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 12:49:35 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/17/t1481975434eyguaw3gu7oix3p.htm/, Retrieved Fri, 01 Nov 2024 03:39:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300729, Retrieved Fri, 01 Nov 2024 03:39:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-17 11:49:35] [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=300729&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=300729&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300729&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
alpha0.447076668976734
beta0.0333439809755555
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.447076668976734 \tabularnewline
beta & 0.0333439809755555 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300729&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]0.447076668976734[/C][/ROW]
[ROW][C]beta[/C][C]0.0333439809755555[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300729&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300729&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
alpha0.447076668976734
beta0.0333439809755555
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
313501778-428
47161974.27085445351-1258.27085445351
520681780.58953977778287.410460222216
613922282.23079710328-890.230797103284
77342244.10517209776-1510.10517209776
87581906.33656142507-1148.33656142507
95581713.18764021994-1155.18764021994
1016201499.75501439981120.244985600189
1131321858.331088426741273.66891157326
1213922751.56307406988-1359.56307406988
139182447.27103863642-1529.27103863642
147762044.30920516728-1268.30920516728
1513481739.11023289823-391.110232898232
165021820.25605136992-1318.25605136992
1712741467.24494620943-193.244946209429
1816381614.3192950380123.6807049619879
199121858.72905715859-946.729057158589
2012501655.17806611844-405.178066118443
2116141687.70177078797-73.7017707879722
2228401867.32209783576972.677902164244
2311502529.25438035224-1379.25438035224
2416522119.131631526-467.131631526005
2515262109.83400412386-583.834004123856
2614122039.65807076008-627.658070760084
278821940.53272249734-1058.53272249734
288481632.99348845703-784.993488457028
298201436.04511805873-616.045118058731
3012261305.44604311589-79.4460431158905
3112121413.56356790919-201.563567909185
3221101464.08042470439645.919575295609
3311781903.1161493615-725.116149361505
3425481718.38425365548829.615746344522
3515682241.10405907727-673.104059077268
3620882081.958724613216.04127538679086
3721782226.53348323333-48.5334832333324
3830162345.98563659089670.014363409107
3955142796.671883528772717.32811647123
4013584203.17241229432-2845.17241229432
4136043080.39484941005523.605150589954
4219623471.52468527389-1509.52468527389
4320362931.1866451124-895.186645112403
4422462652.15997942359-406.159979423594
4534342585.71097133426848.289028665737
4643163092.742559745651223.25744025435
4730323785.64926172549-753.649261725492
4852963583.492212850161712.50778714984
4938504509.42533720078-659.425337200782
5020984365.09223943737-2267.09223943737
5139923468.21251790819523.787482091807
5248603826.878271278561033.12172872144
5373364428.656555047542907.34344495246
5496145911.696327927413702.30367207259
5529887805.33568168095-4817.33568168095
5627565818.22950725546-3062.22950725546
5735404570.14073223192-1030.14073223192
5827104215.19480444775-1505.19480444775
5937303625.42486996486104.575130035137
6035083756.9044501129-248.904450112898
6126403726.64105973911-1086.64105973911
6227883305.64627485746-517.646274857461
6335023131.31906649879370.680933501206
6437003359.668085205340.331914794999
6532503579.52220110133-329.522201101332
6648663494.987878599671371.01212140033
6728364191.16088734077-1355.16088734077
6834983648.32373677575-150.323736775755
6934683641.90024270662-173.900242706621
7039243622.34385703887301.656142961131
7157383819.894519615941918.10548038406
7270284768.715771949572259.28422805043
7356085903.74994611258-295.749946112581
7460305892.07911468166137.920885318335
75119766076.34842421215899.6515757879
7677748924.50106838423-1150.50106838423
7779068603.54406970094-697.544069700936
78109408474.695067346092465.30493265391
7976269796.63314097222-2170.63314097222
8059309013.59314902605-3083.59314902605
8162867776.42194045191-1490.42194045191
8267887229.30221815909-441.302218159095
8369327144.64081507343-212.640815073431
8466607159.03868658976-499.038686589756
8549107037.95542433678-2127.95542433678
8641826156.899389104-1974.899389104
8735505314.83068711697-1764.83068711697
8831844540.36991202833-1356.36991202833
8938723928.3025848571-56.3025848571028
9032263896.62570734209-670.625707342092
9125043580.30206525094-1076.30206525094
9236483066.56521344436581.434786555644
9344483302.631463448021145.36853655198
9429543807.89370657142-853.893706571423
9538423406.60318236097435.396817639025
9639823588.21496897978393.785031020218
9748643757.09337451871106.9066254813
9867964261.29281387232534.7071861277
9958445441.6142526944402.385747305599
10056565674.62301692708-18.623016927083
10161185719.13096603943398.869033960575
10270685956.23593729681111.7640627032
10376966528.633061473491167.36693852651
10470167143.29124193513-127.291241935127
10558207177.24038485194-1357.24038485194
10649046641.07515071245-1737.07515071245
10738605909.19952659865-2049.19952659865
10872225007.23231142992214.7676885701
10977386044.601597123041693.39840287696
11071426874.12286427411267.877135725892
111138047070.320160848496733.67983915151
112796410257.6080851657-2293.60808516569
11397169374.81465400576341.185345994245
11484629675.06205123911-1213.06205123911
11568849262.35820009294-2378.35820009294
11680728293.22269122668-221.222691226678
11773208285.19430364346-965.19430364346
118117007930.1651093353769.834890665
119107929748.255114501081043.74488549892
1201093010363.1333156008566.86668439917
121711210773.2608598083-3661.2608598083
12281969238.51165314859-1042.51165314859
123168188859.003068097967958.99693190204
1241052412622.5062388862-2098.50623888619
1251487811858.25129833993019.7487016601
1261369613427.2650755568268.734924443166

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1350 & 1778 & -428 \tabularnewline
4 & 716 & 1974.27085445351 & -1258.27085445351 \tabularnewline
5 & 2068 & 1780.58953977778 & 287.410460222216 \tabularnewline
6 & 1392 & 2282.23079710328 & -890.230797103284 \tabularnewline
7 & 734 & 2244.10517209776 & -1510.10517209776 \tabularnewline
8 & 758 & 1906.33656142507 & -1148.33656142507 \tabularnewline
9 & 558 & 1713.18764021994 & -1155.18764021994 \tabularnewline
10 & 1620 & 1499.75501439981 & 120.244985600189 \tabularnewline
11 & 3132 & 1858.33108842674 & 1273.66891157326 \tabularnewline
12 & 1392 & 2751.56307406988 & -1359.56307406988 \tabularnewline
13 & 918 & 2447.27103863642 & -1529.27103863642 \tabularnewline
14 & 776 & 2044.30920516728 & -1268.30920516728 \tabularnewline
15 & 1348 & 1739.11023289823 & -391.110232898232 \tabularnewline
16 & 502 & 1820.25605136992 & -1318.25605136992 \tabularnewline
17 & 1274 & 1467.24494620943 & -193.244946209429 \tabularnewline
18 & 1638 & 1614.31929503801 & 23.6807049619879 \tabularnewline
19 & 912 & 1858.72905715859 & -946.729057158589 \tabularnewline
20 & 1250 & 1655.17806611844 & -405.178066118443 \tabularnewline
21 & 1614 & 1687.70177078797 & -73.7017707879722 \tabularnewline
22 & 2840 & 1867.32209783576 & 972.677902164244 \tabularnewline
23 & 1150 & 2529.25438035224 & -1379.25438035224 \tabularnewline
24 & 1652 & 2119.131631526 & -467.131631526005 \tabularnewline
25 & 1526 & 2109.83400412386 & -583.834004123856 \tabularnewline
26 & 1412 & 2039.65807076008 & -627.658070760084 \tabularnewline
27 & 882 & 1940.53272249734 & -1058.53272249734 \tabularnewline
28 & 848 & 1632.99348845703 & -784.993488457028 \tabularnewline
29 & 820 & 1436.04511805873 & -616.045118058731 \tabularnewline
30 & 1226 & 1305.44604311589 & -79.4460431158905 \tabularnewline
31 & 1212 & 1413.56356790919 & -201.563567909185 \tabularnewline
32 & 2110 & 1464.08042470439 & 645.919575295609 \tabularnewline
33 & 1178 & 1903.1161493615 & -725.116149361505 \tabularnewline
34 & 2548 & 1718.38425365548 & 829.615746344522 \tabularnewline
35 & 1568 & 2241.10405907727 & -673.104059077268 \tabularnewline
36 & 2088 & 2081.95872461321 & 6.04127538679086 \tabularnewline
37 & 2178 & 2226.53348323333 & -48.5334832333324 \tabularnewline
38 & 3016 & 2345.98563659089 & 670.014363409107 \tabularnewline
39 & 5514 & 2796.67188352877 & 2717.32811647123 \tabularnewline
40 & 1358 & 4203.17241229432 & -2845.17241229432 \tabularnewline
41 & 3604 & 3080.39484941005 & 523.605150589954 \tabularnewline
42 & 1962 & 3471.52468527389 & -1509.52468527389 \tabularnewline
43 & 2036 & 2931.1866451124 & -895.186645112403 \tabularnewline
44 & 2246 & 2652.15997942359 & -406.159979423594 \tabularnewline
45 & 3434 & 2585.71097133426 & 848.289028665737 \tabularnewline
46 & 4316 & 3092.74255974565 & 1223.25744025435 \tabularnewline
47 & 3032 & 3785.64926172549 & -753.649261725492 \tabularnewline
48 & 5296 & 3583.49221285016 & 1712.50778714984 \tabularnewline
49 & 3850 & 4509.42533720078 & -659.425337200782 \tabularnewline
50 & 2098 & 4365.09223943737 & -2267.09223943737 \tabularnewline
51 & 3992 & 3468.21251790819 & 523.787482091807 \tabularnewline
52 & 4860 & 3826.87827127856 & 1033.12172872144 \tabularnewline
53 & 7336 & 4428.65655504754 & 2907.34344495246 \tabularnewline
54 & 9614 & 5911.69632792741 & 3702.30367207259 \tabularnewline
55 & 2988 & 7805.33568168095 & -4817.33568168095 \tabularnewline
56 & 2756 & 5818.22950725546 & -3062.22950725546 \tabularnewline
57 & 3540 & 4570.14073223192 & -1030.14073223192 \tabularnewline
58 & 2710 & 4215.19480444775 & -1505.19480444775 \tabularnewline
59 & 3730 & 3625.42486996486 & 104.575130035137 \tabularnewline
60 & 3508 & 3756.9044501129 & -248.904450112898 \tabularnewline
61 & 2640 & 3726.64105973911 & -1086.64105973911 \tabularnewline
62 & 2788 & 3305.64627485746 & -517.646274857461 \tabularnewline
63 & 3502 & 3131.31906649879 & 370.680933501206 \tabularnewline
64 & 3700 & 3359.668085205 & 340.331914794999 \tabularnewline
65 & 3250 & 3579.52220110133 & -329.522201101332 \tabularnewline
66 & 4866 & 3494.98787859967 & 1371.01212140033 \tabularnewline
67 & 2836 & 4191.16088734077 & -1355.16088734077 \tabularnewline
68 & 3498 & 3648.32373677575 & -150.323736775755 \tabularnewline
69 & 3468 & 3641.90024270662 & -173.900242706621 \tabularnewline
70 & 3924 & 3622.34385703887 & 301.656142961131 \tabularnewline
71 & 5738 & 3819.89451961594 & 1918.10548038406 \tabularnewline
72 & 7028 & 4768.71577194957 & 2259.28422805043 \tabularnewline
73 & 5608 & 5903.74994611258 & -295.749946112581 \tabularnewline
74 & 6030 & 5892.07911468166 & 137.920885318335 \tabularnewline
75 & 11976 & 6076.3484242121 & 5899.6515757879 \tabularnewline
76 & 7774 & 8924.50106838423 & -1150.50106838423 \tabularnewline
77 & 7906 & 8603.54406970094 & -697.544069700936 \tabularnewline
78 & 10940 & 8474.69506734609 & 2465.30493265391 \tabularnewline
79 & 7626 & 9796.63314097222 & -2170.63314097222 \tabularnewline
80 & 5930 & 9013.59314902605 & -3083.59314902605 \tabularnewline
81 & 6286 & 7776.42194045191 & -1490.42194045191 \tabularnewline
82 & 6788 & 7229.30221815909 & -441.302218159095 \tabularnewline
83 & 6932 & 7144.64081507343 & -212.640815073431 \tabularnewline
84 & 6660 & 7159.03868658976 & -499.038686589756 \tabularnewline
85 & 4910 & 7037.95542433678 & -2127.95542433678 \tabularnewline
86 & 4182 & 6156.899389104 & -1974.899389104 \tabularnewline
87 & 3550 & 5314.83068711697 & -1764.83068711697 \tabularnewline
88 & 3184 & 4540.36991202833 & -1356.36991202833 \tabularnewline
89 & 3872 & 3928.3025848571 & -56.3025848571028 \tabularnewline
90 & 3226 & 3896.62570734209 & -670.625707342092 \tabularnewline
91 & 2504 & 3580.30206525094 & -1076.30206525094 \tabularnewline
92 & 3648 & 3066.56521344436 & 581.434786555644 \tabularnewline
93 & 4448 & 3302.63146344802 & 1145.36853655198 \tabularnewline
94 & 2954 & 3807.89370657142 & -853.893706571423 \tabularnewline
95 & 3842 & 3406.60318236097 & 435.396817639025 \tabularnewline
96 & 3982 & 3588.21496897978 & 393.785031020218 \tabularnewline
97 & 4864 & 3757.0933745187 & 1106.9066254813 \tabularnewline
98 & 6796 & 4261.2928138723 & 2534.7071861277 \tabularnewline
99 & 5844 & 5441.6142526944 & 402.385747305599 \tabularnewline
100 & 5656 & 5674.62301692708 & -18.623016927083 \tabularnewline
101 & 6118 & 5719.13096603943 & 398.869033960575 \tabularnewline
102 & 7068 & 5956.2359372968 & 1111.7640627032 \tabularnewline
103 & 7696 & 6528.63306147349 & 1167.36693852651 \tabularnewline
104 & 7016 & 7143.29124193513 & -127.291241935127 \tabularnewline
105 & 5820 & 7177.24038485194 & -1357.24038485194 \tabularnewline
106 & 4904 & 6641.07515071245 & -1737.07515071245 \tabularnewline
107 & 3860 & 5909.19952659865 & -2049.19952659865 \tabularnewline
108 & 7222 & 5007.2323114299 & 2214.7676885701 \tabularnewline
109 & 7738 & 6044.60159712304 & 1693.39840287696 \tabularnewline
110 & 7142 & 6874.12286427411 & 267.877135725892 \tabularnewline
111 & 13804 & 7070.32016084849 & 6733.67983915151 \tabularnewline
112 & 7964 & 10257.6080851657 & -2293.60808516569 \tabularnewline
113 & 9716 & 9374.81465400576 & 341.185345994245 \tabularnewline
114 & 8462 & 9675.06205123911 & -1213.06205123911 \tabularnewline
115 & 6884 & 9262.35820009294 & -2378.35820009294 \tabularnewline
116 & 8072 & 8293.22269122668 & -221.222691226678 \tabularnewline
117 & 7320 & 8285.19430364346 & -965.19430364346 \tabularnewline
118 & 11700 & 7930.165109335 & 3769.834890665 \tabularnewline
119 & 10792 & 9748.25511450108 & 1043.74488549892 \tabularnewline
120 & 10930 & 10363.1333156008 & 566.86668439917 \tabularnewline
121 & 7112 & 10773.2608598083 & -3661.2608598083 \tabularnewline
122 & 8196 & 9238.51165314859 & -1042.51165314859 \tabularnewline
123 & 16818 & 8859.00306809796 & 7958.99693190204 \tabularnewline
124 & 10524 & 12622.5062388862 & -2098.50623888619 \tabularnewline
125 & 14878 & 11858.2512983399 & 3019.7487016601 \tabularnewline
126 & 13696 & 13427.2650755568 & 268.734924443166 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300729&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]3[/C][C]1350[/C][C]1778[/C][C]-428[/C][/ROW]
[ROW][C]4[/C][C]716[/C][C]1974.27085445351[/C][C]-1258.27085445351[/C][/ROW]
[ROW][C]5[/C][C]2068[/C][C]1780.58953977778[/C][C]287.410460222216[/C][/ROW]
[ROW][C]6[/C][C]1392[/C][C]2282.23079710328[/C][C]-890.230797103284[/C][/ROW]
[ROW][C]7[/C][C]734[/C][C]2244.10517209776[/C][C]-1510.10517209776[/C][/ROW]
[ROW][C]8[/C][C]758[/C][C]1906.33656142507[/C][C]-1148.33656142507[/C][/ROW]
[ROW][C]9[/C][C]558[/C][C]1713.18764021994[/C][C]-1155.18764021994[/C][/ROW]
[ROW][C]10[/C][C]1620[/C][C]1499.75501439981[/C][C]120.244985600189[/C][/ROW]
[ROW][C]11[/C][C]3132[/C][C]1858.33108842674[/C][C]1273.66891157326[/C][/ROW]
[ROW][C]12[/C][C]1392[/C][C]2751.56307406988[/C][C]-1359.56307406988[/C][/ROW]
[ROW][C]13[/C][C]918[/C][C]2447.27103863642[/C][C]-1529.27103863642[/C][/ROW]
[ROW][C]14[/C][C]776[/C][C]2044.30920516728[/C][C]-1268.30920516728[/C][/ROW]
[ROW][C]15[/C][C]1348[/C][C]1739.11023289823[/C][C]-391.110232898232[/C][/ROW]
[ROW][C]16[/C][C]502[/C][C]1820.25605136992[/C][C]-1318.25605136992[/C][/ROW]
[ROW][C]17[/C][C]1274[/C][C]1467.24494620943[/C][C]-193.244946209429[/C][/ROW]
[ROW][C]18[/C][C]1638[/C][C]1614.31929503801[/C][C]23.6807049619879[/C][/ROW]
[ROW][C]19[/C][C]912[/C][C]1858.72905715859[/C][C]-946.729057158589[/C][/ROW]
[ROW][C]20[/C][C]1250[/C][C]1655.17806611844[/C][C]-405.178066118443[/C][/ROW]
[ROW][C]21[/C][C]1614[/C][C]1687.70177078797[/C][C]-73.7017707879722[/C][/ROW]
[ROW][C]22[/C][C]2840[/C][C]1867.32209783576[/C][C]972.677902164244[/C][/ROW]
[ROW][C]23[/C][C]1150[/C][C]2529.25438035224[/C][C]-1379.25438035224[/C][/ROW]
[ROW][C]24[/C][C]1652[/C][C]2119.131631526[/C][C]-467.131631526005[/C][/ROW]
[ROW][C]25[/C][C]1526[/C][C]2109.83400412386[/C][C]-583.834004123856[/C][/ROW]
[ROW][C]26[/C][C]1412[/C][C]2039.65807076008[/C][C]-627.658070760084[/C][/ROW]
[ROW][C]27[/C][C]882[/C][C]1940.53272249734[/C][C]-1058.53272249734[/C][/ROW]
[ROW][C]28[/C][C]848[/C][C]1632.99348845703[/C][C]-784.993488457028[/C][/ROW]
[ROW][C]29[/C][C]820[/C][C]1436.04511805873[/C][C]-616.045118058731[/C][/ROW]
[ROW][C]30[/C][C]1226[/C][C]1305.44604311589[/C][C]-79.4460431158905[/C][/ROW]
[ROW][C]31[/C][C]1212[/C][C]1413.56356790919[/C][C]-201.563567909185[/C][/ROW]
[ROW][C]32[/C][C]2110[/C][C]1464.08042470439[/C][C]645.919575295609[/C][/ROW]
[ROW][C]33[/C][C]1178[/C][C]1903.1161493615[/C][C]-725.116149361505[/C][/ROW]
[ROW][C]34[/C][C]2548[/C][C]1718.38425365548[/C][C]829.615746344522[/C][/ROW]
[ROW][C]35[/C][C]1568[/C][C]2241.10405907727[/C][C]-673.104059077268[/C][/ROW]
[ROW][C]36[/C][C]2088[/C][C]2081.95872461321[/C][C]6.04127538679086[/C][/ROW]
[ROW][C]37[/C][C]2178[/C][C]2226.53348323333[/C][C]-48.5334832333324[/C][/ROW]
[ROW][C]38[/C][C]3016[/C][C]2345.98563659089[/C][C]670.014363409107[/C][/ROW]
[ROW][C]39[/C][C]5514[/C][C]2796.67188352877[/C][C]2717.32811647123[/C][/ROW]
[ROW][C]40[/C][C]1358[/C][C]4203.17241229432[/C][C]-2845.17241229432[/C][/ROW]
[ROW][C]41[/C][C]3604[/C][C]3080.39484941005[/C][C]523.605150589954[/C][/ROW]
[ROW][C]42[/C][C]1962[/C][C]3471.52468527389[/C][C]-1509.52468527389[/C][/ROW]
[ROW][C]43[/C][C]2036[/C][C]2931.1866451124[/C][C]-895.186645112403[/C][/ROW]
[ROW][C]44[/C][C]2246[/C][C]2652.15997942359[/C][C]-406.159979423594[/C][/ROW]
[ROW][C]45[/C][C]3434[/C][C]2585.71097133426[/C][C]848.289028665737[/C][/ROW]
[ROW][C]46[/C][C]4316[/C][C]3092.74255974565[/C][C]1223.25744025435[/C][/ROW]
[ROW][C]47[/C][C]3032[/C][C]3785.64926172549[/C][C]-753.649261725492[/C][/ROW]
[ROW][C]48[/C][C]5296[/C][C]3583.49221285016[/C][C]1712.50778714984[/C][/ROW]
[ROW][C]49[/C][C]3850[/C][C]4509.42533720078[/C][C]-659.425337200782[/C][/ROW]
[ROW][C]50[/C][C]2098[/C][C]4365.09223943737[/C][C]-2267.09223943737[/C][/ROW]
[ROW][C]51[/C][C]3992[/C][C]3468.21251790819[/C][C]523.787482091807[/C][/ROW]
[ROW][C]52[/C][C]4860[/C][C]3826.87827127856[/C][C]1033.12172872144[/C][/ROW]
[ROW][C]53[/C][C]7336[/C][C]4428.65655504754[/C][C]2907.34344495246[/C][/ROW]
[ROW][C]54[/C][C]9614[/C][C]5911.69632792741[/C][C]3702.30367207259[/C][/ROW]
[ROW][C]55[/C][C]2988[/C][C]7805.33568168095[/C][C]-4817.33568168095[/C][/ROW]
[ROW][C]56[/C][C]2756[/C][C]5818.22950725546[/C][C]-3062.22950725546[/C][/ROW]
[ROW][C]57[/C][C]3540[/C][C]4570.14073223192[/C][C]-1030.14073223192[/C][/ROW]
[ROW][C]58[/C][C]2710[/C][C]4215.19480444775[/C][C]-1505.19480444775[/C][/ROW]
[ROW][C]59[/C][C]3730[/C][C]3625.42486996486[/C][C]104.575130035137[/C][/ROW]
[ROW][C]60[/C][C]3508[/C][C]3756.9044501129[/C][C]-248.904450112898[/C][/ROW]
[ROW][C]61[/C][C]2640[/C][C]3726.64105973911[/C][C]-1086.64105973911[/C][/ROW]
[ROW][C]62[/C][C]2788[/C][C]3305.64627485746[/C][C]-517.646274857461[/C][/ROW]
[ROW][C]63[/C][C]3502[/C][C]3131.31906649879[/C][C]370.680933501206[/C][/ROW]
[ROW][C]64[/C][C]3700[/C][C]3359.668085205[/C][C]340.331914794999[/C][/ROW]
[ROW][C]65[/C][C]3250[/C][C]3579.52220110133[/C][C]-329.522201101332[/C][/ROW]
[ROW][C]66[/C][C]4866[/C][C]3494.98787859967[/C][C]1371.01212140033[/C][/ROW]
[ROW][C]67[/C][C]2836[/C][C]4191.16088734077[/C][C]-1355.16088734077[/C][/ROW]
[ROW][C]68[/C][C]3498[/C][C]3648.32373677575[/C][C]-150.323736775755[/C][/ROW]
[ROW][C]69[/C][C]3468[/C][C]3641.90024270662[/C][C]-173.900242706621[/C][/ROW]
[ROW][C]70[/C][C]3924[/C][C]3622.34385703887[/C][C]301.656142961131[/C][/ROW]
[ROW][C]71[/C][C]5738[/C][C]3819.89451961594[/C][C]1918.10548038406[/C][/ROW]
[ROW][C]72[/C][C]7028[/C][C]4768.71577194957[/C][C]2259.28422805043[/C][/ROW]
[ROW][C]73[/C][C]5608[/C][C]5903.74994611258[/C][C]-295.749946112581[/C][/ROW]
[ROW][C]74[/C][C]6030[/C][C]5892.07911468166[/C][C]137.920885318335[/C][/ROW]
[ROW][C]75[/C][C]11976[/C][C]6076.3484242121[/C][C]5899.6515757879[/C][/ROW]
[ROW][C]76[/C][C]7774[/C][C]8924.50106838423[/C][C]-1150.50106838423[/C][/ROW]
[ROW][C]77[/C][C]7906[/C][C]8603.54406970094[/C][C]-697.544069700936[/C][/ROW]
[ROW][C]78[/C][C]10940[/C][C]8474.69506734609[/C][C]2465.30493265391[/C][/ROW]
[ROW][C]79[/C][C]7626[/C][C]9796.63314097222[/C][C]-2170.63314097222[/C][/ROW]
[ROW][C]80[/C][C]5930[/C][C]9013.59314902605[/C][C]-3083.59314902605[/C][/ROW]
[ROW][C]81[/C][C]6286[/C][C]7776.42194045191[/C][C]-1490.42194045191[/C][/ROW]
[ROW][C]82[/C][C]6788[/C][C]7229.30221815909[/C][C]-441.302218159095[/C][/ROW]
[ROW][C]83[/C][C]6932[/C][C]7144.64081507343[/C][C]-212.640815073431[/C][/ROW]
[ROW][C]84[/C][C]6660[/C][C]7159.03868658976[/C][C]-499.038686589756[/C][/ROW]
[ROW][C]85[/C][C]4910[/C][C]7037.95542433678[/C][C]-2127.95542433678[/C][/ROW]
[ROW][C]86[/C][C]4182[/C][C]6156.899389104[/C][C]-1974.899389104[/C][/ROW]
[ROW][C]87[/C][C]3550[/C][C]5314.83068711697[/C][C]-1764.83068711697[/C][/ROW]
[ROW][C]88[/C][C]3184[/C][C]4540.36991202833[/C][C]-1356.36991202833[/C][/ROW]
[ROW][C]89[/C][C]3872[/C][C]3928.3025848571[/C][C]-56.3025848571028[/C][/ROW]
[ROW][C]90[/C][C]3226[/C][C]3896.62570734209[/C][C]-670.625707342092[/C][/ROW]
[ROW][C]91[/C][C]2504[/C][C]3580.30206525094[/C][C]-1076.30206525094[/C][/ROW]
[ROW][C]92[/C][C]3648[/C][C]3066.56521344436[/C][C]581.434786555644[/C][/ROW]
[ROW][C]93[/C][C]4448[/C][C]3302.63146344802[/C][C]1145.36853655198[/C][/ROW]
[ROW][C]94[/C][C]2954[/C][C]3807.89370657142[/C][C]-853.893706571423[/C][/ROW]
[ROW][C]95[/C][C]3842[/C][C]3406.60318236097[/C][C]435.396817639025[/C][/ROW]
[ROW][C]96[/C][C]3982[/C][C]3588.21496897978[/C][C]393.785031020218[/C][/ROW]
[ROW][C]97[/C][C]4864[/C][C]3757.0933745187[/C][C]1106.9066254813[/C][/ROW]
[ROW][C]98[/C][C]6796[/C][C]4261.2928138723[/C][C]2534.7071861277[/C][/ROW]
[ROW][C]99[/C][C]5844[/C][C]5441.6142526944[/C][C]402.385747305599[/C][/ROW]
[ROW][C]100[/C][C]5656[/C][C]5674.62301692708[/C][C]-18.623016927083[/C][/ROW]
[ROW][C]101[/C][C]6118[/C][C]5719.13096603943[/C][C]398.869033960575[/C][/ROW]
[ROW][C]102[/C][C]7068[/C][C]5956.2359372968[/C][C]1111.7640627032[/C][/ROW]
[ROW][C]103[/C][C]7696[/C][C]6528.63306147349[/C][C]1167.36693852651[/C][/ROW]
[ROW][C]104[/C][C]7016[/C][C]7143.29124193513[/C][C]-127.291241935127[/C][/ROW]
[ROW][C]105[/C][C]5820[/C][C]7177.24038485194[/C][C]-1357.24038485194[/C][/ROW]
[ROW][C]106[/C][C]4904[/C][C]6641.07515071245[/C][C]-1737.07515071245[/C][/ROW]
[ROW][C]107[/C][C]3860[/C][C]5909.19952659865[/C][C]-2049.19952659865[/C][/ROW]
[ROW][C]108[/C][C]7222[/C][C]5007.2323114299[/C][C]2214.7676885701[/C][/ROW]
[ROW][C]109[/C][C]7738[/C][C]6044.60159712304[/C][C]1693.39840287696[/C][/ROW]
[ROW][C]110[/C][C]7142[/C][C]6874.12286427411[/C][C]267.877135725892[/C][/ROW]
[ROW][C]111[/C][C]13804[/C][C]7070.32016084849[/C][C]6733.67983915151[/C][/ROW]
[ROW][C]112[/C][C]7964[/C][C]10257.6080851657[/C][C]-2293.60808516569[/C][/ROW]
[ROW][C]113[/C][C]9716[/C][C]9374.81465400576[/C][C]341.185345994245[/C][/ROW]
[ROW][C]114[/C][C]8462[/C][C]9675.06205123911[/C][C]-1213.06205123911[/C][/ROW]
[ROW][C]115[/C][C]6884[/C][C]9262.35820009294[/C][C]-2378.35820009294[/C][/ROW]
[ROW][C]116[/C][C]8072[/C][C]8293.22269122668[/C][C]-221.222691226678[/C][/ROW]
[ROW][C]117[/C][C]7320[/C][C]8285.19430364346[/C][C]-965.19430364346[/C][/ROW]
[ROW][C]118[/C][C]11700[/C][C]7930.165109335[/C][C]3769.834890665[/C][/ROW]
[ROW][C]119[/C][C]10792[/C][C]9748.25511450108[/C][C]1043.74488549892[/C][/ROW]
[ROW][C]120[/C][C]10930[/C][C]10363.1333156008[/C][C]566.86668439917[/C][/ROW]
[ROW][C]121[/C][C]7112[/C][C]10773.2608598083[/C][C]-3661.2608598083[/C][/ROW]
[ROW][C]122[/C][C]8196[/C][C]9238.51165314859[/C][C]-1042.51165314859[/C][/ROW]
[ROW][C]123[/C][C]16818[/C][C]8859.00306809796[/C][C]7958.99693190204[/C][/ROW]
[ROW][C]124[/C][C]10524[/C][C]12622.5062388862[/C][C]-2098.50623888619[/C][/ROW]
[ROW][C]125[/C][C]14878[/C][C]11858.2512983399[/C][C]3019.7487016601[/C][/ROW]
[ROW][C]126[/C][C]13696[/C][C]13427.2650755568[/C][C]268.734924443166[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300729&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300729&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
313501778-428
47161974.27085445351-1258.27085445351
520681780.58953977778287.410460222216
613922282.23079710328-890.230797103284
77342244.10517209776-1510.10517209776
87581906.33656142507-1148.33656142507
95581713.18764021994-1155.18764021994
1016201499.75501439981120.244985600189
1131321858.331088426741273.66891157326
1213922751.56307406988-1359.56307406988
139182447.27103863642-1529.27103863642
147762044.30920516728-1268.30920516728
1513481739.11023289823-391.110232898232
165021820.25605136992-1318.25605136992
1712741467.24494620943-193.244946209429
1816381614.3192950380123.6807049619879
199121858.72905715859-946.729057158589
2012501655.17806611844-405.178066118443
2116141687.70177078797-73.7017707879722
2228401867.32209783576972.677902164244
2311502529.25438035224-1379.25438035224
2416522119.131631526-467.131631526005
2515262109.83400412386-583.834004123856
2614122039.65807076008-627.658070760084
278821940.53272249734-1058.53272249734
288481632.99348845703-784.993488457028
298201436.04511805873-616.045118058731
3012261305.44604311589-79.4460431158905
3112121413.56356790919-201.563567909185
3221101464.08042470439645.919575295609
3311781903.1161493615-725.116149361505
3425481718.38425365548829.615746344522
3515682241.10405907727-673.104059077268
3620882081.958724613216.04127538679086
3721782226.53348323333-48.5334832333324
3830162345.98563659089670.014363409107
3955142796.671883528772717.32811647123
4013584203.17241229432-2845.17241229432
4136043080.39484941005523.605150589954
4219623471.52468527389-1509.52468527389
4320362931.1866451124-895.186645112403
4422462652.15997942359-406.159979423594
4534342585.71097133426848.289028665737
4643163092.742559745651223.25744025435
4730323785.64926172549-753.649261725492
4852963583.492212850161712.50778714984
4938504509.42533720078-659.425337200782
5020984365.09223943737-2267.09223943737
5139923468.21251790819523.787482091807
5248603826.878271278561033.12172872144
5373364428.656555047542907.34344495246
5496145911.696327927413702.30367207259
5529887805.33568168095-4817.33568168095
5627565818.22950725546-3062.22950725546
5735404570.14073223192-1030.14073223192
5827104215.19480444775-1505.19480444775
5937303625.42486996486104.575130035137
6035083756.9044501129-248.904450112898
6126403726.64105973911-1086.64105973911
6227883305.64627485746-517.646274857461
6335023131.31906649879370.680933501206
6437003359.668085205340.331914794999
6532503579.52220110133-329.522201101332
6648663494.987878599671371.01212140033
6728364191.16088734077-1355.16088734077
6834983648.32373677575-150.323736775755
6934683641.90024270662-173.900242706621
7039243622.34385703887301.656142961131
7157383819.894519615941918.10548038406
7270284768.715771949572259.28422805043
7356085903.74994611258-295.749946112581
7460305892.07911468166137.920885318335
75119766076.34842421215899.6515757879
7677748924.50106838423-1150.50106838423
7779068603.54406970094-697.544069700936
78109408474.695067346092465.30493265391
7976269796.63314097222-2170.63314097222
8059309013.59314902605-3083.59314902605
8162867776.42194045191-1490.42194045191
8267887229.30221815909-441.302218159095
8369327144.64081507343-212.640815073431
8466607159.03868658976-499.038686589756
8549107037.95542433678-2127.95542433678
8641826156.899389104-1974.899389104
8735505314.83068711697-1764.83068711697
8831844540.36991202833-1356.36991202833
8938723928.3025848571-56.3025848571028
9032263896.62570734209-670.625707342092
9125043580.30206525094-1076.30206525094
9236483066.56521344436581.434786555644
9344483302.631463448021145.36853655198
9429543807.89370657142-853.893706571423
9538423406.60318236097435.396817639025
9639823588.21496897978393.785031020218
9748643757.09337451871106.9066254813
9867964261.29281387232534.7071861277
9958445441.6142526944402.385747305599
10056565674.62301692708-18.623016927083
10161185719.13096603943398.869033960575
10270685956.23593729681111.7640627032
10376966528.633061473491167.36693852651
10470167143.29124193513-127.291241935127
10558207177.24038485194-1357.24038485194
10649046641.07515071245-1737.07515071245
10738605909.19952659865-2049.19952659865
10872225007.23231142992214.7676885701
10977386044.601597123041693.39840287696
11071426874.12286427411267.877135725892
111138047070.320160848496733.67983915151
112796410257.6080851657-2293.60808516569
11397169374.81465400576341.185345994245
11484629675.06205123911-1213.06205123911
11568849262.35820009294-2378.35820009294
11680728293.22269122668-221.222691226678
11773208285.19430364346-965.19430364346
118117007930.1651093353769.834890665
119107929748.255114501081043.74488549892
1201093010363.1333156008566.86668439917
121711210773.2608598083-3661.2608598083
12281969238.51165314859-1042.51165314859
123168188859.003068097967958.99693190204
1241052412622.5062388862-2098.50623888619
1251487811858.25129833993019.7487016601
1261369613427.2650755568268.734924443166







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12713770.370893370610233.726819054417307.0149676869
12813993.331596326710097.51434754117889.1488451124
12914216.29229928279971.0603818566318461.5242167088
13014439.25300223889851.5284584080319026.9775460695
13114662.21370519489736.9097958693719587.5176145202
13214885.17440815089625.7296131690620144.6192031326
13315108.13511110699516.8742033974320699.3960188163
13415331.09581406299409.4833013808821252.708326745
13515554.0565170199302.8800373826721805.2329966553
13615777.0172199759196.5236505703722357.5107893796
13715999.9779229319089.9765731565722909.9792727055
13816222.93862588718982.8809133018423462.9963384723
13916445.89932884318874.9412724743524016.8573852119
14016668.86003179928765.91194425924571.8081193393
14116891.82073475528655.587213173725128.0542563367
14217114.78143771138543.7938910175125685.768984405
14317337.74214066738430.3854970663226245.0987842683
14417560.70284362338315.2376651981726806.1680220485

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 13770.3708933706 & 10233.7268190544 & 17307.0149676869 \tabularnewline
128 & 13993.3315963267 & 10097.514347541 & 17889.1488451124 \tabularnewline
129 & 14216.2922992827 & 9971.06038185663 & 18461.5242167088 \tabularnewline
130 & 14439.2530022388 & 9851.52845840803 & 19026.9775460695 \tabularnewline
131 & 14662.2137051948 & 9736.90979586937 & 19587.5176145202 \tabularnewline
132 & 14885.1744081508 & 9625.72961316906 & 20144.6192031326 \tabularnewline
133 & 15108.1351111069 & 9516.87420339743 & 20699.3960188163 \tabularnewline
134 & 15331.0958140629 & 9409.48330138088 & 21252.708326745 \tabularnewline
135 & 15554.056517019 & 9302.88003738267 & 21805.2329966553 \tabularnewline
136 & 15777.017219975 & 9196.52365057037 & 22357.5107893796 \tabularnewline
137 & 15999.977922931 & 9089.97657315657 & 22909.9792727055 \tabularnewline
138 & 16222.9386258871 & 8982.88091330184 & 23462.9963384723 \tabularnewline
139 & 16445.8993288431 & 8874.94127247435 & 24016.8573852119 \tabularnewline
140 & 16668.8600317992 & 8765.911944259 & 24571.8081193393 \tabularnewline
141 & 16891.8207347552 & 8655.5872131737 & 25128.0542563367 \tabularnewline
142 & 17114.7814377113 & 8543.79389101751 & 25685.768984405 \tabularnewline
143 & 17337.7421406673 & 8430.38549706632 & 26245.0987842683 \tabularnewline
144 & 17560.7028436233 & 8315.23766519817 & 26806.1680220485 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300729&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]13770.3708933706[/C][C]10233.7268190544[/C][C]17307.0149676869[/C][/ROW]
[ROW][C]128[/C][C]13993.3315963267[/C][C]10097.514347541[/C][C]17889.1488451124[/C][/ROW]
[ROW][C]129[/C][C]14216.2922992827[/C][C]9971.06038185663[/C][C]18461.5242167088[/C][/ROW]
[ROW][C]130[/C][C]14439.2530022388[/C][C]9851.52845840803[/C][C]19026.9775460695[/C][/ROW]
[ROW][C]131[/C][C]14662.2137051948[/C][C]9736.90979586937[/C][C]19587.5176145202[/C][/ROW]
[ROW][C]132[/C][C]14885.1744081508[/C][C]9625.72961316906[/C][C]20144.6192031326[/C][/ROW]
[ROW][C]133[/C][C]15108.1351111069[/C][C]9516.87420339743[/C][C]20699.3960188163[/C][/ROW]
[ROW][C]134[/C][C]15331.0958140629[/C][C]9409.48330138088[/C][C]21252.708326745[/C][/ROW]
[ROW][C]135[/C][C]15554.056517019[/C][C]9302.88003738267[/C][C]21805.2329966553[/C][/ROW]
[ROW][C]136[/C][C]15777.017219975[/C][C]9196.52365057037[/C][C]22357.5107893796[/C][/ROW]
[ROW][C]137[/C][C]15999.977922931[/C][C]9089.97657315657[/C][C]22909.9792727055[/C][/ROW]
[ROW][C]138[/C][C]16222.9386258871[/C][C]8982.88091330184[/C][C]23462.9963384723[/C][/ROW]
[ROW][C]139[/C][C]16445.8993288431[/C][C]8874.94127247435[/C][C]24016.8573852119[/C][/ROW]
[ROW][C]140[/C][C]16668.8600317992[/C][C]8765.911944259[/C][C]24571.8081193393[/C][/ROW]
[ROW][C]141[/C][C]16891.8207347552[/C][C]8655.5872131737[/C][C]25128.0542563367[/C][/ROW]
[ROW][C]142[/C][C]17114.7814377113[/C][C]8543.79389101751[/C][C]25685.768984405[/C][/ROW]
[ROW][C]143[/C][C]17337.7421406673[/C][C]8430.38549706632[/C][C]26245.0987842683[/C][/ROW]
[ROW][C]144[/C][C]17560.7028436233[/C][C]8315.23766519817[/C][C]26806.1680220485[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300729&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300729&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
12713770.370893370610233.726819054417307.0149676869
12813993.331596326710097.51434754117889.1488451124
12914216.29229928279971.0603818566318461.5242167088
13014439.25300223889851.5284584080319026.9775460695
13114662.21370519489736.9097958693719587.5176145202
13214885.17440815089625.7296131690620144.6192031326
13315108.13511110699516.8742033974320699.3960188163
13415331.09581406299409.4833013808821252.708326745
13515554.0565170199302.8800373826721805.2329966553
13615777.0172199759196.5236505703722357.5107893796
13715999.9779229319089.9765731565722909.9792727055
13816222.93862588718982.8809133018423462.9963384723
13916445.89932884318874.9412724743524016.8573852119
14016668.86003179928765.91194425924571.8081193393
14116891.82073475528655.587213173725128.0542563367
14217114.78143771138543.7938910175125685.768984405
14317337.74214066738430.3854970663226245.0987842683
14417560.70284362338315.2376651981726806.1680220485



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 18 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')