Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 03 Aug 2012 08:36:28 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Aug/03/t1343997473a3tks0v823mf303.htm/, Retrieved Mon, 29 Apr 2024 23:27:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=168984, Retrieved Mon, 29 Apr 2024 23:27:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSelleslaghs Tessa
Estimated Impact139
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks A stap 32] [2012-08-03 12:36:28] [5f178b5bce8a01d64692a8a5c649399b] [Current]
- R P     [Exponential Smoothing] [Tijdreeks A stap 32] [2012-08-04 12:29:12] [232e08efb3d57a376dc11ef19bbd5ba5]
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Dataseries X:
3028
3017
3007
2986
3193
3183
3028
2924
2935
2935
2945
2966
2955
3038
3069
3038
3152
3079
2914
2873
2873
2893
2811
2873
2821
2873
2955
2986
3059
3028
2842
2769
2738
2769
2718
2738
2676
2780
2831
2842
3038
3038
2780
2718
2718
2749
2614
2552
2480
2501
2594
2521
2718
2749
2552
2480
2439
2480
2366
2325
2160
2201
2211
2222
2418
2397
2160
2056
2015
2067
1870
1736
1488
1509
1509
1488
1664
1674
1467
1426
1343
1457
1250
1126
889
940
878
899
1054
1085
982
971
971
1106
868
713
444
661
630
641
889
858
744
796
796
982
765
641
444
703
682
692
909
889
816
827
878
992
816
672




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168984&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168984&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168984&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.791736231887363
beta0.0130819811835399
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.791736231887363 \tabularnewline
beta & 0.0130819811835399 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168984&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]0.791736231887363[/C][/ROW]
[ROW][C]beta[/C][C]0.0130819811835399[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168984&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168984&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
alpha0.791736231887363
beta0.0130819811835399
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1329552967.17120726496-12.171207264957
1430383043.40540765421-5.40540765421065
1530693070.77368367282-1.77368367281815
1630383038.62395626122-0.623956261223611
1731523155.37804708463-3.37804708462863
1830793085.04163636722-6.04163636722478
1929142983.74212272255-69.7421227225523
2028732821.7862735057251.2137264942785
2128732865.500997643017.49900235698988
2228932862.3911949027730.6088050972276
2328112892.18695701075-81.186957010751
2428732850.1290715256522.8709284743527
2528212859.20131452154-38.2013145215446
2628732915.26033975697-42.2603397569706
2729552912.8485960206642.1514039793442
2829862914.8133604990571.1866395009456
2930593087.69066313289-28.6906631328943
3030282996.3381717940531.6618282059499
3128422911.59343039243-69.5934303924314
3227692774.91764388329-5.91764388329193
3327382763.67507867414-25.675078674145
3427692738.1493685200830.8506314799224
3527182743.89237127205-25.8923712720521
3627382766.89619716935-28.8961971693457
3726762721.33871592172-45.3387159217182
3827802769.9028486979210.09715130208
3928312826.068021775794.9319782242078
4028422803.7699928185238.2300071814816
4130382928.57035146526109.429648534738
4230382959.3893699479778.6106300520305
4327802891.46158297333-111.461582973326
4427182735.1986625086-17.1986625086006
4527182711.092945564656.90705443534716
4627492723.6566141014825.3433858985186
4726142713.68544424797-99.6854442479739
4825522677.33834716826-125.338347168264
4924802550.70015773927-70.7001577392725
5025012589.16773731071-88.1677373107141
5125942563.8772794518730.1227205481305
5225212566.13931956222-45.1393195622231
5327182636.5788438663981.421156133606
5427492635.3313185103113.668681489704
5525522552.46549810811-0.465498108108022
5624802501.75378252738-21.7537825273826
5724392477.05481179945-38.0548117994458
5824802455.3873224149824.6126775850194
5923662416.31824149944-50.3182414994444
6023252411.74528949168-86.7452894916751
6121602325.47241631677-165.472416316766
6222012282.71653840266-81.7165384026625
6322112284.68520044721-73.6852004472084
6422222185.5250594741736.474940525834
6524182344.2254972291873.7745027708211
6623972340.8466155862556.1533844137521
6721602185.28490792579-25.284907925789
6820562106.84319314327-50.8431931432742
6920152051.77088047624-36.7708804762356
7020672040.237303998126.7626960018997
7118701983.35335425638-113.353354256384
7217361916.72217974802-180.722179748022
7314881734.11042031886-246.110420318861
7415091638.58065212051-129.580652120512
7515091597.45727072019-88.4572707201924
7614881502.52198403398-14.521984033978
7716641621.0643282202542.9356717797521
7816741581.7298456346592.2701543653525
7914671430.3069857695636.6930142304416
8014261388.7590458220337.2409541779707
8113431400.41569963992-57.4156996399188
8214571379.6135883314777.3864116685347
8312501327.99848038525-77.9984803852547
8411261270.06405089914-144.064050899141
858891097.97304053713-208.973040537133
869401051.61504133964-111.615041339642
878781028.96610496569-150.966104965694
88899894.976826565244.02317343475966
8910541035.39894859118.6010514090035
901085982.050962141557102.949037858443
91982822.597374466428159.402625533572
92971874.67727582369996.3227241763007
93971910.36957435116460.630425648836
9411061009.2979314805396.7020685194655
95868939.009425641488-71.0094256414884
96713871.316548211562-158.316548211562
97444672.742637478365-228.742637478365
98661629.12322159875931.8767784012415
99630711.48751627656-81.4875162765604
100641665.10618717959-24.1061871795898
101889786.322551938861102.677448061139
102858818.00757683950639.9924231604938
103744620.714173764716123.285826235284
104796630.935740218085165.064259781915
105796714.20568114161281.7943188583876
106982838.207770773122143.792229226878
107765771.566854102381-6.5668541023814
108641738.672878155473-97.6728781554726
109444576.033964073223-132.033964073223
110703666.84995702207636.1500429779239
111682732.62220172202-50.6222017220196
112692726.582525922417-34.5825259224174
113909869.7543365174539.2456634825498
114889841.3516116654247.6483883345797
115816670.734519928407145.265480071593
116827710.554570812474116.445429187526
117878740.981003971078137.018996028922
118992925.18227188292766.8177281170734
119816769.05012479031946.9498752096812
120672762.874117259745-90.874117259745

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2955 & 2967.17120726496 & -12.171207264957 \tabularnewline
14 & 3038 & 3043.40540765421 & -5.40540765421065 \tabularnewline
15 & 3069 & 3070.77368367282 & -1.77368367281815 \tabularnewline
16 & 3038 & 3038.62395626122 & -0.623956261223611 \tabularnewline
17 & 3152 & 3155.37804708463 & -3.37804708462863 \tabularnewline
18 & 3079 & 3085.04163636722 & -6.04163636722478 \tabularnewline
19 & 2914 & 2983.74212272255 & -69.7421227225523 \tabularnewline
20 & 2873 & 2821.78627350572 & 51.2137264942785 \tabularnewline
21 & 2873 & 2865.50099764301 & 7.49900235698988 \tabularnewline
22 & 2893 & 2862.39119490277 & 30.6088050972276 \tabularnewline
23 & 2811 & 2892.18695701075 & -81.186957010751 \tabularnewline
24 & 2873 & 2850.12907152565 & 22.8709284743527 \tabularnewline
25 & 2821 & 2859.20131452154 & -38.2013145215446 \tabularnewline
26 & 2873 & 2915.26033975697 & -42.2603397569706 \tabularnewline
27 & 2955 & 2912.84859602066 & 42.1514039793442 \tabularnewline
28 & 2986 & 2914.81336049905 & 71.1866395009456 \tabularnewline
29 & 3059 & 3087.69066313289 & -28.6906631328943 \tabularnewline
30 & 3028 & 2996.33817179405 & 31.6618282059499 \tabularnewline
31 & 2842 & 2911.59343039243 & -69.5934303924314 \tabularnewline
32 & 2769 & 2774.91764388329 & -5.91764388329193 \tabularnewline
33 & 2738 & 2763.67507867414 & -25.675078674145 \tabularnewline
34 & 2769 & 2738.14936852008 & 30.8506314799224 \tabularnewline
35 & 2718 & 2743.89237127205 & -25.8923712720521 \tabularnewline
36 & 2738 & 2766.89619716935 & -28.8961971693457 \tabularnewline
37 & 2676 & 2721.33871592172 & -45.3387159217182 \tabularnewline
38 & 2780 & 2769.90284869792 & 10.09715130208 \tabularnewline
39 & 2831 & 2826.06802177579 & 4.9319782242078 \tabularnewline
40 & 2842 & 2803.76999281852 & 38.2300071814816 \tabularnewline
41 & 3038 & 2928.57035146526 & 109.429648534738 \tabularnewline
42 & 3038 & 2959.38936994797 & 78.6106300520305 \tabularnewline
43 & 2780 & 2891.46158297333 & -111.461582973326 \tabularnewline
44 & 2718 & 2735.1986625086 & -17.1986625086006 \tabularnewline
45 & 2718 & 2711.09294556465 & 6.90705443534716 \tabularnewline
46 & 2749 & 2723.65661410148 & 25.3433858985186 \tabularnewline
47 & 2614 & 2713.68544424797 & -99.6854442479739 \tabularnewline
48 & 2552 & 2677.33834716826 & -125.338347168264 \tabularnewline
49 & 2480 & 2550.70015773927 & -70.7001577392725 \tabularnewline
50 & 2501 & 2589.16773731071 & -88.1677373107141 \tabularnewline
51 & 2594 & 2563.87727945187 & 30.1227205481305 \tabularnewline
52 & 2521 & 2566.13931956222 & -45.1393195622231 \tabularnewline
53 & 2718 & 2636.57884386639 & 81.421156133606 \tabularnewline
54 & 2749 & 2635.3313185103 & 113.668681489704 \tabularnewline
55 & 2552 & 2552.46549810811 & -0.465498108108022 \tabularnewline
56 & 2480 & 2501.75378252738 & -21.7537825273826 \tabularnewline
57 & 2439 & 2477.05481179945 & -38.0548117994458 \tabularnewline
58 & 2480 & 2455.38732241498 & 24.6126775850194 \tabularnewline
59 & 2366 & 2416.31824149944 & -50.3182414994444 \tabularnewline
60 & 2325 & 2411.74528949168 & -86.7452894916751 \tabularnewline
61 & 2160 & 2325.47241631677 & -165.472416316766 \tabularnewline
62 & 2201 & 2282.71653840266 & -81.7165384026625 \tabularnewline
63 & 2211 & 2284.68520044721 & -73.6852004472084 \tabularnewline
64 & 2222 & 2185.52505947417 & 36.474940525834 \tabularnewline
65 & 2418 & 2344.22549722918 & 73.7745027708211 \tabularnewline
66 & 2397 & 2340.84661558625 & 56.1533844137521 \tabularnewline
67 & 2160 & 2185.28490792579 & -25.284907925789 \tabularnewline
68 & 2056 & 2106.84319314327 & -50.8431931432742 \tabularnewline
69 & 2015 & 2051.77088047624 & -36.7708804762356 \tabularnewline
70 & 2067 & 2040.2373039981 & 26.7626960018997 \tabularnewline
71 & 1870 & 1983.35335425638 & -113.353354256384 \tabularnewline
72 & 1736 & 1916.72217974802 & -180.722179748022 \tabularnewline
73 & 1488 & 1734.11042031886 & -246.110420318861 \tabularnewline
74 & 1509 & 1638.58065212051 & -129.580652120512 \tabularnewline
75 & 1509 & 1597.45727072019 & -88.4572707201924 \tabularnewline
76 & 1488 & 1502.52198403398 & -14.521984033978 \tabularnewline
77 & 1664 & 1621.06432822025 & 42.9356717797521 \tabularnewline
78 & 1674 & 1581.72984563465 & 92.2701543653525 \tabularnewline
79 & 1467 & 1430.30698576956 & 36.6930142304416 \tabularnewline
80 & 1426 & 1388.75904582203 & 37.2409541779707 \tabularnewline
81 & 1343 & 1400.41569963992 & -57.4156996399188 \tabularnewline
82 & 1457 & 1379.61358833147 & 77.3864116685347 \tabularnewline
83 & 1250 & 1327.99848038525 & -77.9984803852547 \tabularnewline
84 & 1126 & 1270.06405089914 & -144.064050899141 \tabularnewline
85 & 889 & 1097.97304053713 & -208.973040537133 \tabularnewline
86 & 940 & 1051.61504133964 & -111.615041339642 \tabularnewline
87 & 878 & 1028.96610496569 & -150.966104965694 \tabularnewline
88 & 899 & 894.97682656524 & 4.02317343475966 \tabularnewline
89 & 1054 & 1035.398948591 & 18.6010514090035 \tabularnewline
90 & 1085 & 982.050962141557 & 102.949037858443 \tabularnewline
91 & 982 & 822.597374466428 & 159.402625533572 \tabularnewline
92 & 971 & 874.677275823699 & 96.3227241763007 \tabularnewline
93 & 971 & 910.369574351164 & 60.630425648836 \tabularnewline
94 & 1106 & 1009.29793148053 & 96.7020685194655 \tabularnewline
95 & 868 & 939.009425641488 & -71.0094256414884 \tabularnewline
96 & 713 & 871.316548211562 & -158.316548211562 \tabularnewline
97 & 444 & 672.742637478365 & -228.742637478365 \tabularnewline
98 & 661 & 629.123221598759 & 31.8767784012415 \tabularnewline
99 & 630 & 711.48751627656 & -81.4875162765604 \tabularnewline
100 & 641 & 665.10618717959 & -24.1061871795898 \tabularnewline
101 & 889 & 786.322551938861 & 102.677448061139 \tabularnewline
102 & 858 & 818.007576839506 & 39.9924231604938 \tabularnewline
103 & 744 & 620.714173764716 & 123.285826235284 \tabularnewline
104 & 796 & 630.935740218085 & 165.064259781915 \tabularnewline
105 & 796 & 714.205681141612 & 81.7943188583876 \tabularnewline
106 & 982 & 838.207770773122 & 143.792229226878 \tabularnewline
107 & 765 & 771.566854102381 & -6.5668541023814 \tabularnewline
108 & 641 & 738.672878155473 & -97.6728781554726 \tabularnewline
109 & 444 & 576.033964073223 & -132.033964073223 \tabularnewline
110 & 703 & 666.849957022076 & 36.1500429779239 \tabularnewline
111 & 682 & 732.62220172202 & -50.6222017220196 \tabularnewline
112 & 692 & 726.582525922417 & -34.5825259224174 \tabularnewline
113 & 909 & 869.75433651745 & 39.2456634825498 \tabularnewline
114 & 889 & 841.35161166542 & 47.6483883345797 \tabularnewline
115 & 816 & 670.734519928407 & 145.265480071593 \tabularnewline
116 & 827 & 710.554570812474 & 116.445429187526 \tabularnewline
117 & 878 & 740.981003971078 & 137.018996028922 \tabularnewline
118 & 992 & 925.182271882927 & 66.8177281170734 \tabularnewline
119 & 816 & 769.050124790319 & 46.9498752096812 \tabularnewline
120 & 672 & 762.874117259745 & -90.874117259745 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168984&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]2955[/C][C]2967.17120726496[/C][C]-12.171207264957[/C][/ROW]
[ROW][C]14[/C][C]3038[/C][C]3043.40540765421[/C][C]-5.40540765421065[/C][/ROW]
[ROW][C]15[/C][C]3069[/C][C]3070.77368367282[/C][C]-1.77368367281815[/C][/ROW]
[ROW][C]16[/C][C]3038[/C][C]3038.62395626122[/C][C]-0.623956261223611[/C][/ROW]
[ROW][C]17[/C][C]3152[/C][C]3155.37804708463[/C][C]-3.37804708462863[/C][/ROW]
[ROW][C]18[/C][C]3079[/C][C]3085.04163636722[/C][C]-6.04163636722478[/C][/ROW]
[ROW][C]19[/C][C]2914[/C][C]2983.74212272255[/C][C]-69.7421227225523[/C][/ROW]
[ROW][C]20[/C][C]2873[/C][C]2821.78627350572[/C][C]51.2137264942785[/C][/ROW]
[ROW][C]21[/C][C]2873[/C][C]2865.50099764301[/C][C]7.49900235698988[/C][/ROW]
[ROW][C]22[/C][C]2893[/C][C]2862.39119490277[/C][C]30.6088050972276[/C][/ROW]
[ROW][C]23[/C][C]2811[/C][C]2892.18695701075[/C][C]-81.186957010751[/C][/ROW]
[ROW][C]24[/C][C]2873[/C][C]2850.12907152565[/C][C]22.8709284743527[/C][/ROW]
[ROW][C]25[/C][C]2821[/C][C]2859.20131452154[/C][C]-38.2013145215446[/C][/ROW]
[ROW][C]26[/C][C]2873[/C][C]2915.26033975697[/C][C]-42.2603397569706[/C][/ROW]
[ROW][C]27[/C][C]2955[/C][C]2912.84859602066[/C][C]42.1514039793442[/C][/ROW]
[ROW][C]28[/C][C]2986[/C][C]2914.81336049905[/C][C]71.1866395009456[/C][/ROW]
[ROW][C]29[/C][C]3059[/C][C]3087.69066313289[/C][C]-28.6906631328943[/C][/ROW]
[ROW][C]30[/C][C]3028[/C][C]2996.33817179405[/C][C]31.6618282059499[/C][/ROW]
[ROW][C]31[/C][C]2842[/C][C]2911.59343039243[/C][C]-69.5934303924314[/C][/ROW]
[ROW][C]32[/C][C]2769[/C][C]2774.91764388329[/C][C]-5.91764388329193[/C][/ROW]
[ROW][C]33[/C][C]2738[/C][C]2763.67507867414[/C][C]-25.675078674145[/C][/ROW]
[ROW][C]34[/C][C]2769[/C][C]2738.14936852008[/C][C]30.8506314799224[/C][/ROW]
[ROW][C]35[/C][C]2718[/C][C]2743.89237127205[/C][C]-25.8923712720521[/C][/ROW]
[ROW][C]36[/C][C]2738[/C][C]2766.89619716935[/C][C]-28.8961971693457[/C][/ROW]
[ROW][C]37[/C][C]2676[/C][C]2721.33871592172[/C][C]-45.3387159217182[/C][/ROW]
[ROW][C]38[/C][C]2780[/C][C]2769.90284869792[/C][C]10.09715130208[/C][/ROW]
[ROW][C]39[/C][C]2831[/C][C]2826.06802177579[/C][C]4.9319782242078[/C][/ROW]
[ROW][C]40[/C][C]2842[/C][C]2803.76999281852[/C][C]38.2300071814816[/C][/ROW]
[ROW][C]41[/C][C]3038[/C][C]2928.57035146526[/C][C]109.429648534738[/C][/ROW]
[ROW][C]42[/C][C]3038[/C][C]2959.38936994797[/C][C]78.6106300520305[/C][/ROW]
[ROW][C]43[/C][C]2780[/C][C]2891.46158297333[/C][C]-111.461582973326[/C][/ROW]
[ROW][C]44[/C][C]2718[/C][C]2735.1986625086[/C][C]-17.1986625086006[/C][/ROW]
[ROW][C]45[/C][C]2718[/C][C]2711.09294556465[/C][C]6.90705443534716[/C][/ROW]
[ROW][C]46[/C][C]2749[/C][C]2723.65661410148[/C][C]25.3433858985186[/C][/ROW]
[ROW][C]47[/C][C]2614[/C][C]2713.68544424797[/C][C]-99.6854442479739[/C][/ROW]
[ROW][C]48[/C][C]2552[/C][C]2677.33834716826[/C][C]-125.338347168264[/C][/ROW]
[ROW][C]49[/C][C]2480[/C][C]2550.70015773927[/C][C]-70.7001577392725[/C][/ROW]
[ROW][C]50[/C][C]2501[/C][C]2589.16773731071[/C][C]-88.1677373107141[/C][/ROW]
[ROW][C]51[/C][C]2594[/C][C]2563.87727945187[/C][C]30.1227205481305[/C][/ROW]
[ROW][C]52[/C][C]2521[/C][C]2566.13931956222[/C][C]-45.1393195622231[/C][/ROW]
[ROW][C]53[/C][C]2718[/C][C]2636.57884386639[/C][C]81.421156133606[/C][/ROW]
[ROW][C]54[/C][C]2749[/C][C]2635.3313185103[/C][C]113.668681489704[/C][/ROW]
[ROW][C]55[/C][C]2552[/C][C]2552.46549810811[/C][C]-0.465498108108022[/C][/ROW]
[ROW][C]56[/C][C]2480[/C][C]2501.75378252738[/C][C]-21.7537825273826[/C][/ROW]
[ROW][C]57[/C][C]2439[/C][C]2477.05481179945[/C][C]-38.0548117994458[/C][/ROW]
[ROW][C]58[/C][C]2480[/C][C]2455.38732241498[/C][C]24.6126775850194[/C][/ROW]
[ROW][C]59[/C][C]2366[/C][C]2416.31824149944[/C][C]-50.3182414994444[/C][/ROW]
[ROW][C]60[/C][C]2325[/C][C]2411.74528949168[/C][C]-86.7452894916751[/C][/ROW]
[ROW][C]61[/C][C]2160[/C][C]2325.47241631677[/C][C]-165.472416316766[/C][/ROW]
[ROW][C]62[/C][C]2201[/C][C]2282.71653840266[/C][C]-81.7165384026625[/C][/ROW]
[ROW][C]63[/C][C]2211[/C][C]2284.68520044721[/C][C]-73.6852004472084[/C][/ROW]
[ROW][C]64[/C][C]2222[/C][C]2185.52505947417[/C][C]36.474940525834[/C][/ROW]
[ROW][C]65[/C][C]2418[/C][C]2344.22549722918[/C][C]73.7745027708211[/C][/ROW]
[ROW][C]66[/C][C]2397[/C][C]2340.84661558625[/C][C]56.1533844137521[/C][/ROW]
[ROW][C]67[/C][C]2160[/C][C]2185.28490792579[/C][C]-25.284907925789[/C][/ROW]
[ROW][C]68[/C][C]2056[/C][C]2106.84319314327[/C][C]-50.8431931432742[/C][/ROW]
[ROW][C]69[/C][C]2015[/C][C]2051.77088047624[/C][C]-36.7708804762356[/C][/ROW]
[ROW][C]70[/C][C]2067[/C][C]2040.2373039981[/C][C]26.7626960018997[/C][/ROW]
[ROW][C]71[/C][C]1870[/C][C]1983.35335425638[/C][C]-113.353354256384[/C][/ROW]
[ROW][C]72[/C][C]1736[/C][C]1916.72217974802[/C][C]-180.722179748022[/C][/ROW]
[ROW][C]73[/C][C]1488[/C][C]1734.11042031886[/C][C]-246.110420318861[/C][/ROW]
[ROW][C]74[/C][C]1509[/C][C]1638.58065212051[/C][C]-129.580652120512[/C][/ROW]
[ROW][C]75[/C][C]1509[/C][C]1597.45727072019[/C][C]-88.4572707201924[/C][/ROW]
[ROW][C]76[/C][C]1488[/C][C]1502.52198403398[/C][C]-14.521984033978[/C][/ROW]
[ROW][C]77[/C][C]1664[/C][C]1621.06432822025[/C][C]42.9356717797521[/C][/ROW]
[ROW][C]78[/C][C]1674[/C][C]1581.72984563465[/C][C]92.2701543653525[/C][/ROW]
[ROW][C]79[/C][C]1467[/C][C]1430.30698576956[/C][C]36.6930142304416[/C][/ROW]
[ROW][C]80[/C][C]1426[/C][C]1388.75904582203[/C][C]37.2409541779707[/C][/ROW]
[ROW][C]81[/C][C]1343[/C][C]1400.41569963992[/C][C]-57.4156996399188[/C][/ROW]
[ROW][C]82[/C][C]1457[/C][C]1379.61358833147[/C][C]77.3864116685347[/C][/ROW]
[ROW][C]83[/C][C]1250[/C][C]1327.99848038525[/C][C]-77.9984803852547[/C][/ROW]
[ROW][C]84[/C][C]1126[/C][C]1270.06405089914[/C][C]-144.064050899141[/C][/ROW]
[ROW][C]85[/C][C]889[/C][C]1097.97304053713[/C][C]-208.973040537133[/C][/ROW]
[ROW][C]86[/C][C]940[/C][C]1051.61504133964[/C][C]-111.615041339642[/C][/ROW]
[ROW][C]87[/C][C]878[/C][C]1028.96610496569[/C][C]-150.966104965694[/C][/ROW]
[ROW][C]88[/C][C]899[/C][C]894.97682656524[/C][C]4.02317343475966[/C][/ROW]
[ROW][C]89[/C][C]1054[/C][C]1035.398948591[/C][C]18.6010514090035[/C][/ROW]
[ROW][C]90[/C][C]1085[/C][C]982.050962141557[/C][C]102.949037858443[/C][/ROW]
[ROW][C]91[/C][C]982[/C][C]822.597374466428[/C][C]159.402625533572[/C][/ROW]
[ROW][C]92[/C][C]971[/C][C]874.677275823699[/C][C]96.3227241763007[/C][/ROW]
[ROW][C]93[/C][C]971[/C][C]910.369574351164[/C][C]60.630425648836[/C][/ROW]
[ROW][C]94[/C][C]1106[/C][C]1009.29793148053[/C][C]96.7020685194655[/C][/ROW]
[ROW][C]95[/C][C]868[/C][C]939.009425641488[/C][C]-71.0094256414884[/C][/ROW]
[ROW][C]96[/C][C]713[/C][C]871.316548211562[/C][C]-158.316548211562[/C][/ROW]
[ROW][C]97[/C][C]444[/C][C]672.742637478365[/C][C]-228.742637478365[/C][/ROW]
[ROW][C]98[/C][C]661[/C][C]629.123221598759[/C][C]31.8767784012415[/C][/ROW]
[ROW][C]99[/C][C]630[/C][C]711.48751627656[/C][C]-81.4875162765604[/C][/ROW]
[ROW][C]100[/C][C]641[/C][C]665.10618717959[/C][C]-24.1061871795898[/C][/ROW]
[ROW][C]101[/C][C]889[/C][C]786.322551938861[/C][C]102.677448061139[/C][/ROW]
[ROW][C]102[/C][C]858[/C][C]818.007576839506[/C][C]39.9924231604938[/C][/ROW]
[ROW][C]103[/C][C]744[/C][C]620.714173764716[/C][C]123.285826235284[/C][/ROW]
[ROW][C]104[/C][C]796[/C][C]630.935740218085[/C][C]165.064259781915[/C][/ROW]
[ROW][C]105[/C][C]796[/C][C]714.205681141612[/C][C]81.7943188583876[/C][/ROW]
[ROW][C]106[/C][C]982[/C][C]838.207770773122[/C][C]143.792229226878[/C][/ROW]
[ROW][C]107[/C][C]765[/C][C]771.566854102381[/C][C]-6.5668541023814[/C][/ROW]
[ROW][C]108[/C][C]641[/C][C]738.672878155473[/C][C]-97.6728781554726[/C][/ROW]
[ROW][C]109[/C][C]444[/C][C]576.033964073223[/C][C]-132.033964073223[/C][/ROW]
[ROW][C]110[/C][C]703[/C][C]666.849957022076[/C][C]36.1500429779239[/C][/ROW]
[ROW][C]111[/C][C]682[/C][C]732.62220172202[/C][C]-50.6222017220196[/C][/ROW]
[ROW][C]112[/C][C]692[/C][C]726.582525922417[/C][C]-34.5825259224174[/C][/ROW]
[ROW][C]113[/C][C]909[/C][C]869.75433651745[/C][C]39.2456634825498[/C][/ROW]
[ROW][C]114[/C][C]889[/C][C]841.35161166542[/C][C]47.6483883345797[/C][/ROW]
[ROW][C]115[/C][C]816[/C][C]670.734519928407[/C][C]145.265480071593[/C][/ROW]
[ROW][C]116[/C][C]827[/C][C]710.554570812474[/C][C]116.445429187526[/C][/ROW]
[ROW][C]117[/C][C]878[/C][C]740.981003971078[/C][C]137.018996028922[/C][/ROW]
[ROW][C]118[/C][C]992[/C][C]925.182271882927[/C][C]66.8177281170734[/C][/ROW]
[ROW][C]119[/C][C]816[/C][C]769.050124790319[/C][C]46.9498752096812[/C][/ROW]
[ROW][C]120[/C][C]672[/C][C]762.874117259745[/C][C]-90.874117259745[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168984&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168984&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
1329552967.17120726496-12.171207264957
1430383043.40540765421-5.40540765421065
1530693070.77368367282-1.77368367281815
1630383038.62395626122-0.623956261223611
1731523155.37804708463-3.37804708462863
1830793085.04163636722-6.04163636722478
1929142983.74212272255-69.7421227225523
2028732821.7862735057251.2137264942785
2128732865.500997643017.49900235698988
2228932862.3911949027730.6088050972276
2328112892.18695701075-81.186957010751
2428732850.1290715256522.8709284743527
2528212859.20131452154-38.2013145215446
2628732915.26033975697-42.2603397569706
2729552912.8485960206642.1514039793442
2829862914.8133604990571.1866395009456
2930593087.69066313289-28.6906631328943
3030282996.3381717940531.6618282059499
3128422911.59343039243-69.5934303924314
3227692774.91764388329-5.91764388329193
3327382763.67507867414-25.675078674145
3427692738.1493685200830.8506314799224
3527182743.89237127205-25.8923712720521
3627382766.89619716935-28.8961971693457
3726762721.33871592172-45.3387159217182
3827802769.9028486979210.09715130208
3928312826.068021775794.9319782242078
4028422803.7699928185238.2300071814816
4130382928.57035146526109.429648534738
4230382959.3893699479778.6106300520305
4327802891.46158297333-111.461582973326
4427182735.1986625086-17.1986625086006
4527182711.092945564656.90705443534716
4627492723.6566141014825.3433858985186
4726142713.68544424797-99.6854442479739
4825522677.33834716826-125.338347168264
4924802550.70015773927-70.7001577392725
5025012589.16773731071-88.1677373107141
5125942563.8772794518730.1227205481305
5225212566.13931956222-45.1393195622231
5327182636.5788438663981.421156133606
5427492635.3313185103113.668681489704
5525522552.46549810811-0.465498108108022
5624802501.75378252738-21.7537825273826
5724392477.05481179945-38.0548117994458
5824802455.3873224149824.6126775850194
5923662416.31824149944-50.3182414994444
6023252411.74528949168-86.7452894916751
6121602325.47241631677-165.472416316766
6222012282.71653840266-81.7165384026625
6322112284.68520044721-73.6852004472084
6422222185.5250594741736.474940525834
6524182344.2254972291873.7745027708211
6623972340.8466155862556.1533844137521
6721602185.28490792579-25.284907925789
6820562106.84319314327-50.8431931432742
6920152051.77088047624-36.7708804762356
7020672040.237303998126.7626960018997
7118701983.35335425638-113.353354256384
7217361916.72217974802-180.722179748022
7314881734.11042031886-246.110420318861
7415091638.58065212051-129.580652120512
7515091597.45727072019-88.4572707201924
7614881502.52198403398-14.521984033978
7716641621.0643282202542.9356717797521
7816741581.7298456346592.2701543653525
7914671430.3069857695636.6930142304416
8014261388.7590458220337.2409541779707
8113431400.41569963992-57.4156996399188
8214571379.6135883314777.3864116685347
8312501327.99848038525-77.9984803852547
8411261270.06405089914-144.064050899141
858891097.97304053713-208.973040537133
869401051.61504133964-111.615041339642
878781028.96610496569-150.966104965694
88899894.976826565244.02317343475966
8910541035.39894859118.6010514090035
901085982.050962141557102.949037858443
91982822.597374466428159.402625533572
92971874.67727582369996.3227241763007
93971910.36957435116460.630425648836
9411061009.2979314805396.7020685194655
95868939.009425641488-71.0094256414884
96713871.316548211562-158.316548211562
97444672.742637478365-228.742637478365
98661629.12322159875931.8767784012415
99630711.48751627656-81.4875162765604
100641665.10618717959-24.1061871795898
101889786.322551938861102.677448061139
102858818.00757683950639.9924231604938
103744620.714173764716123.285826235284
104796630.935740218085165.064259781915
105796714.20568114161281.7943188583876
106982838.207770773122143.792229226878
107765771.566854102381-6.5668541023814
108641738.672878155473-97.6728781554726
109444576.033964073223-132.033964073223
110703666.84995702207636.1500429779239
111682732.62220172202-50.6222017220196
112692726.582525922417-34.5825259224174
113909869.7543365174539.2456634825498
114889841.3516116654247.6483883345797
115816670.734519928407145.265480071593
116827710.554570812474116.445429187526
117878740.981003971078137.018996028922
118992925.18227188292766.8177281170734
119816769.05012479031946.9498752096812
120672762.874117259745-90.874117259745







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121601.853195975555434.083641155172769.622750795938
122836.990772802851621.9213064230211052.06023918268
123860.454656388808605.8298101237221115.07950265389
124902.743665861838613.1068701755231192.38046154815
1251093.93841061661772.3363310219331415.54049021129
1261041.07392754419689.7121141964091392.43574089197
127857.428938934942477.9856740788451236.87220379104
128779.097244730577372.8951537863891185.29933567476
129723.2706312109291.3794351923511155.16182722945
130784.605733717666327.9079892867061241.30347814863
131570.97887203944190.21421923271241051.74352484617
132497.985976500139-6.217860305415461002.18981330569

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 601.853195975555 & 434.083641155172 & 769.622750795938 \tabularnewline
122 & 836.990772802851 & 621.921306423021 & 1052.06023918268 \tabularnewline
123 & 860.454656388808 & 605.829810123722 & 1115.07950265389 \tabularnewline
124 & 902.743665861838 & 613.106870175523 & 1192.38046154815 \tabularnewline
125 & 1093.93841061661 & 772.336331021933 & 1415.54049021129 \tabularnewline
126 & 1041.07392754419 & 689.712114196409 & 1392.43574089197 \tabularnewline
127 & 857.428938934942 & 477.985674078845 & 1236.87220379104 \tabularnewline
128 & 779.097244730577 & 372.895153786389 & 1185.29933567476 \tabularnewline
129 & 723.2706312109 & 291.379435192351 & 1155.16182722945 \tabularnewline
130 & 784.605733717666 & 327.907989286706 & 1241.30347814863 \tabularnewline
131 & 570.978872039441 & 90.2142192327124 & 1051.74352484617 \tabularnewline
132 & 497.985976500139 & -6.21786030541546 & 1002.18981330569 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168984&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]121[/C][C]601.853195975555[/C][C]434.083641155172[/C][C]769.622750795938[/C][/ROW]
[ROW][C]122[/C][C]836.990772802851[/C][C]621.921306423021[/C][C]1052.06023918268[/C][/ROW]
[ROW][C]123[/C][C]860.454656388808[/C][C]605.829810123722[/C][C]1115.07950265389[/C][/ROW]
[ROW][C]124[/C][C]902.743665861838[/C][C]613.106870175523[/C][C]1192.38046154815[/C][/ROW]
[ROW][C]125[/C][C]1093.93841061661[/C][C]772.336331021933[/C][C]1415.54049021129[/C][/ROW]
[ROW][C]126[/C][C]1041.07392754419[/C][C]689.712114196409[/C][C]1392.43574089197[/C][/ROW]
[ROW][C]127[/C][C]857.428938934942[/C][C]477.985674078845[/C][C]1236.87220379104[/C][/ROW]
[ROW][C]128[/C][C]779.097244730577[/C][C]372.895153786389[/C][C]1185.29933567476[/C][/ROW]
[ROW][C]129[/C][C]723.2706312109[/C][C]291.379435192351[/C][C]1155.16182722945[/C][/ROW]
[ROW][C]130[/C][C]784.605733717666[/C][C]327.907989286706[/C][C]1241.30347814863[/C][/ROW]
[ROW][C]131[/C][C]570.978872039441[/C][C]90.2142192327124[/C][C]1051.74352484617[/C][/ROW]
[ROW][C]132[/C][C]497.985976500139[/C][C]-6.21786030541546[/C][C]1002.18981330569[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168984&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168984&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
121601.853195975555434.083641155172769.622750795938
122836.990772802851621.9213064230211052.06023918268
123860.454656388808605.8298101237221115.07950265389
124902.743665861838613.1068701755231192.38046154815
1251093.93841061661772.3363310219331415.54049021129
1261041.07392754419689.7121141964091392.43574089197
127857.428938934942477.9856740788451236.87220379104
128779.097244730577372.8951537863891185.29933567476
129723.2706312109291.3794351923511155.16182722945
130784.605733717666327.9079892867061241.30347814863
131570.97887203944190.21421923271241051.74352484617
132497.985976500139-6.217860305415461002.18981330569



Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')