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, 12 Dec 2016 14:14:05 +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/12/t1481548471r0gjajvt6fk5wwx.htm/, Retrieved Fri, 01 Nov 2024 03:43:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298893, Retrieved Fri, 01 Nov 2024 03:43:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact134
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2016-12-12 13:14:05] [36884fbde1107444791dd71ee0072a5a] [Current]
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Dataseries X:
3647
1885
4791
3178
2849
4716
3085
2799
3573
2721
3355
5667
2856
1944
4188
2949
3567
4137
3494
2489
3244
2669
2529
3377
3366
2073
4133
4213
3710
5123
3141
3084
3804
3203
2757
2243
5229
2857
3395
4882
7140
8945
6866
4205
3217
3079
2263
4187
2665
2073
3540
3686
2384
4500
1679
868
1869
3710
6904
3415
938
3359
3551
2278
3033
2280
2901
4812
4882
7896
5048
3741
4418
3471
5055
7595
8124
2333
3008
2744
2833
2428
4269
3207
5170
7767
4544
3741
2193
3432
5282
6635
4222
7317
4132
5048
4383
3761
4081
6491
5859
7139
7682
8649
6146
7137
9948
15819
8370
13222
16711
19059
8303
20781
9638
13444
6072
13442
14457
17705
16463
19194
20688
14739
12702
15760




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=298893&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=298893&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298893&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
alpha0.458539244289317
beta0.117560633456458
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.458539244289317 \tabularnewline
beta & 0.117560633456458 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298893&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]0.458539244289317[/C][/ROW]
[ROW][C]beta[/C][C]0.117560633456458[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298893&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298893&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
alpha0.458539244289317
beta0.117560633456458
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
347911234668
43178753.0951660032862424.90483399671
52849485.3604874407192363.63951255928
64716316.9479939410574399.05200605894
730851318.98802601341766.0119739866
827991208.874802732591590.12519726741
935731103.828139475962469.17186052404
1027211534.962452199191186.03754780081
1133551441.664061434161913.33593856584
1256671785.001126079363881.99887392064
1328563240.31107339837-384.311073398366
1419442718.63374581114-774.633745811135
1541881976.220621227092211.77937877291
1629492722.42365590099226.576344099009
1735672570.54705286346996.452947136538
1841372825.404041588631311.59595841137
1934943295.46957541324198.530424586764
2024893265.85289414481-776.852894144811
2132442747.10752347906496.89247652094
2226692839.20995983668-170.209959836679
2325292616.24438314996-87.2443831499572
2433772426.618769271950.381230729
2533662764.01662674368601.98337325632
2620732974.11100839687-901.111008396873
2741332446.402190369451686.59780963055
2842133196.17743636841016.8225636316
2937103693.6474511210216.3525488789783
3051233733.244204556921389.75579544308
3131414477.5166486383-1336.5166486383
3230843899.63970080245-815.63970080245
3338043516.63726749961287.362732500394
3432033654.89535900508-451.895359005076
3527573429.81465855297-672.81465855297
3622433067.16493209601-824.164932096012
3752292590.687595573832638.31240442617
3828573844.11330152711-987.113301527113
3933953381.9275525038113.0724474961858
4048823379.070906485521502.92909351448
4171404140.389143262252999.61085673775
4289455749.692219538353195.30778046165
4368667620.97680064703-754.976800647033
4442057640.20297195694-3435.20297195694
4532176245.26164529032-3028.26164529032
4630794873.67691806702-1794.67691806702
4722633970.99505111739-1707.99505111739
4841873015.988760555921171.01123944408
4926653444.24456271929-779.244562719289
5020732936.2254579756-863.225457975604
5135402343.164643859631196.83535614037
5236862759.23936165541926.760638344588
5323843101.43233343241-717.432333432407
5445002651.024277423351848.97572257665
5516793477.08622053101-1798.08622053101
568682533.89920563778-1665.89920563778
5718691561.52288883316307.477111166839
5837101510.591968622542199.40803137746
5969042445.747272906484458.25272709352
6034154656.99881969501-1241.99881969501
619384187.5099378689-3249.5099378689
6233592622.32980930683736.670190693171
6335512924.68076862729626.319231372714
6422783210.19394967166-932.193949671663
6530332730.81667451249302.183325487515
6622802833.73936618154-553.739366181539
6729012514.33794854305386.662051456953
6848122646.990954244542165.00904575546
6948823711.793179528261170.20682047174
7078964383.520905018583512.47909498142
7150486318.61666340487-1270.61666340487
7237415991.98123710903-2250.98123710903
7344185094.4684162779-676.4684162779
7434714882.46569703006-1411.46569703006
7550554257.35117873406797.648821265937
7675954688.200550398222906.79944960178
7781246242.87266518491881.1273348151
7823337428.63822222792-5095.63822222792
7930085140.5966633499-2132.5966633499
8027444096.26583614756-1352.26583614756
8128333336.85185277977-503.851852779774
8224282939.30825557055-511.308255570551
8342692510.782938369281758.21706163072
8432073217.70278232577-10.7027823257727
8551703112.926511886522057.07348811348
8677674067.195750712093699.80424928791
8745445974.1637660536-1430.1637660536
8837415451.74548185899-1710.74548185899
8921934708.44974319037-2515.44974319037
9034323460.56727420568-28.5672742056809
9152823351.478061016551930.52193898345
9266354244.775167431942390.22483256806
9342225477.7119431462-1255.7119431462
9473174971.153011024562345.84698897544
9541326242.50580246269-2110.50580246269
9650485356.67668066851-308.676680668508
9743835280.41734694203-897.417346942033
9837614885.8209863185-1124.8209863185
9940814326.31634816131-245.316348161306
10064914156.875038832082334.12496116792
10158595296.03252117892562.967478821081
10271395653.392207306181485.60779269382
10376826513.902103054741168.09789694526
10486497291.788927980381357.21107201962
10561468229.5536079523-2083.5536079523
10671377477.27626925091-340.276269250909
10799487506.017015640872441.98298435913
108158198942.17075289516876.8292471049
109837012782.5790293627-4412.57902936273
1101322211208.48535734272013.51464265726
1111671112689.54867201354021.45132798645
1121905915308.11077185413750.88922814585
113830318004.8055808662-9701.80558086616
1142078114009.92475553476771.07524446533
115963817933.5089478609-8295.5089478609
1161344414501.2939446164-1057.29394461637
117607214331.0899181638-8259.08991816385
1181344210413.36395266333028.63604733668
1191445711834.76547266292622.2345273371
1201770513211.1705513424493.82944865796
1211646315688.0204582114774.979541788551
1221919416501.40791345392692.59208654608
1232068818339.24328647442348.7567135256
1241473920146.0291120403-5407.02911204027
1251270218105.010568089-5403.01056808898
1261576015774.5791103412-14.5791103412448

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 4791 & 123 & 4668 \tabularnewline
4 & 3178 & 753.095166003286 & 2424.90483399671 \tabularnewline
5 & 2849 & 485.360487440719 & 2363.63951255928 \tabularnewline
6 & 4716 & 316.947993941057 & 4399.05200605894 \tabularnewline
7 & 3085 & 1318.9880260134 & 1766.0119739866 \tabularnewline
8 & 2799 & 1208.87480273259 & 1590.12519726741 \tabularnewline
9 & 3573 & 1103.82813947596 & 2469.17186052404 \tabularnewline
10 & 2721 & 1534.96245219919 & 1186.03754780081 \tabularnewline
11 & 3355 & 1441.66406143416 & 1913.33593856584 \tabularnewline
12 & 5667 & 1785.00112607936 & 3881.99887392064 \tabularnewline
13 & 2856 & 3240.31107339837 & -384.311073398366 \tabularnewline
14 & 1944 & 2718.63374581114 & -774.633745811135 \tabularnewline
15 & 4188 & 1976.22062122709 & 2211.77937877291 \tabularnewline
16 & 2949 & 2722.42365590099 & 226.576344099009 \tabularnewline
17 & 3567 & 2570.54705286346 & 996.452947136538 \tabularnewline
18 & 4137 & 2825.40404158863 & 1311.59595841137 \tabularnewline
19 & 3494 & 3295.46957541324 & 198.530424586764 \tabularnewline
20 & 2489 & 3265.85289414481 & -776.852894144811 \tabularnewline
21 & 3244 & 2747.10752347906 & 496.89247652094 \tabularnewline
22 & 2669 & 2839.20995983668 & -170.209959836679 \tabularnewline
23 & 2529 & 2616.24438314996 & -87.2443831499572 \tabularnewline
24 & 3377 & 2426.618769271 & 950.381230729 \tabularnewline
25 & 3366 & 2764.01662674368 & 601.98337325632 \tabularnewline
26 & 2073 & 2974.11100839687 & -901.111008396873 \tabularnewline
27 & 4133 & 2446.40219036945 & 1686.59780963055 \tabularnewline
28 & 4213 & 3196.1774363684 & 1016.8225636316 \tabularnewline
29 & 3710 & 3693.64745112102 & 16.3525488789783 \tabularnewline
30 & 5123 & 3733.24420455692 & 1389.75579544308 \tabularnewline
31 & 3141 & 4477.5166486383 & -1336.5166486383 \tabularnewline
32 & 3084 & 3899.63970080245 & -815.63970080245 \tabularnewline
33 & 3804 & 3516.63726749961 & 287.362732500394 \tabularnewline
34 & 3203 & 3654.89535900508 & -451.895359005076 \tabularnewline
35 & 2757 & 3429.81465855297 & -672.81465855297 \tabularnewline
36 & 2243 & 3067.16493209601 & -824.164932096012 \tabularnewline
37 & 5229 & 2590.68759557383 & 2638.31240442617 \tabularnewline
38 & 2857 & 3844.11330152711 & -987.113301527113 \tabularnewline
39 & 3395 & 3381.92755250381 & 13.0724474961858 \tabularnewline
40 & 4882 & 3379.07090648552 & 1502.92909351448 \tabularnewline
41 & 7140 & 4140.38914326225 & 2999.61085673775 \tabularnewline
42 & 8945 & 5749.69221953835 & 3195.30778046165 \tabularnewline
43 & 6866 & 7620.97680064703 & -754.976800647033 \tabularnewline
44 & 4205 & 7640.20297195694 & -3435.20297195694 \tabularnewline
45 & 3217 & 6245.26164529032 & -3028.26164529032 \tabularnewline
46 & 3079 & 4873.67691806702 & -1794.67691806702 \tabularnewline
47 & 2263 & 3970.99505111739 & -1707.99505111739 \tabularnewline
48 & 4187 & 3015.98876055592 & 1171.01123944408 \tabularnewline
49 & 2665 & 3444.24456271929 & -779.244562719289 \tabularnewline
50 & 2073 & 2936.2254579756 & -863.225457975604 \tabularnewline
51 & 3540 & 2343.16464385963 & 1196.83535614037 \tabularnewline
52 & 3686 & 2759.23936165541 & 926.760638344588 \tabularnewline
53 & 2384 & 3101.43233343241 & -717.432333432407 \tabularnewline
54 & 4500 & 2651.02427742335 & 1848.97572257665 \tabularnewline
55 & 1679 & 3477.08622053101 & -1798.08622053101 \tabularnewline
56 & 868 & 2533.89920563778 & -1665.89920563778 \tabularnewline
57 & 1869 & 1561.52288883316 & 307.477111166839 \tabularnewline
58 & 3710 & 1510.59196862254 & 2199.40803137746 \tabularnewline
59 & 6904 & 2445.74727290648 & 4458.25272709352 \tabularnewline
60 & 3415 & 4656.99881969501 & -1241.99881969501 \tabularnewline
61 & 938 & 4187.5099378689 & -3249.5099378689 \tabularnewline
62 & 3359 & 2622.32980930683 & 736.670190693171 \tabularnewline
63 & 3551 & 2924.68076862729 & 626.319231372714 \tabularnewline
64 & 2278 & 3210.19394967166 & -932.193949671663 \tabularnewline
65 & 3033 & 2730.81667451249 & 302.183325487515 \tabularnewline
66 & 2280 & 2833.73936618154 & -553.739366181539 \tabularnewline
67 & 2901 & 2514.33794854305 & 386.662051456953 \tabularnewline
68 & 4812 & 2646.99095424454 & 2165.00904575546 \tabularnewline
69 & 4882 & 3711.79317952826 & 1170.20682047174 \tabularnewline
70 & 7896 & 4383.52090501858 & 3512.47909498142 \tabularnewline
71 & 5048 & 6318.61666340487 & -1270.61666340487 \tabularnewline
72 & 3741 & 5991.98123710903 & -2250.98123710903 \tabularnewline
73 & 4418 & 5094.4684162779 & -676.4684162779 \tabularnewline
74 & 3471 & 4882.46569703006 & -1411.46569703006 \tabularnewline
75 & 5055 & 4257.35117873406 & 797.648821265937 \tabularnewline
76 & 7595 & 4688.20055039822 & 2906.79944960178 \tabularnewline
77 & 8124 & 6242.8726651849 & 1881.1273348151 \tabularnewline
78 & 2333 & 7428.63822222792 & -5095.63822222792 \tabularnewline
79 & 3008 & 5140.5966633499 & -2132.5966633499 \tabularnewline
80 & 2744 & 4096.26583614756 & -1352.26583614756 \tabularnewline
81 & 2833 & 3336.85185277977 & -503.851852779774 \tabularnewline
82 & 2428 & 2939.30825557055 & -511.308255570551 \tabularnewline
83 & 4269 & 2510.78293836928 & 1758.21706163072 \tabularnewline
84 & 3207 & 3217.70278232577 & -10.7027823257727 \tabularnewline
85 & 5170 & 3112.92651188652 & 2057.07348811348 \tabularnewline
86 & 7767 & 4067.19575071209 & 3699.80424928791 \tabularnewline
87 & 4544 & 5974.1637660536 & -1430.1637660536 \tabularnewline
88 & 3741 & 5451.74548185899 & -1710.74548185899 \tabularnewline
89 & 2193 & 4708.44974319037 & -2515.44974319037 \tabularnewline
90 & 3432 & 3460.56727420568 & -28.5672742056809 \tabularnewline
91 & 5282 & 3351.47806101655 & 1930.52193898345 \tabularnewline
92 & 6635 & 4244.77516743194 & 2390.22483256806 \tabularnewline
93 & 4222 & 5477.7119431462 & -1255.7119431462 \tabularnewline
94 & 7317 & 4971.15301102456 & 2345.84698897544 \tabularnewline
95 & 4132 & 6242.50580246269 & -2110.50580246269 \tabularnewline
96 & 5048 & 5356.67668066851 & -308.676680668508 \tabularnewline
97 & 4383 & 5280.41734694203 & -897.417346942033 \tabularnewline
98 & 3761 & 4885.8209863185 & -1124.8209863185 \tabularnewline
99 & 4081 & 4326.31634816131 & -245.316348161306 \tabularnewline
100 & 6491 & 4156.87503883208 & 2334.12496116792 \tabularnewline
101 & 5859 & 5296.03252117892 & 562.967478821081 \tabularnewline
102 & 7139 & 5653.39220730618 & 1485.60779269382 \tabularnewline
103 & 7682 & 6513.90210305474 & 1168.09789694526 \tabularnewline
104 & 8649 & 7291.78892798038 & 1357.21107201962 \tabularnewline
105 & 6146 & 8229.5536079523 & -2083.5536079523 \tabularnewline
106 & 7137 & 7477.27626925091 & -340.276269250909 \tabularnewline
107 & 9948 & 7506.01701564087 & 2441.98298435913 \tabularnewline
108 & 15819 & 8942.1707528951 & 6876.8292471049 \tabularnewline
109 & 8370 & 12782.5790293627 & -4412.57902936273 \tabularnewline
110 & 13222 & 11208.4853573427 & 2013.51464265726 \tabularnewline
111 & 16711 & 12689.5486720135 & 4021.45132798645 \tabularnewline
112 & 19059 & 15308.1107718541 & 3750.88922814585 \tabularnewline
113 & 8303 & 18004.8055808662 & -9701.80558086616 \tabularnewline
114 & 20781 & 14009.9247555347 & 6771.07524446533 \tabularnewline
115 & 9638 & 17933.5089478609 & -8295.5089478609 \tabularnewline
116 & 13444 & 14501.2939446164 & -1057.29394461637 \tabularnewline
117 & 6072 & 14331.0899181638 & -8259.08991816385 \tabularnewline
118 & 13442 & 10413.3639526633 & 3028.63604733668 \tabularnewline
119 & 14457 & 11834.7654726629 & 2622.2345273371 \tabularnewline
120 & 17705 & 13211.170551342 & 4493.82944865796 \tabularnewline
121 & 16463 & 15688.0204582114 & 774.979541788551 \tabularnewline
122 & 19194 & 16501.4079134539 & 2692.59208654608 \tabularnewline
123 & 20688 & 18339.2432864744 & 2348.7567135256 \tabularnewline
124 & 14739 & 20146.0291120403 & -5407.02911204027 \tabularnewline
125 & 12702 & 18105.010568089 & -5403.01056808898 \tabularnewline
126 & 15760 & 15774.5791103412 & -14.5791103412448 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298893&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]4791[/C][C]123[/C][C]4668[/C][/ROW]
[ROW][C]4[/C][C]3178[/C][C]753.095166003286[/C][C]2424.90483399671[/C][/ROW]
[ROW][C]5[/C][C]2849[/C][C]485.360487440719[/C][C]2363.63951255928[/C][/ROW]
[ROW][C]6[/C][C]4716[/C][C]316.947993941057[/C][C]4399.05200605894[/C][/ROW]
[ROW][C]7[/C][C]3085[/C][C]1318.9880260134[/C][C]1766.0119739866[/C][/ROW]
[ROW][C]8[/C][C]2799[/C][C]1208.87480273259[/C][C]1590.12519726741[/C][/ROW]
[ROW][C]9[/C][C]3573[/C][C]1103.82813947596[/C][C]2469.17186052404[/C][/ROW]
[ROW][C]10[/C][C]2721[/C][C]1534.96245219919[/C][C]1186.03754780081[/C][/ROW]
[ROW][C]11[/C][C]3355[/C][C]1441.66406143416[/C][C]1913.33593856584[/C][/ROW]
[ROW][C]12[/C][C]5667[/C][C]1785.00112607936[/C][C]3881.99887392064[/C][/ROW]
[ROW][C]13[/C][C]2856[/C][C]3240.31107339837[/C][C]-384.311073398366[/C][/ROW]
[ROW][C]14[/C][C]1944[/C][C]2718.63374581114[/C][C]-774.633745811135[/C][/ROW]
[ROW][C]15[/C][C]4188[/C][C]1976.22062122709[/C][C]2211.77937877291[/C][/ROW]
[ROW][C]16[/C][C]2949[/C][C]2722.42365590099[/C][C]226.576344099009[/C][/ROW]
[ROW][C]17[/C][C]3567[/C][C]2570.54705286346[/C][C]996.452947136538[/C][/ROW]
[ROW][C]18[/C][C]4137[/C][C]2825.40404158863[/C][C]1311.59595841137[/C][/ROW]
[ROW][C]19[/C][C]3494[/C][C]3295.46957541324[/C][C]198.530424586764[/C][/ROW]
[ROW][C]20[/C][C]2489[/C][C]3265.85289414481[/C][C]-776.852894144811[/C][/ROW]
[ROW][C]21[/C][C]3244[/C][C]2747.10752347906[/C][C]496.89247652094[/C][/ROW]
[ROW][C]22[/C][C]2669[/C][C]2839.20995983668[/C][C]-170.209959836679[/C][/ROW]
[ROW][C]23[/C][C]2529[/C][C]2616.24438314996[/C][C]-87.2443831499572[/C][/ROW]
[ROW][C]24[/C][C]3377[/C][C]2426.618769271[/C][C]950.381230729[/C][/ROW]
[ROW][C]25[/C][C]3366[/C][C]2764.01662674368[/C][C]601.98337325632[/C][/ROW]
[ROW][C]26[/C][C]2073[/C][C]2974.11100839687[/C][C]-901.111008396873[/C][/ROW]
[ROW][C]27[/C][C]4133[/C][C]2446.40219036945[/C][C]1686.59780963055[/C][/ROW]
[ROW][C]28[/C][C]4213[/C][C]3196.1774363684[/C][C]1016.8225636316[/C][/ROW]
[ROW][C]29[/C][C]3710[/C][C]3693.64745112102[/C][C]16.3525488789783[/C][/ROW]
[ROW][C]30[/C][C]5123[/C][C]3733.24420455692[/C][C]1389.75579544308[/C][/ROW]
[ROW][C]31[/C][C]3141[/C][C]4477.5166486383[/C][C]-1336.5166486383[/C][/ROW]
[ROW][C]32[/C][C]3084[/C][C]3899.63970080245[/C][C]-815.63970080245[/C][/ROW]
[ROW][C]33[/C][C]3804[/C][C]3516.63726749961[/C][C]287.362732500394[/C][/ROW]
[ROW][C]34[/C][C]3203[/C][C]3654.89535900508[/C][C]-451.895359005076[/C][/ROW]
[ROW][C]35[/C][C]2757[/C][C]3429.81465855297[/C][C]-672.81465855297[/C][/ROW]
[ROW][C]36[/C][C]2243[/C][C]3067.16493209601[/C][C]-824.164932096012[/C][/ROW]
[ROW][C]37[/C][C]5229[/C][C]2590.68759557383[/C][C]2638.31240442617[/C][/ROW]
[ROW][C]38[/C][C]2857[/C][C]3844.11330152711[/C][C]-987.113301527113[/C][/ROW]
[ROW][C]39[/C][C]3395[/C][C]3381.92755250381[/C][C]13.0724474961858[/C][/ROW]
[ROW][C]40[/C][C]4882[/C][C]3379.07090648552[/C][C]1502.92909351448[/C][/ROW]
[ROW][C]41[/C][C]7140[/C][C]4140.38914326225[/C][C]2999.61085673775[/C][/ROW]
[ROW][C]42[/C][C]8945[/C][C]5749.69221953835[/C][C]3195.30778046165[/C][/ROW]
[ROW][C]43[/C][C]6866[/C][C]7620.97680064703[/C][C]-754.976800647033[/C][/ROW]
[ROW][C]44[/C][C]4205[/C][C]7640.20297195694[/C][C]-3435.20297195694[/C][/ROW]
[ROW][C]45[/C][C]3217[/C][C]6245.26164529032[/C][C]-3028.26164529032[/C][/ROW]
[ROW][C]46[/C][C]3079[/C][C]4873.67691806702[/C][C]-1794.67691806702[/C][/ROW]
[ROW][C]47[/C][C]2263[/C][C]3970.99505111739[/C][C]-1707.99505111739[/C][/ROW]
[ROW][C]48[/C][C]4187[/C][C]3015.98876055592[/C][C]1171.01123944408[/C][/ROW]
[ROW][C]49[/C][C]2665[/C][C]3444.24456271929[/C][C]-779.244562719289[/C][/ROW]
[ROW][C]50[/C][C]2073[/C][C]2936.2254579756[/C][C]-863.225457975604[/C][/ROW]
[ROW][C]51[/C][C]3540[/C][C]2343.16464385963[/C][C]1196.83535614037[/C][/ROW]
[ROW][C]52[/C][C]3686[/C][C]2759.23936165541[/C][C]926.760638344588[/C][/ROW]
[ROW][C]53[/C][C]2384[/C][C]3101.43233343241[/C][C]-717.432333432407[/C][/ROW]
[ROW][C]54[/C][C]4500[/C][C]2651.02427742335[/C][C]1848.97572257665[/C][/ROW]
[ROW][C]55[/C][C]1679[/C][C]3477.08622053101[/C][C]-1798.08622053101[/C][/ROW]
[ROW][C]56[/C][C]868[/C][C]2533.89920563778[/C][C]-1665.89920563778[/C][/ROW]
[ROW][C]57[/C][C]1869[/C][C]1561.52288883316[/C][C]307.477111166839[/C][/ROW]
[ROW][C]58[/C][C]3710[/C][C]1510.59196862254[/C][C]2199.40803137746[/C][/ROW]
[ROW][C]59[/C][C]6904[/C][C]2445.74727290648[/C][C]4458.25272709352[/C][/ROW]
[ROW][C]60[/C][C]3415[/C][C]4656.99881969501[/C][C]-1241.99881969501[/C][/ROW]
[ROW][C]61[/C][C]938[/C][C]4187.5099378689[/C][C]-3249.5099378689[/C][/ROW]
[ROW][C]62[/C][C]3359[/C][C]2622.32980930683[/C][C]736.670190693171[/C][/ROW]
[ROW][C]63[/C][C]3551[/C][C]2924.68076862729[/C][C]626.319231372714[/C][/ROW]
[ROW][C]64[/C][C]2278[/C][C]3210.19394967166[/C][C]-932.193949671663[/C][/ROW]
[ROW][C]65[/C][C]3033[/C][C]2730.81667451249[/C][C]302.183325487515[/C][/ROW]
[ROW][C]66[/C][C]2280[/C][C]2833.73936618154[/C][C]-553.739366181539[/C][/ROW]
[ROW][C]67[/C][C]2901[/C][C]2514.33794854305[/C][C]386.662051456953[/C][/ROW]
[ROW][C]68[/C][C]4812[/C][C]2646.99095424454[/C][C]2165.00904575546[/C][/ROW]
[ROW][C]69[/C][C]4882[/C][C]3711.79317952826[/C][C]1170.20682047174[/C][/ROW]
[ROW][C]70[/C][C]7896[/C][C]4383.52090501858[/C][C]3512.47909498142[/C][/ROW]
[ROW][C]71[/C][C]5048[/C][C]6318.61666340487[/C][C]-1270.61666340487[/C][/ROW]
[ROW][C]72[/C][C]3741[/C][C]5991.98123710903[/C][C]-2250.98123710903[/C][/ROW]
[ROW][C]73[/C][C]4418[/C][C]5094.4684162779[/C][C]-676.4684162779[/C][/ROW]
[ROW][C]74[/C][C]3471[/C][C]4882.46569703006[/C][C]-1411.46569703006[/C][/ROW]
[ROW][C]75[/C][C]5055[/C][C]4257.35117873406[/C][C]797.648821265937[/C][/ROW]
[ROW][C]76[/C][C]7595[/C][C]4688.20055039822[/C][C]2906.79944960178[/C][/ROW]
[ROW][C]77[/C][C]8124[/C][C]6242.8726651849[/C][C]1881.1273348151[/C][/ROW]
[ROW][C]78[/C][C]2333[/C][C]7428.63822222792[/C][C]-5095.63822222792[/C][/ROW]
[ROW][C]79[/C][C]3008[/C][C]5140.5966633499[/C][C]-2132.5966633499[/C][/ROW]
[ROW][C]80[/C][C]2744[/C][C]4096.26583614756[/C][C]-1352.26583614756[/C][/ROW]
[ROW][C]81[/C][C]2833[/C][C]3336.85185277977[/C][C]-503.851852779774[/C][/ROW]
[ROW][C]82[/C][C]2428[/C][C]2939.30825557055[/C][C]-511.308255570551[/C][/ROW]
[ROW][C]83[/C][C]4269[/C][C]2510.78293836928[/C][C]1758.21706163072[/C][/ROW]
[ROW][C]84[/C][C]3207[/C][C]3217.70278232577[/C][C]-10.7027823257727[/C][/ROW]
[ROW][C]85[/C][C]5170[/C][C]3112.92651188652[/C][C]2057.07348811348[/C][/ROW]
[ROW][C]86[/C][C]7767[/C][C]4067.19575071209[/C][C]3699.80424928791[/C][/ROW]
[ROW][C]87[/C][C]4544[/C][C]5974.1637660536[/C][C]-1430.1637660536[/C][/ROW]
[ROW][C]88[/C][C]3741[/C][C]5451.74548185899[/C][C]-1710.74548185899[/C][/ROW]
[ROW][C]89[/C][C]2193[/C][C]4708.44974319037[/C][C]-2515.44974319037[/C][/ROW]
[ROW][C]90[/C][C]3432[/C][C]3460.56727420568[/C][C]-28.5672742056809[/C][/ROW]
[ROW][C]91[/C][C]5282[/C][C]3351.47806101655[/C][C]1930.52193898345[/C][/ROW]
[ROW][C]92[/C][C]6635[/C][C]4244.77516743194[/C][C]2390.22483256806[/C][/ROW]
[ROW][C]93[/C][C]4222[/C][C]5477.7119431462[/C][C]-1255.7119431462[/C][/ROW]
[ROW][C]94[/C][C]7317[/C][C]4971.15301102456[/C][C]2345.84698897544[/C][/ROW]
[ROW][C]95[/C][C]4132[/C][C]6242.50580246269[/C][C]-2110.50580246269[/C][/ROW]
[ROW][C]96[/C][C]5048[/C][C]5356.67668066851[/C][C]-308.676680668508[/C][/ROW]
[ROW][C]97[/C][C]4383[/C][C]5280.41734694203[/C][C]-897.417346942033[/C][/ROW]
[ROW][C]98[/C][C]3761[/C][C]4885.8209863185[/C][C]-1124.8209863185[/C][/ROW]
[ROW][C]99[/C][C]4081[/C][C]4326.31634816131[/C][C]-245.316348161306[/C][/ROW]
[ROW][C]100[/C][C]6491[/C][C]4156.87503883208[/C][C]2334.12496116792[/C][/ROW]
[ROW][C]101[/C][C]5859[/C][C]5296.03252117892[/C][C]562.967478821081[/C][/ROW]
[ROW][C]102[/C][C]7139[/C][C]5653.39220730618[/C][C]1485.60779269382[/C][/ROW]
[ROW][C]103[/C][C]7682[/C][C]6513.90210305474[/C][C]1168.09789694526[/C][/ROW]
[ROW][C]104[/C][C]8649[/C][C]7291.78892798038[/C][C]1357.21107201962[/C][/ROW]
[ROW][C]105[/C][C]6146[/C][C]8229.5536079523[/C][C]-2083.5536079523[/C][/ROW]
[ROW][C]106[/C][C]7137[/C][C]7477.27626925091[/C][C]-340.276269250909[/C][/ROW]
[ROW][C]107[/C][C]9948[/C][C]7506.01701564087[/C][C]2441.98298435913[/C][/ROW]
[ROW][C]108[/C][C]15819[/C][C]8942.1707528951[/C][C]6876.8292471049[/C][/ROW]
[ROW][C]109[/C][C]8370[/C][C]12782.5790293627[/C][C]-4412.57902936273[/C][/ROW]
[ROW][C]110[/C][C]13222[/C][C]11208.4853573427[/C][C]2013.51464265726[/C][/ROW]
[ROW][C]111[/C][C]16711[/C][C]12689.5486720135[/C][C]4021.45132798645[/C][/ROW]
[ROW][C]112[/C][C]19059[/C][C]15308.1107718541[/C][C]3750.88922814585[/C][/ROW]
[ROW][C]113[/C][C]8303[/C][C]18004.8055808662[/C][C]-9701.80558086616[/C][/ROW]
[ROW][C]114[/C][C]20781[/C][C]14009.9247555347[/C][C]6771.07524446533[/C][/ROW]
[ROW][C]115[/C][C]9638[/C][C]17933.5089478609[/C][C]-8295.5089478609[/C][/ROW]
[ROW][C]116[/C][C]13444[/C][C]14501.2939446164[/C][C]-1057.29394461637[/C][/ROW]
[ROW][C]117[/C][C]6072[/C][C]14331.0899181638[/C][C]-8259.08991816385[/C][/ROW]
[ROW][C]118[/C][C]13442[/C][C]10413.3639526633[/C][C]3028.63604733668[/C][/ROW]
[ROW][C]119[/C][C]14457[/C][C]11834.7654726629[/C][C]2622.2345273371[/C][/ROW]
[ROW][C]120[/C][C]17705[/C][C]13211.170551342[/C][C]4493.82944865796[/C][/ROW]
[ROW][C]121[/C][C]16463[/C][C]15688.0204582114[/C][C]774.979541788551[/C][/ROW]
[ROW][C]122[/C][C]19194[/C][C]16501.4079134539[/C][C]2692.59208654608[/C][/ROW]
[ROW][C]123[/C][C]20688[/C][C]18339.2432864744[/C][C]2348.7567135256[/C][/ROW]
[ROW][C]124[/C][C]14739[/C][C]20146.0291120403[/C][C]-5407.02911204027[/C][/ROW]
[ROW][C]125[/C][C]12702[/C][C]18105.010568089[/C][C]-5403.01056808898[/C][/ROW]
[ROW][C]126[/C][C]15760[/C][C]15774.5791103412[/C][C]-14.5791103412448[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298893&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298893&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
347911234668
43178753.0951660032862424.90483399671
52849485.3604874407192363.63951255928
64716316.9479939410574399.05200605894
730851318.98802601341766.0119739866
827991208.874802732591590.12519726741
935731103.828139475962469.17186052404
1027211534.962452199191186.03754780081
1133551441.664061434161913.33593856584
1256671785.001126079363881.99887392064
1328563240.31107339837-384.311073398366
1419442718.63374581114-774.633745811135
1541881976.220621227092211.77937877291
1629492722.42365590099226.576344099009
1735672570.54705286346996.452947136538
1841372825.404041588631311.59595841137
1934943295.46957541324198.530424586764
2024893265.85289414481-776.852894144811
2132442747.10752347906496.89247652094
2226692839.20995983668-170.209959836679
2325292616.24438314996-87.2443831499572
2433772426.618769271950.381230729
2533662764.01662674368601.98337325632
2620732974.11100839687-901.111008396873
2741332446.402190369451686.59780963055
2842133196.17743636841016.8225636316
2937103693.6474511210216.3525488789783
3051233733.244204556921389.75579544308
3131414477.5166486383-1336.5166486383
3230843899.63970080245-815.63970080245
3338043516.63726749961287.362732500394
3432033654.89535900508-451.895359005076
3527573429.81465855297-672.81465855297
3622433067.16493209601-824.164932096012
3752292590.687595573832638.31240442617
3828573844.11330152711-987.113301527113
3933953381.9275525038113.0724474961858
4048823379.070906485521502.92909351448
4171404140.389143262252999.61085673775
4289455749.692219538353195.30778046165
4368667620.97680064703-754.976800647033
4442057640.20297195694-3435.20297195694
4532176245.26164529032-3028.26164529032
4630794873.67691806702-1794.67691806702
4722633970.99505111739-1707.99505111739
4841873015.988760555921171.01123944408
4926653444.24456271929-779.244562719289
5020732936.2254579756-863.225457975604
5135402343.164643859631196.83535614037
5236862759.23936165541926.760638344588
5323843101.43233343241-717.432333432407
5445002651.024277423351848.97572257665
5516793477.08622053101-1798.08622053101
568682533.89920563778-1665.89920563778
5718691561.52288883316307.477111166839
5837101510.591968622542199.40803137746
5969042445.747272906484458.25272709352
6034154656.99881969501-1241.99881969501
619384187.5099378689-3249.5099378689
6233592622.32980930683736.670190693171
6335512924.68076862729626.319231372714
6422783210.19394967166-932.193949671663
6530332730.81667451249302.183325487515
6622802833.73936618154-553.739366181539
6729012514.33794854305386.662051456953
6848122646.990954244542165.00904575546
6948823711.793179528261170.20682047174
7078964383.520905018583512.47909498142
7150486318.61666340487-1270.61666340487
7237415991.98123710903-2250.98123710903
7344185094.4684162779-676.4684162779
7434714882.46569703006-1411.46569703006
7550554257.35117873406797.648821265937
7675954688.200550398222906.79944960178
7781246242.87266518491881.1273348151
7823337428.63822222792-5095.63822222792
7930085140.5966633499-2132.5966633499
8027444096.26583614756-1352.26583614756
8128333336.85185277977-503.851852779774
8224282939.30825557055-511.308255570551
8342692510.782938369281758.21706163072
8432073217.70278232577-10.7027823257727
8551703112.926511886522057.07348811348
8677674067.195750712093699.80424928791
8745445974.1637660536-1430.1637660536
8837415451.74548185899-1710.74548185899
8921934708.44974319037-2515.44974319037
9034323460.56727420568-28.5672742056809
9152823351.478061016551930.52193898345
9266354244.775167431942390.22483256806
9342225477.7119431462-1255.7119431462
9473174971.153011024562345.84698897544
9541326242.50580246269-2110.50580246269
9650485356.67668066851-308.676680668508
9743835280.41734694203-897.417346942033
9837614885.8209863185-1124.8209863185
9940814326.31634816131-245.316348161306
10064914156.875038832082334.12496116792
10158595296.03252117892562.967478821081
10271395653.392207306181485.60779269382
10376826513.902103054741168.09789694526
10486497291.788927980381357.21107201962
10561468229.5536079523-2083.5536079523
10671377477.27626925091-340.276269250909
10799487506.017015640872441.98298435913
108158198942.17075289516876.8292471049
109837012782.5790293627-4412.57902936273
1101322211208.48535734272013.51464265726
1111671112689.54867201354021.45132798645
1121905915308.11077185413750.88922814585
113830318004.8055808662-9701.80558086616
1142078114009.92475553476771.07524446533
115963817933.5089478609-8295.5089478609
1161344414501.2939446164-1057.29394461637
117607214331.0899181638-8259.08991816385
1181344210413.36395266333028.63604733668
1191445711834.76547266292622.2345273371
1201770513211.1705513424493.82944865796
1211646315688.0204582114774.979541788551
1221919416501.40791345392692.59208654608
1232068818339.24328647442348.7567135256
1241473920146.0291120403-5407.02911204027
1251270218105.010568089-5403.01056808898
1261576015774.5791103412-14.5791103412448







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12715914.169037220610779.722062833321048.6160116078
12816060.444058338210291.097643124521829.7904735518
12916206.71907945589745.97200338922667.4661555226
13016352.99410057349149.9778990690623556.0103020777
13116499.2691216918507.7023533243224490.8358900577
13216645.54414280867822.8712868578125468.2169987594
13316791.81916392627098.5273789556426485.1109488968
13416938.09418504386337.1791382451527539.0092318425
13517084.36920616145540.9186204152528627.8197919076
13617230.64422727914711.5119523655429749.7765021926
13717376.91924839673850.4682429431930903.3702538501
13817523.19426951432959.0919771016332087.2965619269
13917669.46929063192038.5230057968533300.4155754669
14017815.74431174951089.76727513434541.721348365
14117962.0193328671113.72063821077635810.3180275234
14218108.2943539847-888.81252185516537105.4012298246
14318254.5693751023-1917.1045862838338426.2433364885
14418400.8443962199-2970.4929753778839772.1817678178

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 15914.1690372206 & 10779.7220628333 & 21048.6160116078 \tabularnewline
128 & 16060.4440583382 & 10291.0976431245 & 21829.7904735518 \tabularnewline
129 & 16206.7190794558 & 9745.972003389 & 22667.4661555226 \tabularnewline
130 & 16352.9941005734 & 9149.97789906906 & 23556.0103020777 \tabularnewline
131 & 16499.269121691 & 8507.70235332432 & 24490.8358900577 \tabularnewline
132 & 16645.5441428086 & 7822.87128685781 & 25468.2169987594 \tabularnewline
133 & 16791.8191639262 & 7098.52737895564 & 26485.1109488968 \tabularnewline
134 & 16938.0941850438 & 6337.17913824515 & 27539.0092318425 \tabularnewline
135 & 17084.3692061614 & 5540.91862041525 & 28627.8197919076 \tabularnewline
136 & 17230.6442272791 & 4711.51195236554 & 29749.7765021926 \tabularnewline
137 & 17376.9192483967 & 3850.46824294319 & 30903.3702538501 \tabularnewline
138 & 17523.1942695143 & 2959.09197710163 & 32087.2965619269 \tabularnewline
139 & 17669.4692906319 & 2038.52300579685 & 33300.4155754669 \tabularnewline
140 & 17815.7443117495 & 1089.767275134 & 34541.721348365 \tabularnewline
141 & 17962.0193328671 & 113.720638210776 & 35810.3180275234 \tabularnewline
142 & 18108.2943539847 & -888.812521855165 & 37105.4012298246 \tabularnewline
143 & 18254.5693751023 & -1917.10458628383 & 38426.2433364885 \tabularnewline
144 & 18400.8443962199 & -2970.49297537788 & 39772.1817678178 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298893&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]15914.1690372206[/C][C]10779.7220628333[/C][C]21048.6160116078[/C][/ROW]
[ROW][C]128[/C][C]16060.4440583382[/C][C]10291.0976431245[/C][C]21829.7904735518[/C][/ROW]
[ROW][C]129[/C][C]16206.7190794558[/C][C]9745.972003389[/C][C]22667.4661555226[/C][/ROW]
[ROW][C]130[/C][C]16352.9941005734[/C][C]9149.97789906906[/C][C]23556.0103020777[/C][/ROW]
[ROW][C]131[/C][C]16499.269121691[/C][C]8507.70235332432[/C][C]24490.8358900577[/C][/ROW]
[ROW][C]132[/C][C]16645.5441428086[/C][C]7822.87128685781[/C][C]25468.2169987594[/C][/ROW]
[ROW][C]133[/C][C]16791.8191639262[/C][C]7098.52737895564[/C][C]26485.1109488968[/C][/ROW]
[ROW][C]134[/C][C]16938.0941850438[/C][C]6337.17913824515[/C][C]27539.0092318425[/C][/ROW]
[ROW][C]135[/C][C]17084.3692061614[/C][C]5540.91862041525[/C][C]28627.8197919076[/C][/ROW]
[ROW][C]136[/C][C]17230.6442272791[/C][C]4711.51195236554[/C][C]29749.7765021926[/C][/ROW]
[ROW][C]137[/C][C]17376.9192483967[/C][C]3850.46824294319[/C][C]30903.3702538501[/C][/ROW]
[ROW][C]138[/C][C]17523.1942695143[/C][C]2959.09197710163[/C][C]32087.2965619269[/C][/ROW]
[ROW][C]139[/C][C]17669.4692906319[/C][C]2038.52300579685[/C][C]33300.4155754669[/C][/ROW]
[ROW][C]140[/C][C]17815.7443117495[/C][C]1089.767275134[/C][C]34541.721348365[/C][/ROW]
[ROW][C]141[/C][C]17962.0193328671[/C][C]113.720638210776[/C][C]35810.3180275234[/C][/ROW]
[ROW][C]142[/C][C]18108.2943539847[/C][C]-888.812521855165[/C][C]37105.4012298246[/C][/ROW]
[ROW][C]143[/C][C]18254.5693751023[/C][C]-1917.10458628383[/C][C]38426.2433364885[/C][/ROW]
[ROW][C]144[/C][C]18400.8443962199[/C][C]-2970.49297537788[/C][C]39772.1817678178[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298893&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298893&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
12715914.169037220610779.722062833321048.6160116078
12816060.444058338210291.097643124521829.7904735518
12916206.71907945589745.97200338922667.4661555226
13016352.99410057349149.9778990690623556.0103020777
13116499.2691216918507.7023533243224490.8358900577
13216645.54414280867822.8712868578125468.2169987594
13316791.81916392627098.5273789556426485.1109488968
13416938.09418504386337.1791382451527539.0092318425
13517084.36920616145540.9186204152528627.8197919076
13617230.64422727914711.5119523655429749.7765021926
13717376.91924839673850.4682429431930903.3702538501
13817523.19426951432959.0919771016332087.2965619269
13917669.46929063192038.5230057968533300.4155754669
14017815.74431174951089.76727513434541.721348365
14117962.0193328671113.72063821077635810.3180275234
14218108.2943539847-888.81252185516537105.4012298246
14318254.5693751023-1917.1045862838338426.2433364885
14418400.8443962199-2970.4929753778839772.1817678178



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):
par4 <- '18'
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
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')