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 computationTue, 04 Dec 2012 15:42:40 -0500
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/Dec/04/t1354653774qjlrwl1x1govhl4.htm/, Retrieved Tue, 23 Apr 2024 13:50:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=196599, Retrieved Tue, 23 Apr 2024 13:50:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [Exponential Smoothing] [Births] [2010-11-30 13:57:06] [b98453cac15ba1066b407e146608df68]
- R PD            [Exponential Smoothing] [Maandelijks geboo...] [2012-12-04 20:42:40] [4cf5995ff1ac45697158e3095d381e89] [Current]
Feedback Forum

Post a new message
Dataseries X:
9769
9321
9939
9336
10195
9464
10010
10213
9563
9890
9305
9391
9928
8686
9843
9627
10074
9503
10119
10000
9313
9866
9172
9241
9659
8904
9755
9080
9435
8971
10063
9793
9454
9759
8820
9403
9676
8642
9402
9610
9294
9448
10319
9548
9801
9596
8923
9746
9829
9125
9782
9441
9162
9915
10444
10209
9985
9842
9429
10132
9849
9172
10313
9819
9955
10048
10082
10541
10208
10233
9439
9963
10158
9225
10474
9757
10490
10281
10444
10640
10695
10786
9832
9747
10411
9511
10402
9701
10540
10112
10915
11183
10384
10834
9886
10216
10943
9867
10203
10837
10573
10647
11502
10656
10866
10835
9945
10331
10718
9462
10579
10633
10346
10757
11207
11013
11015
10765
10042
10661




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196599&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196599&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196599&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.112367224616474
beta0.118429348067127
gamma0.313940620745369

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.112367224616474 \tabularnewline
beta & 0.118429348067127 \tabularnewline
gamma & 0.313940620745369 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196599&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]0.112367224616474[/C][/ROW]
[ROW][C]beta[/C][C]0.118429348067127[/C][/ROW]
[ROW][C]gamma[/C][C]0.313940620745369[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196599&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196599&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
alpha0.112367224616474
beta0.118429348067127
gamma0.313940620745369







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1399289938.65918803419-10.6591880341857
1486868694.00024937159-8.00024937159469
1598439863.4919576645-20.4919576645007
1696279650.43230905813-23.4323090581274
171007410094.8554340655-20.8554340655319
1895039526.5405800661-23.5405800661028
19101199938.11073557739180.889264422611
201000010176.6009698522-176.600969852208
2193139530.19588764204-217.195887642038
2298669814.7555828203151.2444171796851
2391729219.20277572869-47.2027757286851
2492419293.45957621869-52.4595762186927
2596599804.87390962675-145.873909626755
2689048539.06158759441364.938412405594
2797559745.240668253799.75933174620877
2890809533.42575360876-453.425753608763
2994359923.1924705264-488.192470526397
3089719288.33955325027-317.339553250273
31100639706.67737201572356.32262798428
3297939850.40930982878-57.4093098287849
3394549192.81967079502261.180329204979
3497599599.0383958232159.961604176799
3588208982.815489717-162.815489717002
3694039035.62514377689367.374856223114
3796769566.77969024377109.220309756225
3886428473.96707409728168.032925902722
3994029558.41495839574-156.414958395742
4096109196.01326582854413.986734171463
4192949682.26241064693-388.26241064693
4294489116.28066444386331.719335556141
43103199813.94597092407505.054029075929
4495489879.7466619202-331.746661920199
4598019297.10759751067503.892402489333
4695969722.62074426886-126.620744268865
4789239000.66286013763-77.6628601376342
4897469228.33284456518517.667155434818
4998299723.98398277973105.016017220272
5091258666.57898869501458.421011304987
5197829716.6004866542365.3995133457702
5294419564.38114291128-123.381142911277
5391629785.84600688343-623.84600688343
5499159410.04652043995504.95347956005
551044410193.8062824471250.193717552887
561020910012.717718738196.282281261989
5799859744.23600433217240.763995667827
5898429982.94092681934-140.940926819345
5994299291.28624592451137.713754075492
60101329730.19020122117401.809798778826
61984910117.4256429738-268.425642973845
6291729131.1635696033440.8364303966646
631031310033.8085513526279.191448647432
6498199864.91833763432-45.9183376343226
6599559968.56908468689-13.5690846868874
66100489996.9649277939751.0350722060339
671008210673.75065653-591.750656530048
681054110386.8516135945154.148386405468
691020810129.289831095978.7101689040956
701023310244.5202053863-11.5202053863468
7194399647.88387683781-208.883876837814
72996310119.6479810759-156.647981075874
731015810248.1411799755-90.141179975466
7492259361.24575945592-136.24575945592
751047410301.210052141172.789947858986
76975710019.1480484862-262.148048486226
771049010094.0193810587395.980618941267
781028110178.3913000461102.608699953933
791044410674.4905624442-230.490562444236
801064010633.48759015526.5124098448141
811069510333.7968484674361.203151532625
821078610454.8679167519331.132083248069
8398329845.53789675746-13.5378967574579
84974710360.2099001194-613.209900119407
851041110456.2589711929-45.2589711928849
8695119562.48184523508-51.4818452350846
871040210600.1386387376-198.138638737586
88970110152.309396896-451.309396895977
891054010383.9192039728156.08079602721
901011210350.9868258377-238.986825837714
911091510702.7381386019212.261861398107
921118310770.281141243412.718858757047
931038410613.2307711187-229.23077111871
941083410649.8759944431184.124005556869
9598869916.32295341471-30.3229534147104
961021610250.1214868774-34.1214868774332
971094310565.3344585284377.665541471559
9898679718.80006990867148.199930091334
991020310742.137839015-539.137839014966
1001083710185.0152731823651.98472681768
1011057310724.1125038252-151.112503825179
1021064710556.738104614390.2618953856781
1031150211085.7819974408416.218002559166
1041065611249.3663511624-593.366351162371
1051086610804.25139995861.748600042034
1061083510996.5271505466-161.527150546621
107994510167.5227187688-222.522718768816
1081033110479.255184748-148.255184747992
1091071810895.4640418191-177.464041819077
11094629914.29060948983-452.290609489826
1111057910662.3086960732-83.3086960731816
1121063310478.0873818951154.912618104925
1131034610720.6789353216-374.678935321643
1141075710575.6134312936181.386568706381
1151120711187.109709740219.890290259762
1161101311000.931589475712.0684105242763
1171101510790.5680443172224.431955682812
1181076510925.2335226589-160.233522658886
1191004210065.7227601211-23.7227601211089
1201066110409.4806343868251.519365613229

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 9928 & 9938.65918803419 & -10.6591880341857 \tabularnewline
14 & 8686 & 8694.00024937159 & -8.00024937159469 \tabularnewline
15 & 9843 & 9863.4919576645 & -20.4919576645007 \tabularnewline
16 & 9627 & 9650.43230905813 & -23.4323090581274 \tabularnewline
17 & 10074 & 10094.8554340655 & -20.8554340655319 \tabularnewline
18 & 9503 & 9526.5405800661 & -23.5405800661028 \tabularnewline
19 & 10119 & 9938.11073557739 & 180.889264422611 \tabularnewline
20 & 10000 & 10176.6009698522 & -176.600969852208 \tabularnewline
21 & 9313 & 9530.19588764204 & -217.195887642038 \tabularnewline
22 & 9866 & 9814.75558282031 & 51.2444171796851 \tabularnewline
23 & 9172 & 9219.20277572869 & -47.2027757286851 \tabularnewline
24 & 9241 & 9293.45957621869 & -52.4595762186927 \tabularnewline
25 & 9659 & 9804.87390962675 & -145.873909626755 \tabularnewline
26 & 8904 & 8539.06158759441 & 364.938412405594 \tabularnewline
27 & 9755 & 9745.24066825379 & 9.75933174620877 \tabularnewline
28 & 9080 & 9533.42575360876 & -453.425753608763 \tabularnewline
29 & 9435 & 9923.1924705264 & -488.192470526397 \tabularnewline
30 & 8971 & 9288.33955325027 & -317.339553250273 \tabularnewline
31 & 10063 & 9706.67737201572 & 356.32262798428 \tabularnewline
32 & 9793 & 9850.40930982878 & -57.4093098287849 \tabularnewline
33 & 9454 & 9192.81967079502 & 261.180329204979 \tabularnewline
34 & 9759 & 9599.0383958232 & 159.961604176799 \tabularnewline
35 & 8820 & 8982.815489717 & -162.815489717002 \tabularnewline
36 & 9403 & 9035.62514377689 & 367.374856223114 \tabularnewline
37 & 9676 & 9566.77969024377 & 109.220309756225 \tabularnewline
38 & 8642 & 8473.96707409728 & 168.032925902722 \tabularnewline
39 & 9402 & 9558.41495839574 & -156.414958395742 \tabularnewline
40 & 9610 & 9196.01326582854 & 413.986734171463 \tabularnewline
41 & 9294 & 9682.26241064693 & -388.26241064693 \tabularnewline
42 & 9448 & 9116.28066444386 & 331.719335556141 \tabularnewline
43 & 10319 & 9813.94597092407 & 505.054029075929 \tabularnewline
44 & 9548 & 9879.7466619202 & -331.746661920199 \tabularnewline
45 & 9801 & 9297.10759751067 & 503.892402489333 \tabularnewline
46 & 9596 & 9722.62074426886 & -126.620744268865 \tabularnewline
47 & 8923 & 9000.66286013763 & -77.6628601376342 \tabularnewline
48 & 9746 & 9228.33284456518 & 517.667155434818 \tabularnewline
49 & 9829 & 9723.98398277973 & 105.016017220272 \tabularnewline
50 & 9125 & 8666.57898869501 & 458.421011304987 \tabularnewline
51 & 9782 & 9716.60048665423 & 65.3995133457702 \tabularnewline
52 & 9441 & 9564.38114291128 & -123.381142911277 \tabularnewline
53 & 9162 & 9785.84600688343 & -623.84600688343 \tabularnewline
54 & 9915 & 9410.04652043995 & 504.95347956005 \tabularnewline
55 & 10444 & 10193.8062824471 & 250.193717552887 \tabularnewline
56 & 10209 & 10012.717718738 & 196.282281261989 \tabularnewline
57 & 9985 & 9744.23600433217 & 240.763995667827 \tabularnewline
58 & 9842 & 9982.94092681934 & -140.940926819345 \tabularnewline
59 & 9429 & 9291.28624592451 & 137.713754075492 \tabularnewline
60 & 10132 & 9730.19020122117 & 401.809798778826 \tabularnewline
61 & 9849 & 10117.4256429738 & -268.425642973845 \tabularnewline
62 & 9172 & 9131.16356960334 & 40.8364303966646 \tabularnewline
63 & 10313 & 10033.8085513526 & 279.191448647432 \tabularnewline
64 & 9819 & 9864.91833763432 & -45.9183376343226 \tabularnewline
65 & 9955 & 9968.56908468689 & -13.5690846868874 \tabularnewline
66 & 10048 & 9996.96492779397 & 51.0350722060339 \tabularnewline
67 & 10082 & 10673.75065653 & -591.750656530048 \tabularnewline
68 & 10541 & 10386.8516135945 & 154.148386405468 \tabularnewline
69 & 10208 & 10129.2898310959 & 78.7101689040956 \tabularnewline
70 & 10233 & 10244.5202053863 & -11.5202053863468 \tabularnewline
71 & 9439 & 9647.88387683781 & -208.883876837814 \tabularnewline
72 & 9963 & 10119.6479810759 & -156.647981075874 \tabularnewline
73 & 10158 & 10248.1411799755 & -90.141179975466 \tabularnewline
74 & 9225 & 9361.24575945592 & -136.24575945592 \tabularnewline
75 & 10474 & 10301.210052141 & 172.789947858986 \tabularnewline
76 & 9757 & 10019.1480484862 & -262.148048486226 \tabularnewline
77 & 10490 & 10094.0193810587 & 395.980618941267 \tabularnewline
78 & 10281 & 10178.3913000461 & 102.608699953933 \tabularnewline
79 & 10444 & 10674.4905624442 & -230.490562444236 \tabularnewline
80 & 10640 & 10633.4875901552 & 6.5124098448141 \tabularnewline
81 & 10695 & 10333.7968484674 & 361.203151532625 \tabularnewline
82 & 10786 & 10454.8679167519 & 331.132083248069 \tabularnewline
83 & 9832 & 9845.53789675746 & -13.5378967574579 \tabularnewline
84 & 9747 & 10360.2099001194 & -613.209900119407 \tabularnewline
85 & 10411 & 10456.2589711929 & -45.2589711928849 \tabularnewline
86 & 9511 & 9562.48184523508 & -51.4818452350846 \tabularnewline
87 & 10402 & 10600.1386387376 & -198.138638737586 \tabularnewline
88 & 9701 & 10152.309396896 & -451.309396895977 \tabularnewline
89 & 10540 & 10383.9192039728 & 156.08079602721 \tabularnewline
90 & 10112 & 10350.9868258377 & -238.986825837714 \tabularnewline
91 & 10915 & 10702.7381386019 & 212.261861398107 \tabularnewline
92 & 11183 & 10770.281141243 & 412.718858757047 \tabularnewline
93 & 10384 & 10613.2307711187 & -229.23077111871 \tabularnewline
94 & 10834 & 10649.8759944431 & 184.124005556869 \tabularnewline
95 & 9886 & 9916.32295341471 & -30.3229534147104 \tabularnewline
96 & 10216 & 10250.1214868774 & -34.1214868774332 \tabularnewline
97 & 10943 & 10565.3344585284 & 377.665541471559 \tabularnewline
98 & 9867 & 9718.80006990867 & 148.199930091334 \tabularnewline
99 & 10203 & 10742.137839015 & -539.137839014966 \tabularnewline
100 & 10837 & 10185.0152731823 & 651.98472681768 \tabularnewline
101 & 10573 & 10724.1125038252 & -151.112503825179 \tabularnewline
102 & 10647 & 10556.7381046143 & 90.2618953856781 \tabularnewline
103 & 11502 & 11085.7819974408 & 416.218002559166 \tabularnewline
104 & 10656 & 11249.3663511624 & -593.366351162371 \tabularnewline
105 & 10866 & 10804.251399958 & 61.748600042034 \tabularnewline
106 & 10835 & 10996.5271505466 & -161.527150546621 \tabularnewline
107 & 9945 & 10167.5227187688 & -222.522718768816 \tabularnewline
108 & 10331 & 10479.255184748 & -148.255184747992 \tabularnewline
109 & 10718 & 10895.4640418191 & -177.464041819077 \tabularnewline
110 & 9462 & 9914.29060948983 & -452.290609489826 \tabularnewline
111 & 10579 & 10662.3086960732 & -83.3086960731816 \tabularnewline
112 & 10633 & 10478.0873818951 & 154.912618104925 \tabularnewline
113 & 10346 & 10720.6789353216 & -374.678935321643 \tabularnewline
114 & 10757 & 10575.6134312936 & 181.386568706381 \tabularnewline
115 & 11207 & 11187.1097097402 & 19.890290259762 \tabularnewline
116 & 11013 & 11000.9315894757 & 12.0684105242763 \tabularnewline
117 & 11015 & 10790.5680443172 & 224.431955682812 \tabularnewline
118 & 10765 & 10925.2335226589 & -160.233522658886 \tabularnewline
119 & 10042 & 10065.7227601211 & -23.7227601211089 \tabularnewline
120 & 10661 & 10409.4806343868 & 251.519365613229 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196599&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]9928[/C][C]9938.65918803419[/C][C]-10.6591880341857[/C][/ROW]
[ROW][C]14[/C][C]8686[/C][C]8694.00024937159[/C][C]-8.00024937159469[/C][/ROW]
[ROW][C]15[/C][C]9843[/C][C]9863.4919576645[/C][C]-20.4919576645007[/C][/ROW]
[ROW][C]16[/C][C]9627[/C][C]9650.43230905813[/C][C]-23.4323090581274[/C][/ROW]
[ROW][C]17[/C][C]10074[/C][C]10094.8554340655[/C][C]-20.8554340655319[/C][/ROW]
[ROW][C]18[/C][C]9503[/C][C]9526.5405800661[/C][C]-23.5405800661028[/C][/ROW]
[ROW][C]19[/C][C]10119[/C][C]9938.11073557739[/C][C]180.889264422611[/C][/ROW]
[ROW][C]20[/C][C]10000[/C][C]10176.6009698522[/C][C]-176.600969852208[/C][/ROW]
[ROW][C]21[/C][C]9313[/C][C]9530.19588764204[/C][C]-217.195887642038[/C][/ROW]
[ROW][C]22[/C][C]9866[/C][C]9814.75558282031[/C][C]51.2444171796851[/C][/ROW]
[ROW][C]23[/C][C]9172[/C][C]9219.20277572869[/C][C]-47.2027757286851[/C][/ROW]
[ROW][C]24[/C][C]9241[/C][C]9293.45957621869[/C][C]-52.4595762186927[/C][/ROW]
[ROW][C]25[/C][C]9659[/C][C]9804.87390962675[/C][C]-145.873909626755[/C][/ROW]
[ROW][C]26[/C][C]8904[/C][C]8539.06158759441[/C][C]364.938412405594[/C][/ROW]
[ROW][C]27[/C][C]9755[/C][C]9745.24066825379[/C][C]9.75933174620877[/C][/ROW]
[ROW][C]28[/C][C]9080[/C][C]9533.42575360876[/C][C]-453.425753608763[/C][/ROW]
[ROW][C]29[/C][C]9435[/C][C]9923.1924705264[/C][C]-488.192470526397[/C][/ROW]
[ROW][C]30[/C][C]8971[/C][C]9288.33955325027[/C][C]-317.339553250273[/C][/ROW]
[ROW][C]31[/C][C]10063[/C][C]9706.67737201572[/C][C]356.32262798428[/C][/ROW]
[ROW][C]32[/C][C]9793[/C][C]9850.40930982878[/C][C]-57.4093098287849[/C][/ROW]
[ROW][C]33[/C][C]9454[/C][C]9192.81967079502[/C][C]261.180329204979[/C][/ROW]
[ROW][C]34[/C][C]9759[/C][C]9599.0383958232[/C][C]159.961604176799[/C][/ROW]
[ROW][C]35[/C][C]8820[/C][C]8982.815489717[/C][C]-162.815489717002[/C][/ROW]
[ROW][C]36[/C][C]9403[/C][C]9035.62514377689[/C][C]367.374856223114[/C][/ROW]
[ROW][C]37[/C][C]9676[/C][C]9566.77969024377[/C][C]109.220309756225[/C][/ROW]
[ROW][C]38[/C][C]8642[/C][C]8473.96707409728[/C][C]168.032925902722[/C][/ROW]
[ROW][C]39[/C][C]9402[/C][C]9558.41495839574[/C][C]-156.414958395742[/C][/ROW]
[ROW][C]40[/C][C]9610[/C][C]9196.01326582854[/C][C]413.986734171463[/C][/ROW]
[ROW][C]41[/C][C]9294[/C][C]9682.26241064693[/C][C]-388.26241064693[/C][/ROW]
[ROW][C]42[/C][C]9448[/C][C]9116.28066444386[/C][C]331.719335556141[/C][/ROW]
[ROW][C]43[/C][C]10319[/C][C]9813.94597092407[/C][C]505.054029075929[/C][/ROW]
[ROW][C]44[/C][C]9548[/C][C]9879.7466619202[/C][C]-331.746661920199[/C][/ROW]
[ROW][C]45[/C][C]9801[/C][C]9297.10759751067[/C][C]503.892402489333[/C][/ROW]
[ROW][C]46[/C][C]9596[/C][C]9722.62074426886[/C][C]-126.620744268865[/C][/ROW]
[ROW][C]47[/C][C]8923[/C][C]9000.66286013763[/C][C]-77.6628601376342[/C][/ROW]
[ROW][C]48[/C][C]9746[/C][C]9228.33284456518[/C][C]517.667155434818[/C][/ROW]
[ROW][C]49[/C][C]9829[/C][C]9723.98398277973[/C][C]105.016017220272[/C][/ROW]
[ROW][C]50[/C][C]9125[/C][C]8666.57898869501[/C][C]458.421011304987[/C][/ROW]
[ROW][C]51[/C][C]9782[/C][C]9716.60048665423[/C][C]65.3995133457702[/C][/ROW]
[ROW][C]52[/C][C]9441[/C][C]9564.38114291128[/C][C]-123.381142911277[/C][/ROW]
[ROW][C]53[/C][C]9162[/C][C]9785.84600688343[/C][C]-623.84600688343[/C][/ROW]
[ROW][C]54[/C][C]9915[/C][C]9410.04652043995[/C][C]504.95347956005[/C][/ROW]
[ROW][C]55[/C][C]10444[/C][C]10193.8062824471[/C][C]250.193717552887[/C][/ROW]
[ROW][C]56[/C][C]10209[/C][C]10012.717718738[/C][C]196.282281261989[/C][/ROW]
[ROW][C]57[/C][C]9985[/C][C]9744.23600433217[/C][C]240.763995667827[/C][/ROW]
[ROW][C]58[/C][C]9842[/C][C]9982.94092681934[/C][C]-140.940926819345[/C][/ROW]
[ROW][C]59[/C][C]9429[/C][C]9291.28624592451[/C][C]137.713754075492[/C][/ROW]
[ROW][C]60[/C][C]10132[/C][C]9730.19020122117[/C][C]401.809798778826[/C][/ROW]
[ROW][C]61[/C][C]9849[/C][C]10117.4256429738[/C][C]-268.425642973845[/C][/ROW]
[ROW][C]62[/C][C]9172[/C][C]9131.16356960334[/C][C]40.8364303966646[/C][/ROW]
[ROW][C]63[/C][C]10313[/C][C]10033.8085513526[/C][C]279.191448647432[/C][/ROW]
[ROW][C]64[/C][C]9819[/C][C]9864.91833763432[/C][C]-45.9183376343226[/C][/ROW]
[ROW][C]65[/C][C]9955[/C][C]9968.56908468689[/C][C]-13.5690846868874[/C][/ROW]
[ROW][C]66[/C][C]10048[/C][C]9996.96492779397[/C][C]51.0350722060339[/C][/ROW]
[ROW][C]67[/C][C]10082[/C][C]10673.75065653[/C][C]-591.750656530048[/C][/ROW]
[ROW][C]68[/C][C]10541[/C][C]10386.8516135945[/C][C]154.148386405468[/C][/ROW]
[ROW][C]69[/C][C]10208[/C][C]10129.2898310959[/C][C]78.7101689040956[/C][/ROW]
[ROW][C]70[/C][C]10233[/C][C]10244.5202053863[/C][C]-11.5202053863468[/C][/ROW]
[ROW][C]71[/C][C]9439[/C][C]9647.88387683781[/C][C]-208.883876837814[/C][/ROW]
[ROW][C]72[/C][C]9963[/C][C]10119.6479810759[/C][C]-156.647981075874[/C][/ROW]
[ROW][C]73[/C][C]10158[/C][C]10248.1411799755[/C][C]-90.141179975466[/C][/ROW]
[ROW][C]74[/C][C]9225[/C][C]9361.24575945592[/C][C]-136.24575945592[/C][/ROW]
[ROW][C]75[/C][C]10474[/C][C]10301.210052141[/C][C]172.789947858986[/C][/ROW]
[ROW][C]76[/C][C]9757[/C][C]10019.1480484862[/C][C]-262.148048486226[/C][/ROW]
[ROW][C]77[/C][C]10490[/C][C]10094.0193810587[/C][C]395.980618941267[/C][/ROW]
[ROW][C]78[/C][C]10281[/C][C]10178.3913000461[/C][C]102.608699953933[/C][/ROW]
[ROW][C]79[/C][C]10444[/C][C]10674.4905624442[/C][C]-230.490562444236[/C][/ROW]
[ROW][C]80[/C][C]10640[/C][C]10633.4875901552[/C][C]6.5124098448141[/C][/ROW]
[ROW][C]81[/C][C]10695[/C][C]10333.7968484674[/C][C]361.203151532625[/C][/ROW]
[ROW][C]82[/C][C]10786[/C][C]10454.8679167519[/C][C]331.132083248069[/C][/ROW]
[ROW][C]83[/C][C]9832[/C][C]9845.53789675746[/C][C]-13.5378967574579[/C][/ROW]
[ROW][C]84[/C][C]9747[/C][C]10360.2099001194[/C][C]-613.209900119407[/C][/ROW]
[ROW][C]85[/C][C]10411[/C][C]10456.2589711929[/C][C]-45.2589711928849[/C][/ROW]
[ROW][C]86[/C][C]9511[/C][C]9562.48184523508[/C][C]-51.4818452350846[/C][/ROW]
[ROW][C]87[/C][C]10402[/C][C]10600.1386387376[/C][C]-198.138638737586[/C][/ROW]
[ROW][C]88[/C][C]9701[/C][C]10152.309396896[/C][C]-451.309396895977[/C][/ROW]
[ROW][C]89[/C][C]10540[/C][C]10383.9192039728[/C][C]156.08079602721[/C][/ROW]
[ROW][C]90[/C][C]10112[/C][C]10350.9868258377[/C][C]-238.986825837714[/C][/ROW]
[ROW][C]91[/C][C]10915[/C][C]10702.7381386019[/C][C]212.261861398107[/C][/ROW]
[ROW][C]92[/C][C]11183[/C][C]10770.281141243[/C][C]412.718858757047[/C][/ROW]
[ROW][C]93[/C][C]10384[/C][C]10613.2307711187[/C][C]-229.23077111871[/C][/ROW]
[ROW][C]94[/C][C]10834[/C][C]10649.8759944431[/C][C]184.124005556869[/C][/ROW]
[ROW][C]95[/C][C]9886[/C][C]9916.32295341471[/C][C]-30.3229534147104[/C][/ROW]
[ROW][C]96[/C][C]10216[/C][C]10250.1214868774[/C][C]-34.1214868774332[/C][/ROW]
[ROW][C]97[/C][C]10943[/C][C]10565.3344585284[/C][C]377.665541471559[/C][/ROW]
[ROW][C]98[/C][C]9867[/C][C]9718.80006990867[/C][C]148.199930091334[/C][/ROW]
[ROW][C]99[/C][C]10203[/C][C]10742.137839015[/C][C]-539.137839014966[/C][/ROW]
[ROW][C]100[/C][C]10837[/C][C]10185.0152731823[/C][C]651.98472681768[/C][/ROW]
[ROW][C]101[/C][C]10573[/C][C]10724.1125038252[/C][C]-151.112503825179[/C][/ROW]
[ROW][C]102[/C][C]10647[/C][C]10556.7381046143[/C][C]90.2618953856781[/C][/ROW]
[ROW][C]103[/C][C]11502[/C][C]11085.7819974408[/C][C]416.218002559166[/C][/ROW]
[ROW][C]104[/C][C]10656[/C][C]11249.3663511624[/C][C]-593.366351162371[/C][/ROW]
[ROW][C]105[/C][C]10866[/C][C]10804.251399958[/C][C]61.748600042034[/C][/ROW]
[ROW][C]106[/C][C]10835[/C][C]10996.5271505466[/C][C]-161.527150546621[/C][/ROW]
[ROW][C]107[/C][C]9945[/C][C]10167.5227187688[/C][C]-222.522718768816[/C][/ROW]
[ROW][C]108[/C][C]10331[/C][C]10479.255184748[/C][C]-148.255184747992[/C][/ROW]
[ROW][C]109[/C][C]10718[/C][C]10895.4640418191[/C][C]-177.464041819077[/C][/ROW]
[ROW][C]110[/C][C]9462[/C][C]9914.29060948983[/C][C]-452.290609489826[/C][/ROW]
[ROW][C]111[/C][C]10579[/C][C]10662.3086960732[/C][C]-83.3086960731816[/C][/ROW]
[ROW][C]112[/C][C]10633[/C][C]10478.0873818951[/C][C]154.912618104925[/C][/ROW]
[ROW][C]113[/C][C]10346[/C][C]10720.6789353216[/C][C]-374.678935321643[/C][/ROW]
[ROW][C]114[/C][C]10757[/C][C]10575.6134312936[/C][C]181.386568706381[/C][/ROW]
[ROW][C]115[/C][C]11207[/C][C]11187.1097097402[/C][C]19.890290259762[/C][/ROW]
[ROW][C]116[/C][C]11013[/C][C]11000.9315894757[/C][C]12.0684105242763[/C][/ROW]
[ROW][C]117[/C][C]11015[/C][C]10790.5680443172[/C][C]224.431955682812[/C][/ROW]
[ROW][C]118[/C][C]10765[/C][C]10925.2335226589[/C][C]-160.233522658886[/C][/ROW]
[ROW][C]119[/C][C]10042[/C][C]10065.7227601211[/C][C]-23.7227601211089[/C][/ROW]
[ROW][C]120[/C][C]10661[/C][C]10409.4806343868[/C][C]251.519365613229[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196599&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196599&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
1399289938.65918803419-10.6591880341857
1486868694.00024937159-8.00024937159469
1598439863.4919576645-20.4919576645007
1696279650.43230905813-23.4323090581274
171007410094.8554340655-20.8554340655319
1895039526.5405800661-23.5405800661028
19101199938.11073557739180.889264422611
201000010176.6009698522-176.600969852208
2193139530.19588764204-217.195887642038
2298669814.7555828203151.2444171796851
2391729219.20277572869-47.2027757286851
2492419293.45957621869-52.4595762186927
2596599804.87390962675-145.873909626755
2689048539.06158759441364.938412405594
2797559745.240668253799.75933174620877
2890809533.42575360876-453.425753608763
2994359923.1924705264-488.192470526397
3089719288.33955325027-317.339553250273
31100639706.67737201572356.32262798428
3297939850.40930982878-57.4093098287849
3394549192.81967079502261.180329204979
3497599599.0383958232159.961604176799
3588208982.815489717-162.815489717002
3694039035.62514377689367.374856223114
3796769566.77969024377109.220309756225
3886428473.96707409728168.032925902722
3994029558.41495839574-156.414958395742
4096109196.01326582854413.986734171463
4192949682.26241064693-388.26241064693
4294489116.28066444386331.719335556141
43103199813.94597092407505.054029075929
4495489879.7466619202-331.746661920199
4598019297.10759751067503.892402489333
4695969722.62074426886-126.620744268865
4789239000.66286013763-77.6628601376342
4897469228.33284456518517.667155434818
4998299723.98398277973105.016017220272
5091258666.57898869501458.421011304987
5197829716.6004866542365.3995133457702
5294419564.38114291128-123.381142911277
5391629785.84600688343-623.84600688343
5499159410.04652043995504.95347956005
551044410193.8062824471250.193717552887
561020910012.717718738196.282281261989
5799859744.23600433217240.763995667827
5898429982.94092681934-140.940926819345
5994299291.28624592451137.713754075492
60101329730.19020122117401.809798778826
61984910117.4256429738-268.425642973845
6291729131.1635696033440.8364303966646
631031310033.8085513526279.191448647432
6498199864.91833763432-45.9183376343226
6599559968.56908468689-13.5690846868874
66100489996.9649277939751.0350722060339
671008210673.75065653-591.750656530048
681054110386.8516135945154.148386405468
691020810129.289831095978.7101689040956
701023310244.5202053863-11.5202053863468
7194399647.88387683781-208.883876837814
72996310119.6479810759-156.647981075874
731015810248.1411799755-90.141179975466
7492259361.24575945592-136.24575945592
751047410301.210052141172.789947858986
76975710019.1480484862-262.148048486226
771049010094.0193810587395.980618941267
781028110178.3913000461102.608699953933
791044410674.4905624442-230.490562444236
801064010633.48759015526.5124098448141
811069510333.7968484674361.203151532625
821078610454.8679167519331.132083248069
8398329845.53789675746-13.5378967574579
84974710360.2099001194-613.209900119407
851041110456.2589711929-45.2589711928849
8695119562.48184523508-51.4818452350846
871040210600.1386387376-198.138638737586
88970110152.309396896-451.309396895977
891054010383.9192039728156.08079602721
901011210350.9868258377-238.986825837714
911091510702.7381386019212.261861398107
921118310770.281141243412.718858757047
931038410613.2307711187-229.23077111871
941083410649.8759944431184.124005556869
9598869916.32295341471-30.3229534147104
961021610250.1214868774-34.1214868774332
971094310565.3344585284377.665541471559
9898679718.80006990867148.199930091334
991020310742.137839015-539.137839014966
1001083710185.0152731823651.98472681768
1011057310724.1125038252-151.112503825179
1021064710556.738104614390.2618953856781
1031150211085.7819974408416.218002559166
1041065611249.3663511624-593.366351162371
1051086610804.25139995861.748600042034
1061083510996.5271505466-161.527150546621
107994510167.5227187688-222.522718768816
1081033110479.255184748-148.255184747992
1091071810895.4640418191-177.464041819077
11094629914.29060948983-452.290609489826
1111057910662.3086960732-83.3086960731816
1121063310478.0873818951154.912618104925
1131034610720.6789353216-374.678935321643
1141075710575.6134312936181.386568706381
1151120711187.109709740219.890290259762
1161101311000.931589475712.0684105242763
1171101510790.5680443172224.431955682812
1181076510925.2335226589-160.233522658886
1191004210065.7227601211-23.7227601211089
1201066110409.4806343868251.519365613229







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12110856.782744064210315.347015889411398.218472239
1229815.638956023239269.9442187058210361.3336933406
12310719.993314330710169.134609507611270.8520191538
12410615.317165633910058.321495522311172.3128357456
12510694.6623119710130.496407633511258.8282163064
12610753.378724159110180.957449479511325.7999988387
12711303.800940244510721.996118554411885.6057619346
12811117.254474901610524.903901446511709.6050483566
12910968.598654106910364.515051079711572.6822571342
13010971.752022517510354.731704365811588.7723406692
13110171.31831013049540.1493531006410802.4872671601
13210597.78902593389951.2587736541211244.3192782136

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 10856.7827440642 & 10315.3470158894 & 11398.218472239 \tabularnewline
122 & 9815.63895602323 & 9269.94421870582 & 10361.3336933406 \tabularnewline
123 & 10719.9933143307 & 10169.1346095076 & 11270.8520191538 \tabularnewline
124 & 10615.3171656339 & 10058.3214955223 & 11172.3128357456 \tabularnewline
125 & 10694.66231197 & 10130.4964076335 & 11258.8282163064 \tabularnewline
126 & 10753.3787241591 & 10180.9574494795 & 11325.7999988387 \tabularnewline
127 & 11303.8009402445 & 10721.9961185544 & 11885.6057619346 \tabularnewline
128 & 11117.2544749016 & 10524.9039014465 & 11709.6050483566 \tabularnewline
129 & 10968.5986541069 & 10364.5150510797 & 11572.6822571342 \tabularnewline
130 & 10971.7520225175 & 10354.7317043658 & 11588.7723406692 \tabularnewline
131 & 10171.3183101304 & 9540.14935310064 & 10802.4872671601 \tabularnewline
132 & 10597.7890259338 & 9951.25877365412 & 11244.3192782136 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196599&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]10856.7827440642[/C][C]10315.3470158894[/C][C]11398.218472239[/C][/ROW]
[ROW][C]122[/C][C]9815.63895602323[/C][C]9269.94421870582[/C][C]10361.3336933406[/C][/ROW]
[ROW][C]123[/C][C]10719.9933143307[/C][C]10169.1346095076[/C][C]11270.8520191538[/C][/ROW]
[ROW][C]124[/C][C]10615.3171656339[/C][C]10058.3214955223[/C][C]11172.3128357456[/C][/ROW]
[ROW][C]125[/C][C]10694.66231197[/C][C]10130.4964076335[/C][C]11258.8282163064[/C][/ROW]
[ROW][C]126[/C][C]10753.3787241591[/C][C]10180.9574494795[/C][C]11325.7999988387[/C][/ROW]
[ROW][C]127[/C][C]11303.8009402445[/C][C]10721.9961185544[/C][C]11885.6057619346[/C][/ROW]
[ROW][C]128[/C][C]11117.2544749016[/C][C]10524.9039014465[/C][C]11709.6050483566[/C][/ROW]
[ROW][C]129[/C][C]10968.5986541069[/C][C]10364.5150510797[/C][C]11572.6822571342[/C][/ROW]
[ROW][C]130[/C][C]10971.7520225175[/C][C]10354.7317043658[/C][C]11588.7723406692[/C][/ROW]
[ROW][C]131[/C][C]10171.3183101304[/C][C]9540.14935310064[/C][C]10802.4872671601[/C][/ROW]
[ROW][C]132[/C][C]10597.7890259338[/C][C]9951.25877365412[/C][C]11244.3192782136[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196599&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196599&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
12110856.782744064210315.347015889411398.218472239
1229815.638956023239269.9442187058210361.3336933406
12310719.993314330710169.134609507611270.8520191538
12410615.317165633910058.321495522311172.3128357456
12510694.6623119710130.496407633511258.8282163064
12610753.378724159110180.957449479511325.7999988387
12711303.800940244510721.996118554411885.6057619346
12811117.254474901610524.903901446511709.6050483566
12910968.598654106910364.515051079711572.6822571342
13010971.752022517510354.731704365811588.7723406692
13110171.31831013049540.1493531006410802.4872671601
13210597.78902593389951.2587736541211244.3192782136



Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
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')