[ROW][C]95[/C][C]3842[/C][C]3450.72780135477[/C][C]391.272198645232[/C][/ROW]
[ROW][C]96[/C][C]3982[/C][C]3619.14876023171[/C][C]362.851239768294[/C][/ROW]
[ROW][C]97[/C][C]4864[/C][C]3775.33607418618[/C][C]1088.66392581382[/C][/ROW]
[ROW][C]98[/C][C]6796[/C][C]4243.94545383327[/C][C]2552.05454616673[/C][/ROW]
[ROW][C]99[/C][C]5844[/C][C]5342.46325105957[/C][C]501.536748940434[/C][/ROW]
[ROW][C]100[/C][C]5656[/C][C]5558.34697717413[/C][C]97.6530228258716[/C][/ROW]
[ROW][C]101[/C][C]6118[/C][C]5600.38118200266[/C][C]517.618817997337[/C][/ROW]
[ROW][C]102[/C][C]7068[/C][C]5823.18734600233[/C][C]1244.81265399767[/C][/ROW]
[ROW][C]103[/C][C]7696[/C][C]6359.0100840715[/C][C]1336.9899159285[/C][/ROW]
[ROW][C]104[/C][C]7016[/C][C]6934.51001590705[/C][C]81.4899840929547[/C][/ROW]
[ROW][C]105[/C][C]5820[/C][C]6969.58692990023[/C][C]-1149.58692990023[/C][/ROW]
[ROW][C]106[/C][C]4904[/C][C]6474.75357931571[/C][C]-1570.75357931571[/C][/ROW]
[ROW][C]107[/C][C]3860[/C][C]5798.63136847701[/C][C]-1938.63136847701[/C][/ROW]
[ROW][C]108[/C][C]7222[/C][C]4964.15819323398[/C][C]2257.84180676602[/C][/ROW]
[ROW][C]109[/C][C]7738[/C][C]5936.03374024355[/C][C]1801.96625975645[/C][/ROW]
[ROW][C]110[/C][C]7142[/C][C]6711.68017355236[/C][C]430.31982644764[/C][/ROW]
[ROW][C]111[/C][C]13804[/C][C]6896.90896835304[/C][C]6907.09103164696[/C][/ROW]
[ROW][C]112[/C][C]7964[/C][C]9870.02818977528[/C][C]-1906.02818977528[/C][/ROW]
[ROW][C]113[/C][C]9716[/C][C]9049.58887290091[/C][C]666.411127099091[/C][/ROW]
[ROW][C]114[/C][C]8462[/C][C]9336.4418653213[/C][C]-874.4418653213[/C][/ROW]
[ROW][C]115[/C][C]6884[/C][C]8960.04318954141[/C][C]-2076.04318954141[/C][/ROW]
[ROW][C]116[/C][C]8072[/C][C]8066.42185415609[/C][C]5.5781458439069[/C][/ROW]
[ROW][C]117[/C][C]7320[/C][C]8068.82293625454[/C][C]-748.822936254537[/C][/ROW]
[ROW][C]118[/C][C]11700[/C][C]7746.49623532942[/C][C]3953.50376467058[/C][/ROW]
[ROW][C]119[/C][C]10792[/C][C]9448.26011550005[/C][C]1343.73988449995[/C][/ROW]
[ROW][C]120[/C][C]10930[/C][C]10026.665534061[/C][C]903.334465938977[/C][/ROW]
[ROW][C]121[/C][C]7112[/C][C]10415.5008703482[/C][C]-3303.50087034817[/C][/ROW]
[ROW][C]122[/C][C]8196[/C][C]8993.52714933941[/C][C]-797.527149339412[/C][/ROW]
[ROW][C]123[/C][C]16818[/C][C]8650.23598864051[/C][C]8167.76401135949[/C][/ROW]
[ROW][C]124[/C][C]10524[/C][C]12166.004937819[/C][C]-1642.00493781901[/C][/ROW]
[ROW][C]125[/C][C]14878[/C][C]11459.2129728757[/C][C]3418.78702712428[/C][/ROW]
[ROW][C]126[/C][C]13696[/C][C]12930.8109839227[/C][C]765.189016077285[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300733&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300733&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
21384990394
313501159.59512591816190.40487408184
47161241.5538533175-525.553853317503
520681015.332097149591052.66790285041
613921468.44718733721-76.447187337209
77341435.54091738152-701.540917381516
87581133.56650057933-375.566500579333
9558971.905972771224-413.905972771224
101620793.742430714335826.257569285665
1131321149.400442145391982.59955785461
1213922002.79948189067-610.799481890673
139181739.88421528662-821.884215286623
147761386.1086899524-610.108689952401
1513481123.49077092641224.509229073592
165021220.129529745-718.129529744999
171274911.014636286491362.985363713509
1816381067.25968315309570.740316846906
199121312.93170320949-400.931703209495
2012501140.35286389377109.647136106233
2116141187.54986860063426.450131399375
2228401371.112974520661468.88702547934
2311502003.38728935751-853.387289357514
2416521636.0514396226315.9485603773724
2515261642.91640943332-116.916409433323
2614121592.59038613448-180.590386134481
278821514.85625091599-632.856250915987
288481242.44676979367-394.446769793673
298201072.65933428309-252.65933428309
301226963.903518008625262.096481991375
3112121076.72150244018135.278497559816
3221101134.95138525155975.048614748454
3311781554.65568117691-376.655681176906
3425481392.526321590641155.47367840936
3515681889.89359058799-321.89359058799
3620881751.33627071992336.663729280078
3721781896.25131528676281.748684713245
3830162017.52848193959998.471518060405
3955142447.315037348613066.68496265139
4013583767.35265763336-2409.35265763336
4136042730.26010090091873.739899099088
4219623106.35661919388-1144.35661919388
4320362613.77462699219-577.77462699219
4422462365.07472694889-119.074726948894
4534342313.819667785021120.18033221498
4643162795.995110660771520.00488933923
4730323450.27282792906-418.27282792906
4852963270.229597165672025.77040283433
4938504142.21128891687-292.211288916867
5020984016.43055201696-1918.43055201696
5139923190.65270675157801.347293248427
5248603535.588227316661324.41177268334
5373364105.673966798193230.32603320181
5496145496.149982934164117.85001706584
5529887268.65580058995-4280.65580058995
5627565426.07113177432-2670.07113177432
5735404276.75374648572-736.753746485717
5827103959.62216169911-1249.62216169911
5937303421.72919757859308.270802421406
6035083554.42266345055-46.4226634505499
6126403534.44028412732-894.44028412732
6227883149.43339932314-361.433399323138
6335022993.85638696467508.14361303533
6437003212.58400127237487.415998727625
6532503422.38952837577-172.389528375769
6648663348.185407127391517.81459287261
6728364001.52032336762-1165.52032336762
6834983499.82853148512-1.82853148511776
6934683499.04145019714-31.0414501971381
7039243485.6798292457438.320170754298
7157383674.352328107492063.64767189251
7270284562.638081318982465.36191868102
7356085623.83951541174-15.8395154117361
7460305617.02148340479412.978516595208
75119765794.785807068396181.21419293161
7677748455.45534863529-681.455348635287
7779068162.12665406827-256.126654068268
78109408051.878349124852888.12165087515
7976269295.05437716327-1669.05437716327
8059308576.61913031235-2646.61913031235
8162867437.39652964551-1151.39652964551
8267886941.78424683596-153.78424683596
8369326875.5886663629356.4113336370701
8466606899.87061365072-239.870613650723
8549106796.61963160463-1886.61963160463
8641825984.53462149889-1802.53462149889
8735505208.64354001425-1658.64354001425
8831844494.6895805674-1310.6895805674
8938723930.51048296347-58.5104829634683
9032263905.32496843118-679.32496843118
9125043612.91328426764-1108.91328426764
9236483135.58768000954512.412319990462
9344483356.152735671471091.84726432853
9429543826.13236581663-872.132365816635
9538423450.72780135477391.272198645232
9639823619.14876023171362.851239768294
9748643775.336074186181088.66392581382
9867964243.945453833272552.05454616673
9958445342.46325105957501.536748940434
10056565558.3469771741397.6530228258716
10161185600.38118200266517.618817997337
10270685823.187346002331244.81265399767
10376966359.01008407151336.9899159285
10470166934.5100159070581.4899840929547
10558206969.58692990023-1149.58692990023
10649046474.75357931571-1570.75357931571
10738605798.63136847701-1938.63136847701
10872224964.158193233982257.84180676602
10977385936.033740243551801.96625975645
11071426711.68017355236430.31982644764
111138046896.908968353046907.09103164696
11279649870.02818977528-1906.02818977528
11397169049.58887290091666.411127099091
11484629336.4418653213-874.4418653213
11568848960.04318954141-2076.04318954141
11680728066.421854156095.5781458439069
11773208068.82293625454-748.822936254537
118117007746.496235329423953.50376467058
119107929448.260115500051343.73988449995
1201093010026.665534061903.334465938977
121711210415.5008703482-3303.50087034817
12281968993.52714933941-797.527149339412
123168188650.235988640518167.76401135949
1241052412166.004937819-1642.00493781901
1251487811459.21297287573418.78702712428
1261369612930.8109839227765.189016077285







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12713260.18237359999813.5180997356116706.8466474642
12813260.18237359999507.7756113863517012.5891358135
12913260.18237359999225.1336252599817295.2311219399
13013260.18237359998961.0335864731817559.3311607267
13113260.18237359998712.2441389460217808.1206082538
13213260.18237359998476.3759311735118043.9888160263
13313260.18237359998251.6031368328718268.761610367
13413260.18237359998036.4932688246818483.8714783752
13513260.18237359997829.8978731597118690.4668740401
13613260.18237359997630.8794284658918889.485318734
13713260.18237359997438.6607906743519081.7039565255
13813260.18237359997252.5892255212519267.7755216786
13913260.18237359997072.1101919576119448.2545552422
14013260.18237359996896.7478278857119623.6169193141
14113260.18237359996726.0901558574619794.2745913424
14213260.18237359996559.7776841549519960.5870630449
14313260.18237359996397.4944967757320122.8702504241
14413260.18237359996238.9611986843220281.4035485155

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 13260.1823735999 & 9813.51809973561 & 16706.8466474642 \tabularnewline
128 & 13260.1823735999 & 9507.77561138635 & 17012.5891358135 \tabularnewline
129 & 13260.1823735999 & 9225.13362525998 & 17295.2311219399 \tabularnewline
130 & 13260.1823735999 & 8961.03358647318 & 17559.3311607267 \tabularnewline
131 & 13260.1823735999 & 8712.24413894602 & 17808.1206082538 \tabularnewline
132 & 13260.1823735999 & 8476.37593117351 & 18043.9888160263 \tabularnewline
133 & 13260.1823735999 & 8251.60313683287 & 18268.761610367 \tabularnewline
134 & 13260.1823735999 & 8036.49326882468 & 18483.8714783752 \tabularnewline
135 & 13260.1823735999 & 7829.89787315971 & 18690.4668740401 \tabularnewline
136 & 13260.1823735999 & 7630.87942846589 & 18889.485318734 \tabularnewline
137 & 13260.1823735999 & 7438.66079067435 & 19081.7039565255 \tabularnewline
138 & 13260.1823735999 & 7252.58922552125 & 19267.7755216786 \tabularnewline
139 & 13260.1823735999 & 7072.11019195761 & 19448.2545552422 \tabularnewline
140 & 13260.1823735999 & 6896.74782788571 & 19623.6169193141 \tabularnewline
141 & 13260.1823735999 & 6726.09015585746 & 19794.2745913424 \tabularnewline
142 & 13260.1823735999 & 6559.77768415495 & 19960.5870630449 \tabularnewline
143 & 13260.1823735999 & 6397.49449677573 & 20122.8702504241 \tabularnewline
144 & 13260.1823735999 & 6238.96119868432 & 20281.4035485155 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300733&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]127[/C][C]13260.1823735999[/C][C]9813.51809973561[/C][C]16706.8466474642[/C][/ROW]
[ROW][C]128[/C][C]13260.1823735999[/C][C]9507.77561138635[/C][C]17012.5891358135[/C][/ROW]
[ROW][C]129[/C][C]13260.1823735999[/C][C]9225.13362525998[/C][C]17295.2311219399[/C][/ROW]
[ROW][C]130[/C][C]13260.1823735999[/C][C]8961.03358647318[/C][C]17559.3311607267[/C][/ROW]
[ROW][C]131[/C][C]13260.1823735999[/C][C]8712.24413894602[/C][C]17808.1206082538[/C][/ROW]
[ROW][C]132[/C][C]13260.1823735999[/C][C]8476.37593117351[/C][C]18043.9888160263[/C][/ROW]
[ROW][C]133[/C][C]13260.1823735999[/C][C]8251.60313683287[/C][C]18268.761610367[/C][/ROW]
[ROW][C]134[/C][C]13260.1823735999[/C][C]8036.49326882468[/C][C]18483.8714783752[/C][/ROW]
[ROW][C]135[/C][C]13260.1823735999[/C][C]7829.89787315971[/C][C]18690.4668740401[/C][/ROW]
[ROW][C]136[/C][C]13260.1823735999[/C][C]7630.87942846589[/C][C]18889.485318734[/C][/ROW]
[ROW][C]137[/C][C]13260.1823735999[/C][C]7438.66079067435[/C][C]19081.7039565255[/C][/ROW]
[ROW][C]138[/C][C]13260.1823735999[/C][C]7252.58922552125[/C][C]19267.7755216786[/C][/ROW]
[ROW][C]139[/C][C]13260.1823735999[/C][C]7072.11019195761[/C][C]19448.2545552422[/C][/ROW]
[ROW][C]140[/C][C]13260.1823735999[/C][C]6896.74782788571[/C][C]19623.6169193141[/C][/ROW]
[ROW][C]141[/C][C]13260.1823735999[/C][C]6726.09015585746[/C][C]19794.2745913424[/C][/ROW]
[ROW][C]142[/C][C]13260.1823735999[/C][C]6559.77768415495[/C][C]19960.5870630449[/C][/ROW]
[ROW][C]143[/C][C]13260.1823735999[/C][C]6397.49449677573[/C][C]20122.8702504241[/C][/ROW]
[ROW][C]144[/C][C]13260.1823735999[/C][C]6238.96119868432[/C][C]20281.4035485155[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300733&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300733&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
12713260.18237359999813.5180997356116706.8466474642
12813260.18237359999507.7756113863517012.5891358135
12913260.18237359999225.1336252599817295.2311219399
13013260.18237359998961.0335864731817559.3311607267
13113260.18237359998712.2441389460217808.1206082538
13213260.18237359998476.3759311735118043.9888160263
13313260.18237359998251.6031368328718268.761610367
13413260.18237359998036.4932688246818483.8714783752
13513260.18237359997829.8978731597118690.4668740401
13613260.18237359997630.8794284658918889.485318734
13713260.18237359997438.6607906743519081.7039565255
13813260.18237359997252.5892255212519267.7755216786
13913260.18237359997072.1101919576119448.2545552422
14013260.18237359996896.7478278857119623.6169193141
14113260.18237359996726.0901558574619794.2745913424
14213260.18237359996559.7776841549519960.5870630449
14313260.18237359996397.4944967757320122.8702504241
14413260.18237359996238.9611986843220281.4035485155



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 18 ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 18 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')