Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 17 Aug 2013 09:59:15 -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/17/t1376748118hoyki28b38ykhyt.htm/, Retrieved Mon, 29 Apr 2024 05:11:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211143, Retrieved Mon, 29 Apr 2024 05:11:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsDe Laere Dieter
Estimated Impact166
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 1 - Sta...] [2013-08-17 13:59:15] [bc2cf5f41ec5ca561b7a550898b8dd0d] [Current]
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Dataseries X:
145756
145472
145160
144588
150460
150172
145756
142820
143108
143108
143392
143992
143992
141340
140172
141340
145472
144872
139288
134560
133676
131908
133104
134560
133988
132792
130456
132792
134872
134272
127492
124556
121620
119256
118972
120736
118372
117488
116604
121620
122192
119256
111304
107772
102188
99820
100988
102756
102756
101304
100988
105720
109540
107772
101872
98940
92756
88936
91872
94808
94808
90988
90704
95688
98940
97768
91872
88052
79788
76568
77736
82752
83036
75684
78336
84804
87740
85972
78024
72436
65968
60952
63004
67420
66252
59784
61836
68304
71840
69788
61836
58304
53004
47416
48300
52716
53288
47988
48872
56252
58016
55056
44168
38584
31204
23852
26216
29436
28868
23252
26500
34452
37984
36220
29152
23568
17668
10884
12084
14136




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 3 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211143&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211143&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211143&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 time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.400851431469249
beta0.0368982697384306
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.400851431469249 \tabularnewline
beta & 0.0368982697384306 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211143&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]0.400851431469249[/C][/ROW]
[ROW][C]beta[/C][C]0.0368982697384306[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211143&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211143&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
alpha0.400851431469249
beta0.0368982697384306
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13143992146316.667735043-2324.66773504278
14141340142758.159854306-1418.159854306
15140172141149.551343863-977.551343862637
16141340142161.602693187-821.602693187189
17145472146223.680850165-751.680850164819
18144872145497.002707168-625.002707168431
19139288139315.692769768-27.6927697682404
20134560135957.572446351-1397.57244635123
21133676135387.996118304-1711.99611830449
22131908134342.227615443-2434.22761544253
23133104133254.947593695-150.947593694931
24134560133482.1910128771077.80898712348
25133988132286.7701628281701.22983717185
26132792130773.6984525252018.30154747522
27130456130745.934592013-289.934592012985
28132792132076.569080721715.430919278937
29134872136768.911343229-1896.91134322865
30134272135614.374566948-1342.37456694845
31127492129448.081658447-1956.08165844684
32124556124412.379344828143.620655172228
33121620124211.178250443-2591.17825044291
34119256122306.232888966-3050.2328889655
35118972122256.907589218-3284.9075892179
36120736121834.610227513-1098.61022751259
37118372119978.603336273-1606.60333627294
38117488117118.942782945369.057217054884
39116604114812.0948330981791.90516690223
40121620117375.3872341524244.61276584833
41122192121765.21127813426.788721870224
42119256121756.737435294-2500.73743529449
43111304114623.632882067-3319.63288206654
44107772110144.436328563-2372.43632856257
45102188107103.958620483-4915.95862048271
4699820103765.533884307-3945.53388430737
47100988102976.93283215-1988.93283214995
48102756104163.426090765-1407.42609076524
49102756101654.0793136211101.92068637865
50101304100878.722455175425.277544824814
5110098899262.61312674881725.38687325116
52105720103083.4992779372636.50072206285
53109540104332.2018109875207.79818901268
54107772104347.8302577943424.16974220575
5510187299048.37776878172823.62223121834
569894097639.37304830711300.62695169295
579275694641.7753077107-1885.77530771068
588893693238.7261213526-4302.72612135261
599187293613.2492771038-1741.24927710382
609480895385.1097020167-577.109702016736
619480894862.0228751032-54.0228751031827
629098893350.7522809675-2362.75228096754
639070491487.6365339141-783.636533914148
649568894903.1800306595784.81996934046
659894096977.34559217141962.65440782861
669776894602.61976369923165.3802363008
679187288814.91095046083057.08904953921
688805286565.74144124191486.25855875808
697978881714.9218140276-1926.92181402764
707656878828.1535553301-2260.15355533009
717773681567.2483439991-3831.24834399913
728275283179.0079226853-427.007922685269
738303683011.902157996124.0978420039173
747568480132.2357340269-4448.23573402689
757833678331.99137576744.00862423256331
768480482967.36734957611836.63265042393
778774086148.77373824831591.22626175167
788597284320.20056343661651.79943656338
797802477812.9299534567211.070046543275
807243673391.7158736878-955.715873687848
816596865390.8536554303577.146344569657
826095263219.054853739-2267.05485373904
836300464924.8274501293-1920.82745012932
846742069281.0476595513-1861.04765955133
856625268727.1938057777-2475.1938057777
865978462046.9335725517-2262.93357255172
876183663703.391835058-1867.39183505803
886830468572.1142368585-268.114236858455
897184070617.15012459291222.84987540706
906978868526.11171361821261.88828638177
916183660842.4732756126993.526724387375
925830455890.54262862752413.45737137255
935300450063.17571203562940.82428796444
944741647074.2672092586341.7327907414
954830050011.3092676085-1711.30926760846
965271654468.5225890377-1752.52258903773
975328853573.0020178141-285.002017814099
984798847913.048872719374.9511272806994
994887250793.4089973255-1921.40899732548
1005625256647.6536407486-395.653640748635
1015801659581.9580041035-1565.95800410349
1025505656402.2470969177-1346.24709691769
1034416847479.6045264197-3311.60452641972
1043858441556.2883753638-2972.28837536379
1053120433709.9327255689-2505.9327255689
1062385226723.8044717416-2871.80447174155
1072621626838.4503091876-622.450309187625
1082943631419.3784140592-1983.37841405922
1092886831019.1042934329-2151.10429343287
1102325224507.7082763234-1255.70827632341
1112650025319.79543178011180.20456821992
1123445233038.59563010811413.4043698919
1133798435730.74976023592253.25023976413
1143622034003.97473382372216.02526617626
1152915225174.78295062953977.21704937051
1162356822327.35899993591240.6410000641
1171766816462.34756940811205.65243059186
1181088410812.868166460571.1318335395372
1191208413566.4858815692-1482.48588156923
1201413617086.1431415946-2950.14314159457

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 143992 & 146316.667735043 & -2324.66773504278 \tabularnewline
14 & 141340 & 142758.159854306 & -1418.159854306 \tabularnewline
15 & 140172 & 141149.551343863 & -977.551343862637 \tabularnewline
16 & 141340 & 142161.602693187 & -821.602693187189 \tabularnewline
17 & 145472 & 146223.680850165 & -751.680850164819 \tabularnewline
18 & 144872 & 145497.002707168 & -625.002707168431 \tabularnewline
19 & 139288 & 139315.692769768 & -27.6927697682404 \tabularnewline
20 & 134560 & 135957.572446351 & -1397.57244635123 \tabularnewline
21 & 133676 & 135387.996118304 & -1711.99611830449 \tabularnewline
22 & 131908 & 134342.227615443 & -2434.22761544253 \tabularnewline
23 & 133104 & 133254.947593695 & -150.947593694931 \tabularnewline
24 & 134560 & 133482.191012877 & 1077.80898712348 \tabularnewline
25 & 133988 & 132286.770162828 & 1701.22983717185 \tabularnewline
26 & 132792 & 130773.698452525 & 2018.30154747522 \tabularnewline
27 & 130456 & 130745.934592013 & -289.934592012985 \tabularnewline
28 & 132792 & 132076.569080721 & 715.430919278937 \tabularnewline
29 & 134872 & 136768.911343229 & -1896.91134322865 \tabularnewline
30 & 134272 & 135614.374566948 & -1342.37456694845 \tabularnewline
31 & 127492 & 129448.081658447 & -1956.08165844684 \tabularnewline
32 & 124556 & 124412.379344828 & 143.620655172228 \tabularnewline
33 & 121620 & 124211.178250443 & -2591.17825044291 \tabularnewline
34 & 119256 & 122306.232888966 & -3050.2328889655 \tabularnewline
35 & 118972 & 122256.907589218 & -3284.9075892179 \tabularnewline
36 & 120736 & 121834.610227513 & -1098.61022751259 \tabularnewline
37 & 118372 & 119978.603336273 & -1606.60333627294 \tabularnewline
38 & 117488 & 117118.942782945 & 369.057217054884 \tabularnewline
39 & 116604 & 114812.094833098 & 1791.90516690223 \tabularnewline
40 & 121620 & 117375.387234152 & 4244.61276584833 \tabularnewline
41 & 122192 & 121765.21127813 & 426.788721870224 \tabularnewline
42 & 119256 & 121756.737435294 & -2500.73743529449 \tabularnewline
43 & 111304 & 114623.632882067 & -3319.63288206654 \tabularnewline
44 & 107772 & 110144.436328563 & -2372.43632856257 \tabularnewline
45 & 102188 & 107103.958620483 & -4915.95862048271 \tabularnewline
46 & 99820 & 103765.533884307 & -3945.53388430737 \tabularnewline
47 & 100988 & 102976.93283215 & -1988.93283214995 \tabularnewline
48 & 102756 & 104163.426090765 & -1407.42609076524 \tabularnewline
49 & 102756 & 101654.079313621 & 1101.92068637865 \tabularnewline
50 & 101304 & 100878.722455175 & 425.277544824814 \tabularnewline
51 & 100988 & 99262.6131267488 & 1725.38687325116 \tabularnewline
52 & 105720 & 103083.499277937 & 2636.50072206285 \tabularnewline
53 & 109540 & 104332.201810987 & 5207.79818901268 \tabularnewline
54 & 107772 & 104347.830257794 & 3424.16974220575 \tabularnewline
55 & 101872 & 99048.3777687817 & 2823.62223121834 \tabularnewline
56 & 98940 & 97639.3730483071 & 1300.62695169295 \tabularnewline
57 & 92756 & 94641.7753077107 & -1885.77530771068 \tabularnewline
58 & 88936 & 93238.7261213526 & -4302.72612135261 \tabularnewline
59 & 91872 & 93613.2492771038 & -1741.24927710382 \tabularnewline
60 & 94808 & 95385.1097020167 & -577.109702016736 \tabularnewline
61 & 94808 & 94862.0228751032 & -54.0228751031827 \tabularnewline
62 & 90988 & 93350.7522809675 & -2362.75228096754 \tabularnewline
63 & 90704 & 91487.6365339141 & -783.636533914148 \tabularnewline
64 & 95688 & 94903.1800306595 & 784.81996934046 \tabularnewline
65 & 98940 & 96977.3455921714 & 1962.65440782861 \tabularnewline
66 & 97768 & 94602.6197636992 & 3165.3802363008 \tabularnewline
67 & 91872 & 88814.9109504608 & 3057.08904953921 \tabularnewline
68 & 88052 & 86565.7414412419 & 1486.25855875808 \tabularnewline
69 & 79788 & 81714.9218140276 & -1926.92181402764 \tabularnewline
70 & 76568 & 78828.1535553301 & -2260.15355533009 \tabularnewline
71 & 77736 & 81567.2483439991 & -3831.24834399913 \tabularnewline
72 & 82752 & 83179.0079226853 & -427.007922685269 \tabularnewline
73 & 83036 & 83011.9021579961 & 24.0978420039173 \tabularnewline
74 & 75684 & 80132.2357340269 & -4448.23573402689 \tabularnewline
75 & 78336 & 78331.9913757674 & 4.00862423256331 \tabularnewline
76 & 84804 & 82967.3673495761 & 1836.63265042393 \tabularnewline
77 & 87740 & 86148.7737382483 & 1591.22626175167 \tabularnewline
78 & 85972 & 84320.2005634366 & 1651.79943656338 \tabularnewline
79 & 78024 & 77812.9299534567 & 211.070046543275 \tabularnewline
80 & 72436 & 73391.7158736878 & -955.715873687848 \tabularnewline
81 & 65968 & 65390.8536554303 & 577.146344569657 \tabularnewline
82 & 60952 & 63219.054853739 & -2267.05485373904 \tabularnewline
83 & 63004 & 64924.8274501293 & -1920.82745012932 \tabularnewline
84 & 67420 & 69281.0476595513 & -1861.04765955133 \tabularnewline
85 & 66252 & 68727.1938057777 & -2475.1938057777 \tabularnewline
86 & 59784 & 62046.9335725517 & -2262.93357255172 \tabularnewline
87 & 61836 & 63703.391835058 & -1867.39183505803 \tabularnewline
88 & 68304 & 68572.1142368585 & -268.114236858455 \tabularnewline
89 & 71840 & 70617.1501245929 & 1222.84987540706 \tabularnewline
90 & 69788 & 68526.1117136182 & 1261.88828638177 \tabularnewline
91 & 61836 & 60842.4732756126 & 993.526724387375 \tabularnewline
92 & 58304 & 55890.5426286275 & 2413.45737137255 \tabularnewline
93 & 53004 & 50063.1757120356 & 2940.82428796444 \tabularnewline
94 & 47416 & 47074.2672092586 & 341.7327907414 \tabularnewline
95 & 48300 & 50011.3092676085 & -1711.30926760846 \tabularnewline
96 & 52716 & 54468.5225890377 & -1752.52258903773 \tabularnewline
97 & 53288 & 53573.0020178141 & -285.002017814099 \tabularnewline
98 & 47988 & 47913.0488727193 & 74.9511272806994 \tabularnewline
99 & 48872 & 50793.4089973255 & -1921.40899732548 \tabularnewline
100 & 56252 & 56647.6536407486 & -395.653640748635 \tabularnewline
101 & 58016 & 59581.9580041035 & -1565.95800410349 \tabularnewline
102 & 55056 & 56402.2470969177 & -1346.24709691769 \tabularnewline
103 & 44168 & 47479.6045264197 & -3311.60452641972 \tabularnewline
104 & 38584 & 41556.2883753638 & -2972.28837536379 \tabularnewline
105 & 31204 & 33709.9327255689 & -2505.9327255689 \tabularnewline
106 & 23852 & 26723.8044717416 & -2871.80447174155 \tabularnewline
107 & 26216 & 26838.4503091876 & -622.450309187625 \tabularnewline
108 & 29436 & 31419.3784140592 & -1983.37841405922 \tabularnewline
109 & 28868 & 31019.1042934329 & -2151.10429343287 \tabularnewline
110 & 23252 & 24507.7082763234 & -1255.70827632341 \tabularnewline
111 & 26500 & 25319.7954317801 & 1180.20456821992 \tabularnewline
112 & 34452 & 33038.5956301081 & 1413.4043698919 \tabularnewline
113 & 37984 & 35730.7497602359 & 2253.25023976413 \tabularnewline
114 & 36220 & 34003.9747338237 & 2216.02526617626 \tabularnewline
115 & 29152 & 25174.7829506295 & 3977.21704937051 \tabularnewline
116 & 23568 & 22327.3589999359 & 1240.6410000641 \tabularnewline
117 & 17668 & 16462.3475694081 & 1205.65243059186 \tabularnewline
118 & 10884 & 10812.8681664605 & 71.1318335395372 \tabularnewline
119 & 12084 & 13566.4858815692 & -1482.48588156923 \tabularnewline
120 & 14136 & 17086.1431415946 & -2950.14314159457 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211143&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]143992[/C][C]146316.667735043[/C][C]-2324.66773504278[/C][/ROW]
[ROW][C]14[/C][C]141340[/C][C]142758.159854306[/C][C]-1418.159854306[/C][/ROW]
[ROW][C]15[/C][C]140172[/C][C]141149.551343863[/C][C]-977.551343862637[/C][/ROW]
[ROW][C]16[/C][C]141340[/C][C]142161.602693187[/C][C]-821.602693187189[/C][/ROW]
[ROW][C]17[/C][C]145472[/C][C]146223.680850165[/C][C]-751.680850164819[/C][/ROW]
[ROW][C]18[/C][C]144872[/C][C]145497.002707168[/C][C]-625.002707168431[/C][/ROW]
[ROW][C]19[/C][C]139288[/C][C]139315.692769768[/C][C]-27.6927697682404[/C][/ROW]
[ROW][C]20[/C][C]134560[/C][C]135957.572446351[/C][C]-1397.57244635123[/C][/ROW]
[ROW][C]21[/C][C]133676[/C][C]135387.996118304[/C][C]-1711.99611830449[/C][/ROW]
[ROW][C]22[/C][C]131908[/C][C]134342.227615443[/C][C]-2434.22761544253[/C][/ROW]
[ROW][C]23[/C][C]133104[/C][C]133254.947593695[/C][C]-150.947593694931[/C][/ROW]
[ROW][C]24[/C][C]134560[/C][C]133482.191012877[/C][C]1077.80898712348[/C][/ROW]
[ROW][C]25[/C][C]133988[/C][C]132286.770162828[/C][C]1701.22983717185[/C][/ROW]
[ROW][C]26[/C][C]132792[/C][C]130773.698452525[/C][C]2018.30154747522[/C][/ROW]
[ROW][C]27[/C][C]130456[/C][C]130745.934592013[/C][C]-289.934592012985[/C][/ROW]
[ROW][C]28[/C][C]132792[/C][C]132076.569080721[/C][C]715.430919278937[/C][/ROW]
[ROW][C]29[/C][C]134872[/C][C]136768.911343229[/C][C]-1896.91134322865[/C][/ROW]
[ROW][C]30[/C][C]134272[/C][C]135614.374566948[/C][C]-1342.37456694845[/C][/ROW]
[ROW][C]31[/C][C]127492[/C][C]129448.081658447[/C][C]-1956.08165844684[/C][/ROW]
[ROW][C]32[/C][C]124556[/C][C]124412.379344828[/C][C]143.620655172228[/C][/ROW]
[ROW][C]33[/C][C]121620[/C][C]124211.178250443[/C][C]-2591.17825044291[/C][/ROW]
[ROW][C]34[/C][C]119256[/C][C]122306.232888966[/C][C]-3050.2328889655[/C][/ROW]
[ROW][C]35[/C][C]118972[/C][C]122256.907589218[/C][C]-3284.9075892179[/C][/ROW]
[ROW][C]36[/C][C]120736[/C][C]121834.610227513[/C][C]-1098.61022751259[/C][/ROW]
[ROW][C]37[/C][C]118372[/C][C]119978.603336273[/C][C]-1606.60333627294[/C][/ROW]
[ROW][C]38[/C][C]117488[/C][C]117118.942782945[/C][C]369.057217054884[/C][/ROW]
[ROW][C]39[/C][C]116604[/C][C]114812.094833098[/C][C]1791.90516690223[/C][/ROW]
[ROW][C]40[/C][C]121620[/C][C]117375.387234152[/C][C]4244.61276584833[/C][/ROW]
[ROW][C]41[/C][C]122192[/C][C]121765.21127813[/C][C]426.788721870224[/C][/ROW]
[ROW][C]42[/C][C]119256[/C][C]121756.737435294[/C][C]-2500.73743529449[/C][/ROW]
[ROW][C]43[/C][C]111304[/C][C]114623.632882067[/C][C]-3319.63288206654[/C][/ROW]
[ROW][C]44[/C][C]107772[/C][C]110144.436328563[/C][C]-2372.43632856257[/C][/ROW]
[ROW][C]45[/C][C]102188[/C][C]107103.958620483[/C][C]-4915.95862048271[/C][/ROW]
[ROW][C]46[/C][C]99820[/C][C]103765.533884307[/C][C]-3945.53388430737[/C][/ROW]
[ROW][C]47[/C][C]100988[/C][C]102976.93283215[/C][C]-1988.93283214995[/C][/ROW]
[ROW][C]48[/C][C]102756[/C][C]104163.426090765[/C][C]-1407.42609076524[/C][/ROW]
[ROW][C]49[/C][C]102756[/C][C]101654.079313621[/C][C]1101.92068637865[/C][/ROW]
[ROW][C]50[/C][C]101304[/C][C]100878.722455175[/C][C]425.277544824814[/C][/ROW]
[ROW][C]51[/C][C]100988[/C][C]99262.6131267488[/C][C]1725.38687325116[/C][/ROW]
[ROW][C]52[/C][C]105720[/C][C]103083.499277937[/C][C]2636.50072206285[/C][/ROW]
[ROW][C]53[/C][C]109540[/C][C]104332.201810987[/C][C]5207.79818901268[/C][/ROW]
[ROW][C]54[/C][C]107772[/C][C]104347.830257794[/C][C]3424.16974220575[/C][/ROW]
[ROW][C]55[/C][C]101872[/C][C]99048.3777687817[/C][C]2823.62223121834[/C][/ROW]
[ROW][C]56[/C][C]98940[/C][C]97639.3730483071[/C][C]1300.62695169295[/C][/ROW]
[ROW][C]57[/C][C]92756[/C][C]94641.7753077107[/C][C]-1885.77530771068[/C][/ROW]
[ROW][C]58[/C][C]88936[/C][C]93238.7261213526[/C][C]-4302.72612135261[/C][/ROW]
[ROW][C]59[/C][C]91872[/C][C]93613.2492771038[/C][C]-1741.24927710382[/C][/ROW]
[ROW][C]60[/C][C]94808[/C][C]95385.1097020167[/C][C]-577.109702016736[/C][/ROW]
[ROW][C]61[/C][C]94808[/C][C]94862.0228751032[/C][C]-54.0228751031827[/C][/ROW]
[ROW][C]62[/C][C]90988[/C][C]93350.7522809675[/C][C]-2362.75228096754[/C][/ROW]
[ROW][C]63[/C][C]90704[/C][C]91487.6365339141[/C][C]-783.636533914148[/C][/ROW]
[ROW][C]64[/C][C]95688[/C][C]94903.1800306595[/C][C]784.81996934046[/C][/ROW]
[ROW][C]65[/C][C]98940[/C][C]96977.3455921714[/C][C]1962.65440782861[/C][/ROW]
[ROW][C]66[/C][C]97768[/C][C]94602.6197636992[/C][C]3165.3802363008[/C][/ROW]
[ROW][C]67[/C][C]91872[/C][C]88814.9109504608[/C][C]3057.08904953921[/C][/ROW]
[ROW][C]68[/C][C]88052[/C][C]86565.7414412419[/C][C]1486.25855875808[/C][/ROW]
[ROW][C]69[/C][C]79788[/C][C]81714.9218140276[/C][C]-1926.92181402764[/C][/ROW]
[ROW][C]70[/C][C]76568[/C][C]78828.1535553301[/C][C]-2260.15355533009[/C][/ROW]
[ROW][C]71[/C][C]77736[/C][C]81567.2483439991[/C][C]-3831.24834399913[/C][/ROW]
[ROW][C]72[/C][C]82752[/C][C]83179.0079226853[/C][C]-427.007922685269[/C][/ROW]
[ROW][C]73[/C][C]83036[/C][C]83011.9021579961[/C][C]24.0978420039173[/C][/ROW]
[ROW][C]74[/C][C]75684[/C][C]80132.2357340269[/C][C]-4448.23573402689[/C][/ROW]
[ROW][C]75[/C][C]78336[/C][C]78331.9913757674[/C][C]4.00862423256331[/C][/ROW]
[ROW][C]76[/C][C]84804[/C][C]82967.3673495761[/C][C]1836.63265042393[/C][/ROW]
[ROW][C]77[/C][C]87740[/C][C]86148.7737382483[/C][C]1591.22626175167[/C][/ROW]
[ROW][C]78[/C][C]85972[/C][C]84320.2005634366[/C][C]1651.79943656338[/C][/ROW]
[ROW][C]79[/C][C]78024[/C][C]77812.9299534567[/C][C]211.070046543275[/C][/ROW]
[ROW][C]80[/C][C]72436[/C][C]73391.7158736878[/C][C]-955.715873687848[/C][/ROW]
[ROW][C]81[/C][C]65968[/C][C]65390.8536554303[/C][C]577.146344569657[/C][/ROW]
[ROW][C]82[/C][C]60952[/C][C]63219.054853739[/C][C]-2267.05485373904[/C][/ROW]
[ROW][C]83[/C][C]63004[/C][C]64924.8274501293[/C][C]-1920.82745012932[/C][/ROW]
[ROW][C]84[/C][C]67420[/C][C]69281.0476595513[/C][C]-1861.04765955133[/C][/ROW]
[ROW][C]85[/C][C]66252[/C][C]68727.1938057777[/C][C]-2475.1938057777[/C][/ROW]
[ROW][C]86[/C][C]59784[/C][C]62046.9335725517[/C][C]-2262.93357255172[/C][/ROW]
[ROW][C]87[/C][C]61836[/C][C]63703.391835058[/C][C]-1867.39183505803[/C][/ROW]
[ROW][C]88[/C][C]68304[/C][C]68572.1142368585[/C][C]-268.114236858455[/C][/ROW]
[ROW][C]89[/C][C]71840[/C][C]70617.1501245929[/C][C]1222.84987540706[/C][/ROW]
[ROW][C]90[/C][C]69788[/C][C]68526.1117136182[/C][C]1261.88828638177[/C][/ROW]
[ROW][C]91[/C][C]61836[/C][C]60842.4732756126[/C][C]993.526724387375[/C][/ROW]
[ROW][C]92[/C][C]58304[/C][C]55890.5426286275[/C][C]2413.45737137255[/C][/ROW]
[ROW][C]93[/C][C]53004[/C][C]50063.1757120356[/C][C]2940.82428796444[/C][/ROW]
[ROW][C]94[/C][C]47416[/C][C]47074.2672092586[/C][C]341.7327907414[/C][/ROW]
[ROW][C]95[/C][C]48300[/C][C]50011.3092676085[/C][C]-1711.30926760846[/C][/ROW]
[ROW][C]96[/C][C]52716[/C][C]54468.5225890377[/C][C]-1752.52258903773[/C][/ROW]
[ROW][C]97[/C][C]53288[/C][C]53573.0020178141[/C][C]-285.002017814099[/C][/ROW]
[ROW][C]98[/C][C]47988[/C][C]47913.0488727193[/C][C]74.9511272806994[/C][/ROW]
[ROW][C]99[/C][C]48872[/C][C]50793.4089973255[/C][C]-1921.40899732548[/C][/ROW]
[ROW][C]100[/C][C]56252[/C][C]56647.6536407486[/C][C]-395.653640748635[/C][/ROW]
[ROW][C]101[/C][C]58016[/C][C]59581.9580041035[/C][C]-1565.95800410349[/C][/ROW]
[ROW][C]102[/C][C]55056[/C][C]56402.2470969177[/C][C]-1346.24709691769[/C][/ROW]
[ROW][C]103[/C][C]44168[/C][C]47479.6045264197[/C][C]-3311.60452641972[/C][/ROW]
[ROW][C]104[/C][C]38584[/C][C]41556.2883753638[/C][C]-2972.28837536379[/C][/ROW]
[ROW][C]105[/C][C]31204[/C][C]33709.9327255689[/C][C]-2505.9327255689[/C][/ROW]
[ROW][C]106[/C][C]23852[/C][C]26723.8044717416[/C][C]-2871.80447174155[/C][/ROW]
[ROW][C]107[/C][C]26216[/C][C]26838.4503091876[/C][C]-622.450309187625[/C][/ROW]
[ROW][C]108[/C][C]29436[/C][C]31419.3784140592[/C][C]-1983.37841405922[/C][/ROW]
[ROW][C]109[/C][C]28868[/C][C]31019.1042934329[/C][C]-2151.10429343287[/C][/ROW]
[ROW][C]110[/C][C]23252[/C][C]24507.7082763234[/C][C]-1255.70827632341[/C][/ROW]
[ROW][C]111[/C][C]26500[/C][C]25319.7954317801[/C][C]1180.20456821992[/C][/ROW]
[ROW][C]112[/C][C]34452[/C][C]33038.5956301081[/C][C]1413.4043698919[/C][/ROW]
[ROW][C]113[/C][C]37984[/C][C]35730.7497602359[/C][C]2253.25023976413[/C][/ROW]
[ROW][C]114[/C][C]36220[/C][C]34003.9747338237[/C][C]2216.02526617626[/C][/ROW]
[ROW][C]115[/C][C]29152[/C][C]25174.7829506295[/C][C]3977.21704937051[/C][/ROW]
[ROW][C]116[/C][C]23568[/C][C]22327.3589999359[/C][C]1240.6410000641[/C][/ROW]
[ROW][C]117[/C][C]17668[/C][C]16462.3475694081[/C][C]1205.65243059186[/C][/ROW]
[ROW][C]118[/C][C]10884[/C][C]10812.8681664605[/C][C]71.1318335395372[/C][/ROW]
[ROW][C]119[/C][C]12084[/C][C]13566.4858815692[/C][C]-1482.48588156923[/C][/ROW]
[ROW][C]120[/C][C]14136[/C][C]17086.1431415946[/C][C]-2950.14314159457[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211143&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211143&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
13143992146316.667735043-2324.66773504278
14141340142758.159854306-1418.159854306
15140172141149.551343863-977.551343862637
16141340142161.602693187-821.602693187189
17145472146223.680850165-751.680850164819
18144872145497.002707168-625.002707168431
19139288139315.692769768-27.6927697682404
20134560135957.572446351-1397.57244635123
21133676135387.996118304-1711.99611830449
22131908134342.227615443-2434.22761544253
23133104133254.947593695-150.947593694931
24134560133482.1910128771077.80898712348
25133988132286.7701628281701.22983717185
26132792130773.6984525252018.30154747522
27130456130745.934592013-289.934592012985
28132792132076.569080721715.430919278937
29134872136768.911343229-1896.91134322865
30134272135614.374566948-1342.37456694845
31127492129448.081658447-1956.08165844684
32124556124412.379344828143.620655172228
33121620124211.178250443-2591.17825044291
34119256122306.232888966-3050.2328889655
35118972122256.907589218-3284.9075892179
36120736121834.610227513-1098.61022751259
37118372119978.603336273-1606.60333627294
38117488117118.942782945369.057217054884
39116604114812.0948330981791.90516690223
40121620117375.3872341524244.61276584833
41122192121765.21127813426.788721870224
42119256121756.737435294-2500.73743529449
43111304114623.632882067-3319.63288206654
44107772110144.436328563-2372.43632856257
45102188107103.958620483-4915.95862048271
4699820103765.533884307-3945.53388430737
47100988102976.93283215-1988.93283214995
48102756104163.426090765-1407.42609076524
49102756101654.0793136211101.92068637865
50101304100878.722455175425.277544824814
5110098899262.61312674881725.38687325116
52105720103083.4992779372636.50072206285
53109540104332.2018109875207.79818901268
54107772104347.8302577943424.16974220575
5510187299048.37776878172823.62223121834
569894097639.37304830711300.62695169295
579275694641.7753077107-1885.77530771068
588893693238.7261213526-4302.72612135261
599187293613.2492771038-1741.24927710382
609480895385.1097020167-577.109702016736
619480894862.0228751032-54.0228751031827
629098893350.7522809675-2362.75228096754
639070491487.6365339141-783.636533914148
649568894903.1800306595784.81996934046
659894096977.34559217141962.65440782861
669776894602.61976369923165.3802363008
679187288814.91095046083057.08904953921
688805286565.74144124191486.25855875808
697978881714.9218140276-1926.92181402764
707656878828.1535553301-2260.15355533009
717773681567.2483439991-3831.24834399913
728275283179.0079226853-427.007922685269
738303683011.902157996124.0978420039173
747568480132.2357340269-4448.23573402689
757833678331.99137576744.00862423256331
768480482967.36734957611836.63265042393
778774086148.77373824831591.22626175167
788597284320.20056343661651.79943656338
797802477812.9299534567211.070046543275
807243673391.7158736878-955.715873687848
816596865390.8536554303577.146344569657
826095263219.054853739-2267.05485373904
836300464924.8274501293-1920.82745012932
846742069281.0476595513-1861.04765955133
856625268727.1938057777-2475.1938057777
865978462046.9335725517-2262.93357255172
876183663703.391835058-1867.39183505803
886830468572.1142368585-268.114236858455
897184070617.15012459291222.84987540706
906978868526.11171361821261.88828638177
916183660842.4732756126993.526724387375
925830455890.54262862752413.45737137255
935300450063.17571203562940.82428796444
944741647074.2672092586341.7327907414
954830050011.3092676085-1711.30926760846
965271654468.5225890377-1752.52258903773
975328853573.0020178141-285.002017814099
984798847913.048872719374.9511272806994
994887250793.4089973255-1921.40899732548
1005625256647.6536407486-395.653640748635
1015801659581.9580041035-1565.95800410349
1025505656402.2470969177-1346.24709691769
1034416847479.6045264197-3311.60452641972
1043858441556.2883753638-2972.28837536379
1053120433709.9327255689-2505.9327255689
1062385226723.8044717416-2871.80447174155
1072621626838.4503091876-622.450309187625
1082943631419.3784140592-1983.37841405922
1092886831019.1042934329-2151.10429343287
1102325224507.7082763234-1255.70827632341
1112650025319.79543178011180.20456821992
1123445233038.59563010811413.4043698919
1133798435730.74976023592253.25023976413
1143622034003.97473382372216.02526617626
1152915225174.78295062953977.21704937051
1162356822327.35899993591240.6410000641
1171766816462.34756940811205.65243059186
1181088410812.868166460571.1318335395372
1191208413566.4858815692-1482.48588156923
1201413617086.1431415946-2950.14314159457







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12116282.421896380712237.762375685720327.0814170757
12211286.16536774696906.0429852944615666.2877501993
12314196.04252328889482.6154825806318909.469563997
12421698.985124192916653.274522541326744.6957258445
12524424.369031665619046.541143317429802.1969200139
12621835.347420139816124.912750158427545.7820901212
12713203.57294260037159.5306582741519247.6152269264
1287093.93297111632714.87821909378713472.9877231388
129663.968238873396-6051.826501340037379.76297908683
130-6213.05476064401-13267.5769424554841.467421167372
131-4484.35996643888-11879.80788262952911.0879497517
132-1293.42561877736-9032.169488666726445.31825111201

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 16282.4218963807 & 12237.7623756857 & 20327.0814170757 \tabularnewline
122 & 11286.1653677469 & 6906.04298529446 & 15666.2877501993 \tabularnewline
123 & 14196.0425232888 & 9482.61548258063 & 18909.469563997 \tabularnewline
124 & 21698.9851241929 & 16653.2745225413 & 26744.6957258445 \tabularnewline
125 & 24424.3690316656 & 19046.5411433174 & 29802.1969200139 \tabularnewline
126 & 21835.3474201398 & 16124.9127501584 & 27545.7820901212 \tabularnewline
127 & 13203.5729426003 & 7159.53065827415 & 19247.6152269264 \tabularnewline
128 & 7093.93297111632 & 714.878219093787 & 13472.9877231388 \tabularnewline
129 & 663.968238873396 & -6051.82650134003 & 7379.76297908683 \tabularnewline
130 & -6213.05476064401 & -13267.5769424554 & 841.467421167372 \tabularnewline
131 & -4484.35996643888 & -11879.8078826295 & 2911.0879497517 \tabularnewline
132 & -1293.42561877736 & -9032.16948866672 & 6445.31825111201 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211143&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]16282.4218963807[/C][C]12237.7623756857[/C][C]20327.0814170757[/C][/ROW]
[ROW][C]122[/C][C]11286.1653677469[/C][C]6906.04298529446[/C][C]15666.2877501993[/C][/ROW]
[ROW][C]123[/C][C]14196.0425232888[/C][C]9482.61548258063[/C][C]18909.469563997[/C][/ROW]
[ROW][C]124[/C][C]21698.9851241929[/C][C]16653.2745225413[/C][C]26744.6957258445[/C][/ROW]
[ROW][C]125[/C][C]24424.3690316656[/C][C]19046.5411433174[/C][C]29802.1969200139[/C][/ROW]
[ROW][C]126[/C][C]21835.3474201398[/C][C]16124.9127501584[/C][C]27545.7820901212[/C][/ROW]
[ROW][C]127[/C][C]13203.5729426003[/C][C]7159.53065827415[/C][C]19247.6152269264[/C][/ROW]
[ROW][C]128[/C][C]7093.93297111632[/C][C]714.878219093787[/C][C]13472.9877231388[/C][/ROW]
[ROW][C]129[/C][C]663.968238873396[/C][C]-6051.82650134003[/C][C]7379.76297908683[/C][/ROW]
[ROW][C]130[/C][C]-6213.05476064401[/C][C]-13267.5769424554[/C][C]841.467421167372[/C][/ROW]
[ROW][C]131[/C][C]-4484.35996643888[/C][C]-11879.8078826295[/C][C]2911.0879497517[/C][/ROW]
[ROW][C]132[/C][C]-1293.42561877736[/C][C]-9032.16948866672[/C][C]6445.31825111201[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211143&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211143&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
12116282.421896380712237.762375685720327.0814170757
12211286.16536774696906.0429852944615666.2877501993
12314196.04252328889482.6154825806318909.469563997
12421698.985124192916653.274522541326744.6957258445
12524424.369031665619046.541143317429802.1969200139
12621835.347420139816124.912750158427545.7820901212
12713203.57294260037159.5306582741519247.6152269264
1287093.93297111632714.87821909378713472.9877231388
129663.968238873396-6051.826501340037379.76297908683
130-6213.05476064401-13267.5769424554841.467421167372
131-4484.35996643888-11879.80788262952911.0879497517
132-1293.42561877736-9032.169488666726445.31825111201



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