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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 12 Aug 2013 11:06:04 -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/2013/Aug/12/t1376321596qw3nmg3s0iym4lq.htm/, Retrieved Sat, 27 Apr 2024 17:45:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211047, Retrieved Sat, 27 Apr 2024 17:45:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsAnthony Van Dyck
Estimated Impact123

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Tijdreeks 1 - stap 2] [2013-08-12 11:07:04] [c4bfab449d963e708b9482b0c0d301bf]
-   P   [Univariate Data Series] [Tijdreeks A - Stap 2] [2013-08-12 11:17:51] [fffbdc2eb6bf36a612a50d50ad291a0a]
- RMP     [Histogram] [Tijdreeks A - Stap 3] [2013-08-12 11:22:38] [fffbdc2eb6bf36a612a50d50ad291a0a]
- R P       [Histogram] [Tijdreeks A -stap 5] [2013-08-12 11:38:26] [c4bfab449d963e708b9482b0c0d301bf]
-   P         [Histogram] [Tijdreeks A -stap 5] [2013-08-12 11:42:06] [c4bfab449d963e708b9482b0c0d301bf]
- RMP           [Harrell-Davis Quantiles] [Tijdreeks A - sta...] [2013-08-12 12:35:57] [fffbdc2eb6bf36a612a50d50ad291a0a]
- R P             [Harrell-Davis Quantiles] [Tijdreeks A - sta...] [2013-08-12 12:48:29] [c4bfab449d963e708b9482b0c0d301bf]
- RMP               [(Partial) Autocorrelation Function] [Tijdreeks A - sta...] [2013-08-12 13:54:06] [fffbdc2eb6bf36a612a50d50ad291a0a]
- RM                    [Exponential Smoothing] [Tijdreeks A - sta...] [2013-08-12 15:06:04] [c43b2753d6eee680db8e2d052715ef09] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
36439
36368
36290
36147
37615
37543
36439
35705
35777
35777
35848
35998
35998
35335
35043
35335
36368
36218
34822
33640
33419
32977
33276
33640
33497
33198
32614
33198
33718
33568
31873
31139
30405
29814
29743
30184
29593
29372
29151
30405
30548
29814
27826
26943
25547
24955
25247
25689
25689
25326
25247
26430
27385
26943
25468
24735
23189
22234
22968
23702
23702
22747
22676
23922
24735
24442
22968
22013
19947
19142
19434
20688
20759
18921
19584
21201
21935
21493
19506
18109
16492
15238
15751
16855
16563
14946
15459
17076
17960
17447
15459
14576
13251
11854
12075
13179
13322
11997
12218
14063
14504
13764
11042
9646
7801
5963
6554
7359
7217
5813
6625
8613
9496
9055
7288
5892
4417
2721
3021
3534

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 & 6 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211047&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]6 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=211047&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211047&T=0

As an alternative you can also use a QR Code:  
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 time6 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.400851431469901
beta0.0368982697385969
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.400851431469901 \tabularnewline
beta & 0.0368982697385969 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211047&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]0.400851431469901[/C][/ROW]
[ROW][C]beta[/C][C]0.0368982697385969[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211047&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211047&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.400851431469901
beta0.0368982697385969
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133599836579.1669337607-581.16693376068
143533535689.5399635761-354.539963576055
153504335287.3878359651-244.387835965084
163533535540.4006732962-205.400673296201
173636836555.9202125406-187.920212540615
183621836374.2506767915-156.250676791526
193482234828.9231924415-6.92319244149985
203364033989.3931115873-349.393111587349
213341933846.9990295755-427.999029575491
223297733585.5569038598-608.556903859811
233327633313.7368984226-37.7368984226414
243364033370.5477532183269.452246781744
253349733071.6925407069425.307459293072
263319832693.4246131314504.575386868601
273261432686.4836480036-72.483648003632
283319833019.1422701804178.85772981964
293371834192.2278358073-474.227835807251
303356833903.5936417367-335.593641736719
313187332362.020414611-489.020414611023
323113931103.094836206235.9051637938101
333040531052.7945626103-647.794562610303
342981430576.5582222407-762.558222240714
352974330564.2268973031-821.226897303099
363018430458.6525568761-274.652556876128
372959329994.6508340664-401.650834066357
382937229279.735695734492.2643042655654
392915128703.0237082734447.976291726627
403040529343.84680853731061.15319146266
413054830441.3028195331106.697180466927
422981430439.1843588241-625.184358824114
432782628655.9082205165-829.908220516507
442694327536.1090821396-593.109082139603
452554726775.9896551198-1228.98965511977
462495525941.3834710755-986.38347107554
472524725744.2332080358-497.233208035843
482568926040.8565226892-351.856522689202
492568925413.5198284032275.480171596821
502532625219.6806137918106.31938620823
512524724815.6532816852431.346718314759
522643025770.8748194824659.125180517636
532738526083.05045274621301.94954725383
542694326086.9575644496856.04243555036
552546824762.0944421972705.905557802751
562473524409.8432620785325.156737921458
572318923660.4438269297-471.443826929681
582223423309.6815303395-1075.68153033948
592296823403.312319276-435.312319275989
602370223846.2774255036-144.277425503555
612370223715.5057187745-13.505718774526
622274723337.6880702404-590.688070240445
632267622871.9091334764-195.909133476358
642392223725.7950076623196.204992337665
652473524244.3363980404490.663601959612
662444223650.6549409235791.345059076477
672296822203.7277376153764.272262384744
682201321641.4353603116371.564639688422
691994720428.730453509-481.730453509001
701914219707.0383888348-565.038388834771
711943420391.8120860012-957.812086001177
722068820794.7519806714-106.751980671412
732075920752.97553949856.02446050145954
741892120033.0589335063-1112.05893350627
751958419582.99784394011.00215605992344
762120120741.8418373918459.158162608222
772193521537.1934345597397.806565440274
782149321080.050140857412.949859143038
791950619453.232488362652.7675116373757
801810918347.9289684212-238.928968421187
811649216347.713413858144.286586141985
821523815804.7637134364-566.763713436354
831575116231.2068625341-480.20686253408
841685517320.2619148887-465.261914888699
851656317181.7984514444-618.798451444429
861494615511.733393138-565.733393137991
871545915925.8479587634-466.847958763421
881707617143.0285592124-67.0285592123691
891796017654.2875311455305.712468854501
901744717131.5279284018315.472071598178
911545915210.6183189009248.381681099079
921457613972.6356571554603.364342844588
931325112515.7939280085735.206071991533
941185411768.566802315985.4331976840822
951207512502.827316904-427.827316904044
961317913617.1306472611-438.130647261058
971332213393.2505044547-71.2505044547106
981199711978.26221818118.7377818189925
991221812698.3522493321-480.352249332122
1001406314161.9134101866-98.9134101865729
1011450414895.4895010243-391.489501024265
1021376414100.5617742269-336.561774226931
1031104211869.9011316021-827.901131602121
104964610389.0720938376-743.07209383762
10578018427.48318138887-626.483181388874
10659636680.95111793313-717.951117933126
10765546709.61257729581-155.612577295813
10873597854.84460351474-495.844603514735
10972177754.77607335814-537.776073358142
11058136126.92706908066-313.927069080661
11166256329.94885794505295.051142054952
11286138259.64890752688353.35109247312
11394968932.68744005857563.312559941431
11490558500.9936834552554.006316544797
11572886293.69573765668994.304262343319
11658925581.83974998347310.160250016534
11744174115.58689235116301.41310764884
11827212703.2170416145617.7829583854427
11930213391.6214703919-370.621470391897
12035344271.53578539867-737.535785398671

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 35998 & 36579.1669337607 & -581.16693376068 \tabularnewline
14 & 35335 & 35689.5399635761 & -354.539963576055 \tabularnewline
15 & 35043 & 35287.3878359651 & -244.387835965084 \tabularnewline
16 & 35335 & 35540.4006732962 & -205.400673296201 \tabularnewline
17 & 36368 & 36555.9202125406 & -187.920212540615 \tabularnewline
18 & 36218 & 36374.2506767915 & -156.250676791526 \tabularnewline
19 & 34822 & 34828.9231924415 & -6.92319244149985 \tabularnewline
20 & 33640 & 33989.3931115873 & -349.393111587349 \tabularnewline
21 & 33419 & 33846.9990295755 & -427.999029575491 \tabularnewline
22 & 32977 & 33585.5569038598 & -608.556903859811 \tabularnewline
23 & 33276 & 33313.7368984226 & -37.7368984226414 \tabularnewline
24 & 33640 & 33370.5477532183 & 269.452246781744 \tabularnewline
25 & 33497 & 33071.6925407069 & 425.307459293072 \tabularnewline
26 & 33198 & 32693.4246131314 & 504.575386868601 \tabularnewline
27 & 32614 & 32686.4836480036 & -72.483648003632 \tabularnewline
28 & 33198 & 33019.1422701804 & 178.85772981964 \tabularnewline
29 & 33718 & 34192.2278358073 & -474.227835807251 \tabularnewline
30 & 33568 & 33903.5936417367 & -335.593641736719 \tabularnewline
31 & 31873 & 32362.020414611 & -489.020414611023 \tabularnewline
32 & 31139 & 31103.0948362062 & 35.9051637938101 \tabularnewline
33 & 30405 & 31052.7945626103 & -647.794562610303 \tabularnewline
34 & 29814 & 30576.5582222407 & -762.558222240714 \tabularnewline
35 & 29743 & 30564.2268973031 & -821.226897303099 \tabularnewline
36 & 30184 & 30458.6525568761 & -274.652556876128 \tabularnewline
37 & 29593 & 29994.6508340664 & -401.650834066357 \tabularnewline
38 & 29372 & 29279.7356957344 & 92.2643042655654 \tabularnewline
39 & 29151 & 28703.0237082734 & 447.976291726627 \tabularnewline
40 & 30405 & 29343.8468085373 & 1061.15319146266 \tabularnewline
41 & 30548 & 30441.3028195331 & 106.697180466927 \tabularnewline
42 & 29814 & 30439.1843588241 & -625.184358824114 \tabularnewline
43 & 27826 & 28655.9082205165 & -829.908220516507 \tabularnewline
44 & 26943 & 27536.1090821396 & -593.109082139603 \tabularnewline
45 & 25547 & 26775.9896551198 & -1228.98965511977 \tabularnewline
46 & 24955 & 25941.3834710755 & -986.38347107554 \tabularnewline
47 & 25247 & 25744.2332080358 & -497.233208035843 \tabularnewline
48 & 25689 & 26040.8565226892 & -351.856522689202 \tabularnewline
49 & 25689 & 25413.5198284032 & 275.480171596821 \tabularnewline
50 & 25326 & 25219.6806137918 & 106.31938620823 \tabularnewline
51 & 25247 & 24815.6532816852 & 431.346718314759 \tabularnewline
52 & 26430 & 25770.8748194824 & 659.125180517636 \tabularnewline
53 & 27385 & 26083.0504527462 & 1301.94954725383 \tabularnewline
54 & 26943 & 26086.9575644496 & 856.04243555036 \tabularnewline
55 & 25468 & 24762.0944421972 & 705.905557802751 \tabularnewline
56 & 24735 & 24409.8432620785 & 325.156737921458 \tabularnewline
57 & 23189 & 23660.4438269297 & -471.443826929681 \tabularnewline
58 & 22234 & 23309.6815303395 & -1075.68153033948 \tabularnewline
59 & 22968 & 23403.312319276 & -435.312319275989 \tabularnewline
60 & 23702 & 23846.2774255036 & -144.277425503555 \tabularnewline
61 & 23702 & 23715.5057187745 & -13.505718774526 \tabularnewline
62 & 22747 & 23337.6880702404 & -590.688070240445 \tabularnewline
63 & 22676 & 22871.9091334764 & -195.909133476358 \tabularnewline
64 & 23922 & 23725.7950076623 & 196.204992337665 \tabularnewline
65 & 24735 & 24244.3363980404 & 490.663601959612 \tabularnewline
66 & 24442 & 23650.6549409235 & 791.345059076477 \tabularnewline
67 & 22968 & 22203.7277376153 & 764.272262384744 \tabularnewline
68 & 22013 & 21641.4353603116 & 371.564639688422 \tabularnewline
69 & 19947 & 20428.730453509 & -481.730453509001 \tabularnewline
70 & 19142 & 19707.0383888348 & -565.038388834771 \tabularnewline
71 & 19434 & 20391.8120860012 & -957.812086001177 \tabularnewline
72 & 20688 & 20794.7519806714 & -106.751980671412 \tabularnewline
73 & 20759 & 20752.9755394985 & 6.02446050145954 \tabularnewline
74 & 18921 & 20033.0589335063 & -1112.05893350627 \tabularnewline
75 & 19584 & 19582.9978439401 & 1.00215605992344 \tabularnewline
76 & 21201 & 20741.8418373918 & 459.158162608222 \tabularnewline
77 & 21935 & 21537.1934345597 & 397.806565440274 \tabularnewline
78 & 21493 & 21080.050140857 & 412.949859143038 \tabularnewline
79 & 19506 & 19453.2324883626 & 52.7675116373757 \tabularnewline
80 & 18109 & 18347.9289684212 & -238.928968421187 \tabularnewline
81 & 16492 & 16347.713413858 & 144.286586141985 \tabularnewline
82 & 15238 & 15804.7637134364 & -566.763713436354 \tabularnewline
83 & 15751 & 16231.2068625341 & -480.20686253408 \tabularnewline
84 & 16855 & 17320.2619148887 & -465.261914888699 \tabularnewline
85 & 16563 & 17181.7984514444 & -618.798451444429 \tabularnewline
86 & 14946 & 15511.733393138 & -565.733393137991 \tabularnewline
87 & 15459 & 15925.8479587634 & -466.847958763421 \tabularnewline
88 & 17076 & 17143.0285592124 & -67.0285592123691 \tabularnewline
89 & 17960 & 17654.2875311455 & 305.712468854501 \tabularnewline
90 & 17447 & 17131.5279284018 & 315.472071598178 \tabularnewline
91 & 15459 & 15210.6183189009 & 248.381681099079 \tabularnewline
92 & 14576 & 13972.6356571554 & 603.364342844588 \tabularnewline
93 & 13251 & 12515.7939280085 & 735.206071991533 \tabularnewline
94 & 11854 & 11768.5668023159 & 85.4331976840822 \tabularnewline
95 & 12075 & 12502.827316904 & -427.827316904044 \tabularnewline
96 & 13179 & 13617.1306472611 & -438.130647261058 \tabularnewline
97 & 13322 & 13393.2505044547 & -71.2505044547106 \tabularnewline
98 & 11997 & 11978.262218181 & 18.7377818189925 \tabularnewline
99 & 12218 & 12698.3522493321 & -480.352249332122 \tabularnewline
100 & 14063 & 14161.9134101866 & -98.9134101865729 \tabularnewline
101 & 14504 & 14895.4895010243 & -391.489501024265 \tabularnewline
102 & 13764 & 14100.5617742269 & -336.561774226931 \tabularnewline
103 & 11042 & 11869.9011316021 & -827.901131602121 \tabularnewline
104 & 9646 & 10389.0720938376 & -743.07209383762 \tabularnewline
105 & 7801 & 8427.48318138887 & -626.483181388874 \tabularnewline
106 & 5963 & 6680.95111793313 & -717.951117933126 \tabularnewline
107 & 6554 & 6709.61257729581 & -155.612577295813 \tabularnewline
108 & 7359 & 7854.84460351474 & -495.844603514735 \tabularnewline
109 & 7217 & 7754.77607335814 & -537.776073358142 \tabularnewline
110 & 5813 & 6126.92706908066 & -313.927069080661 \tabularnewline
111 & 6625 & 6329.94885794505 & 295.051142054952 \tabularnewline
112 & 8613 & 8259.64890752688 & 353.35109247312 \tabularnewline
113 & 9496 & 8932.68744005857 & 563.312559941431 \tabularnewline
114 & 9055 & 8500.9936834552 & 554.006316544797 \tabularnewline
115 & 7288 & 6293.69573765668 & 994.304262343319 \tabularnewline
116 & 5892 & 5581.83974998347 & 310.160250016534 \tabularnewline
117 & 4417 & 4115.58689235116 & 301.41310764884 \tabularnewline
118 & 2721 & 2703.21704161456 & 17.7829583854427 \tabularnewline
119 & 3021 & 3391.6214703919 & -370.621470391897 \tabularnewline
120 & 3534 & 4271.53578539867 & -737.535785398671 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211047&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]35998[/C][C]36579.1669337607[/C][C]-581.16693376068[/C][/ROW]
[ROW][C]14[/C][C]35335[/C][C]35689.5399635761[/C][C]-354.539963576055[/C][/ROW]
[ROW][C]15[/C][C]35043[/C][C]35287.3878359651[/C][C]-244.387835965084[/C][/ROW]
[ROW][C]16[/C][C]35335[/C][C]35540.4006732962[/C][C]-205.400673296201[/C][/ROW]
[ROW][C]17[/C][C]36368[/C][C]36555.9202125406[/C][C]-187.920212540615[/C][/ROW]
[ROW][C]18[/C][C]36218[/C][C]36374.2506767915[/C][C]-156.250676791526[/C][/ROW]
[ROW][C]19[/C][C]34822[/C][C]34828.9231924415[/C][C]-6.92319244149985[/C][/ROW]
[ROW][C]20[/C][C]33640[/C][C]33989.3931115873[/C][C]-349.393111587349[/C][/ROW]
[ROW][C]21[/C][C]33419[/C][C]33846.9990295755[/C][C]-427.999029575491[/C][/ROW]
[ROW][C]22[/C][C]32977[/C][C]33585.5569038598[/C][C]-608.556903859811[/C][/ROW]
[ROW][C]23[/C][C]33276[/C][C]33313.7368984226[/C][C]-37.7368984226414[/C][/ROW]
[ROW][C]24[/C][C]33640[/C][C]33370.5477532183[/C][C]269.452246781744[/C][/ROW]
[ROW][C]25[/C][C]33497[/C][C]33071.6925407069[/C][C]425.307459293072[/C][/ROW]
[ROW][C]26[/C][C]33198[/C][C]32693.4246131314[/C][C]504.575386868601[/C][/ROW]
[ROW][C]27[/C][C]32614[/C][C]32686.4836480036[/C][C]-72.483648003632[/C][/ROW]
[ROW][C]28[/C][C]33198[/C][C]33019.1422701804[/C][C]178.85772981964[/C][/ROW]
[ROW][C]29[/C][C]33718[/C][C]34192.2278358073[/C][C]-474.227835807251[/C][/ROW]
[ROW][C]30[/C][C]33568[/C][C]33903.5936417367[/C][C]-335.593641736719[/C][/ROW]
[ROW][C]31[/C][C]31873[/C][C]32362.020414611[/C][C]-489.020414611023[/C][/ROW]
[ROW][C]32[/C][C]31139[/C][C]31103.0948362062[/C][C]35.9051637938101[/C][/ROW]
[ROW][C]33[/C][C]30405[/C][C]31052.7945626103[/C][C]-647.794562610303[/C][/ROW]
[ROW][C]34[/C][C]29814[/C][C]30576.5582222407[/C][C]-762.558222240714[/C][/ROW]
[ROW][C]35[/C][C]29743[/C][C]30564.2268973031[/C][C]-821.226897303099[/C][/ROW]
[ROW][C]36[/C][C]30184[/C][C]30458.6525568761[/C][C]-274.652556876128[/C][/ROW]
[ROW][C]37[/C][C]29593[/C][C]29994.6508340664[/C][C]-401.650834066357[/C][/ROW]
[ROW][C]38[/C][C]29372[/C][C]29279.7356957344[/C][C]92.2643042655654[/C][/ROW]
[ROW][C]39[/C][C]29151[/C][C]28703.0237082734[/C][C]447.976291726627[/C][/ROW]
[ROW][C]40[/C][C]30405[/C][C]29343.8468085373[/C][C]1061.15319146266[/C][/ROW]
[ROW][C]41[/C][C]30548[/C][C]30441.3028195331[/C][C]106.697180466927[/C][/ROW]
[ROW][C]42[/C][C]29814[/C][C]30439.1843588241[/C][C]-625.184358824114[/C][/ROW]
[ROW][C]43[/C][C]27826[/C][C]28655.9082205165[/C][C]-829.908220516507[/C][/ROW]
[ROW][C]44[/C][C]26943[/C][C]27536.1090821396[/C][C]-593.109082139603[/C][/ROW]
[ROW][C]45[/C][C]25547[/C][C]26775.9896551198[/C][C]-1228.98965511977[/C][/ROW]
[ROW][C]46[/C][C]24955[/C][C]25941.3834710755[/C][C]-986.38347107554[/C][/ROW]
[ROW][C]47[/C][C]25247[/C][C]25744.2332080358[/C][C]-497.233208035843[/C][/ROW]
[ROW][C]48[/C][C]25689[/C][C]26040.8565226892[/C][C]-351.856522689202[/C][/ROW]
[ROW][C]49[/C][C]25689[/C][C]25413.5198284032[/C][C]275.480171596821[/C][/ROW]
[ROW][C]50[/C][C]25326[/C][C]25219.6806137918[/C][C]106.31938620823[/C][/ROW]
[ROW][C]51[/C][C]25247[/C][C]24815.6532816852[/C][C]431.346718314759[/C][/ROW]
[ROW][C]52[/C][C]26430[/C][C]25770.8748194824[/C][C]659.125180517636[/C][/ROW]
[ROW][C]53[/C][C]27385[/C][C]26083.0504527462[/C][C]1301.94954725383[/C][/ROW]
[ROW][C]54[/C][C]26943[/C][C]26086.9575644496[/C][C]856.04243555036[/C][/ROW]
[ROW][C]55[/C][C]25468[/C][C]24762.0944421972[/C][C]705.905557802751[/C][/ROW]
[ROW][C]56[/C][C]24735[/C][C]24409.8432620785[/C][C]325.156737921458[/C][/ROW]
[ROW][C]57[/C][C]23189[/C][C]23660.4438269297[/C][C]-471.443826929681[/C][/ROW]
[ROW][C]58[/C][C]22234[/C][C]23309.6815303395[/C][C]-1075.68153033948[/C][/ROW]
[ROW][C]59[/C][C]22968[/C][C]23403.312319276[/C][C]-435.312319275989[/C][/ROW]
[ROW][C]60[/C][C]23702[/C][C]23846.2774255036[/C][C]-144.277425503555[/C][/ROW]
[ROW][C]61[/C][C]23702[/C][C]23715.5057187745[/C][C]-13.505718774526[/C][/ROW]
[ROW][C]62[/C][C]22747[/C][C]23337.6880702404[/C][C]-590.688070240445[/C][/ROW]
[ROW][C]63[/C][C]22676[/C][C]22871.9091334764[/C][C]-195.909133476358[/C][/ROW]
[ROW][C]64[/C][C]23922[/C][C]23725.7950076623[/C][C]196.204992337665[/C][/ROW]
[ROW][C]65[/C][C]24735[/C][C]24244.3363980404[/C][C]490.663601959612[/C][/ROW]
[ROW][C]66[/C][C]24442[/C][C]23650.6549409235[/C][C]791.345059076477[/C][/ROW]
[ROW][C]67[/C][C]22968[/C][C]22203.7277376153[/C][C]764.272262384744[/C][/ROW]
[ROW][C]68[/C][C]22013[/C][C]21641.4353603116[/C][C]371.564639688422[/C][/ROW]
[ROW][C]69[/C][C]19947[/C][C]20428.730453509[/C][C]-481.730453509001[/C][/ROW]
[ROW][C]70[/C][C]19142[/C][C]19707.0383888348[/C][C]-565.038388834771[/C][/ROW]
[ROW][C]71[/C][C]19434[/C][C]20391.8120860012[/C][C]-957.812086001177[/C][/ROW]
[ROW][C]72[/C][C]20688[/C][C]20794.7519806714[/C][C]-106.751980671412[/C][/ROW]
[ROW][C]73[/C][C]20759[/C][C]20752.9755394985[/C][C]6.02446050145954[/C][/ROW]
[ROW][C]74[/C][C]18921[/C][C]20033.0589335063[/C][C]-1112.05893350627[/C][/ROW]
[ROW][C]75[/C][C]19584[/C][C]19582.9978439401[/C][C]1.00215605992344[/C][/ROW]
[ROW][C]76[/C][C]21201[/C][C]20741.8418373918[/C][C]459.158162608222[/C][/ROW]
[ROW][C]77[/C][C]21935[/C][C]21537.1934345597[/C][C]397.806565440274[/C][/ROW]
[ROW][C]78[/C][C]21493[/C][C]21080.050140857[/C][C]412.949859143038[/C][/ROW]
[ROW][C]79[/C][C]19506[/C][C]19453.2324883626[/C][C]52.7675116373757[/C][/ROW]
[ROW][C]80[/C][C]18109[/C][C]18347.9289684212[/C][C]-238.928968421187[/C][/ROW]
[ROW][C]81[/C][C]16492[/C][C]16347.713413858[/C][C]144.286586141985[/C][/ROW]
[ROW][C]82[/C][C]15238[/C][C]15804.7637134364[/C][C]-566.763713436354[/C][/ROW]
[ROW][C]83[/C][C]15751[/C][C]16231.2068625341[/C][C]-480.20686253408[/C][/ROW]
[ROW][C]84[/C][C]16855[/C][C]17320.2619148887[/C][C]-465.261914888699[/C][/ROW]
[ROW][C]85[/C][C]16563[/C][C]17181.7984514444[/C][C]-618.798451444429[/C][/ROW]
[ROW][C]86[/C][C]14946[/C][C]15511.733393138[/C][C]-565.733393137991[/C][/ROW]
[ROW][C]87[/C][C]15459[/C][C]15925.8479587634[/C][C]-466.847958763421[/C][/ROW]
[ROW][C]88[/C][C]17076[/C][C]17143.0285592124[/C][C]-67.0285592123691[/C][/ROW]
[ROW][C]89[/C][C]17960[/C][C]17654.2875311455[/C][C]305.712468854501[/C][/ROW]
[ROW][C]90[/C][C]17447[/C][C]17131.5279284018[/C][C]315.472071598178[/C][/ROW]
[ROW][C]91[/C][C]15459[/C][C]15210.6183189009[/C][C]248.381681099079[/C][/ROW]
[ROW][C]92[/C][C]14576[/C][C]13972.6356571554[/C][C]603.364342844588[/C][/ROW]
[ROW][C]93[/C][C]13251[/C][C]12515.7939280085[/C][C]735.206071991533[/C][/ROW]
[ROW][C]94[/C][C]11854[/C][C]11768.5668023159[/C][C]85.4331976840822[/C][/ROW]
[ROW][C]95[/C][C]12075[/C][C]12502.827316904[/C][C]-427.827316904044[/C][/ROW]
[ROW][C]96[/C][C]13179[/C][C]13617.1306472611[/C][C]-438.130647261058[/C][/ROW]
[ROW][C]97[/C][C]13322[/C][C]13393.2505044547[/C][C]-71.2505044547106[/C][/ROW]
[ROW][C]98[/C][C]11997[/C][C]11978.262218181[/C][C]18.7377818189925[/C][/ROW]
[ROW][C]99[/C][C]12218[/C][C]12698.3522493321[/C][C]-480.352249332122[/C][/ROW]
[ROW][C]100[/C][C]14063[/C][C]14161.9134101866[/C][C]-98.9134101865729[/C][/ROW]
[ROW][C]101[/C][C]14504[/C][C]14895.4895010243[/C][C]-391.489501024265[/C][/ROW]
[ROW][C]102[/C][C]13764[/C][C]14100.5617742269[/C][C]-336.561774226931[/C][/ROW]
[ROW][C]103[/C][C]11042[/C][C]11869.9011316021[/C][C]-827.901131602121[/C][/ROW]
[ROW][C]104[/C][C]9646[/C][C]10389.0720938376[/C][C]-743.07209383762[/C][/ROW]
[ROW][C]105[/C][C]7801[/C][C]8427.48318138887[/C][C]-626.483181388874[/C][/ROW]
[ROW][C]106[/C][C]5963[/C][C]6680.95111793313[/C][C]-717.951117933126[/C][/ROW]
[ROW][C]107[/C][C]6554[/C][C]6709.61257729581[/C][C]-155.612577295813[/C][/ROW]
[ROW][C]108[/C][C]7359[/C][C]7854.84460351474[/C][C]-495.844603514735[/C][/ROW]
[ROW][C]109[/C][C]7217[/C][C]7754.77607335814[/C][C]-537.776073358142[/C][/ROW]
[ROW][C]110[/C][C]5813[/C][C]6126.92706908066[/C][C]-313.927069080661[/C][/ROW]
[ROW][C]111[/C][C]6625[/C][C]6329.94885794505[/C][C]295.051142054952[/C][/ROW]
[ROW][C]112[/C][C]8613[/C][C]8259.64890752688[/C][C]353.35109247312[/C][/ROW]
[ROW][C]113[/C][C]9496[/C][C]8932.68744005857[/C][C]563.312559941431[/C][/ROW]
[ROW][C]114[/C][C]9055[/C][C]8500.9936834552[/C][C]554.006316544797[/C][/ROW]
[ROW][C]115[/C][C]7288[/C][C]6293.69573765668[/C][C]994.304262343319[/C][/ROW]
[ROW][C]116[/C][C]5892[/C][C]5581.83974998347[/C][C]310.160250016534[/C][/ROW]
[ROW][C]117[/C][C]4417[/C][C]4115.58689235116[/C][C]301.41310764884[/C][/ROW]
[ROW][C]118[/C][C]2721[/C][C]2703.21704161456[/C][C]17.7829583854427[/C][/ROW]
[ROW][C]119[/C][C]3021[/C][C]3391.6214703919[/C][C]-370.621470391897[/C][/ROW]
[ROW][C]120[/C][C]3534[/C][C]4271.53578539867[/C][C]-737.535785398671[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211047&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211047&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133599836579.1669337607-581.16693376068
143533535689.5399635761-354.539963576055
153504335287.3878359651-244.387835965084
163533535540.4006732962-205.400673296201
173636836555.9202125406-187.920212540615
183621836374.2506767915-156.250676791526
193482234828.9231924415-6.92319244149985
203364033989.3931115873-349.393111587349
213341933846.9990295755-427.999029575491
223297733585.5569038598-608.556903859811
233327633313.7368984226-37.7368984226414
243364033370.5477532183269.452246781744
253349733071.6925407069425.307459293072
263319832693.4246131314504.575386868601
273261432686.4836480036-72.483648003632
283319833019.1422701804178.85772981964
293371834192.2278358073-474.227835807251
303356833903.5936417367-335.593641736719
313187332362.020414611-489.020414611023
323113931103.094836206235.9051637938101
333040531052.7945626103-647.794562610303
342981430576.5582222407-762.558222240714
352974330564.2268973031-821.226897303099
363018430458.6525568761-274.652556876128
372959329994.6508340664-401.650834066357
382937229279.735695734492.2643042655654
392915128703.0237082734447.976291726627
403040529343.84680853731061.15319146266
413054830441.3028195331106.697180466927
422981430439.1843588241-625.184358824114
432782628655.9082205165-829.908220516507
442694327536.1090821396-593.109082139603
452554726775.9896551198-1228.98965511977
462495525941.3834710755-986.38347107554
472524725744.2332080358-497.233208035843
482568926040.8565226892-351.856522689202
492568925413.5198284032275.480171596821
502532625219.6806137918106.31938620823
512524724815.6532816852431.346718314759
522643025770.8748194824659.125180517636
532738526083.05045274621301.94954725383
542694326086.9575644496856.04243555036
552546824762.0944421972705.905557802751
562473524409.8432620785325.156737921458
572318923660.4438269297-471.443826929681
582223423309.6815303395-1075.68153033948
592296823403.312319276-435.312319275989
602370223846.2774255036-144.277425503555
612370223715.5057187745-13.505718774526
622274723337.6880702404-590.688070240445
632267622871.9091334764-195.909133476358
642392223725.7950076623196.204992337665
652473524244.3363980404490.663601959612
662444223650.6549409235791.345059076477
672296822203.7277376153764.272262384744
682201321641.4353603116371.564639688422
691994720428.730453509-481.730453509001
701914219707.0383888348-565.038388834771
711943420391.8120860012-957.812086001177
722068820794.7519806714-106.751980671412
732075920752.97553949856.02446050145954
741892120033.0589335063-1112.05893350627
751958419582.99784394011.00215605992344
762120120741.8418373918459.158162608222
772193521537.1934345597397.806565440274
782149321080.050140857412.949859143038
791950619453.232488362652.7675116373757
801810918347.9289684212-238.928968421187
811649216347.713413858144.286586141985
821523815804.7637134364-566.763713436354
831575116231.2068625341-480.20686253408
841685517320.2619148887-465.261914888699
851656317181.7984514444-618.798451444429
861494615511.733393138-565.733393137991
871545915925.8479587634-466.847958763421
881707617143.0285592124-67.0285592123691
891796017654.2875311455305.712468854501
901744717131.5279284018315.472071598178
911545915210.6183189009248.381681099079
921457613972.6356571554603.364342844588
931325112515.7939280085735.206071991533
941185411768.566802315985.4331976840822
951207512502.827316904-427.827316904044
961317913617.1306472611-438.130647261058
971332213393.2505044547-71.2505044547106
981199711978.26221818118.7377818189925
991221812698.3522493321-480.352249332122
1001406314161.9134101866-98.9134101865729
1011450414895.4895010243-391.489501024265
1021376414100.5617742269-336.561774226931
1031104211869.9011316021-827.901131602121
104964610389.0720938376-743.07209383762
10578018427.48318138887-626.483181388874
10659636680.95111793313-717.951117933126
10765546709.61257729581-155.612577295813
10873597854.84460351474-495.844603514735
10972177754.77607335814-537.776073358142
11058136126.92706908066-313.927069080661
11166256329.94885794505295.051142054952
11286138259.64890752688353.35109247312
11394968932.68744005857563.312559941431
11490558500.9936834552554.006316544797
11572886293.69573765668994.304262343319
11658925581.83974998347310.160250016534
11744174115.58689235116301.41310764884
11827212703.2170416145617.7829583854427
11930213391.6214703919-370.621470391897
12035344271.53578539867-737.535785398671






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1214070.605474095223059.440593921215081.77035426923
1222821.541341937151726.510746323473916.57193755083
1233549.010630822722370.653870644794727.36739100065
1245424.746281048684163.318630634596686.17393146278
1256106.092257916564761.635285827977450.54923000514
1265458.836855034594031.22818753746886.44552253179
1273300.893235648881789.882664565164811.90380673259
1281773.48324277748178.7195547693153368.24693078564
129165.992059716155-1512.956625340081844.94074477239
130-1553.26369016352-3316.8942356196210.366855292569
131-1121.08999161225-2969.9519706635727.771987438999
132-323.356404696447-2258.042372172771611.32956277988

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 4070.60547409522 & 3059.44059392121 & 5081.77035426923 \tabularnewline
122 & 2821.54134193715 & 1726.51074632347 & 3916.57193755083 \tabularnewline
123 & 3549.01063082272 & 2370.65387064479 & 4727.36739100065 \tabularnewline
124 & 5424.74628104868 & 4163.31863063459 & 6686.17393146278 \tabularnewline
125 & 6106.09225791656 & 4761.63528582797 & 7450.54923000514 \tabularnewline
126 & 5458.83685503459 & 4031.2281875374 & 6886.44552253179 \tabularnewline
127 & 3300.89323564888 & 1789.88266456516 & 4811.90380673259 \tabularnewline
128 & 1773.48324277748 & 178.719554769315 & 3368.24693078564 \tabularnewline
129 & 165.992059716155 & -1512.95662534008 & 1844.94074477239 \tabularnewline
130 & -1553.26369016352 & -3316.8942356196 & 210.366855292569 \tabularnewline
131 & -1121.08999161225 & -2969.9519706635 & 727.771987438999 \tabularnewline
132 & -323.356404696447 & -2258.04237217277 & 1611.32956277988 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211047&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]4070.60547409522[/C][C]3059.44059392121[/C][C]5081.77035426923[/C][/ROW]
[ROW][C]122[/C][C]2821.54134193715[/C][C]1726.51074632347[/C][C]3916.57193755083[/C][/ROW]
[ROW][C]123[/C][C]3549.01063082272[/C][C]2370.65387064479[/C][C]4727.36739100065[/C][/ROW]
[ROW][C]124[/C][C]5424.74628104868[/C][C]4163.31863063459[/C][C]6686.17393146278[/C][/ROW]
[ROW][C]125[/C][C]6106.09225791656[/C][C]4761.63528582797[/C][C]7450.54923000514[/C][/ROW]
[ROW][C]126[/C][C]5458.83685503459[/C][C]4031.2281875374[/C][C]6886.44552253179[/C][/ROW]
[ROW][C]127[/C][C]3300.89323564888[/C][C]1789.88266456516[/C][C]4811.90380673259[/C][/ROW]
[ROW][C]128[/C][C]1773.48324277748[/C][C]178.719554769315[/C][C]3368.24693078564[/C][/ROW]
[ROW][C]129[/C][C]165.992059716155[/C][C]-1512.95662534008[/C][C]1844.94074477239[/C][/ROW]
[ROW][C]130[/C][C]-1553.26369016352[/C][C]-3316.8942356196[/C][C]210.366855292569[/C][/ROW]
[ROW][C]131[/C][C]-1121.08999161225[/C][C]-2969.9519706635[/C][C]727.771987438999[/C][/ROW]
[ROW][C]132[/C][C]-323.356404696447[/C][C]-2258.04237217277[/C][C]1611.32956277988[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211047&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211047&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1214070.605474095223059.440593921215081.77035426923
1222821.541341937151726.510746323473916.57193755083
1233549.010630822722370.653870644794727.36739100065
1245424.746281048684163.318630634596686.17393146278
1256106.092257916564761.635285827977450.54923000514
1265458.836855034594031.22818753746886.44552253179
1273300.893235648881789.882664565164811.90380673259
1281773.48324277748178.7195547693153368.24693078564
129165.992059716155-1512.956625340081844.94074477239
130-1553.26369016352-3316.8942356196210.366855292569
131-1121.08999161225-2969.9519706635727.771987438999
132-323.356404696447-2258.042372172771611.32956277988


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 60 ; par2 = 1 ; par3 = 1 ; 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')