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Description of Statistical Computation

Author's title

Exponential Smoothing - Koers BEL 20 van Januari 2000 tot Januari 2009 - Cl...

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 Jun 2009 01:41:47 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/02/t12439286024q0yhdl9etcouyt.htm/, Retrieved Fri, 10 May 2024 15:23:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41162, Retrieved Fri, 10 May 2024 15:23:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact134

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2009-06-02 07:41:47] [fbcf875f1b36dfb87c2c6a55976f6e7b] [Current]
-   PD    [Exponential Smoothing] [Opgave 10 OEFENIN...] [2009-06-08 01:29:27] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1635,25
1765,9
1833,42
1862,83
1905,41
1910,43
1940,49
1946,81
1959,67
1969,6
1995,37
2014,45
2042
2061,41
2065,81
2091,48
2120,88
2174,56
2196,72
2197,82
2214,95
2304,98
2350,44
2407,6
2408,64
2440,25
2448,05
2452,62
2472,81
2497,84
2555,28
2604,42
2638,53
2641,65
2645,64
2659,81
2720,25
2735,7
2745,88
2756,76
2767,63
2794,83
2799,43
2803,47
2811,7
2833,18
2845,26
2848,96
2849,27
2863,36
2882,6
2892,63
2897,06
2915,02
2921,44
2962,34
2981,85
2987,1
2995,55
3012,61
3013,24
3030,29
3032,6
3032,93
3045,78
3047,03
3061,26
3080,58
3097,31
3106,22
3110,52
3119,31
3142,95
3161,69
3257,16
3277,01
3295,32
3363,99
3494,17
3504,37
3570,12
3667,03
3674,4
3701,61
3720,98
3801,06
3801,06
3813,06
3844,49
3857,62
3862,27
3895,51
3917,96
3970,1
4105,18
4116,68
4138,52
4199,75
4202,52
4290,89
4296,49
4356,98
4435,23
4443,91
4502,64
4562,84
4591,27
4621,4
4696,96

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41162&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41162&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41162&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0887765523093223
gamma0.518290651633152

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0887765523093223 \tabularnewline
gamma & 0.518290651633152 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41162&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0887765523093223[/C][/ROW]
[ROW][C]gamma[/C][C]0.518290651633152[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41162&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41162&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
alpha1
beta0.0887765523093223
gamma0.518290651633152






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1320421916.84015491453125.159845085471
142061.412073.58958995384-12.1795899538370
152065.812076.94791128253-11.1379112825284
162091.482098.11370925227-6.63370925227082
172120.882122.76687474917-1.8868747491656
182174.562173.872281180960.687718819038764
192196.722228.46166782001-31.7416678200075
202197.822201.51041865307-3.69041865306599
212214.952216.08779600847-1.13779600846965
222304.982232.9726197349472.0073802650613
232350.442345.940186695704.49981330430319
242407.62383.6313312735623.9686687264434
252408.642449.6908537132-41.0508537132
262440.252439.493167117850.756832882145773
272448.052456.19993946514-8.14993946514005
282452.622481.03099927123-28.4109992712279
292472.812482.6508520416-9.8408520415992
302497.842523.84013179223-26.0001317922256
312555.282547.410263065467.86973693454229
322604.422559.2555778447545.1644221552451
332638.532626.2101195307412.3198804692597
342641.652661.269669377-19.6196693769971
352645.642679.19290277226-33.5529027722582
362659.812672.03585841083-12.2258584108349
372720.252691.8921555187628.3578444812356
382735.72747.2563338494-11.5563338493994
392745.882746.70998570625-0.829985706248408
402756.762774.57088577011-17.8108857701141
412767.632783.4417800712-15.8117800712025
422794.832814.78098141727-19.9509814172734
432799.432841.05813540519-41.6281354051944
442803.472795.669199731527.80080026847736
452811.72814.20672788461-2.50672788461179
462833.182822.0700225587711.1099774412291
472845.262861.08132805224-15.8213280522368
482848.962863.58843176147-14.6284317614727
492849.272872.76143669066-23.4914366906628
502863.362863.39261459914-0.0326145991393787
512882.62862.5093025208120.0906974791924
522892.632901.28746870983-8.65746870983185
532897.062910.12097181938-13.0609718193814
542915.022935.26438043811-20.2443804381132
552921.442952.27548747251-30.8354874725128
562962.342909.6646858725952.6753141274071
572981.852969.0460186526412.8039813473647
582987.12989.54854530582-2.44854530581961
592995.553011.12617189540-15.5761718953950
603012.613010.025039723012.58496027698720
613013.243034.08619025093-20.8461902509262
623030.293025.272204018335.01779598166922
633032.63027.797249979114.80275002089047
643032.933048.2882049009-15.3582049009001
653045.783046.82683975347-1.04683975347189
663047.033081.45682159600-34.4268215960042
673061.263080.49886040108-19.2388604010766
683080.583046.7275673709833.8524326290240
693097.313082.8578696270614.4521303729357
703106.223100.726713268435.49328673156879
713110.523126.66938832531-16.1493883253056
723119.313121.36736797455-2.05736797454892
733142.953136.74638860566.20361139439774
743161.693153.343790503738.3462094962697
753257.163157.8543215409999.3056784590049
763277.013279.89492063266-2.88492063265585
773295.323299.06089065854-3.74089065853696
783363.993338.9117039499725.0782960500283
793494.173410.6564019444283.513598055581
803504.373501.957117917412.41288208259266
813570.123526.1763252698343.9436747301711
823667.033595.6833265415171.3466734584918
833674.43715.47223822989-41.0722382298923
843701.613711.02765319088-9.4176531908829
853720.983744.17325307642-23.1932530764170
863801.063753.8909026981247.1690973018781
873801.063823.18799586546-22.1279958654600
883813.063838.97813201634-25.9181320163420
893844.493848.24929294697-3.75929294696743
903857.623901.21847254668-43.5984725466801
913862.273911.32628380137-49.056283801367
923895.513865.3279027230430.1820972769592
933917.963915.052365260752.90763473924517
943970.13937.6163283816132.4836716183877
954105.184009.1851167542495.9948832457599
964116.684144.6188781948-27.9388781948019
974138.524160.41022757995-21.8902275799446
984199.754172.713555312827.0364446872036
994202.524221.37334099216-18.8533409921629
1004290.894240.224189712750.6658102873016
1014296.494332.6642090033-36.1742090032985
1024356.984356.925704112130.0542958878668287
1034435.234418.2688576472016.9611423528031
1044443.914451.73127605517-7.82127605517326
1054502.644473.5219301323429.1180698676644
1064562.844534.6927653184228.147234681579
1074591.274613.93657977049-22.6665797704927
1084621.44632.18598563249-10.7859856324922
1094696.964668.1301096814528.8298903185523

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2042 & 1916.84015491453 & 125.159845085471 \tabularnewline
14 & 2061.41 & 2073.58958995384 & -12.1795899538370 \tabularnewline
15 & 2065.81 & 2076.94791128253 & -11.1379112825284 \tabularnewline
16 & 2091.48 & 2098.11370925227 & -6.63370925227082 \tabularnewline
17 & 2120.88 & 2122.76687474917 & -1.8868747491656 \tabularnewline
18 & 2174.56 & 2173.87228118096 & 0.687718819038764 \tabularnewline
19 & 2196.72 & 2228.46166782001 & -31.7416678200075 \tabularnewline
20 & 2197.82 & 2201.51041865307 & -3.69041865306599 \tabularnewline
21 & 2214.95 & 2216.08779600847 & -1.13779600846965 \tabularnewline
22 & 2304.98 & 2232.97261973494 & 72.0073802650613 \tabularnewline
23 & 2350.44 & 2345.94018669570 & 4.49981330430319 \tabularnewline
24 & 2407.6 & 2383.63133127356 & 23.9686687264434 \tabularnewline
25 & 2408.64 & 2449.6908537132 & -41.0508537132 \tabularnewline
26 & 2440.25 & 2439.49316711785 & 0.756832882145773 \tabularnewline
27 & 2448.05 & 2456.19993946514 & -8.14993946514005 \tabularnewline
28 & 2452.62 & 2481.03099927123 & -28.4109992712279 \tabularnewline
29 & 2472.81 & 2482.6508520416 & -9.8408520415992 \tabularnewline
30 & 2497.84 & 2523.84013179223 & -26.0001317922256 \tabularnewline
31 & 2555.28 & 2547.41026306546 & 7.86973693454229 \tabularnewline
32 & 2604.42 & 2559.25557784475 & 45.1644221552451 \tabularnewline
33 & 2638.53 & 2626.21011953074 & 12.3198804692597 \tabularnewline
34 & 2641.65 & 2661.269669377 & -19.6196693769971 \tabularnewline
35 & 2645.64 & 2679.19290277226 & -33.5529027722582 \tabularnewline
36 & 2659.81 & 2672.03585841083 & -12.2258584108349 \tabularnewline
37 & 2720.25 & 2691.89215551876 & 28.3578444812356 \tabularnewline
38 & 2735.7 & 2747.2563338494 & -11.5563338493994 \tabularnewline
39 & 2745.88 & 2746.70998570625 & -0.829985706248408 \tabularnewline
40 & 2756.76 & 2774.57088577011 & -17.8108857701141 \tabularnewline
41 & 2767.63 & 2783.4417800712 & -15.8117800712025 \tabularnewline
42 & 2794.83 & 2814.78098141727 & -19.9509814172734 \tabularnewline
43 & 2799.43 & 2841.05813540519 & -41.6281354051944 \tabularnewline
44 & 2803.47 & 2795.66919973152 & 7.80080026847736 \tabularnewline
45 & 2811.7 & 2814.20672788461 & -2.50672788461179 \tabularnewline
46 & 2833.18 & 2822.07002255877 & 11.1099774412291 \tabularnewline
47 & 2845.26 & 2861.08132805224 & -15.8213280522368 \tabularnewline
48 & 2848.96 & 2863.58843176147 & -14.6284317614727 \tabularnewline
49 & 2849.27 & 2872.76143669066 & -23.4914366906628 \tabularnewline
50 & 2863.36 & 2863.39261459914 & -0.0326145991393787 \tabularnewline
51 & 2882.6 & 2862.50930252081 & 20.0906974791924 \tabularnewline
52 & 2892.63 & 2901.28746870983 & -8.65746870983185 \tabularnewline
53 & 2897.06 & 2910.12097181938 & -13.0609718193814 \tabularnewline
54 & 2915.02 & 2935.26438043811 & -20.2443804381132 \tabularnewline
55 & 2921.44 & 2952.27548747251 & -30.8354874725128 \tabularnewline
56 & 2962.34 & 2909.66468587259 & 52.6753141274071 \tabularnewline
57 & 2981.85 & 2969.04601865264 & 12.8039813473647 \tabularnewline
58 & 2987.1 & 2989.54854530582 & -2.44854530581961 \tabularnewline
59 & 2995.55 & 3011.12617189540 & -15.5761718953950 \tabularnewline
60 & 3012.61 & 3010.02503972301 & 2.58496027698720 \tabularnewline
61 & 3013.24 & 3034.08619025093 & -20.8461902509262 \tabularnewline
62 & 3030.29 & 3025.27220401833 & 5.01779598166922 \tabularnewline
63 & 3032.6 & 3027.79724997911 & 4.80275002089047 \tabularnewline
64 & 3032.93 & 3048.2882049009 & -15.3582049009001 \tabularnewline
65 & 3045.78 & 3046.82683975347 & -1.04683975347189 \tabularnewline
66 & 3047.03 & 3081.45682159600 & -34.4268215960042 \tabularnewline
67 & 3061.26 & 3080.49886040108 & -19.2388604010766 \tabularnewline
68 & 3080.58 & 3046.72756737098 & 33.8524326290240 \tabularnewline
69 & 3097.31 & 3082.85786962706 & 14.4521303729357 \tabularnewline
70 & 3106.22 & 3100.72671326843 & 5.49328673156879 \tabularnewline
71 & 3110.52 & 3126.66938832531 & -16.1493883253056 \tabularnewline
72 & 3119.31 & 3121.36736797455 & -2.05736797454892 \tabularnewline
73 & 3142.95 & 3136.7463886056 & 6.20361139439774 \tabularnewline
74 & 3161.69 & 3153.34379050373 & 8.3462094962697 \tabularnewline
75 & 3257.16 & 3157.85432154099 & 99.3056784590049 \tabularnewline
76 & 3277.01 & 3279.89492063266 & -2.88492063265585 \tabularnewline
77 & 3295.32 & 3299.06089065854 & -3.74089065853696 \tabularnewline
78 & 3363.99 & 3338.91170394997 & 25.0782960500283 \tabularnewline
79 & 3494.17 & 3410.65640194442 & 83.513598055581 \tabularnewline
80 & 3504.37 & 3501.95711791741 & 2.41288208259266 \tabularnewline
81 & 3570.12 & 3526.17632526983 & 43.9436747301711 \tabularnewline
82 & 3667.03 & 3595.68332654151 & 71.3466734584918 \tabularnewline
83 & 3674.4 & 3715.47223822989 & -41.0722382298923 \tabularnewline
84 & 3701.61 & 3711.02765319088 & -9.4176531908829 \tabularnewline
85 & 3720.98 & 3744.17325307642 & -23.1932530764170 \tabularnewline
86 & 3801.06 & 3753.89090269812 & 47.1690973018781 \tabularnewline
87 & 3801.06 & 3823.18799586546 & -22.1279958654600 \tabularnewline
88 & 3813.06 & 3838.97813201634 & -25.9181320163420 \tabularnewline
89 & 3844.49 & 3848.24929294697 & -3.75929294696743 \tabularnewline
90 & 3857.62 & 3901.21847254668 & -43.5984725466801 \tabularnewline
91 & 3862.27 & 3911.32628380137 & -49.056283801367 \tabularnewline
92 & 3895.51 & 3865.32790272304 & 30.1820972769592 \tabularnewline
93 & 3917.96 & 3915.05236526075 & 2.90763473924517 \tabularnewline
94 & 3970.1 & 3937.61632838161 & 32.4836716183877 \tabularnewline
95 & 4105.18 & 4009.18511675424 & 95.9948832457599 \tabularnewline
96 & 4116.68 & 4144.6188781948 & -27.9388781948019 \tabularnewline
97 & 4138.52 & 4160.41022757995 & -21.8902275799446 \tabularnewline
98 & 4199.75 & 4172.7135553128 & 27.0364446872036 \tabularnewline
99 & 4202.52 & 4221.37334099216 & -18.8533409921629 \tabularnewline
100 & 4290.89 & 4240.2241897127 & 50.6658102873016 \tabularnewline
101 & 4296.49 & 4332.6642090033 & -36.1742090032985 \tabularnewline
102 & 4356.98 & 4356.92570411213 & 0.0542958878668287 \tabularnewline
103 & 4435.23 & 4418.26885764720 & 16.9611423528031 \tabularnewline
104 & 4443.91 & 4451.73127605517 & -7.82127605517326 \tabularnewline
105 & 4502.64 & 4473.52193013234 & 29.1180698676644 \tabularnewline
106 & 4562.84 & 4534.69276531842 & 28.147234681579 \tabularnewline
107 & 4591.27 & 4613.93657977049 & -22.6665797704927 \tabularnewline
108 & 4621.4 & 4632.18598563249 & -10.7859856324922 \tabularnewline
109 & 4696.96 & 4668.13010968145 & 28.8298903185523 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41162&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]2042[/C][C]1916.84015491453[/C][C]125.159845085471[/C][/ROW]
[ROW][C]14[/C][C]2061.41[/C][C]2073.58958995384[/C][C]-12.1795899538370[/C][/ROW]
[ROW][C]15[/C][C]2065.81[/C][C]2076.94791128253[/C][C]-11.1379112825284[/C][/ROW]
[ROW][C]16[/C][C]2091.48[/C][C]2098.11370925227[/C][C]-6.63370925227082[/C][/ROW]
[ROW][C]17[/C][C]2120.88[/C][C]2122.76687474917[/C][C]-1.8868747491656[/C][/ROW]
[ROW][C]18[/C][C]2174.56[/C][C]2173.87228118096[/C][C]0.687718819038764[/C][/ROW]
[ROW][C]19[/C][C]2196.72[/C][C]2228.46166782001[/C][C]-31.7416678200075[/C][/ROW]
[ROW][C]20[/C][C]2197.82[/C][C]2201.51041865307[/C][C]-3.69041865306599[/C][/ROW]
[ROW][C]21[/C][C]2214.95[/C][C]2216.08779600847[/C][C]-1.13779600846965[/C][/ROW]
[ROW][C]22[/C][C]2304.98[/C][C]2232.97261973494[/C][C]72.0073802650613[/C][/ROW]
[ROW][C]23[/C][C]2350.44[/C][C]2345.94018669570[/C][C]4.49981330430319[/C][/ROW]
[ROW][C]24[/C][C]2407.6[/C][C]2383.63133127356[/C][C]23.9686687264434[/C][/ROW]
[ROW][C]25[/C][C]2408.64[/C][C]2449.6908537132[/C][C]-41.0508537132[/C][/ROW]
[ROW][C]26[/C][C]2440.25[/C][C]2439.49316711785[/C][C]0.756832882145773[/C][/ROW]
[ROW][C]27[/C][C]2448.05[/C][C]2456.19993946514[/C][C]-8.14993946514005[/C][/ROW]
[ROW][C]28[/C][C]2452.62[/C][C]2481.03099927123[/C][C]-28.4109992712279[/C][/ROW]
[ROW][C]29[/C][C]2472.81[/C][C]2482.6508520416[/C][C]-9.8408520415992[/C][/ROW]
[ROW][C]30[/C][C]2497.84[/C][C]2523.84013179223[/C][C]-26.0001317922256[/C][/ROW]
[ROW][C]31[/C][C]2555.28[/C][C]2547.41026306546[/C][C]7.86973693454229[/C][/ROW]
[ROW][C]32[/C][C]2604.42[/C][C]2559.25557784475[/C][C]45.1644221552451[/C][/ROW]
[ROW][C]33[/C][C]2638.53[/C][C]2626.21011953074[/C][C]12.3198804692597[/C][/ROW]
[ROW][C]34[/C][C]2641.65[/C][C]2661.269669377[/C][C]-19.6196693769971[/C][/ROW]
[ROW][C]35[/C][C]2645.64[/C][C]2679.19290277226[/C][C]-33.5529027722582[/C][/ROW]
[ROW][C]36[/C][C]2659.81[/C][C]2672.03585841083[/C][C]-12.2258584108349[/C][/ROW]
[ROW][C]37[/C][C]2720.25[/C][C]2691.89215551876[/C][C]28.3578444812356[/C][/ROW]
[ROW][C]38[/C][C]2735.7[/C][C]2747.2563338494[/C][C]-11.5563338493994[/C][/ROW]
[ROW][C]39[/C][C]2745.88[/C][C]2746.70998570625[/C][C]-0.829985706248408[/C][/ROW]
[ROW][C]40[/C][C]2756.76[/C][C]2774.57088577011[/C][C]-17.8108857701141[/C][/ROW]
[ROW][C]41[/C][C]2767.63[/C][C]2783.4417800712[/C][C]-15.8117800712025[/C][/ROW]
[ROW][C]42[/C][C]2794.83[/C][C]2814.78098141727[/C][C]-19.9509814172734[/C][/ROW]
[ROW][C]43[/C][C]2799.43[/C][C]2841.05813540519[/C][C]-41.6281354051944[/C][/ROW]
[ROW][C]44[/C][C]2803.47[/C][C]2795.66919973152[/C][C]7.80080026847736[/C][/ROW]
[ROW][C]45[/C][C]2811.7[/C][C]2814.20672788461[/C][C]-2.50672788461179[/C][/ROW]
[ROW][C]46[/C][C]2833.18[/C][C]2822.07002255877[/C][C]11.1099774412291[/C][/ROW]
[ROW][C]47[/C][C]2845.26[/C][C]2861.08132805224[/C][C]-15.8213280522368[/C][/ROW]
[ROW][C]48[/C][C]2848.96[/C][C]2863.58843176147[/C][C]-14.6284317614727[/C][/ROW]
[ROW][C]49[/C][C]2849.27[/C][C]2872.76143669066[/C][C]-23.4914366906628[/C][/ROW]
[ROW][C]50[/C][C]2863.36[/C][C]2863.39261459914[/C][C]-0.0326145991393787[/C][/ROW]
[ROW][C]51[/C][C]2882.6[/C][C]2862.50930252081[/C][C]20.0906974791924[/C][/ROW]
[ROW][C]52[/C][C]2892.63[/C][C]2901.28746870983[/C][C]-8.65746870983185[/C][/ROW]
[ROW][C]53[/C][C]2897.06[/C][C]2910.12097181938[/C][C]-13.0609718193814[/C][/ROW]
[ROW][C]54[/C][C]2915.02[/C][C]2935.26438043811[/C][C]-20.2443804381132[/C][/ROW]
[ROW][C]55[/C][C]2921.44[/C][C]2952.27548747251[/C][C]-30.8354874725128[/C][/ROW]
[ROW][C]56[/C][C]2962.34[/C][C]2909.66468587259[/C][C]52.6753141274071[/C][/ROW]
[ROW][C]57[/C][C]2981.85[/C][C]2969.04601865264[/C][C]12.8039813473647[/C][/ROW]
[ROW][C]58[/C][C]2987.1[/C][C]2989.54854530582[/C][C]-2.44854530581961[/C][/ROW]
[ROW][C]59[/C][C]2995.55[/C][C]3011.12617189540[/C][C]-15.5761718953950[/C][/ROW]
[ROW][C]60[/C][C]3012.61[/C][C]3010.02503972301[/C][C]2.58496027698720[/C][/ROW]
[ROW][C]61[/C][C]3013.24[/C][C]3034.08619025093[/C][C]-20.8461902509262[/C][/ROW]
[ROW][C]62[/C][C]3030.29[/C][C]3025.27220401833[/C][C]5.01779598166922[/C][/ROW]
[ROW][C]63[/C][C]3032.6[/C][C]3027.79724997911[/C][C]4.80275002089047[/C][/ROW]
[ROW][C]64[/C][C]3032.93[/C][C]3048.2882049009[/C][C]-15.3582049009001[/C][/ROW]
[ROW][C]65[/C][C]3045.78[/C][C]3046.82683975347[/C][C]-1.04683975347189[/C][/ROW]
[ROW][C]66[/C][C]3047.03[/C][C]3081.45682159600[/C][C]-34.4268215960042[/C][/ROW]
[ROW][C]67[/C][C]3061.26[/C][C]3080.49886040108[/C][C]-19.2388604010766[/C][/ROW]
[ROW][C]68[/C][C]3080.58[/C][C]3046.72756737098[/C][C]33.8524326290240[/C][/ROW]
[ROW][C]69[/C][C]3097.31[/C][C]3082.85786962706[/C][C]14.4521303729357[/C][/ROW]
[ROW][C]70[/C][C]3106.22[/C][C]3100.72671326843[/C][C]5.49328673156879[/C][/ROW]
[ROW][C]71[/C][C]3110.52[/C][C]3126.66938832531[/C][C]-16.1493883253056[/C][/ROW]
[ROW][C]72[/C][C]3119.31[/C][C]3121.36736797455[/C][C]-2.05736797454892[/C][/ROW]
[ROW][C]73[/C][C]3142.95[/C][C]3136.7463886056[/C][C]6.20361139439774[/C][/ROW]
[ROW][C]74[/C][C]3161.69[/C][C]3153.34379050373[/C][C]8.3462094962697[/C][/ROW]
[ROW][C]75[/C][C]3257.16[/C][C]3157.85432154099[/C][C]99.3056784590049[/C][/ROW]
[ROW][C]76[/C][C]3277.01[/C][C]3279.89492063266[/C][C]-2.88492063265585[/C][/ROW]
[ROW][C]77[/C][C]3295.32[/C][C]3299.06089065854[/C][C]-3.74089065853696[/C][/ROW]
[ROW][C]78[/C][C]3363.99[/C][C]3338.91170394997[/C][C]25.0782960500283[/C][/ROW]
[ROW][C]79[/C][C]3494.17[/C][C]3410.65640194442[/C][C]83.513598055581[/C][/ROW]
[ROW][C]80[/C][C]3504.37[/C][C]3501.95711791741[/C][C]2.41288208259266[/C][/ROW]
[ROW][C]81[/C][C]3570.12[/C][C]3526.17632526983[/C][C]43.9436747301711[/C][/ROW]
[ROW][C]82[/C][C]3667.03[/C][C]3595.68332654151[/C][C]71.3466734584918[/C][/ROW]
[ROW][C]83[/C][C]3674.4[/C][C]3715.47223822989[/C][C]-41.0722382298923[/C][/ROW]
[ROW][C]84[/C][C]3701.61[/C][C]3711.02765319088[/C][C]-9.4176531908829[/C][/ROW]
[ROW][C]85[/C][C]3720.98[/C][C]3744.17325307642[/C][C]-23.1932530764170[/C][/ROW]
[ROW][C]86[/C][C]3801.06[/C][C]3753.89090269812[/C][C]47.1690973018781[/C][/ROW]
[ROW][C]87[/C][C]3801.06[/C][C]3823.18799586546[/C][C]-22.1279958654600[/C][/ROW]
[ROW][C]88[/C][C]3813.06[/C][C]3838.97813201634[/C][C]-25.9181320163420[/C][/ROW]
[ROW][C]89[/C][C]3844.49[/C][C]3848.24929294697[/C][C]-3.75929294696743[/C][/ROW]
[ROW][C]90[/C][C]3857.62[/C][C]3901.21847254668[/C][C]-43.5984725466801[/C][/ROW]
[ROW][C]91[/C][C]3862.27[/C][C]3911.32628380137[/C][C]-49.056283801367[/C][/ROW]
[ROW][C]92[/C][C]3895.51[/C][C]3865.32790272304[/C][C]30.1820972769592[/C][/ROW]
[ROW][C]93[/C][C]3917.96[/C][C]3915.05236526075[/C][C]2.90763473924517[/C][/ROW]
[ROW][C]94[/C][C]3970.1[/C][C]3937.61632838161[/C][C]32.4836716183877[/C][/ROW]
[ROW][C]95[/C][C]4105.18[/C][C]4009.18511675424[/C][C]95.9948832457599[/C][/ROW]
[ROW][C]96[/C][C]4116.68[/C][C]4144.6188781948[/C][C]-27.9388781948019[/C][/ROW]
[ROW][C]97[/C][C]4138.52[/C][C]4160.41022757995[/C][C]-21.8902275799446[/C][/ROW]
[ROW][C]98[/C][C]4199.75[/C][C]4172.7135553128[/C][C]27.0364446872036[/C][/ROW]
[ROW][C]99[/C][C]4202.52[/C][C]4221.37334099216[/C][C]-18.8533409921629[/C][/ROW]
[ROW][C]100[/C][C]4290.89[/C][C]4240.2241897127[/C][C]50.6658102873016[/C][/ROW]
[ROW][C]101[/C][C]4296.49[/C][C]4332.6642090033[/C][C]-36.1742090032985[/C][/ROW]
[ROW][C]102[/C][C]4356.98[/C][C]4356.92570411213[/C][C]0.0542958878668287[/C][/ROW]
[ROW][C]103[/C][C]4435.23[/C][C]4418.26885764720[/C][C]16.9611423528031[/C][/ROW]
[ROW][C]104[/C][C]4443.91[/C][C]4451.73127605517[/C][C]-7.82127605517326[/C][/ROW]
[ROW][C]105[/C][C]4502.64[/C][C]4473.52193013234[/C][C]29.1180698676644[/C][/ROW]
[ROW][C]106[/C][C]4562.84[/C][C]4534.69276531842[/C][C]28.147234681579[/C][/ROW]
[ROW][C]107[/C][C]4591.27[/C][C]4613.93657977049[/C][C]-22.6665797704927[/C][/ROW]
[ROW][C]108[/C][C]4621.4[/C][C]4632.18598563249[/C][C]-10.7859856324922[/C][/ROW]
[ROW][C]109[/C][C]4696.96[/C][C]4668.13010968145[/C][C]28.8298903185523[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41162&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41162&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
1320421916.84015491453125.159845085471
142061.412073.58958995384-12.1795899538370
152065.812076.94791128253-11.1379112825284
162091.482098.11370925227-6.63370925227082
172120.882122.76687474917-1.8868747491656
182174.562173.872281180960.687718819038764
192196.722228.46166782001-31.7416678200075
202197.822201.51041865307-3.69041865306599
212214.952216.08779600847-1.13779600846965
222304.982232.9726197349472.0073802650613
232350.442345.940186695704.49981330430319
242407.62383.6313312735623.9686687264434
252408.642449.6908537132-41.0508537132
262440.252439.493167117850.756832882145773
272448.052456.19993946514-8.14993946514005
282452.622481.03099927123-28.4109992712279
292472.812482.6508520416-9.8408520415992
302497.842523.84013179223-26.0001317922256
312555.282547.410263065467.86973693454229
322604.422559.2555778447545.1644221552451
332638.532626.2101195307412.3198804692597
342641.652661.269669377-19.6196693769971
352645.642679.19290277226-33.5529027722582
362659.812672.03585841083-12.2258584108349
372720.252691.8921555187628.3578444812356
382735.72747.2563338494-11.5563338493994
392745.882746.70998570625-0.829985706248408
402756.762774.57088577011-17.8108857701141
412767.632783.4417800712-15.8117800712025
422794.832814.78098141727-19.9509814172734
432799.432841.05813540519-41.6281354051944
442803.472795.669199731527.80080026847736
452811.72814.20672788461-2.50672788461179
462833.182822.0700225587711.1099774412291
472845.262861.08132805224-15.8213280522368
482848.962863.58843176147-14.6284317614727
492849.272872.76143669066-23.4914366906628
502863.362863.39261459914-0.0326145991393787
512882.62862.5093025208120.0906974791924
522892.632901.28746870983-8.65746870983185
532897.062910.12097181938-13.0609718193814
542915.022935.26438043811-20.2443804381132
552921.442952.27548747251-30.8354874725128
562962.342909.6646858725952.6753141274071
572981.852969.0460186526412.8039813473647
582987.12989.54854530582-2.44854530581961
592995.553011.12617189540-15.5761718953950
603012.613010.025039723012.58496027698720
613013.243034.08619025093-20.8461902509262
623030.293025.272204018335.01779598166922
633032.63027.797249979114.80275002089047
643032.933048.2882049009-15.3582049009001
653045.783046.82683975347-1.04683975347189
663047.033081.45682159600-34.4268215960042
673061.263080.49886040108-19.2388604010766
683080.583046.7275673709833.8524326290240
693097.313082.8578696270614.4521303729357
703106.223100.726713268435.49328673156879
713110.523126.66938832531-16.1493883253056
723119.313121.36736797455-2.05736797454892
733142.953136.74638860566.20361139439774
743161.693153.343790503738.3462094962697
753257.163157.8543215409999.3056784590049
763277.013279.89492063266-2.88492063265585
773295.323299.06089065854-3.74089065853696
783363.993338.9117039499725.0782960500283
793494.173410.6564019444283.513598055581
803504.373501.957117917412.41288208259266
813570.123526.1763252698343.9436747301711
823667.033595.6833265415171.3466734584918
833674.43715.47223822989-41.0722382298923
843701.613711.02765319088-9.4176531908829
853720.983744.17325307642-23.1932530764170
863801.063753.8909026981247.1690973018781
873801.063823.18799586546-22.1279958654600
883813.063838.97813201634-25.9181320163420
893844.493848.24929294697-3.75929294696743
903857.623901.21847254668-43.5984725466801
913862.273911.32628380137-49.056283801367
923895.513865.3279027230430.1820972769592
933917.963915.052365260752.90763473924517
943970.13937.6163283816132.4836716183877
954105.184009.1851167542495.9948832457599
964116.684144.6188781948-27.9388781948019
974138.524160.41022757995-21.8902275799446
984199.754172.713555312827.0364446872036
994202.524221.37334099216-18.8533409921629
1004290.894240.224189712750.6658102873016
1014296.494332.6642090033-36.1742090032985
1024356.984356.925704112130.0542958878668287
1034435.234418.2688576472016.9611423528031
1044443.914451.73127605517-7.82127605517326
1054502.644473.5219301323429.1180698676644
1064562.844534.6927653184228.147234681579
1074591.274613.93657977049-22.6665797704927
1084621.44632.18598563249-10.7859856324922
1094696.964668.1301096814528.8298903185523






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1104738.656194614054675.74028158354801.5721076446
1114765.381972561444672.37202726424858.39191785867
1124809.862333842154690.951829201734928.77283848258
1134853.914778456214710.780640808814997.0489161036
1144919.840139736924753.238025880225086.44225359363
1154986.613834350984796.854113290685176.37355541127
1165007.094195631694794.239225699595219.9491655638
1175041.379556912414805.341173415315277.41794040952
1185075.520751526464816.114145610325334.92735744261
1195126.206946140524843.182849939365409.23104234167
1205168.724807421234861.789849042075475.6597658004
1215218.014335368624886.844483471115549.18418726612

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
110 & 4738.65619461405 & 4675.7402815835 & 4801.5721076446 \tabularnewline
111 & 4765.38197256144 & 4672.3720272642 & 4858.39191785867 \tabularnewline
112 & 4809.86233384215 & 4690.95182920173 & 4928.77283848258 \tabularnewline
113 & 4853.91477845621 & 4710.78064080881 & 4997.0489161036 \tabularnewline
114 & 4919.84013973692 & 4753.23802588022 & 5086.44225359363 \tabularnewline
115 & 4986.61383435098 & 4796.85411329068 & 5176.37355541127 \tabularnewline
116 & 5007.09419563169 & 4794.23922569959 & 5219.9491655638 \tabularnewline
117 & 5041.37955691241 & 4805.34117341531 & 5277.41794040952 \tabularnewline
118 & 5075.52075152646 & 4816.11414561032 & 5334.92735744261 \tabularnewline
119 & 5126.20694614052 & 4843.18284993936 & 5409.23104234167 \tabularnewline
120 & 5168.72480742123 & 4861.78984904207 & 5475.6597658004 \tabularnewline
121 & 5218.01433536862 & 4886.84448347111 & 5549.18418726612 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41162&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]110[/C][C]4738.65619461405[/C][C]4675.7402815835[/C][C]4801.5721076446[/C][/ROW]
[ROW][C]111[/C][C]4765.38197256144[/C][C]4672.3720272642[/C][C]4858.39191785867[/C][/ROW]
[ROW][C]112[/C][C]4809.86233384215[/C][C]4690.95182920173[/C][C]4928.77283848258[/C][/ROW]
[ROW][C]113[/C][C]4853.91477845621[/C][C]4710.78064080881[/C][C]4997.0489161036[/C][/ROW]
[ROW][C]114[/C][C]4919.84013973692[/C][C]4753.23802588022[/C][C]5086.44225359363[/C][/ROW]
[ROW][C]115[/C][C]4986.61383435098[/C][C]4796.85411329068[/C][C]5176.37355541127[/C][/ROW]
[ROW][C]116[/C][C]5007.09419563169[/C][C]4794.23922569959[/C][C]5219.9491655638[/C][/ROW]
[ROW][C]117[/C][C]5041.37955691241[/C][C]4805.34117341531[/C][C]5277.41794040952[/C][/ROW]
[ROW][C]118[/C][C]5075.52075152646[/C][C]4816.11414561032[/C][C]5334.92735744261[/C][/ROW]
[ROW][C]119[/C][C]5126.20694614052[/C][C]4843.18284993936[/C][C]5409.23104234167[/C][/ROW]
[ROW][C]120[/C][C]5168.72480742123[/C][C]4861.78984904207[/C][C]5475.6597658004[/C][/ROW]
[ROW][C]121[/C][C]5218.01433536862[/C][C]4886.84448347111[/C][C]5549.18418726612[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41162&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41162&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
1104738.656194614054675.74028158354801.5721076446
1114765.381972561444672.37202726424858.39191785867
1124809.862333842154690.951829201734928.77283848258
1134853.914778456214710.780640808814997.0489161036
1144919.840139736924753.238025880225086.44225359363
1154986.613834350984796.854113290685176.37355541127
1165007.094195631694794.239225699595219.9491655638
1175041.379556912414805.341173415315277.41794040952
1185075.520751526464816.114145610325334.92735744261
1195126.206946140524843.182849939365409.23104234167
1205168.724807421234861.789849042075475.6597658004
1215218.014335368624886.844483471115549.18418726612


Figures (Output of Computation)

Input Parameters & R Code

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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')