Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 05 Aug 2012 06:20:29 -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/05/t13441620543pxs392ikxwfxd6.htm/, Retrieved Sat, 04 May 2024 16:45:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169019, Retrieved Sat, 04 May 2024 16:45:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsBlij Arnaud
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks A - Sta...] [2012-08-05 10:20:29] [50083fea611f0183deb36cab794727ad] [Current]
Feedback Forum

Post a new message
Dataseries X:
161949
161634
161287
160652
167176
166856
161949
158687
159007
159007
159323
159990
159990
157043
155745
157043
161634
160967
154763
149510
148527
146563
147892
149510
148874
147545
144950
147545
149856
149190
141656
138394
135132
132505
132190
134150
131523
130541
129559
135132
135768
132505
123670
119745
113541
110910
112208
114172
114172
112559
112208
117465
121710
119745
113190
109932
103061
98817
102079
105341
105341
101097
100781
106319
109932
108630
102079
97835
88652
85075
86372
91946
92261
84092
87039
94226
97488
95523
86692
80484
73297
67724
70004
74910
73613
66426
68706
75893
79821
77541
68706
64782
58893
52684
53666
58573
59208
53319
54302
62502
64462
61173
49075
42871
34671
26502
29129
32706
32075
25835
29444
38280
42204
40244
32391
26186
19631
12093
13427
15707




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169019&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169019&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169019&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.40085366746159
beta0.036898409056069
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.40085366746159 \tabularnewline
beta & 0.036898409056069 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169019&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]0.40085366746159[/C][/ROW]
[ROW][C]beta[/C][C]0.036898409056069[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169019&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169019&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
alpha0.40085366746159
beta0.036898409056069
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13159990162572.917200855-2582.91720085469
14157043158618.661142053-1575.66114205323
15155745156831.111981049-1086.11198104906
16157043157955.860863563-912.860863563197
17161634162469.181092313-835.181092313229
18160967161661.453160146-694.453160145902
19154763154793.364974433-30.3649744327122
20149510151062.488182649-1552.48818264939
21148527150429.791747803-1902.79174780296
22146563149267.614246187-2704.61424618706
23147892148060.019677757-168.019677756645
24149510148312.7431889781197.25681102209
25148874146984.4058806641889.59411933611
26147545145302.5823901852242.4176098147
27144950145271.424591431-321.424591430841
28147545146750.403283785794.596716214757
29149856151963.859759528-2107.85975952842
30149190150680.620589306-1490.62058930617
31141656143829.825816361-2173.82581636118
32138394138234.610758077159.389241923462
33135132138010.414125463-2878.41412546256
34132505135894.486064604-3389.48606460399
35132190135839.759862025-3649.75986202495
36134150135370.927924927-1220.92792492729
37131523133308.40919015-1785.40919014951
38130541130130.829010887410.170989112637
39129559127567.9802398461991.01976015395
40135132130415.6623089034716.33769109652
41135768135293.264320415474.735679585341
42132505135284.380838889-2779.3808388894
43123670127357.876261712-3687.87626171242
44119745122381.526037238-2636.52603723774
45113541119002.974028157-5461.97402815668
46110910115293.482811312-4383.48281131219
47112208114417.938391006-2209.93839100623
48114172115736.357234874-1564.35723487432
49114172112947.7544224661224.24557753437
50112559112086.382297565472.617702435484
51112208110290.9519955461917.04800445422
52117465114535.9790837922929.02091620762
53121710115923.4849904855786.51500951484
54119745115940.4182232053804.58177679546
55113190110052.4424594053137.55754059482
56109932108486.6040444841445.3959555164
57103061105156.42278894-2095.42278894027
5898817103597.368391061-4780.36839106113
59102079104013.900169291-1934.90016929121
60105341105982.332798329-641.332798328978
61105341105401.127315289-60.1273152893846
62101097103722.195988998-2625.19598899801
63100781101652.222956952-871.222956952188
64106319105446.442461719872.557538281413
65109932107751.8089189442180.1910810564
66108630105112.4696407913517.5303592086
6710207998682.34109021893396.65890978109
689783596182.90228591771652.09771408225
698865290793.5572050506-2141.55720505056
708507587586.0995605007-2511.09956050075
718637290629.4575786053-4257.45757860529
729194692419.8977281858-473.897728185824
739226192234.489879558126.5101204419188
748409289035.1709798336-4943.17097983362
758703987034.365812844.63418716001615
769422692184.8603688292041.13963117103
779748895719.81023670341768.18976329658
789552393688.17593984011834.82406015988
798669286457.815331393234.184668607049
808048481545.3705840083-1061.37058400831
817329772655.1637128826641.836287117432
826772470242.9947616446-2518.9947616446
837000472137.7123317068-2133.7123317068
847491076978.6299588477-2068.62995884774
857361376362.45830719-2749.45830719001
866642668940.4300427701-2514.43004277012
876870670781.1910465009-2075.19104650088
887589376190.9195274912-297.919527491191
897982178462.89006790811358.10993209195
907754176138.91005391111402.08994608889
916870667601.78124938651104.21875061349
926478262100.44631269322681.55368730685
935889355625.01622804743267.98377195257
945268452304.5324982633379.467501736726
955366655567.605310062-1901.60531006202
965857360519.6462747208-1946.64627472082
975920859525.3491877655-317.34918776554
985331953235.92286354983.077136450971
995430256436.35770917-2134.35770917
1006250262941.624732119-439.624732118951
1016446266201.3102597781-1739.31025977814
1026117362668.56901077-1495.56901077004
1034907552755.0762210019-3680.07622100189
1044287146173.8713606947-3302.87136069467
1053467137455.2829932991-2784.28299329906
1062650229692.9267692106-3190.92676921061
1072912929820.1330874874-691.133087487382
1083270634910.3496351672-2204.34963516721
1093207534465.0664123612-2390.06641236123
1102583527230.1683020331-1395.1683020331
1112944428133.08111304461310.91888695538
1123828036709.35758174431570.64241825569
1134220439700.46247599842503.5375240016
1144024437781.57259974672462.42740025331
1153239127971.41348749994419.5865125001
1162618624808.38583011051377.61416988945
1171963118291.32277224981339.67722775015
1181209312014.05412989678.9458701039839
1191342715073.7294708366-1646.72947083657
1201570718984.105830513-3277.10583051302

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 159990 & 162572.917200855 & -2582.91720085469 \tabularnewline
14 & 157043 & 158618.661142053 & -1575.66114205323 \tabularnewline
15 & 155745 & 156831.111981049 & -1086.11198104906 \tabularnewline
16 & 157043 & 157955.860863563 & -912.860863563197 \tabularnewline
17 & 161634 & 162469.181092313 & -835.181092313229 \tabularnewline
18 & 160967 & 161661.453160146 & -694.453160145902 \tabularnewline
19 & 154763 & 154793.364974433 & -30.3649744327122 \tabularnewline
20 & 149510 & 151062.488182649 & -1552.48818264939 \tabularnewline
21 & 148527 & 150429.791747803 & -1902.79174780296 \tabularnewline
22 & 146563 & 149267.614246187 & -2704.61424618706 \tabularnewline
23 & 147892 & 148060.019677757 & -168.019677756645 \tabularnewline
24 & 149510 & 148312.743188978 & 1197.25681102209 \tabularnewline
25 & 148874 & 146984.405880664 & 1889.59411933611 \tabularnewline
26 & 147545 & 145302.582390185 & 2242.4176098147 \tabularnewline
27 & 144950 & 145271.424591431 & -321.424591430841 \tabularnewline
28 & 147545 & 146750.403283785 & 794.596716214757 \tabularnewline
29 & 149856 & 151963.859759528 & -2107.85975952842 \tabularnewline
30 & 149190 & 150680.620589306 & -1490.62058930617 \tabularnewline
31 & 141656 & 143829.825816361 & -2173.82581636118 \tabularnewline
32 & 138394 & 138234.610758077 & 159.389241923462 \tabularnewline
33 & 135132 & 138010.414125463 & -2878.41412546256 \tabularnewline
34 & 132505 & 135894.486064604 & -3389.48606460399 \tabularnewline
35 & 132190 & 135839.759862025 & -3649.75986202495 \tabularnewline
36 & 134150 & 135370.927924927 & -1220.92792492729 \tabularnewline
37 & 131523 & 133308.40919015 & -1785.40919014951 \tabularnewline
38 & 130541 & 130130.829010887 & 410.170989112637 \tabularnewline
39 & 129559 & 127567.980239846 & 1991.01976015395 \tabularnewline
40 & 135132 & 130415.662308903 & 4716.33769109652 \tabularnewline
41 & 135768 & 135293.264320415 & 474.735679585341 \tabularnewline
42 & 132505 & 135284.380838889 & -2779.3808388894 \tabularnewline
43 & 123670 & 127357.876261712 & -3687.87626171242 \tabularnewline
44 & 119745 & 122381.526037238 & -2636.52603723774 \tabularnewline
45 & 113541 & 119002.974028157 & -5461.97402815668 \tabularnewline
46 & 110910 & 115293.482811312 & -4383.48281131219 \tabularnewline
47 & 112208 & 114417.938391006 & -2209.93839100623 \tabularnewline
48 & 114172 & 115736.357234874 & -1564.35723487432 \tabularnewline
49 & 114172 & 112947.754422466 & 1224.24557753437 \tabularnewline
50 & 112559 & 112086.382297565 & 472.617702435484 \tabularnewline
51 & 112208 & 110290.951995546 & 1917.04800445422 \tabularnewline
52 & 117465 & 114535.979083792 & 2929.02091620762 \tabularnewline
53 & 121710 & 115923.484990485 & 5786.51500951484 \tabularnewline
54 & 119745 & 115940.418223205 & 3804.58177679546 \tabularnewline
55 & 113190 & 110052.442459405 & 3137.55754059482 \tabularnewline
56 & 109932 & 108486.604044484 & 1445.3959555164 \tabularnewline
57 & 103061 & 105156.42278894 & -2095.42278894027 \tabularnewline
58 & 98817 & 103597.368391061 & -4780.36839106113 \tabularnewline
59 & 102079 & 104013.900169291 & -1934.90016929121 \tabularnewline
60 & 105341 & 105982.332798329 & -641.332798328978 \tabularnewline
61 & 105341 & 105401.127315289 & -60.1273152893846 \tabularnewline
62 & 101097 & 103722.195988998 & -2625.19598899801 \tabularnewline
63 & 100781 & 101652.222956952 & -871.222956952188 \tabularnewline
64 & 106319 & 105446.442461719 & 872.557538281413 \tabularnewline
65 & 109932 & 107751.808918944 & 2180.1910810564 \tabularnewline
66 & 108630 & 105112.469640791 & 3517.5303592086 \tabularnewline
67 & 102079 & 98682.3410902189 & 3396.65890978109 \tabularnewline
68 & 97835 & 96182.9022859177 & 1652.09771408225 \tabularnewline
69 & 88652 & 90793.5572050506 & -2141.55720505056 \tabularnewline
70 & 85075 & 87586.0995605007 & -2511.09956050075 \tabularnewline
71 & 86372 & 90629.4575786053 & -4257.45757860529 \tabularnewline
72 & 91946 & 92419.8977281858 & -473.897728185824 \tabularnewline
73 & 92261 & 92234.4898795581 & 26.5101204419188 \tabularnewline
74 & 84092 & 89035.1709798336 & -4943.17097983362 \tabularnewline
75 & 87039 & 87034.36581284 & 4.63418716001615 \tabularnewline
76 & 94226 & 92184.860368829 & 2041.13963117103 \tabularnewline
77 & 97488 & 95719.8102367034 & 1768.18976329658 \tabularnewline
78 & 95523 & 93688.1759398401 & 1834.82406015988 \tabularnewline
79 & 86692 & 86457.815331393 & 234.184668607049 \tabularnewline
80 & 80484 & 81545.3705840083 & -1061.37058400831 \tabularnewline
81 & 73297 & 72655.1637128826 & 641.836287117432 \tabularnewline
82 & 67724 & 70242.9947616446 & -2518.9947616446 \tabularnewline
83 & 70004 & 72137.7123317068 & -2133.7123317068 \tabularnewline
84 & 74910 & 76978.6299588477 & -2068.62995884774 \tabularnewline
85 & 73613 & 76362.45830719 & -2749.45830719001 \tabularnewline
86 & 66426 & 68940.4300427701 & -2514.43004277012 \tabularnewline
87 & 68706 & 70781.1910465009 & -2075.19104650088 \tabularnewline
88 & 75893 & 76190.9195274912 & -297.919527491191 \tabularnewline
89 & 79821 & 78462.8900679081 & 1358.10993209195 \tabularnewline
90 & 77541 & 76138.9100539111 & 1402.08994608889 \tabularnewline
91 & 68706 & 67601.7812493865 & 1104.21875061349 \tabularnewline
92 & 64782 & 62100.4463126932 & 2681.55368730685 \tabularnewline
93 & 58893 & 55625.0162280474 & 3267.98377195257 \tabularnewline
94 & 52684 & 52304.5324982633 & 379.467501736726 \tabularnewline
95 & 53666 & 55567.605310062 & -1901.60531006202 \tabularnewline
96 & 58573 & 60519.6462747208 & -1946.64627472082 \tabularnewline
97 & 59208 & 59525.3491877655 & -317.34918776554 \tabularnewline
98 & 53319 & 53235.922863549 & 83.077136450971 \tabularnewline
99 & 54302 & 56436.35770917 & -2134.35770917 \tabularnewline
100 & 62502 & 62941.624732119 & -439.624732118951 \tabularnewline
101 & 64462 & 66201.3102597781 & -1739.31025977814 \tabularnewline
102 & 61173 & 62668.56901077 & -1495.56901077004 \tabularnewline
103 & 49075 & 52755.0762210019 & -3680.07622100189 \tabularnewline
104 & 42871 & 46173.8713606947 & -3302.87136069467 \tabularnewline
105 & 34671 & 37455.2829932991 & -2784.28299329906 \tabularnewline
106 & 26502 & 29692.9267692106 & -3190.92676921061 \tabularnewline
107 & 29129 & 29820.1330874874 & -691.133087487382 \tabularnewline
108 & 32706 & 34910.3496351672 & -2204.34963516721 \tabularnewline
109 & 32075 & 34465.0664123612 & -2390.06641236123 \tabularnewline
110 & 25835 & 27230.1683020331 & -1395.1683020331 \tabularnewline
111 & 29444 & 28133.0811130446 & 1310.91888695538 \tabularnewline
112 & 38280 & 36709.3575817443 & 1570.64241825569 \tabularnewline
113 & 42204 & 39700.4624759984 & 2503.5375240016 \tabularnewline
114 & 40244 & 37781.5725997467 & 2462.42740025331 \tabularnewline
115 & 32391 & 27971.4134874999 & 4419.5865125001 \tabularnewline
116 & 26186 & 24808.3858301105 & 1377.61416988945 \tabularnewline
117 & 19631 & 18291.3227722498 & 1339.67722775015 \tabularnewline
118 & 12093 & 12014.054129896 & 78.9458701039839 \tabularnewline
119 & 13427 & 15073.7294708366 & -1646.72947083657 \tabularnewline
120 & 15707 & 18984.105830513 & -3277.10583051302 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169019&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]159990[/C][C]162572.917200855[/C][C]-2582.91720085469[/C][/ROW]
[ROW][C]14[/C][C]157043[/C][C]158618.661142053[/C][C]-1575.66114205323[/C][/ROW]
[ROW][C]15[/C][C]155745[/C][C]156831.111981049[/C][C]-1086.11198104906[/C][/ROW]
[ROW][C]16[/C][C]157043[/C][C]157955.860863563[/C][C]-912.860863563197[/C][/ROW]
[ROW][C]17[/C][C]161634[/C][C]162469.181092313[/C][C]-835.181092313229[/C][/ROW]
[ROW][C]18[/C][C]160967[/C][C]161661.453160146[/C][C]-694.453160145902[/C][/ROW]
[ROW][C]19[/C][C]154763[/C][C]154793.364974433[/C][C]-30.3649744327122[/C][/ROW]
[ROW][C]20[/C][C]149510[/C][C]151062.488182649[/C][C]-1552.48818264939[/C][/ROW]
[ROW][C]21[/C][C]148527[/C][C]150429.791747803[/C][C]-1902.79174780296[/C][/ROW]
[ROW][C]22[/C][C]146563[/C][C]149267.614246187[/C][C]-2704.61424618706[/C][/ROW]
[ROW][C]23[/C][C]147892[/C][C]148060.019677757[/C][C]-168.019677756645[/C][/ROW]
[ROW][C]24[/C][C]149510[/C][C]148312.743188978[/C][C]1197.25681102209[/C][/ROW]
[ROW][C]25[/C][C]148874[/C][C]146984.405880664[/C][C]1889.59411933611[/C][/ROW]
[ROW][C]26[/C][C]147545[/C][C]145302.582390185[/C][C]2242.4176098147[/C][/ROW]
[ROW][C]27[/C][C]144950[/C][C]145271.424591431[/C][C]-321.424591430841[/C][/ROW]
[ROW][C]28[/C][C]147545[/C][C]146750.403283785[/C][C]794.596716214757[/C][/ROW]
[ROW][C]29[/C][C]149856[/C][C]151963.859759528[/C][C]-2107.85975952842[/C][/ROW]
[ROW][C]30[/C][C]149190[/C][C]150680.620589306[/C][C]-1490.62058930617[/C][/ROW]
[ROW][C]31[/C][C]141656[/C][C]143829.825816361[/C][C]-2173.82581636118[/C][/ROW]
[ROW][C]32[/C][C]138394[/C][C]138234.610758077[/C][C]159.389241923462[/C][/ROW]
[ROW][C]33[/C][C]135132[/C][C]138010.414125463[/C][C]-2878.41412546256[/C][/ROW]
[ROW][C]34[/C][C]132505[/C][C]135894.486064604[/C][C]-3389.48606460399[/C][/ROW]
[ROW][C]35[/C][C]132190[/C][C]135839.759862025[/C][C]-3649.75986202495[/C][/ROW]
[ROW][C]36[/C][C]134150[/C][C]135370.927924927[/C][C]-1220.92792492729[/C][/ROW]
[ROW][C]37[/C][C]131523[/C][C]133308.40919015[/C][C]-1785.40919014951[/C][/ROW]
[ROW][C]38[/C][C]130541[/C][C]130130.829010887[/C][C]410.170989112637[/C][/ROW]
[ROW][C]39[/C][C]129559[/C][C]127567.980239846[/C][C]1991.01976015395[/C][/ROW]
[ROW][C]40[/C][C]135132[/C][C]130415.662308903[/C][C]4716.33769109652[/C][/ROW]
[ROW][C]41[/C][C]135768[/C][C]135293.264320415[/C][C]474.735679585341[/C][/ROW]
[ROW][C]42[/C][C]132505[/C][C]135284.380838889[/C][C]-2779.3808388894[/C][/ROW]
[ROW][C]43[/C][C]123670[/C][C]127357.876261712[/C][C]-3687.87626171242[/C][/ROW]
[ROW][C]44[/C][C]119745[/C][C]122381.526037238[/C][C]-2636.52603723774[/C][/ROW]
[ROW][C]45[/C][C]113541[/C][C]119002.974028157[/C][C]-5461.97402815668[/C][/ROW]
[ROW][C]46[/C][C]110910[/C][C]115293.482811312[/C][C]-4383.48281131219[/C][/ROW]
[ROW][C]47[/C][C]112208[/C][C]114417.938391006[/C][C]-2209.93839100623[/C][/ROW]
[ROW][C]48[/C][C]114172[/C][C]115736.357234874[/C][C]-1564.35723487432[/C][/ROW]
[ROW][C]49[/C][C]114172[/C][C]112947.754422466[/C][C]1224.24557753437[/C][/ROW]
[ROW][C]50[/C][C]112559[/C][C]112086.382297565[/C][C]472.617702435484[/C][/ROW]
[ROW][C]51[/C][C]112208[/C][C]110290.951995546[/C][C]1917.04800445422[/C][/ROW]
[ROW][C]52[/C][C]117465[/C][C]114535.979083792[/C][C]2929.02091620762[/C][/ROW]
[ROW][C]53[/C][C]121710[/C][C]115923.484990485[/C][C]5786.51500951484[/C][/ROW]
[ROW][C]54[/C][C]119745[/C][C]115940.418223205[/C][C]3804.58177679546[/C][/ROW]
[ROW][C]55[/C][C]113190[/C][C]110052.442459405[/C][C]3137.55754059482[/C][/ROW]
[ROW][C]56[/C][C]109932[/C][C]108486.604044484[/C][C]1445.3959555164[/C][/ROW]
[ROW][C]57[/C][C]103061[/C][C]105156.42278894[/C][C]-2095.42278894027[/C][/ROW]
[ROW][C]58[/C][C]98817[/C][C]103597.368391061[/C][C]-4780.36839106113[/C][/ROW]
[ROW][C]59[/C][C]102079[/C][C]104013.900169291[/C][C]-1934.90016929121[/C][/ROW]
[ROW][C]60[/C][C]105341[/C][C]105982.332798329[/C][C]-641.332798328978[/C][/ROW]
[ROW][C]61[/C][C]105341[/C][C]105401.127315289[/C][C]-60.1273152893846[/C][/ROW]
[ROW][C]62[/C][C]101097[/C][C]103722.195988998[/C][C]-2625.19598899801[/C][/ROW]
[ROW][C]63[/C][C]100781[/C][C]101652.222956952[/C][C]-871.222956952188[/C][/ROW]
[ROW][C]64[/C][C]106319[/C][C]105446.442461719[/C][C]872.557538281413[/C][/ROW]
[ROW][C]65[/C][C]109932[/C][C]107751.808918944[/C][C]2180.1910810564[/C][/ROW]
[ROW][C]66[/C][C]108630[/C][C]105112.469640791[/C][C]3517.5303592086[/C][/ROW]
[ROW][C]67[/C][C]102079[/C][C]98682.3410902189[/C][C]3396.65890978109[/C][/ROW]
[ROW][C]68[/C][C]97835[/C][C]96182.9022859177[/C][C]1652.09771408225[/C][/ROW]
[ROW][C]69[/C][C]88652[/C][C]90793.5572050506[/C][C]-2141.55720505056[/C][/ROW]
[ROW][C]70[/C][C]85075[/C][C]87586.0995605007[/C][C]-2511.09956050075[/C][/ROW]
[ROW][C]71[/C][C]86372[/C][C]90629.4575786053[/C][C]-4257.45757860529[/C][/ROW]
[ROW][C]72[/C][C]91946[/C][C]92419.8977281858[/C][C]-473.897728185824[/C][/ROW]
[ROW][C]73[/C][C]92261[/C][C]92234.4898795581[/C][C]26.5101204419188[/C][/ROW]
[ROW][C]74[/C][C]84092[/C][C]89035.1709798336[/C][C]-4943.17097983362[/C][/ROW]
[ROW][C]75[/C][C]87039[/C][C]87034.36581284[/C][C]4.63418716001615[/C][/ROW]
[ROW][C]76[/C][C]94226[/C][C]92184.860368829[/C][C]2041.13963117103[/C][/ROW]
[ROW][C]77[/C][C]97488[/C][C]95719.8102367034[/C][C]1768.18976329658[/C][/ROW]
[ROW][C]78[/C][C]95523[/C][C]93688.1759398401[/C][C]1834.82406015988[/C][/ROW]
[ROW][C]79[/C][C]86692[/C][C]86457.815331393[/C][C]234.184668607049[/C][/ROW]
[ROW][C]80[/C][C]80484[/C][C]81545.3705840083[/C][C]-1061.37058400831[/C][/ROW]
[ROW][C]81[/C][C]73297[/C][C]72655.1637128826[/C][C]641.836287117432[/C][/ROW]
[ROW][C]82[/C][C]67724[/C][C]70242.9947616446[/C][C]-2518.9947616446[/C][/ROW]
[ROW][C]83[/C][C]70004[/C][C]72137.7123317068[/C][C]-2133.7123317068[/C][/ROW]
[ROW][C]84[/C][C]74910[/C][C]76978.6299588477[/C][C]-2068.62995884774[/C][/ROW]
[ROW][C]85[/C][C]73613[/C][C]76362.45830719[/C][C]-2749.45830719001[/C][/ROW]
[ROW][C]86[/C][C]66426[/C][C]68940.4300427701[/C][C]-2514.43004277012[/C][/ROW]
[ROW][C]87[/C][C]68706[/C][C]70781.1910465009[/C][C]-2075.19104650088[/C][/ROW]
[ROW][C]88[/C][C]75893[/C][C]76190.9195274912[/C][C]-297.919527491191[/C][/ROW]
[ROW][C]89[/C][C]79821[/C][C]78462.8900679081[/C][C]1358.10993209195[/C][/ROW]
[ROW][C]90[/C][C]77541[/C][C]76138.9100539111[/C][C]1402.08994608889[/C][/ROW]
[ROW][C]91[/C][C]68706[/C][C]67601.7812493865[/C][C]1104.21875061349[/C][/ROW]
[ROW][C]92[/C][C]64782[/C][C]62100.4463126932[/C][C]2681.55368730685[/C][/ROW]
[ROW][C]93[/C][C]58893[/C][C]55625.0162280474[/C][C]3267.98377195257[/C][/ROW]
[ROW][C]94[/C][C]52684[/C][C]52304.5324982633[/C][C]379.467501736726[/C][/ROW]
[ROW][C]95[/C][C]53666[/C][C]55567.605310062[/C][C]-1901.60531006202[/C][/ROW]
[ROW][C]96[/C][C]58573[/C][C]60519.6462747208[/C][C]-1946.64627472082[/C][/ROW]
[ROW][C]97[/C][C]59208[/C][C]59525.3491877655[/C][C]-317.34918776554[/C][/ROW]
[ROW][C]98[/C][C]53319[/C][C]53235.922863549[/C][C]83.077136450971[/C][/ROW]
[ROW][C]99[/C][C]54302[/C][C]56436.35770917[/C][C]-2134.35770917[/C][/ROW]
[ROW][C]100[/C][C]62502[/C][C]62941.624732119[/C][C]-439.624732118951[/C][/ROW]
[ROW][C]101[/C][C]64462[/C][C]66201.3102597781[/C][C]-1739.31025977814[/C][/ROW]
[ROW][C]102[/C][C]61173[/C][C]62668.56901077[/C][C]-1495.56901077004[/C][/ROW]
[ROW][C]103[/C][C]49075[/C][C]52755.0762210019[/C][C]-3680.07622100189[/C][/ROW]
[ROW][C]104[/C][C]42871[/C][C]46173.8713606947[/C][C]-3302.87136069467[/C][/ROW]
[ROW][C]105[/C][C]34671[/C][C]37455.2829932991[/C][C]-2784.28299329906[/C][/ROW]
[ROW][C]106[/C][C]26502[/C][C]29692.9267692106[/C][C]-3190.92676921061[/C][/ROW]
[ROW][C]107[/C][C]29129[/C][C]29820.1330874874[/C][C]-691.133087487382[/C][/ROW]
[ROW][C]108[/C][C]32706[/C][C]34910.3496351672[/C][C]-2204.34963516721[/C][/ROW]
[ROW][C]109[/C][C]32075[/C][C]34465.0664123612[/C][C]-2390.06641236123[/C][/ROW]
[ROW][C]110[/C][C]25835[/C][C]27230.1683020331[/C][C]-1395.1683020331[/C][/ROW]
[ROW][C]111[/C][C]29444[/C][C]28133.0811130446[/C][C]1310.91888695538[/C][/ROW]
[ROW][C]112[/C][C]38280[/C][C]36709.3575817443[/C][C]1570.64241825569[/C][/ROW]
[ROW][C]113[/C][C]42204[/C][C]39700.4624759984[/C][C]2503.5375240016[/C][/ROW]
[ROW][C]114[/C][C]40244[/C][C]37781.5725997467[/C][C]2462.42740025331[/C][/ROW]
[ROW][C]115[/C][C]32391[/C][C]27971.4134874999[/C][C]4419.5865125001[/C][/ROW]
[ROW][C]116[/C][C]26186[/C][C]24808.3858301105[/C][C]1377.61416988945[/C][/ROW]
[ROW][C]117[/C][C]19631[/C][C]18291.3227722498[/C][C]1339.67722775015[/C][/ROW]
[ROW][C]118[/C][C]12093[/C][C]12014.054129896[/C][C]78.9458701039839[/C][/ROW]
[ROW][C]119[/C][C]13427[/C][C]15073.7294708366[/C][C]-1646.72947083657[/C][/ROW]
[ROW][C]120[/C][C]15707[/C][C]18984.105830513[/C][C]-3277.10583051302[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169019&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169019&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
13159990162572.917200855-2582.91720085469
14157043158618.661142053-1575.66114205323
15155745156831.111981049-1086.11198104906
16157043157955.860863563-912.860863563197
17161634162469.181092313-835.181092313229
18160967161661.453160146-694.453160145902
19154763154793.364974433-30.3649744327122
20149510151062.488182649-1552.48818264939
21148527150429.791747803-1902.79174780296
22146563149267.614246187-2704.61424618706
23147892148060.019677757-168.019677756645
24149510148312.7431889781197.25681102209
25148874146984.4058806641889.59411933611
26147545145302.5823901852242.4176098147
27144950145271.424591431-321.424591430841
28147545146750.403283785794.596716214757
29149856151963.859759528-2107.85975952842
30149190150680.620589306-1490.62058930617
31141656143829.825816361-2173.82581636118
32138394138234.610758077159.389241923462
33135132138010.414125463-2878.41412546256
34132505135894.486064604-3389.48606460399
35132190135839.759862025-3649.75986202495
36134150135370.927924927-1220.92792492729
37131523133308.40919015-1785.40919014951
38130541130130.829010887410.170989112637
39129559127567.9802398461991.01976015395
40135132130415.6623089034716.33769109652
41135768135293.264320415474.735679585341
42132505135284.380838889-2779.3808388894
43123670127357.876261712-3687.87626171242
44119745122381.526037238-2636.52603723774
45113541119002.974028157-5461.97402815668
46110910115293.482811312-4383.48281131219
47112208114417.938391006-2209.93839100623
48114172115736.357234874-1564.35723487432
49114172112947.7544224661224.24557753437
50112559112086.382297565472.617702435484
51112208110290.9519955461917.04800445422
52117465114535.9790837922929.02091620762
53121710115923.4849904855786.51500951484
54119745115940.4182232053804.58177679546
55113190110052.4424594053137.55754059482
56109932108486.6040444841445.3959555164
57103061105156.42278894-2095.42278894027
5898817103597.368391061-4780.36839106113
59102079104013.900169291-1934.90016929121
60105341105982.332798329-641.332798328978
61105341105401.127315289-60.1273152893846
62101097103722.195988998-2625.19598899801
63100781101652.222956952-871.222956952188
64106319105446.442461719872.557538281413
65109932107751.8089189442180.1910810564
66108630105112.4696407913517.5303592086
6710207998682.34109021893396.65890978109
689783596182.90228591771652.09771408225
698865290793.5572050506-2141.55720505056
708507587586.0995605007-2511.09956050075
718637290629.4575786053-4257.45757860529
729194692419.8977281858-473.897728185824
739226192234.489879558126.5101204419188
748409289035.1709798336-4943.17097983362
758703987034.365812844.63418716001615
769422692184.8603688292041.13963117103
779748895719.81023670341768.18976329658
789552393688.17593984011834.82406015988
798669286457.815331393234.184668607049
808048481545.3705840083-1061.37058400831
817329772655.1637128826641.836287117432
826772470242.9947616446-2518.9947616446
837000472137.7123317068-2133.7123317068
847491076978.6299588477-2068.62995884774
857361376362.45830719-2749.45830719001
866642668940.4300427701-2514.43004277012
876870670781.1910465009-2075.19104650088
887589376190.9195274912-297.919527491191
897982178462.89006790811358.10993209195
907754176138.91005391111402.08994608889
916870667601.78124938651104.21875061349
926478262100.44631269322681.55368730685
935889355625.01622804743267.98377195257
945268452304.5324982633379.467501736726
955366655567.605310062-1901.60531006202
965857360519.6462747208-1946.64627472082
975920859525.3491877655-317.34918776554
985331953235.92286354983.077136450971
995430256436.35770917-2134.35770917
1006250262941.624732119-439.624732118951
1016446266201.3102597781-1739.31025977814
1026117362668.56901077-1495.56901077004
1034907552755.0762210019-3680.07622100189
1044287146173.8713606947-3302.87136069467
1053467137455.2829932991-2784.28299329906
1062650229692.9267692106-3190.92676921061
1072912929820.1330874874-691.133087487382
1083270634910.3496351672-2204.34963516721
1093207534465.0664123612-2390.06641236123
1102583527230.1683020331-1395.1683020331
1112944428133.08111304461310.91888695538
1123828036709.35758174431570.64241825569
1134220439700.46247599842503.5375240016
1144024437781.57259974672462.42740025331
1153239127971.41348749994419.5865125001
1162618624808.38583011051377.61416988945
1171963118291.32277224981339.67722775015
1181209312014.05412989678.9458701039839
1191342715073.7294708366-1646.72947083657
1201570718984.105830513-3277.10583051302







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12118091.51810883613597.444278288122585.591939384
12212540.11286559927673.2977882125417406.9279429858
12315773.598390835810536.440288734321010.7564929374
12424110.583164896318504.216747184629716.949582608
12527138.382358269521162.992486835833113.7722297031
12624261.631216001417916.674088265630606.5883437373
12714670.92424045957955.2878767476221386.5606041714
1287882.23353794272794.35702840330214970.1100474821
129738.373895920904-6723.662202615538200.40999445734
130-6902.93193950007-14741.3358958033935.472016803136
131-4981.66216317405-13198.87652096633235.55219461824
132-1436.49349439702-10035.15183412977162.16484533567

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 18091.518108836 & 13597.4442782881 & 22585.591939384 \tabularnewline
122 & 12540.1128655992 & 7673.29778821254 & 17406.9279429858 \tabularnewline
123 & 15773.5983908358 & 10536.4402887343 & 21010.7564929374 \tabularnewline
124 & 24110.5831648963 & 18504.2167471846 & 29716.949582608 \tabularnewline
125 & 27138.3823582695 & 21162.9924868358 & 33113.7722297031 \tabularnewline
126 & 24261.6312160014 & 17916.6740882656 & 30606.5883437373 \tabularnewline
127 & 14670.9242404595 & 7955.28787674762 & 21386.5606041714 \tabularnewline
128 & 7882.23353794272 & 794.357028403302 & 14970.1100474821 \tabularnewline
129 & 738.373895920904 & -6723.66220261553 & 8200.40999445734 \tabularnewline
130 & -6902.93193950007 & -14741.3358958033 & 935.472016803136 \tabularnewline
131 & -4981.66216317405 & -13198.8765209663 & 3235.55219461824 \tabularnewline
132 & -1436.49349439702 & -10035.1518341297 & 7162.16484533567 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169019&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]18091.518108836[/C][C]13597.4442782881[/C][C]22585.591939384[/C][/ROW]
[ROW][C]122[/C][C]12540.1128655992[/C][C]7673.29778821254[/C][C]17406.9279429858[/C][/ROW]
[ROW][C]123[/C][C]15773.5983908358[/C][C]10536.4402887343[/C][C]21010.7564929374[/C][/ROW]
[ROW][C]124[/C][C]24110.5831648963[/C][C]18504.2167471846[/C][C]29716.949582608[/C][/ROW]
[ROW][C]125[/C][C]27138.3823582695[/C][C]21162.9924868358[/C][C]33113.7722297031[/C][/ROW]
[ROW][C]126[/C][C]24261.6312160014[/C][C]17916.6740882656[/C][C]30606.5883437373[/C][/ROW]
[ROW][C]127[/C][C]14670.9242404595[/C][C]7955.28787674762[/C][C]21386.5606041714[/C][/ROW]
[ROW][C]128[/C][C]7882.23353794272[/C][C]794.357028403302[/C][C]14970.1100474821[/C][/ROW]
[ROW][C]129[/C][C]738.373895920904[/C][C]-6723.66220261553[/C][C]8200.40999445734[/C][/ROW]
[ROW][C]130[/C][C]-6902.93193950007[/C][C]-14741.3358958033[/C][C]935.472016803136[/C][/ROW]
[ROW][C]131[/C][C]-4981.66216317405[/C][C]-13198.8765209663[/C][C]3235.55219461824[/C][/ROW]
[ROW][C]132[/C][C]-1436.49349439702[/C][C]-10035.1518341297[/C][C]7162.16484533567[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169019&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169019&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
12118091.51810883613597.444278288122585.591939384
12212540.11286559927673.2977882125417406.9279429858
12315773.598390835810536.440288734321010.7564929374
12424110.583164896318504.216747184629716.949582608
12527138.382358269521162.992486835833113.7722297031
12624261.631216001417916.674088265630606.5883437373
12714670.92424045957955.2878767476221386.5606041714
1287882.23353794272794.35702840330214970.1100474821
129738.373895920904-6723.662202615538200.40999445734
130-6902.93193950007-14741.3358958033935.472016803136
131-4981.66216317405-13198.87652096633235.55219461824
132-1436.49349439702-10035.15183412977162.16484533567



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
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')