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 computationMon, 27 Dec 2010 18:28:16 +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/2010/Dec/27/t1293474378giqx8j1yw3e8udc.htm/, Retrieved Mon, 06 May 2024 13:52:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116076, Retrieved Mon, 06 May 2024 13:52:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact158
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:56:43] [74be16979710d4c4e7c6647856088456]
-  MPD    [Exponential Smoothing] [Aantal openstaand...] [2010-12-27 18:28:16] [f0b33ae54e73edcd25a3e2f31270d1c9] [Current]
Feedback Forum

Post a new message
Dataseries X:
27.951
29.781
32.914
33.488
35.652
36.488
35.387
35.676
34.844
32.447
31.068
29.010
29.812
30.951
32.974
32.936
34.012
32.946
31.948
30.599
27.691
25.073
23.406
22.248
22.896
25.317
26.558
26.471
27.543
26.198
24.725
25.005
23.462
20.780
19.815
19.761
21.454
23.899
24.939
23.580
24.562
24.696
23.785
23.812
21.917
19.713
19.282
18.788
21.453
24.482
27.474
27.264
27.349
30.632
29.429
30.084
26.290
24.379
23.335
21.346
21.106
24.514
28.353
30.805
31.348
34.556
33.855
34.787
32.529
29.998
29.257
28.155
30.466
35.704
39.327
39.351
42.234
43.630
43.722
43.121
37.985
37.135
34.646
33.026
35.087
38.846
42.013
43.908
42.868
44.423
44.167
43.636
44.382
42.142
43.452
36.912
42.413
45.344
44.873
47.510
49.554
47.369
45.998
48.140
48.441
44.928
40.454
38.661
37.246
36.843
36.424
37.594
38.144
38.737
34.560
36.080
33.508
35.462
33.374
32.110
35.533
35.532
37.903
36.763
40.399
44.164
44.496
43.110
43.880
43.930
44.327




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116076&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116076&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116076&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 time3 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.94592858766538
beta0.0390410580898643
gamma0.774358779506533

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.94592858766538 \tabularnewline
beta & 0.0390410580898643 \tabularnewline
gamma & 0.774358779506533 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116076&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]0.94592858766538[/C][/ROW]
[ROW][C]beta[/C][C]0.0390410580898643[/C][/ROW]
[ROW][C]gamma[/C][C]0.774358779506533[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116076&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116076&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
alpha0.94592858766538
beta0.0390410580898643
gamma0.774358779506533







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1329.81230.4108518601392-0.598851860139202
1430.95131.0277203611790-0.0767203611790386
1532.97433.1828321772309-0.208832177230875
1632.93633.249221569499-0.313221569499035
1734.01234.3593559417831-0.347355941783128
1832.94633.2493306419754-0.303330641975421
1931.94831.65535680191760.292643198082377
2030.59931.7001352790484-1.10113527904840
2127.69129.4968068936204-1.80580689362036
2225.07325.4577397593152-0.384739759315206
2323.40623.6621771137398-0.256177113739838
2422.24821.59782796163870.650172038361298
2522.89622.60714867557630.288851324423700
2625.31723.62048087685031.69651912314973
2726.55826.9221072279287-0.36410722792866
2826.47126.6602191539865-0.189219153986528
2927.54327.47894514098190.0640548590181105
3026.19826.7928178426481-0.594817842648137
3124.72525.0794719940671-0.354471994067122
3225.00524.35803847689440.646961523105634
3323.46223.9090564767751-0.447056476775064
3420.7821.5302491452802-0.750249145280151
3519.81519.58431792413240.230682075867612
3619.76118.26562268815291.49537731184706
3721.45420.03942024646131.41457975353869
3823.89922.20994593374191.68905406625807
3924.93925.4276607847813-0.488660784781327
4023.5825.1501356347057-1.57013563470565
4124.56224.5980484598158-0.0360484598158379
4224.69623.90002450067620.795975499323752
4323.78523.67485719581570.110142804184282
4423.81223.56870955402760.24329044597237
4521.91722.8451750415451-0.928175041545053
4619.71320.1933602161703-0.480360216170343
4719.28218.68472408594580.597275914054247
4818.78817.90122600287840.886773997121558
4921.45319.14614626960942.30685373039060
5024.48222.28977160733212.19222839266788
5127.47426.08548054118821.3885194588118
5227.26427.8050665240494-0.54106652404943
5327.34928.7855240097176-1.43652400971756
5430.63226.99310881340423.63889118659579
5529.42929.5911524772775-0.162152477277477
5630.08429.57360491931550.510395080684464
5726.2929.1809859682926-2.89098596829262
5824.37924.6190217369547-0.240021736954745
5923.33523.444077155783-0.109077155783009
6021.34621.9685466339507-0.622546633950737
6121.10622.0727240154377-0.96672401543771
6224.51422.11286160553652.40113839446347
6328.35326.09356926175282.25943073824721
6430.80528.62805531986372.17694468013628
6531.34832.5008305921727-1.15283059217267
6634.55631.33555556805003.22044443194997
6733.85533.41169220475950.443307795240472
6834.78734.20056288908660.586437110913359
6932.52933.7395689877443-1.21056898774427
7029.99830.7127497827325-0.714749782732468
7129.25729.09508643245810.161913567541873
7228.15527.719528695220.435471304779995
7330.46629.3037962070331.16220379296698
7435.70432.37768414883723.32631585116278
7539.32738.4205232333710.906476766628963
7639.35140.1684440499140-0.817444049913959
7742.23441.76848900501560.465510994984413
7843.6342.6391538634730.990846136527011
7943.72242.38900930035291.33299069964707
8043.12144.3427201392084-1.22172013920841
8137.98541.9708497812421-3.9858497812421
8237.13536.07136923631261.06363076368743
8334.64636.0739805912821-1.42798059128206
8433.02632.97923187492460.04676812507536
8535.08734.47566887717950.611331122820509
8638.84637.43757045688021.40842954311976
8742.01341.75500787987060.257992120129366
8843.90842.79929969734381.10870030265615
8942.86846.5348530217785-3.66685302177846
9044.42343.39112112163811.03187887836193
9144.16743.04349329919011.12350670080986
9243.63644.5618201396121-0.925820139612135
9344.38242.20103833733692.18096166266308
9442.14242.09908649920320.0429135007968355
9543.45240.91017559490562.54182440509438
9636.91241.3642332326973-4.45223323269729
9742.41338.82291769154383.59008230845622
9845.34445.23102721237830.112972787621679
9944.87348.8288267624973-3.95582676249727
10047.5145.91717102565381.59282897434619
10149.55450.0413328798024-0.487332879802373
10247.36950.2350603672695-2.86606036726945
10345.99846.0411439298867-0.0431439298867033
10448.1446.27854693588061.86145306411944
10548.44146.52518810006331.91581189993671
10644.92845.8500197481911-0.922019748191069
10740.45443.7143775324225-3.2603775324225
10838.66138.30326069482230.357739305177731
10937.24640.6562035443757-3.41020354437566
11036.84339.6721259494619-2.82912594946193
11136.42439.2988683660116-2.87486836601157
11237.59437.05426299091560.539737009084412
11338.14439.1388326121083-0.994832612108254
11438.73738.17569277228650.561307227713549
11534.5637.2507179739447-2.69071797394471
11636.0834.54685675245391.5331432475461
11733.50834.4595659913753-0.951565991375311
11835.46231.30865905961574.15334094038426
11933.37433.8781803729084-0.50418037290838
12032.1131.40388702837880.706112971621174
12135.53333.40556207888842.12743792111159
12235.53237.5401587191845-2.00815871918453
12337.90337.85930909424760.0436909057523636
12436.76338.6635397739057-1.90053977390566
12540.39938.36870623368442.03029376631564
12644.16440.48262847077933.68137152922071
12744.49642.4127960557422.08320394425800
12843.1144.8981254831121-1.78812548311215
12943.8841.56417136882542.31582863117459
13043.9341.52121164369012.40878835630993
13144.32742.19744920510252.12955079489754

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 29.812 & 30.4108518601392 & -0.598851860139202 \tabularnewline
14 & 30.951 & 31.0277203611790 & -0.0767203611790386 \tabularnewline
15 & 32.974 & 33.1828321772309 & -0.208832177230875 \tabularnewline
16 & 32.936 & 33.249221569499 & -0.313221569499035 \tabularnewline
17 & 34.012 & 34.3593559417831 & -0.347355941783128 \tabularnewline
18 & 32.946 & 33.2493306419754 & -0.303330641975421 \tabularnewline
19 & 31.948 & 31.6553568019176 & 0.292643198082377 \tabularnewline
20 & 30.599 & 31.7001352790484 & -1.10113527904840 \tabularnewline
21 & 27.691 & 29.4968068936204 & -1.80580689362036 \tabularnewline
22 & 25.073 & 25.4577397593152 & -0.384739759315206 \tabularnewline
23 & 23.406 & 23.6621771137398 & -0.256177113739838 \tabularnewline
24 & 22.248 & 21.5978279616387 & 0.650172038361298 \tabularnewline
25 & 22.896 & 22.6071486755763 & 0.288851324423700 \tabularnewline
26 & 25.317 & 23.6204808768503 & 1.69651912314973 \tabularnewline
27 & 26.558 & 26.9221072279287 & -0.36410722792866 \tabularnewline
28 & 26.471 & 26.6602191539865 & -0.189219153986528 \tabularnewline
29 & 27.543 & 27.4789451409819 & 0.0640548590181105 \tabularnewline
30 & 26.198 & 26.7928178426481 & -0.594817842648137 \tabularnewline
31 & 24.725 & 25.0794719940671 & -0.354471994067122 \tabularnewline
32 & 25.005 & 24.3580384768944 & 0.646961523105634 \tabularnewline
33 & 23.462 & 23.9090564767751 & -0.447056476775064 \tabularnewline
34 & 20.78 & 21.5302491452802 & -0.750249145280151 \tabularnewline
35 & 19.815 & 19.5843179241324 & 0.230682075867612 \tabularnewline
36 & 19.761 & 18.2656226881529 & 1.49537731184706 \tabularnewline
37 & 21.454 & 20.0394202464613 & 1.41457975353869 \tabularnewline
38 & 23.899 & 22.2099459337419 & 1.68905406625807 \tabularnewline
39 & 24.939 & 25.4276607847813 & -0.488660784781327 \tabularnewline
40 & 23.58 & 25.1501356347057 & -1.57013563470565 \tabularnewline
41 & 24.562 & 24.5980484598158 & -0.0360484598158379 \tabularnewline
42 & 24.696 & 23.9000245006762 & 0.795975499323752 \tabularnewline
43 & 23.785 & 23.6748571958157 & 0.110142804184282 \tabularnewline
44 & 23.812 & 23.5687095540276 & 0.24329044597237 \tabularnewline
45 & 21.917 & 22.8451750415451 & -0.928175041545053 \tabularnewline
46 & 19.713 & 20.1933602161703 & -0.480360216170343 \tabularnewline
47 & 19.282 & 18.6847240859458 & 0.597275914054247 \tabularnewline
48 & 18.788 & 17.9012260028784 & 0.886773997121558 \tabularnewline
49 & 21.453 & 19.1461462696094 & 2.30685373039060 \tabularnewline
50 & 24.482 & 22.2897716073321 & 2.19222839266788 \tabularnewline
51 & 27.474 & 26.0854805411882 & 1.3885194588118 \tabularnewline
52 & 27.264 & 27.8050665240494 & -0.54106652404943 \tabularnewline
53 & 27.349 & 28.7855240097176 & -1.43652400971756 \tabularnewline
54 & 30.632 & 26.9931088134042 & 3.63889118659579 \tabularnewline
55 & 29.429 & 29.5911524772775 & -0.162152477277477 \tabularnewline
56 & 30.084 & 29.5736049193155 & 0.510395080684464 \tabularnewline
57 & 26.29 & 29.1809859682926 & -2.89098596829262 \tabularnewline
58 & 24.379 & 24.6190217369547 & -0.240021736954745 \tabularnewline
59 & 23.335 & 23.444077155783 & -0.109077155783009 \tabularnewline
60 & 21.346 & 21.9685466339507 & -0.622546633950737 \tabularnewline
61 & 21.106 & 22.0727240154377 & -0.96672401543771 \tabularnewline
62 & 24.514 & 22.1128616055365 & 2.40113839446347 \tabularnewline
63 & 28.353 & 26.0935692617528 & 2.25943073824721 \tabularnewline
64 & 30.805 & 28.6280553198637 & 2.17694468013628 \tabularnewline
65 & 31.348 & 32.5008305921727 & -1.15283059217267 \tabularnewline
66 & 34.556 & 31.3355555680500 & 3.22044443194997 \tabularnewline
67 & 33.855 & 33.4116922047595 & 0.443307795240472 \tabularnewline
68 & 34.787 & 34.2005628890866 & 0.586437110913359 \tabularnewline
69 & 32.529 & 33.7395689877443 & -1.21056898774427 \tabularnewline
70 & 29.998 & 30.7127497827325 & -0.714749782732468 \tabularnewline
71 & 29.257 & 29.0950864324581 & 0.161913567541873 \tabularnewline
72 & 28.155 & 27.71952869522 & 0.435471304779995 \tabularnewline
73 & 30.466 & 29.303796207033 & 1.16220379296698 \tabularnewline
74 & 35.704 & 32.3776841488372 & 3.32631585116278 \tabularnewline
75 & 39.327 & 38.420523233371 & 0.906476766628963 \tabularnewline
76 & 39.351 & 40.1684440499140 & -0.817444049913959 \tabularnewline
77 & 42.234 & 41.7684890050156 & 0.465510994984413 \tabularnewline
78 & 43.63 & 42.639153863473 & 0.990846136527011 \tabularnewline
79 & 43.722 & 42.3890093003529 & 1.33299069964707 \tabularnewline
80 & 43.121 & 44.3427201392084 & -1.22172013920841 \tabularnewline
81 & 37.985 & 41.9708497812421 & -3.9858497812421 \tabularnewline
82 & 37.135 & 36.0713692363126 & 1.06363076368743 \tabularnewline
83 & 34.646 & 36.0739805912821 & -1.42798059128206 \tabularnewline
84 & 33.026 & 32.9792318749246 & 0.04676812507536 \tabularnewline
85 & 35.087 & 34.4756688771795 & 0.611331122820509 \tabularnewline
86 & 38.846 & 37.4375704568802 & 1.40842954311976 \tabularnewline
87 & 42.013 & 41.7550078798706 & 0.257992120129366 \tabularnewline
88 & 43.908 & 42.7992996973438 & 1.10870030265615 \tabularnewline
89 & 42.868 & 46.5348530217785 & -3.66685302177846 \tabularnewline
90 & 44.423 & 43.3911211216381 & 1.03187887836193 \tabularnewline
91 & 44.167 & 43.0434932991901 & 1.12350670080986 \tabularnewline
92 & 43.636 & 44.5618201396121 & -0.925820139612135 \tabularnewline
93 & 44.382 & 42.2010383373369 & 2.18096166266308 \tabularnewline
94 & 42.142 & 42.0990864992032 & 0.0429135007968355 \tabularnewline
95 & 43.452 & 40.9101755949056 & 2.54182440509438 \tabularnewline
96 & 36.912 & 41.3642332326973 & -4.45223323269729 \tabularnewline
97 & 42.413 & 38.8229176915438 & 3.59008230845622 \tabularnewline
98 & 45.344 & 45.2310272123783 & 0.112972787621679 \tabularnewline
99 & 44.873 & 48.8288267624973 & -3.95582676249727 \tabularnewline
100 & 47.51 & 45.9171710256538 & 1.59282897434619 \tabularnewline
101 & 49.554 & 50.0413328798024 & -0.487332879802373 \tabularnewline
102 & 47.369 & 50.2350603672695 & -2.86606036726945 \tabularnewline
103 & 45.998 & 46.0411439298867 & -0.0431439298867033 \tabularnewline
104 & 48.14 & 46.2785469358806 & 1.86145306411944 \tabularnewline
105 & 48.441 & 46.5251881000633 & 1.91581189993671 \tabularnewline
106 & 44.928 & 45.8500197481911 & -0.922019748191069 \tabularnewline
107 & 40.454 & 43.7143775324225 & -3.2603775324225 \tabularnewline
108 & 38.661 & 38.3032606948223 & 0.357739305177731 \tabularnewline
109 & 37.246 & 40.6562035443757 & -3.41020354437566 \tabularnewline
110 & 36.843 & 39.6721259494619 & -2.82912594946193 \tabularnewline
111 & 36.424 & 39.2988683660116 & -2.87486836601157 \tabularnewline
112 & 37.594 & 37.0542629909156 & 0.539737009084412 \tabularnewline
113 & 38.144 & 39.1388326121083 & -0.994832612108254 \tabularnewline
114 & 38.737 & 38.1756927722865 & 0.561307227713549 \tabularnewline
115 & 34.56 & 37.2507179739447 & -2.69071797394471 \tabularnewline
116 & 36.08 & 34.5468567524539 & 1.5331432475461 \tabularnewline
117 & 33.508 & 34.4595659913753 & -0.951565991375311 \tabularnewline
118 & 35.462 & 31.3086590596157 & 4.15334094038426 \tabularnewline
119 & 33.374 & 33.8781803729084 & -0.50418037290838 \tabularnewline
120 & 32.11 & 31.4038870283788 & 0.706112971621174 \tabularnewline
121 & 35.533 & 33.4055620788884 & 2.12743792111159 \tabularnewline
122 & 35.532 & 37.5401587191845 & -2.00815871918453 \tabularnewline
123 & 37.903 & 37.8593090942476 & 0.0436909057523636 \tabularnewline
124 & 36.763 & 38.6635397739057 & -1.90053977390566 \tabularnewline
125 & 40.399 & 38.3687062336844 & 2.03029376631564 \tabularnewline
126 & 44.164 & 40.4826284707793 & 3.68137152922071 \tabularnewline
127 & 44.496 & 42.412796055742 & 2.08320394425800 \tabularnewline
128 & 43.11 & 44.8981254831121 & -1.78812548311215 \tabularnewline
129 & 43.88 & 41.5641713688254 & 2.31582863117459 \tabularnewline
130 & 43.93 & 41.5212116436901 & 2.40878835630993 \tabularnewline
131 & 44.327 & 42.1974492051025 & 2.12955079489754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116076&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]29.812[/C][C]30.4108518601392[/C][C]-0.598851860139202[/C][/ROW]
[ROW][C]14[/C][C]30.951[/C][C]31.0277203611790[/C][C]-0.0767203611790386[/C][/ROW]
[ROW][C]15[/C][C]32.974[/C][C]33.1828321772309[/C][C]-0.208832177230875[/C][/ROW]
[ROW][C]16[/C][C]32.936[/C][C]33.249221569499[/C][C]-0.313221569499035[/C][/ROW]
[ROW][C]17[/C][C]34.012[/C][C]34.3593559417831[/C][C]-0.347355941783128[/C][/ROW]
[ROW][C]18[/C][C]32.946[/C][C]33.2493306419754[/C][C]-0.303330641975421[/C][/ROW]
[ROW][C]19[/C][C]31.948[/C][C]31.6553568019176[/C][C]0.292643198082377[/C][/ROW]
[ROW][C]20[/C][C]30.599[/C][C]31.7001352790484[/C][C]-1.10113527904840[/C][/ROW]
[ROW][C]21[/C][C]27.691[/C][C]29.4968068936204[/C][C]-1.80580689362036[/C][/ROW]
[ROW][C]22[/C][C]25.073[/C][C]25.4577397593152[/C][C]-0.384739759315206[/C][/ROW]
[ROW][C]23[/C][C]23.406[/C][C]23.6621771137398[/C][C]-0.256177113739838[/C][/ROW]
[ROW][C]24[/C][C]22.248[/C][C]21.5978279616387[/C][C]0.650172038361298[/C][/ROW]
[ROW][C]25[/C][C]22.896[/C][C]22.6071486755763[/C][C]0.288851324423700[/C][/ROW]
[ROW][C]26[/C][C]25.317[/C][C]23.6204808768503[/C][C]1.69651912314973[/C][/ROW]
[ROW][C]27[/C][C]26.558[/C][C]26.9221072279287[/C][C]-0.36410722792866[/C][/ROW]
[ROW][C]28[/C][C]26.471[/C][C]26.6602191539865[/C][C]-0.189219153986528[/C][/ROW]
[ROW][C]29[/C][C]27.543[/C][C]27.4789451409819[/C][C]0.0640548590181105[/C][/ROW]
[ROW][C]30[/C][C]26.198[/C][C]26.7928178426481[/C][C]-0.594817842648137[/C][/ROW]
[ROW][C]31[/C][C]24.725[/C][C]25.0794719940671[/C][C]-0.354471994067122[/C][/ROW]
[ROW][C]32[/C][C]25.005[/C][C]24.3580384768944[/C][C]0.646961523105634[/C][/ROW]
[ROW][C]33[/C][C]23.462[/C][C]23.9090564767751[/C][C]-0.447056476775064[/C][/ROW]
[ROW][C]34[/C][C]20.78[/C][C]21.5302491452802[/C][C]-0.750249145280151[/C][/ROW]
[ROW][C]35[/C][C]19.815[/C][C]19.5843179241324[/C][C]0.230682075867612[/C][/ROW]
[ROW][C]36[/C][C]19.761[/C][C]18.2656226881529[/C][C]1.49537731184706[/C][/ROW]
[ROW][C]37[/C][C]21.454[/C][C]20.0394202464613[/C][C]1.41457975353869[/C][/ROW]
[ROW][C]38[/C][C]23.899[/C][C]22.2099459337419[/C][C]1.68905406625807[/C][/ROW]
[ROW][C]39[/C][C]24.939[/C][C]25.4276607847813[/C][C]-0.488660784781327[/C][/ROW]
[ROW][C]40[/C][C]23.58[/C][C]25.1501356347057[/C][C]-1.57013563470565[/C][/ROW]
[ROW][C]41[/C][C]24.562[/C][C]24.5980484598158[/C][C]-0.0360484598158379[/C][/ROW]
[ROW][C]42[/C][C]24.696[/C][C]23.9000245006762[/C][C]0.795975499323752[/C][/ROW]
[ROW][C]43[/C][C]23.785[/C][C]23.6748571958157[/C][C]0.110142804184282[/C][/ROW]
[ROW][C]44[/C][C]23.812[/C][C]23.5687095540276[/C][C]0.24329044597237[/C][/ROW]
[ROW][C]45[/C][C]21.917[/C][C]22.8451750415451[/C][C]-0.928175041545053[/C][/ROW]
[ROW][C]46[/C][C]19.713[/C][C]20.1933602161703[/C][C]-0.480360216170343[/C][/ROW]
[ROW][C]47[/C][C]19.282[/C][C]18.6847240859458[/C][C]0.597275914054247[/C][/ROW]
[ROW][C]48[/C][C]18.788[/C][C]17.9012260028784[/C][C]0.886773997121558[/C][/ROW]
[ROW][C]49[/C][C]21.453[/C][C]19.1461462696094[/C][C]2.30685373039060[/C][/ROW]
[ROW][C]50[/C][C]24.482[/C][C]22.2897716073321[/C][C]2.19222839266788[/C][/ROW]
[ROW][C]51[/C][C]27.474[/C][C]26.0854805411882[/C][C]1.3885194588118[/C][/ROW]
[ROW][C]52[/C][C]27.264[/C][C]27.8050665240494[/C][C]-0.54106652404943[/C][/ROW]
[ROW][C]53[/C][C]27.349[/C][C]28.7855240097176[/C][C]-1.43652400971756[/C][/ROW]
[ROW][C]54[/C][C]30.632[/C][C]26.9931088134042[/C][C]3.63889118659579[/C][/ROW]
[ROW][C]55[/C][C]29.429[/C][C]29.5911524772775[/C][C]-0.162152477277477[/C][/ROW]
[ROW][C]56[/C][C]30.084[/C][C]29.5736049193155[/C][C]0.510395080684464[/C][/ROW]
[ROW][C]57[/C][C]26.29[/C][C]29.1809859682926[/C][C]-2.89098596829262[/C][/ROW]
[ROW][C]58[/C][C]24.379[/C][C]24.6190217369547[/C][C]-0.240021736954745[/C][/ROW]
[ROW][C]59[/C][C]23.335[/C][C]23.444077155783[/C][C]-0.109077155783009[/C][/ROW]
[ROW][C]60[/C][C]21.346[/C][C]21.9685466339507[/C][C]-0.622546633950737[/C][/ROW]
[ROW][C]61[/C][C]21.106[/C][C]22.0727240154377[/C][C]-0.96672401543771[/C][/ROW]
[ROW][C]62[/C][C]24.514[/C][C]22.1128616055365[/C][C]2.40113839446347[/C][/ROW]
[ROW][C]63[/C][C]28.353[/C][C]26.0935692617528[/C][C]2.25943073824721[/C][/ROW]
[ROW][C]64[/C][C]30.805[/C][C]28.6280553198637[/C][C]2.17694468013628[/C][/ROW]
[ROW][C]65[/C][C]31.348[/C][C]32.5008305921727[/C][C]-1.15283059217267[/C][/ROW]
[ROW][C]66[/C][C]34.556[/C][C]31.3355555680500[/C][C]3.22044443194997[/C][/ROW]
[ROW][C]67[/C][C]33.855[/C][C]33.4116922047595[/C][C]0.443307795240472[/C][/ROW]
[ROW][C]68[/C][C]34.787[/C][C]34.2005628890866[/C][C]0.586437110913359[/C][/ROW]
[ROW][C]69[/C][C]32.529[/C][C]33.7395689877443[/C][C]-1.21056898774427[/C][/ROW]
[ROW][C]70[/C][C]29.998[/C][C]30.7127497827325[/C][C]-0.714749782732468[/C][/ROW]
[ROW][C]71[/C][C]29.257[/C][C]29.0950864324581[/C][C]0.161913567541873[/C][/ROW]
[ROW][C]72[/C][C]28.155[/C][C]27.71952869522[/C][C]0.435471304779995[/C][/ROW]
[ROW][C]73[/C][C]30.466[/C][C]29.303796207033[/C][C]1.16220379296698[/C][/ROW]
[ROW][C]74[/C][C]35.704[/C][C]32.3776841488372[/C][C]3.32631585116278[/C][/ROW]
[ROW][C]75[/C][C]39.327[/C][C]38.420523233371[/C][C]0.906476766628963[/C][/ROW]
[ROW][C]76[/C][C]39.351[/C][C]40.1684440499140[/C][C]-0.817444049913959[/C][/ROW]
[ROW][C]77[/C][C]42.234[/C][C]41.7684890050156[/C][C]0.465510994984413[/C][/ROW]
[ROW][C]78[/C][C]43.63[/C][C]42.639153863473[/C][C]0.990846136527011[/C][/ROW]
[ROW][C]79[/C][C]43.722[/C][C]42.3890093003529[/C][C]1.33299069964707[/C][/ROW]
[ROW][C]80[/C][C]43.121[/C][C]44.3427201392084[/C][C]-1.22172013920841[/C][/ROW]
[ROW][C]81[/C][C]37.985[/C][C]41.9708497812421[/C][C]-3.9858497812421[/C][/ROW]
[ROW][C]82[/C][C]37.135[/C][C]36.0713692363126[/C][C]1.06363076368743[/C][/ROW]
[ROW][C]83[/C][C]34.646[/C][C]36.0739805912821[/C][C]-1.42798059128206[/C][/ROW]
[ROW][C]84[/C][C]33.026[/C][C]32.9792318749246[/C][C]0.04676812507536[/C][/ROW]
[ROW][C]85[/C][C]35.087[/C][C]34.4756688771795[/C][C]0.611331122820509[/C][/ROW]
[ROW][C]86[/C][C]38.846[/C][C]37.4375704568802[/C][C]1.40842954311976[/C][/ROW]
[ROW][C]87[/C][C]42.013[/C][C]41.7550078798706[/C][C]0.257992120129366[/C][/ROW]
[ROW][C]88[/C][C]43.908[/C][C]42.7992996973438[/C][C]1.10870030265615[/C][/ROW]
[ROW][C]89[/C][C]42.868[/C][C]46.5348530217785[/C][C]-3.66685302177846[/C][/ROW]
[ROW][C]90[/C][C]44.423[/C][C]43.3911211216381[/C][C]1.03187887836193[/C][/ROW]
[ROW][C]91[/C][C]44.167[/C][C]43.0434932991901[/C][C]1.12350670080986[/C][/ROW]
[ROW][C]92[/C][C]43.636[/C][C]44.5618201396121[/C][C]-0.925820139612135[/C][/ROW]
[ROW][C]93[/C][C]44.382[/C][C]42.2010383373369[/C][C]2.18096166266308[/C][/ROW]
[ROW][C]94[/C][C]42.142[/C][C]42.0990864992032[/C][C]0.0429135007968355[/C][/ROW]
[ROW][C]95[/C][C]43.452[/C][C]40.9101755949056[/C][C]2.54182440509438[/C][/ROW]
[ROW][C]96[/C][C]36.912[/C][C]41.3642332326973[/C][C]-4.45223323269729[/C][/ROW]
[ROW][C]97[/C][C]42.413[/C][C]38.8229176915438[/C][C]3.59008230845622[/C][/ROW]
[ROW][C]98[/C][C]45.344[/C][C]45.2310272123783[/C][C]0.112972787621679[/C][/ROW]
[ROW][C]99[/C][C]44.873[/C][C]48.8288267624973[/C][C]-3.95582676249727[/C][/ROW]
[ROW][C]100[/C][C]47.51[/C][C]45.9171710256538[/C][C]1.59282897434619[/C][/ROW]
[ROW][C]101[/C][C]49.554[/C][C]50.0413328798024[/C][C]-0.487332879802373[/C][/ROW]
[ROW][C]102[/C][C]47.369[/C][C]50.2350603672695[/C][C]-2.86606036726945[/C][/ROW]
[ROW][C]103[/C][C]45.998[/C][C]46.0411439298867[/C][C]-0.0431439298867033[/C][/ROW]
[ROW][C]104[/C][C]48.14[/C][C]46.2785469358806[/C][C]1.86145306411944[/C][/ROW]
[ROW][C]105[/C][C]48.441[/C][C]46.5251881000633[/C][C]1.91581189993671[/C][/ROW]
[ROW][C]106[/C][C]44.928[/C][C]45.8500197481911[/C][C]-0.922019748191069[/C][/ROW]
[ROW][C]107[/C][C]40.454[/C][C]43.7143775324225[/C][C]-3.2603775324225[/C][/ROW]
[ROW][C]108[/C][C]38.661[/C][C]38.3032606948223[/C][C]0.357739305177731[/C][/ROW]
[ROW][C]109[/C][C]37.246[/C][C]40.6562035443757[/C][C]-3.41020354437566[/C][/ROW]
[ROW][C]110[/C][C]36.843[/C][C]39.6721259494619[/C][C]-2.82912594946193[/C][/ROW]
[ROW][C]111[/C][C]36.424[/C][C]39.2988683660116[/C][C]-2.87486836601157[/C][/ROW]
[ROW][C]112[/C][C]37.594[/C][C]37.0542629909156[/C][C]0.539737009084412[/C][/ROW]
[ROW][C]113[/C][C]38.144[/C][C]39.1388326121083[/C][C]-0.994832612108254[/C][/ROW]
[ROW][C]114[/C][C]38.737[/C][C]38.1756927722865[/C][C]0.561307227713549[/C][/ROW]
[ROW][C]115[/C][C]34.56[/C][C]37.2507179739447[/C][C]-2.69071797394471[/C][/ROW]
[ROW][C]116[/C][C]36.08[/C][C]34.5468567524539[/C][C]1.5331432475461[/C][/ROW]
[ROW][C]117[/C][C]33.508[/C][C]34.4595659913753[/C][C]-0.951565991375311[/C][/ROW]
[ROW][C]118[/C][C]35.462[/C][C]31.3086590596157[/C][C]4.15334094038426[/C][/ROW]
[ROW][C]119[/C][C]33.374[/C][C]33.8781803729084[/C][C]-0.50418037290838[/C][/ROW]
[ROW][C]120[/C][C]32.11[/C][C]31.4038870283788[/C][C]0.706112971621174[/C][/ROW]
[ROW][C]121[/C][C]35.533[/C][C]33.4055620788884[/C][C]2.12743792111159[/C][/ROW]
[ROW][C]122[/C][C]35.532[/C][C]37.5401587191845[/C][C]-2.00815871918453[/C][/ROW]
[ROW][C]123[/C][C]37.903[/C][C]37.8593090942476[/C][C]0.0436909057523636[/C][/ROW]
[ROW][C]124[/C][C]36.763[/C][C]38.6635397739057[/C][C]-1.90053977390566[/C][/ROW]
[ROW][C]125[/C][C]40.399[/C][C]38.3687062336844[/C][C]2.03029376631564[/C][/ROW]
[ROW][C]126[/C][C]44.164[/C][C]40.4826284707793[/C][C]3.68137152922071[/C][/ROW]
[ROW][C]127[/C][C]44.496[/C][C]42.412796055742[/C][C]2.08320394425800[/C][/ROW]
[ROW][C]128[/C][C]43.11[/C][C]44.8981254831121[/C][C]-1.78812548311215[/C][/ROW]
[ROW][C]129[/C][C]43.88[/C][C]41.5641713688254[/C][C]2.31582863117459[/C][/ROW]
[ROW][C]130[/C][C]43.93[/C][C]41.5212116436901[/C][C]2.40878835630993[/C][/ROW]
[ROW][C]131[/C][C]44.327[/C][C]42.1974492051025[/C][C]2.12955079489754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116076&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116076&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
1329.81230.4108518601392-0.598851860139202
1430.95131.0277203611790-0.0767203611790386
1532.97433.1828321772309-0.208832177230875
1632.93633.249221569499-0.313221569499035
1734.01234.3593559417831-0.347355941783128
1832.94633.2493306419754-0.303330641975421
1931.94831.65535680191760.292643198082377
2030.59931.7001352790484-1.10113527904840
2127.69129.4968068936204-1.80580689362036
2225.07325.4577397593152-0.384739759315206
2323.40623.6621771137398-0.256177113739838
2422.24821.59782796163870.650172038361298
2522.89622.60714867557630.288851324423700
2625.31723.62048087685031.69651912314973
2726.55826.9221072279287-0.36410722792866
2826.47126.6602191539865-0.189219153986528
2927.54327.47894514098190.0640548590181105
3026.19826.7928178426481-0.594817842648137
3124.72525.0794719940671-0.354471994067122
3225.00524.35803847689440.646961523105634
3323.46223.9090564767751-0.447056476775064
3420.7821.5302491452802-0.750249145280151
3519.81519.58431792413240.230682075867612
3619.76118.26562268815291.49537731184706
3721.45420.03942024646131.41457975353869
3823.89922.20994593374191.68905406625807
3924.93925.4276607847813-0.488660784781327
4023.5825.1501356347057-1.57013563470565
4124.56224.5980484598158-0.0360484598158379
4224.69623.90002450067620.795975499323752
4323.78523.67485719581570.110142804184282
4423.81223.56870955402760.24329044597237
4521.91722.8451750415451-0.928175041545053
4619.71320.1933602161703-0.480360216170343
4719.28218.68472408594580.597275914054247
4818.78817.90122600287840.886773997121558
4921.45319.14614626960942.30685373039060
5024.48222.28977160733212.19222839266788
5127.47426.08548054118821.3885194588118
5227.26427.8050665240494-0.54106652404943
5327.34928.7855240097176-1.43652400971756
5430.63226.99310881340423.63889118659579
5529.42929.5911524772775-0.162152477277477
5630.08429.57360491931550.510395080684464
5726.2929.1809859682926-2.89098596829262
5824.37924.6190217369547-0.240021736954745
5923.33523.444077155783-0.109077155783009
6021.34621.9685466339507-0.622546633950737
6121.10622.0727240154377-0.96672401543771
6224.51422.11286160553652.40113839446347
6328.35326.09356926175282.25943073824721
6430.80528.62805531986372.17694468013628
6531.34832.5008305921727-1.15283059217267
6634.55631.33555556805003.22044443194997
6733.85533.41169220475950.443307795240472
6834.78734.20056288908660.586437110913359
6932.52933.7395689877443-1.21056898774427
7029.99830.7127497827325-0.714749782732468
7129.25729.09508643245810.161913567541873
7228.15527.719528695220.435471304779995
7330.46629.3037962070331.16220379296698
7435.70432.37768414883723.32631585116278
7539.32738.4205232333710.906476766628963
7639.35140.1684440499140-0.817444049913959
7742.23441.76848900501560.465510994984413
7843.6342.6391538634730.990846136527011
7943.72242.38900930035291.33299069964707
8043.12144.3427201392084-1.22172013920841
8137.98541.9708497812421-3.9858497812421
8237.13536.07136923631261.06363076368743
8334.64636.0739805912821-1.42798059128206
8433.02632.97923187492460.04676812507536
8535.08734.47566887717950.611331122820509
8638.84637.43757045688021.40842954311976
8742.01341.75500787987060.257992120129366
8843.90842.79929969734381.10870030265615
8942.86846.5348530217785-3.66685302177846
9044.42343.39112112163811.03187887836193
9144.16743.04349329919011.12350670080986
9243.63644.5618201396121-0.925820139612135
9344.38242.20103833733692.18096166266308
9442.14242.09908649920320.0429135007968355
9543.45240.91017559490562.54182440509438
9636.91241.3642332326973-4.45223323269729
9742.41338.82291769154383.59008230845622
9845.34445.23102721237830.112972787621679
9944.87348.8288267624973-3.95582676249727
10047.5145.91717102565381.59282897434619
10149.55450.0413328798024-0.487332879802373
10247.36950.2350603672695-2.86606036726945
10345.99846.0411439298867-0.0431439298867033
10448.1446.27854693588061.86145306411944
10548.44146.52518810006331.91581189993671
10644.92845.8500197481911-0.922019748191069
10740.45443.7143775324225-3.2603775324225
10838.66138.30326069482230.357739305177731
10937.24640.6562035443757-3.41020354437566
11036.84339.6721259494619-2.82912594946193
11136.42439.2988683660116-2.87486836601157
11237.59437.05426299091560.539737009084412
11338.14439.1388326121083-0.994832612108254
11438.73738.17569277228650.561307227713549
11534.5637.2507179739447-2.69071797394471
11636.0834.54685675245391.5331432475461
11733.50834.4595659913753-0.951565991375311
11835.46231.30865905961574.15334094038426
11933.37433.8781803729084-0.50418037290838
12032.1131.40388702837880.706112971621174
12135.53333.40556207888842.12743792111159
12235.53237.5401587191845-2.00815871918453
12337.90337.85930909424760.0436909057523636
12436.76338.6635397739057-1.90053977390566
12540.39938.36870623368442.03029376631564
12644.16440.48262847077933.68137152922071
12744.49642.4127960557422.08320394425800
12843.1144.8981254831121-1.78812548311215
12943.8841.56417136882542.31582863117459
13043.9341.52121164369012.40878835630993
13144.32742.19744920510252.12955079489754







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
13242.037050955412338.716787532670145.3573143781545
13344.240579393891439.451622149387349.0295366383954
13446.963449281118740.849536740638353.0773618215991
13550.428521084825942.970717629457157.8863245401946
13651.757330496274343.268769916446260.2458910761025
13754.652162163796844.909523862553664.39480046504
13855.440767307905644.801315406395266.080219209416
13953.665133545620442.61981950065364.7104475905877
14054.263277114000342.369619827568166.1569344004326
14152.64805518003740.389930264528864.9061800955453
14250.1009197997237.722945181607662.4788944178323
14348.297233328126833.421932868157263.1725337880964

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
132 & 42.0370509554123 & 38.7167875326701 & 45.3573143781545 \tabularnewline
133 & 44.2405793938914 & 39.4516221493873 & 49.0295366383954 \tabularnewline
134 & 46.9634492811187 & 40.8495367406383 & 53.0773618215991 \tabularnewline
135 & 50.4285210848259 & 42.9707176294571 & 57.8863245401946 \tabularnewline
136 & 51.7573304962743 & 43.2687699164462 & 60.2458910761025 \tabularnewline
137 & 54.6521621637968 & 44.9095238625536 & 64.39480046504 \tabularnewline
138 & 55.4407673079056 & 44.8013154063952 & 66.080219209416 \tabularnewline
139 & 53.6651335456204 & 42.619819500653 & 64.7104475905877 \tabularnewline
140 & 54.2632771140003 & 42.3696198275681 & 66.1569344004326 \tabularnewline
141 & 52.648055180037 & 40.3899302645288 & 64.9061800955453 \tabularnewline
142 & 50.10091979972 & 37.7229451816076 & 62.4788944178323 \tabularnewline
143 & 48.2972333281268 & 33.4219328681572 & 63.1725337880964 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116076&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]132[/C][C]42.0370509554123[/C][C]38.7167875326701[/C][C]45.3573143781545[/C][/ROW]
[ROW][C]133[/C][C]44.2405793938914[/C][C]39.4516221493873[/C][C]49.0295366383954[/C][/ROW]
[ROW][C]134[/C][C]46.9634492811187[/C][C]40.8495367406383[/C][C]53.0773618215991[/C][/ROW]
[ROW][C]135[/C][C]50.4285210848259[/C][C]42.9707176294571[/C][C]57.8863245401946[/C][/ROW]
[ROW][C]136[/C][C]51.7573304962743[/C][C]43.2687699164462[/C][C]60.2458910761025[/C][/ROW]
[ROW][C]137[/C][C]54.6521621637968[/C][C]44.9095238625536[/C][C]64.39480046504[/C][/ROW]
[ROW][C]138[/C][C]55.4407673079056[/C][C]44.8013154063952[/C][C]66.080219209416[/C][/ROW]
[ROW][C]139[/C][C]53.6651335456204[/C][C]42.619819500653[/C][C]64.7104475905877[/C][/ROW]
[ROW][C]140[/C][C]54.2632771140003[/C][C]42.3696198275681[/C][C]66.1569344004326[/C][/ROW]
[ROW][C]141[/C][C]52.648055180037[/C][C]40.3899302645288[/C][C]64.9061800955453[/C][/ROW]
[ROW][C]142[/C][C]50.10091979972[/C][C]37.7229451816076[/C][C]62.4788944178323[/C][/ROW]
[ROW][C]143[/C][C]48.2972333281268[/C][C]33.4219328681572[/C][C]63.1725337880964[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116076&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116076&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
13242.037050955412338.716787532670145.3573143781545
13344.240579393891439.451622149387349.0295366383954
13446.963449281118740.849536740638353.0773618215991
13550.428521084825942.970717629457157.8863245401946
13651.757330496274343.268769916446260.2458910761025
13754.652162163796844.909523862553664.39480046504
13855.440767307905644.801315406395266.080219209416
13953.665133545620442.61981950065364.7104475905877
14054.263277114000342.369619827568166.1569344004326
14152.64805518003740.389930264528864.9061800955453
14250.1009197997237.722945181607662.4788944178323
14348.297233328126833.421932868157263.1725337880964



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')