Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 18 Aug 2014 10:53:45 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Aug/18/t14083557597y08c5ldb5m04ws.htm/, Retrieved Thu, 16 May 2024 23:20:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235698, Retrieved Thu, 16 May 2024 23:20:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Reusel Raphael
Estimated Impact117
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 1] [2014-08-18 09:53:45] [bf566d88435d8cc6ce5d208f6f8dd684] [Current]
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Dataseries X:
1095
1085
1075
1054
1261
1250
1095
992
1002
1002
1013
1033
1095
1075
1106
1157
1447
1447
1385
1323
1374
1436
1447
1478
1571
1509
1509
1602
1860
1881
1829
1705
1798
1798
1808
1860
1901
1922
1922
1984
2222
2284
2294
2139
2222
2191
2129
2263
2294
2242
2253
2325
2594
2728
2728
2666
2759
2666
2614
2811
2842
2769
2955
3028
3245
3389
3369
3358
3441
3431
3307
3493
3555
3493
3751
3875
4164
4278
4247
4185
4237
4299
4092
4257
4361
4319
4588
4681
5074
5146
5053
5105
5136
5167
4970
5156
5259
5156
5456
5549
5952
6014
6034
6138
6138
6179
5993
6086
6148
6034
6365
6427
6840
6913
7016
7109
7119
7130
6944
7130




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=235698&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=235698&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235698&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
alpha0.214206319405539
beta0.107901309125031
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.214206319405539 \tabularnewline
beta & 0.107901309125031 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235698&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]0.214206319405539[/C][/ROW]
[ROW][C]beta[/C][C]0.107901309125031[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235698&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235698&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
alpha0.214206319405539
beta0.107901309125031
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310951032.5970992907762.4029007092267
1410751024.3799181475850.6200818524219
1511061060.5143751461345.4856248538686
1611571111.9789633738945.0210366261092
1714471391.8050426486655.1949573513359
1814471393.7060012648753.2939987351344
1913851304.0351058917780.9648941082316
2013231224.7433096567598.256690343248
2113741287.0704731183186.9295268816882
2214361330.56406695638105.435933043615
2314471387.0190034840659.9809965159388
2414781442.6402515768435.3597484231634
2515711620.20525476594-49.2052547659421
2615091569.22517806431-60.2251780643091
2715091589.45761857804-80.4576185780415
2816021630.59309649077-28.5930964907723
2918602012.41596808684-152.415968086838
3018811957.52174502126-76.5217450212649
3118291825.427030218233.57296978177033
3217051705.81327294001-0.813272940009483
3317981734.6878616741463.3121383258567
3417981784.4621925218313.5378074781729
3518081770.7358416897337.2641583102668
3618601793.3179184321566.6820815678509
3719011920.07360347627-19.0736034762745
3819221843.5176734009878.4823265990196
3919221871.7231720248850.2768279751233
4019841999.67394239745-15.6739423974543
4122222349.24743675855-127.247436758547
4222842362.33748083819-78.3374808381895
4322942274.6746373724519.3253626275514
4421392120.2207966252918.7792033747073
4522222218.766467297933.23353270207281
4621912210.55029731839-19.5502973183929
4721292202.84876776815-73.8487677681537
4822632224.0643894170638.9356105829415
4922942277.6281789499516.3718210500542
5022422277.67324023745-35.6732402374532
5122532247.034896080255.96510391974562
5223252313.6883078936511.3116921063456
5325942612.94398966306-18.9439896630611
5427282691.8493535635836.150646436422
5527282700.1826109778927.8173890221119
5626662512.91147978167153.088520218326
5727592640.67249959929118.327500400714
5826662633.1682336646232.8317663353846
5926142584.5149252904729.485074709527
6028112746.5421824117764.4578175882257
6128422797.0779329377644.9220670622376
6227692755.8661235216613.1338764783413
6329552775.24438474942179.75561525058
6430282908.81598504939119.184014950612
6532453290.20055112138-45.2005511213829
6633893451.14569658567-62.1456965856682
6733693438.84609320494-69.8460932049425
6833583308.9963965157349.0036034842715
6934413405.5441346899635.4558653100412
7034313289.8127510937141.187248906301
7133073249.7732156323457.2267843676609
7234933493.25173545575-0.251735455752168
7335553520.8532509860634.1467490139426
7434933434.7817883900758.2182116099257
7537513630.09440842603120.905591573973
7638753713.06895733536161.931042664639
7741644027.71970729545136.280292704548
7842784256.7610008311821.2389991688242
7942474259.88405581555-12.8840558155462
8041854236.26907521299-51.2690752129884
8142374324.21608487815-87.216084878145
8242994255.3078689039243.6921310960779
8340924093.78717302474-1.78717302474115
8442574320.84773009177-63.8477300917684
8543614370.46342290285-9.46342290284974
8643194271.8643816912747.1356183087337
8745884560.1119934352327.8880065647663
8846814665.4026234215215.5973765784802
8950744968.7431480932105.256851906798
9051465109.2134627960436.7865372039641
9150535070.78881379662-17.7888137966174
9251054993.96986372255111.030136277448
9351365093.6947862228842.3052137771192
9451675160.641640840896.35835915910593
9549704908.0322485479661.967751452039
9651565131.3630214912324.6369785087654
9752595261.986266309-2.98626630900344
9851565196.06983536433-40.0698353643347
9954565498.93153473704-42.9315347370375
10055495591.06009366594-42.0600936659366
10159526015.82744215245-63.8274421524466
10260146066.6947074284-52.694707428398
10360345937.8136210180496.1863789819554
10461385981.18868708287156.811312917127
10561386031.25016413297106.749835867034
10661796081.0788568171497.9211431828562
10759935847.85698685773145.143013142272
10860866088.40294859928-2.40294859927599
10961486205.35638470757-57.3563847075675
11060346076.08552564274-42.0855256427376
11163656425.01700794251-60.017007942507
11264276526.0096482716-99.0096482715953
11368406985.76797014414-145.767970144138
11469137031.36863186484-118.368631864842
11570166995.335486562420.6645134375967
11671097069.1953271302239.8046728697764
11771197036.9383437621182.0616562378855
11871307062.6245360016667.375463998339
11969446813.0929822473130.907017752698
12071306932.63064074562197.369359254379

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1095 & 1032.59709929077 & 62.4029007092267 \tabularnewline
14 & 1075 & 1024.37991814758 & 50.6200818524219 \tabularnewline
15 & 1106 & 1060.51437514613 & 45.4856248538686 \tabularnewline
16 & 1157 & 1111.97896337389 & 45.0210366261092 \tabularnewline
17 & 1447 & 1391.80504264866 & 55.1949573513359 \tabularnewline
18 & 1447 & 1393.70600126487 & 53.2939987351344 \tabularnewline
19 & 1385 & 1304.03510589177 & 80.9648941082316 \tabularnewline
20 & 1323 & 1224.74330965675 & 98.256690343248 \tabularnewline
21 & 1374 & 1287.07047311831 & 86.9295268816882 \tabularnewline
22 & 1436 & 1330.56406695638 & 105.435933043615 \tabularnewline
23 & 1447 & 1387.01900348406 & 59.9809965159388 \tabularnewline
24 & 1478 & 1442.64025157684 & 35.3597484231634 \tabularnewline
25 & 1571 & 1620.20525476594 & -49.2052547659421 \tabularnewline
26 & 1509 & 1569.22517806431 & -60.2251780643091 \tabularnewline
27 & 1509 & 1589.45761857804 & -80.4576185780415 \tabularnewline
28 & 1602 & 1630.59309649077 & -28.5930964907723 \tabularnewline
29 & 1860 & 2012.41596808684 & -152.415968086838 \tabularnewline
30 & 1881 & 1957.52174502126 & -76.5217450212649 \tabularnewline
31 & 1829 & 1825.42703021823 & 3.57296978177033 \tabularnewline
32 & 1705 & 1705.81327294001 & -0.813272940009483 \tabularnewline
33 & 1798 & 1734.68786167414 & 63.3121383258567 \tabularnewline
34 & 1798 & 1784.46219252183 & 13.5378074781729 \tabularnewline
35 & 1808 & 1770.73584168973 & 37.2641583102668 \tabularnewline
36 & 1860 & 1793.31791843215 & 66.6820815678509 \tabularnewline
37 & 1901 & 1920.07360347627 & -19.0736034762745 \tabularnewline
38 & 1922 & 1843.51767340098 & 78.4823265990196 \tabularnewline
39 & 1922 & 1871.72317202488 & 50.2768279751233 \tabularnewline
40 & 1984 & 1999.67394239745 & -15.6739423974543 \tabularnewline
41 & 2222 & 2349.24743675855 & -127.247436758547 \tabularnewline
42 & 2284 & 2362.33748083819 & -78.3374808381895 \tabularnewline
43 & 2294 & 2274.67463737245 & 19.3253626275514 \tabularnewline
44 & 2139 & 2120.22079662529 & 18.7792033747073 \tabularnewline
45 & 2222 & 2218.76646729793 & 3.23353270207281 \tabularnewline
46 & 2191 & 2210.55029731839 & -19.5502973183929 \tabularnewline
47 & 2129 & 2202.84876776815 & -73.8487677681537 \tabularnewline
48 & 2263 & 2224.06438941706 & 38.9356105829415 \tabularnewline
49 & 2294 & 2277.62817894995 & 16.3718210500542 \tabularnewline
50 & 2242 & 2277.67324023745 & -35.6732402374532 \tabularnewline
51 & 2253 & 2247.03489608025 & 5.96510391974562 \tabularnewline
52 & 2325 & 2313.68830789365 & 11.3116921063456 \tabularnewline
53 & 2594 & 2612.94398966306 & -18.9439896630611 \tabularnewline
54 & 2728 & 2691.84935356358 & 36.150646436422 \tabularnewline
55 & 2728 & 2700.18261097789 & 27.8173890221119 \tabularnewline
56 & 2666 & 2512.91147978167 & 153.088520218326 \tabularnewline
57 & 2759 & 2640.67249959929 & 118.327500400714 \tabularnewline
58 & 2666 & 2633.16823366462 & 32.8317663353846 \tabularnewline
59 & 2614 & 2584.51492529047 & 29.485074709527 \tabularnewline
60 & 2811 & 2746.54218241177 & 64.4578175882257 \tabularnewline
61 & 2842 & 2797.07793293776 & 44.9220670622376 \tabularnewline
62 & 2769 & 2755.86612352166 & 13.1338764783413 \tabularnewline
63 & 2955 & 2775.24438474942 & 179.75561525058 \tabularnewline
64 & 3028 & 2908.81598504939 & 119.184014950612 \tabularnewline
65 & 3245 & 3290.20055112138 & -45.2005511213829 \tabularnewline
66 & 3389 & 3451.14569658567 & -62.1456965856682 \tabularnewline
67 & 3369 & 3438.84609320494 & -69.8460932049425 \tabularnewline
68 & 3358 & 3308.99639651573 & 49.0036034842715 \tabularnewline
69 & 3441 & 3405.54413468996 & 35.4558653100412 \tabularnewline
70 & 3431 & 3289.8127510937 & 141.187248906301 \tabularnewline
71 & 3307 & 3249.77321563234 & 57.2267843676609 \tabularnewline
72 & 3493 & 3493.25173545575 & -0.251735455752168 \tabularnewline
73 & 3555 & 3520.85325098606 & 34.1467490139426 \tabularnewline
74 & 3493 & 3434.78178839007 & 58.2182116099257 \tabularnewline
75 & 3751 & 3630.09440842603 & 120.905591573973 \tabularnewline
76 & 3875 & 3713.06895733536 & 161.931042664639 \tabularnewline
77 & 4164 & 4027.71970729545 & 136.280292704548 \tabularnewline
78 & 4278 & 4256.76100083118 & 21.2389991688242 \tabularnewline
79 & 4247 & 4259.88405581555 & -12.8840558155462 \tabularnewline
80 & 4185 & 4236.26907521299 & -51.2690752129884 \tabularnewline
81 & 4237 & 4324.21608487815 & -87.216084878145 \tabularnewline
82 & 4299 & 4255.30786890392 & 43.6921310960779 \tabularnewline
83 & 4092 & 4093.78717302474 & -1.78717302474115 \tabularnewline
84 & 4257 & 4320.84773009177 & -63.8477300917684 \tabularnewline
85 & 4361 & 4370.46342290285 & -9.46342290284974 \tabularnewline
86 & 4319 & 4271.86438169127 & 47.1356183087337 \tabularnewline
87 & 4588 & 4560.11199343523 & 27.8880065647663 \tabularnewline
88 & 4681 & 4665.40262342152 & 15.5973765784802 \tabularnewline
89 & 5074 & 4968.7431480932 & 105.256851906798 \tabularnewline
90 & 5146 & 5109.21346279604 & 36.7865372039641 \tabularnewline
91 & 5053 & 5070.78881379662 & -17.7888137966174 \tabularnewline
92 & 5105 & 4993.96986372255 & 111.030136277448 \tabularnewline
93 & 5136 & 5093.69478622288 & 42.3052137771192 \tabularnewline
94 & 5167 & 5160.64164084089 & 6.35835915910593 \tabularnewline
95 & 4970 & 4908.03224854796 & 61.967751452039 \tabularnewline
96 & 5156 & 5131.36302149123 & 24.6369785087654 \tabularnewline
97 & 5259 & 5261.986266309 & -2.98626630900344 \tabularnewline
98 & 5156 & 5196.06983536433 & -40.0698353643347 \tabularnewline
99 & 5456 & 5498.93153473704 & -42.9315347370375 \tabularnewline
100 & 5549 & 5591.06009366594 & -42.0600936659366 \tabularnewline
101 & 5952 & 6015.82744215245 & -63.8274421524466 \tabularnewline
102 & 6014 & 6066.6947074284 & -52.694707428398 \tabularnewline
103 & 6034 & 5937.81362101804 & 96.1863789819554 \tabularnewline
104 & 6138 & 5981.18868708287 & 156.811312917127 \tabularnewline
105 & 6138 & 6031.25016413297 & 106.749835867034 \tabularnewline
106 & 6179 & 6081.07885681714 & 97.9211431828562 \tabularnewline
107 & 5993 & 5847.85698685773 & 145.143013142272 \tabularnewline
108 & 6086 & 6088.40294859928 & -2.40294859927599 \tabularnewline
109 & 6148 & 6205.35638470757 & -57.3563847075675 \tabularnewline
110 & 6034 & 6076.08552564274 & -42.0855256427376 \tabularnewline
111 & 6365 & 6425.01700794251 & -60.017007942507 \tabularnewline
112 & 6427 & 6526.0096482716 & -99.0096482715953 \tabularnewline
113 & 6840 & 6985.76797014414 & -145.767970144138 \tabularnewline
114 & 6913 & 7031.36863186484 & -118.368631864842 \tabularnewline
115 & 7016 & 6995.3354865624 & 20.6645134375967 \tabularnewline
116 & 7109 & 7069.19532713022 & 39.8046728697764 \tabularnewline
117 & 7119 & 7036.93834376211 & 82.0616562378855 \tabularnewline
118 & 7130 & 7062.62453600166 & 67.375463998339 \tabularnewline
119 & 6944 & 6813.0929822473 & 130.907017752698 \tabularnewline
120 & 7130 & 6932.63064074562 & 197.369359254379 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235698&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]1095[/C][C]1032.59709929077[/C][C]62.4029007092267[/C][/ROW]
[ROW][C]14[/C][C]1075[/C][C]1024.37991814758[/C][C]50.6200818524219[/C][/ROW]
[ROW][C]15[/C][C]1106[/C][C]1060.51437514613[/C][C]45.4856248538686[/C][/ROW]
[ROW][C]16[/C][C]1157[/C][C]1111.97896337389[/C][C]45.0210366261092[/C][/ROW]
[ROW][C]17[/C][C]1447[/C][C]1391.80504264866[/C][C]55.1949573513359[/C][/ROW]
[ROW][C]18[/C][C]1447[/C][C]1393.70600126487[/C][C]53.2939987351344[/C][/ROW]
[ROW][C]19[/C][C]1385[/C][C]1304.03510589177[/C][C]80.9648941082316[/C][/ROW]
[ROW][C]20[/C][C]1323[/C][C]1224.74330965675[/C][C]98.256690343248[/C][/ROW]
[ROW][C]21[/C][C]1374[/C][C]1287.07047311831[/C][C]86.9295268816882[/C][/ROW]
[ROW][C]22[/C][C]1436[/C][C]1330.56406695638[/C][C]105.435933043615[/C][/ROW]
[ROW][C]23[/C][C]1447[/C][C]1387.01900348406[/C][C]59.9809965159388[/C][/ROW]
[ROW][C]24[/C][C]1478[/C][C]1442.64025157684[/C][C]35.3597484231634[/C][/ROW]
[ROW][C]25[/C][C]1571[/C][C]1620.20525476594[/C][C]-49.2052547659421[/C][/ROW]
[ROW][C]26[/C][C]1509[/C][C]1569.22517806431[/C][C]-60.2251780643091[/C][/ROW]
[ROW][C]27[/C][C]1509[/C][C]1589.45761857804[/C][C]-80.4576185780415[/C][/ROW]
[ROW][C]28[/C][C]1602[/C][C]1630.59309649077[/C][C]-28.5930964907723[/C][/ROW]
[ROW][C]29[/C][C]1860[/C][C]2012.41596808684[/C][C]-152.415968086838[/C][/ROW]
[ROW][C]30[/C][C]1881[/C][C]1957.52174502126[/C][C]-76.5217450212649[/C][/ROW]
[ROW][C]31[/C][C]1829[/C][C]1825.42703021823[/C][C]3.57296978177033[/C][/ROW]
[ROW][C]32[/C][C]1705[/C][C]1705.81327294001[/C][C]-0.813272940009483[/C][/ROW]
[ROW][C]33[/C][C]1798[/C][C]1734.68786167414[/C][C]63.3121383258567[/C][/ROW]
[ROW][C]34[/C][C]1798[/C][C]1784.46219252183[/C][C]13.5378074781729[/C][/ROW]
[ROW][C]35[/C][C]1808[/C][C]1770.73584168973[/C][C]37.2641583102668[/C][/ROW]
[ROW][C]36[/C][C]1860[/C][C]1793.31791843215[/C][C]66.6820815678509[/C][/ROW]
[ROW][C]37[/C][C]1901[/C][C]1920.07360347627[/C][C]-19.0736034762745[/C][/ROW]
[ROW][C]38[/C][C]1922[/C][C]1843.51767340098[/C][C]78.4823265990196[/C][/ROW]
[ROW][C]39[/C][C]1922[/C][C]1871.72317202488[/C][C]50.2768279751233[/C][/ROW]
[ROW][C]40[/C][C]1984[/C][C]1999.67394239745[/C][C]-15.6739423974543[/C][/ROW]
[ROW][C]41[/C][C]2222[/C][C]2349.24743675855[/C][C]-127.247436758547[/C][/ROW]
[ROW][C]42[/C][C]2284[/C][C]2362.33748083819[/C][C]-78.3374808381895[/C][/ROW]
[ROW][C]43[/C][C]2294[/C][C]2274.67463737245[/C][C]19.3253626275514[/C][/ROW]
[ROW][C]44[/C][C]2139[/C][C]2120.22079662529[/C][C]18.7792033747073[/C][/ROW]
[ROW][C]45[/C][C]2222[/C][C]2218.76646729793[/C][C]3.23353270207281[/C][/ROW]
[ROW][C]46[/C][C]2191[/C][C]2210.55029731839[/C][C]-19.5502973183929[/C][/ROW]
[ROW][C]47[/C][C]2129[/C][C]2202.84876776815[/C][C]-73.8487677681537[/C][/ROW]
[ROW][C]48[/C][C]2263[/C][C]2224.06438941706[/C][C]38.9356105829415[/C][/ROW]
[ROW][C]49[/C][C]2294[/C][C]2277.62817894995[/C][C]16.3718210500542[/C][/ROW]
[ROW][C]50[/C][C]2242[/C][C]2277.67324023745[/C][C]-35.6732402374532[/C][/ROW]
[ROW][C]51[/C][C]2253[/C][C]2247.03489608025[/C][C]5.96510391974562[/C][/ROW]
[ROW][C]52[/C][C]2325[/C][C]2313.68830789365[/C][C]11.3116921063456[/C][/ROW]
[ROW][C]53[/C][C]2594[/C][C]2612.94398966306[/C][C]-18.9439896630611[/C][/ROW]
[ROW][C]54[/C][C]2728[/C][C]2691.84935356358[/C][C]36.150646436422[/C][/ROW]
[ROW][C]55[/C][C]2728[/C][C]2700.18261097789[/C][C]27.8173890221119[/C][/ROW]
[ROW][C]56[/C][C]2666[/C][C]2512.91147978167[/C][C]153.088520218326[/C][/ROW]
[ROW][C]57[/C][C]2759[/C][C]2640.67249959929[/C][C]118.327500400714[/C][/ROW]
[ROW][C]58[/C][C]2666[/C][C]2633.16823366462[/C][C]32.8317663353846[/C][/ROW]
[ROW][C]59[/C][C]2614[/C][C]2584.51492529047[/C][C]29.485074709527[/C][/ROW]
[ROW][C]60[/C][C]2811[/C][C]2746.54218241177[/C][C]64.4578175882257[/C][/ROW]
[ROW][C]61[/C][C]2842[/C][C]2797.07793293776[/C][C]44.9220670622376[/C][/ROW]
[ROW][C]62[/C][C]2769[/C][C]2755.86612352166[/C][C]13.1338764783413[/C][/ROW]
[ROW][C]63[/C][C]2955[/C][C]2775.24438474942[/C][C]179.75561525058[/C][/ROW]
[ROW][C]64[/C][C]3028[/C][C]2908.81598504939[/C][C]119.184014950612[/C][/ROW]
[ROW][C]65[/C][C]3245[/C][C]3290.20055112138[/C][C]-45.2005511213829[/C][/ROW]
[ROW][C]66[/C][C]3389[/C][C]3451.14569658567[/C][C]-62.1456965856682[/C][/ROW]
[ROW][C]67[/C][C]3369[/C][C]3438.84609320494[/C][C]-69.8460932049425[/C][/ROW]
[ROW][C]68[/C][C]3358[/C][C]3308.99639651573[/C][C]49.0036034842715[/C][/ROW]
[ROW][C]69[/C][C]3441[/C][C]3405.54413468996[/C][C]35.4558653100412[/C][/ROW]
[ROW][C]70[/C][C]3431[/C][C]3289.8127510937[/C][C]141.187248906301[/C][/ROW]
[ROW][C]71[/C][C]3307[/C][C]3249.77321563234[/C][C]57.2267843676609[/C][/ROW]
[ROW][C]72[/C][C]3493[/C][C]3493.25173545575[/C][C]-0.251735455752168[/C][/ROW]
[ROW][C]73[/C][C]3555[/C][C]3520.85325098606[/C][C]34.1467490139426[/C][/ROW]
[ROW][C]74[/C][C]3493[/C][C]3434.78178839007[/C][C]58.2182116099257[/C][/ROW]
[ROW][C]75[/C][C]3751[/C][C]3630.09440842603[/C][C]120.905591573973[/C][/ROW]
[ROW][C]76[/C][C]3875[/C][C]3713.06895733536[/C][C]161.931042664639[/C][/ROW]
[ROW][C]77[/C][C]4164[/C][C]4027.71970729545[/C][C]136.280292704548[/C][/ROW]
[ROW][C]78[/C][C]4278[/C][C]4256.76100083118[/C][C]21.2389991688242[/C][/ROW]
[ROW][C]79[/C][C]4247[/C][C]4259.88405581555[/C][C]-12.8840558155462[/C][/ROW]
[ROW][C]80[/C][C]4185[/C][C]4236.26907521299[/C][C]-51.2690752129884[/C][/ROW]
[ROW][C]81[/C][C]4237[/C][C]4324.21608487815[/C][C]-87.216084878145[/C][/ROW]
[ROW][C]82[/C][C]4299[/C][C]4255.30786890392[/C][C]43.6921310960779[/C][/ROW]
[ROW][C]83[/C][C]4092[/C][C]4093.78717302474[/C][C]-1.78717302474115[/C][/ROW]
[ROW][C]84[/C][C]4257[/C][C]4320.84773009177[/C][C]-63.8477300917684[/C][/ROW]
[ROW][C]85[/C][C]4361[/C][C]4370.46342290285[/C][C]-9.46342290284974[/C][/ROW]
[ROW][C]86[/C][C]4319[/C][C]4271.86438169127[/C][C]47.1356183087337[/C][/ROW]
[ROW][C]87[/C][C]4588[/C][C]4560.11199343523[/C][C]27.8880065647663[/C][/ROW]
[ROW][C]88[/C][C]4681[/C][C]4665.40262342152[/C][C]15.5973765784802[/C][/ROW]
[ROW][C]89[/C][C]5074[/C][C]4968.7431480932[/C][C]105.256851906798[/C][/ROW]
[ROW][C]90[/C][C]5146[/C][C]5109.21346279604[/C][C]36.7865372039641[/C][/ROW]
[ROW][C]91[/C][C]5053[/C][C]5070.78881379662[/C][C]-17.7888137966174[/C][/ROW]
[ROW][C]92[/C][C]5105[/C][C]4993.96986372255[/C][C]111.030136277448[/C][/ROW]
[ROW][C]93[/C][C]5136[/C][C]5093.69478622288[/C][C]42.3052137771192[/C][/ROW]
[ROW][C]94[/C][C]5167[/C][C]5160.64164084089[/C][C]6.35835915910593[/C][/ROW]
[ROW][C]95[/C][C]4970[/C][C]4908.03224854796[/C][C]61.967751452039[/C][/ROW]
[ROW][C]96[/C][C]5156[/C][C]5131.36302149123[/C][C]24.6369785087654[/C][/ROW]
[ROW][C]97[/C][C]5259[/C][C]5261.986266309[/C][C]-2.98626630900344[/C][/ROW]
[ROW][C]98[/C][C]5156[/C][C]5196.06983536433[/C][C]-40.0698353643347[/C][/ROW]
[ROW][C]99[/C][C]5456[/C][C]5498.93153473704[/C][C]-42.9315347370375[/C][/ROW]
[ROW][C]100[/C][C]5549[/C][C]5591.06009366594[/C][C]-42.0600936659366[/C][/ROW]
[ROW][C]101[/C][C]5952[/C][C]6015.82744215245[/C][C]-63.8274421524466[/C][/ROW]
[ROW][C]102[/C][C]6014[/C][C]6066.6947074284[/C][C]-52.694707428398[/C][/ROW]
[ROW][C]103[/C][C]6034[/C][C]5937.81362101804[/C][C]96.1863789819554[/C][/ROW]
[ROW][C]104[/C][C]6138[/C][C]5981.18868708287[/C][C]156.811312917127[/C][/ROW]
[ROW][C]105[/C][C]6138[/C][C]6031.25016413297[/C][C]106.749835867034[/C][/ROW]
[ROW][C]106[/C][C]6179[/C][C]6081.07885681714[/C][C]97.9211431828562[/C][/ROW]
[ROW][C]107[/C][C]5993[/C][C]5847.85698685773[/C][C]145.143013142272[/C][/ROW]
[ROW][C]108[/C][C]6086[/C][C]6088.40294859928[/C][C]-2.40294859927599[/C][/ROW]
[ROW][C]109[/C][C]6148[/C][C]6205.35638470757[/C][C]-57.3563847075675[/C][/ROW]
[ROW][C]110[/C][C]6034[/C][C]6076.08552564274[/C][C]-42.0855256427376[/C][/ROW]
[ROW][C]111[/C][C]6365[/C][C]6425.01700794251[/C][C]-60.017007942507[/C][/ROW]
[ROW][C]112[/C][C]6427[/C][C]6526.0096482716[/C][C]-99.0096482715953[/C][/ROW]
[ROW][C]113[/C][C]6840[/C][C]6985.76797014414[/C][C]-145.767970144138[/C][/ROW]
[ROW][C]114[/C][C]6913[/C][C]7031.36863186484[/C][C]-118.368631864842[/C][/ROW]
[ROW][C]115[/C][C]7016[/C][C]6995.3354865624[/C][C]20.6645134375967[/C][/ROW]
[ROW][C]116[/C][C]7109[/C][C]7069.19532713022[/C][C]39.8046728697764[/C][/ROW]
[ROW][C]117[/C][C]7119[/C][C]7036.93834376211[/C][C]82.0616562378855[/C][/ROW]
[ROW][C]118[/C][C]7130[/C][C]7062.62453600166[/C][C]67.375463998339[/C][/ROW]
[ROW][C]119[/C][C]6944[/C][C]6813.0929822473[/C][C]130.907017752698[/C][/ROW]
[ROW][C]120[/C][C]7130[/C][C]6932.63064074562[/C][C]197.369359254379[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235698&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235698&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
1310951032.5970992907762.4029007092267
1410751024.3799181475850.6200818524219
1511061060.5143751461345.4856248538686
1611571111.9789633738945.0210366261092
1714471391.8050426486655.1949573513359
1814471393.7060012648753.2939987351344
1913851304.0351058917780.9648941082316
2013231224.7433096567598.256690343248
2113741287.0704731183186.9295268816882
2214361330.56406695638105.435933043615
2314471387.0190034840659.9809965159388
2414781442.6402515768435.3597484231634
2515711620.20525476594-49.2052547659421
2615091569.22517806431-60.2251780643091
2715091589.45761857804-80.4576185780415
2816021630.59309649077-28.5930964907723
2918602012.41596808684-152.415968086838
3018811957.52174502126-76.5217450212649
3118291825.427030218233.57296978177033
3217051705.81327294001-0.813272940009483
3317981734.6878616741463.3121383258567
3417981784.4621925218313.5378074781729
3518081770.7358416897337.2641583102668
3618601793.3179184321566.6820815678509
3719011920.07360347627-19.0736034762745
3819221843.5176734009878.4823265990196
3919221871.7231720248850.2768279751233
4019841999.67394239745-15.6739423974543
4122222349.24743675855-127.247436758547
4222842362.33748083819-78.3374808381895
4322942274.6746373724519.3253626275514
4421392120.2207966252918.7792033747073
4522222218.766467297933.23353270207281
4621912210.55029731839-19.5502973183929
4721292202.84876776815-73.8487677681537
4822632224.0643894170638.9356105829415
4922942277.6281789499516.3718210500542
5022422277.67324023745-35.6732402374532
5122532247.034896080255.96510391974562
5223252313.6883078936511.3116921063456
5325942612.94398966306-18.9439896630611
5427282691.8493535635836.150646436422
5527282700.1826109778927.8173890221119
5626662512.91147978167153.088520218326
5727592640.67249959929118.327500400714
5826662633.1682336646232.8317663353846
5926142584.5149252904729.485074709527
6028112746.5421824117764.4578175882257
6128422797.0779329377644.9220670622376
6227692755.8661235216613.1338764783413
6329552775.24438474942179.75561525058
6430282908.81598504939119.184014950612
6532453290.20055112138-45.2005511213829
6633893451.14569658567-62.1456965856682
6733693438.84609320494-69.8460932049425
6833583308.9963965157349.0036034842715
6934413405.5441346899635.4558653100412
7034313289.8127510937141.187248906301
7133073249.7732156323457.2267843676609
7234933493.25173545575-0.251735455752168
7335553520.8532509860634.1467490139426
7434933434.7817883900758.2182116099257
7537513630.09440842603120.905591573973
7638753713.06895733536161.931042664639
7741644027.71970729545136.280292704548
7842784256.7610008311821.2389991688242
7942474259.88405581555-12.8840558155462
8041854236.26907521299-51.2690752129884
8142374324.21608487815-87.216084878145
8242994255.3078689039243.6921310960779
8340924093.78717302474-1.78717302474115
8442574320.84773009177-63.8477300917684
8543614370.46342290285-9.46342290284974
8643194271.8643816912747.1356183087337
8745884560.1119934352327.8880065647663
8846814665.4026234215215.5973765784802
8950744968.7431480932105.256851906798
9051465109.2134627960436.7865372039641
9150535070.78881379662-17.7888137966174
9251054993.96986372255111.030136277448
9351365093.6947862228842.3052137771192
9451675160.641640840896.35835915910593
9549704908.0322485479661.967751452039
9651565131.3630214912324.6369785087654
9752595261.986266309-2.98626630900344
9851565196.06983536433-40.0698353643347
9954565498.93153473704-42.9315347370375
10055495591.06009366594-42.0600936659366
10159526015.82744215245-63.8274421524466
10260146066.6947074284-52.694707428398
10360345937.8136210180496.1863789819554
10461385981.18868708287156.811312917127
10561386031.25016413297106.749835867034
10661796081.0788568171497.9211431828562
10759935847.85698685773145.143013142272
10860866088.40294859928-2.40294859927599
10961486205.35638470757-57.3563847075675
11060346076.08552564274-42.0855256427376
11163656425.01700794251-60.017007942507
11264276526.0096482716-99.0096482715953
11368406985.76797014414-145.767970144138
11469137031.36863186484-118.368631864842
11570166995.335486562420.6645134375967
11671097069.1953271302239.8046728697764
11771197036.9383437621182.0616562378855
11871307062.6245360016667.375463998339
11969446813.0929822473130.907017752698
12071306932.63064074562197.369359254379







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1217048.963084433766908.165889713617189.7602791539
1226919.307725614166774.824042737677063.79140849064
1237305.015384958297155.278736313737454.75203360285
1247393.229187219697238.149260059567548.30911437982
1257898.789727827217735.51286907638062.06658657812
1268010.594431179387840.2036979238180.98516443577
1278126.251136102987948.012597062928304.48967514304
1288224.978597746738038.36659193518411.59060355835
1298215.980047272038021.583317965788410.37677657828
1308209.877432888738007.317709774798412.43715600268
1317959.454734252347751.875833773748167.03363473093
1328116.440814860257949.091754282748283.78987543776

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 7048.96308443376 & 6908.16588971361 & 7189.7602791539 \tabularnewline
122 & 6919.30772561416 & 6774.82404273767 & 7063.79140849064 \tabularnewline
123 & 7305.01538495829 & 7155.27873631373 & 7454.75203360285 \tabularnewline
124 & 7393.22918721969 & 7238.14926005956 & 7548.30911437982 \tabularnewline
125 & 7898.78972782721 & 7735.5128690763 & 8062.06658657812 \tabularnewline
126 & 8010.59443117938 & 7840.203697923 & 8180.98516443577 \tabularnewline
127 & 8126.25113610298 & 7948.01259706292 & 8304.48967514304 \tabularnewline
128 & 8224.97859774673 & 8038.3665919351 & 8411.59060355835 \tabularnewline
129 & 8215.98004727203 & 8021.58331796578 & 8410.37677657828 \tabularnewline
130 & 8209.87743288873 & 8007.31770977479 & 8412.43715600268 \tabularnewline
131 & 7959.45473425234 & 7751.87583377374 & 8167.03363473093 \tabularnewline
132 & 8116.44081486025 & 7949.09175428274 & 8283.78987543776 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235698&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]7048.96308443376[/C][C]6908.16588971361[/C][C]7189.7602791539[/C][/ROW]
[ROW][C]122[/C][C]6919.30772561416[/C][C]6774.82404273767[/C][C]7063.79140849064[/C][/ROW]
[ROW][C]123[/C][C]7305.01538495829[/C][C]7155.27873631373[/C][C]7454.75203360285[/C][/ROW]
[ROW][C]124[/C][C]7393.22918721969[/C][C]7238.14926005956[/C][C]7548.30911437982[/C][/ROW]
[ROW][C]125[/C][C]7898.78972782721[/C][C]7735.5128690763[/C][C]8062.06658657812[/C][/ROW]
[ROW][C]126[/C][C]8010.59443117938[/C][C]7840.203697923[/C][C]8180.98516443577[/C][/ROW]
[ROW][C]127[/C][C]8126.25113610298[/C][C]7948.01259706292[/C][C]8304.48967514304[/C][/ROW]
[ROW][C]128[/C][C]8224.97859774673[/C][C]8038.3665919351[/C][C]8411.59060355835[/C][/ROW]
[ROW][C]129[/C][C]8215.98004727203[/C][C]8021.58331796578[/C][C]8410.37677657828[/C][/ROW]
[ROW][C]130[/C][C]8209.87743288873[/C][C]8007.31770977479[/C][C]8412.43715600268[/C][/ROW]
[ROW][C]131[/C][C]7959.45473425234[/C][C]7751.87583377374[/C][C]8167.03363473093[/C][/ROW]
[ROW][C]132[/C][C]8116.44081486025[/C][C]7949.09175428274[/C][C]8283.78987543776[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235698&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235698&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
1217048.963084433766908.165889713617189.7602791539
1226919.307725614166774.824042737677063.79140849064
1237305.015384958297155.278736313737454.75203360285
1247393.229187219697238.149260059567548.30911437982
1257898.789727827217735.51286907638062.06658657812
1268010.594431179387840.2036979238180.98516443577
1278126.251136102987948.012597062928304.48967514304
1288224.978597746738038.36659193518411.59060355835
1298215.980047272038021.583317965788410.37677657828
1308209.877432888738007.317709774798412.43715600268
1317959.454734252347751.875833773748167.03363473093
1328116.440814860257949.091754282748283.78987543776



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')