Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 11 Dec 2016 12:58:00 +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/2016/Dec/11/t1481457625et2o5iu93wnivvh.htm/, Retrieved Thu, 02 May 2024 06:48:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298768, Retrieved Thu, 02 May 2024 06:48:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [f1 n2131] [2016-12-11 11:58:00] [6e17bb30248b72d8119c893128a7a697] [Current]
Feedback Forum

Post a new message
Dataseries X:
7149.3
7566.6
9954.9
5566.2
4397.4
3970.5
5805.3
7112.1
5622.6
11673.3
13034.4
11737.8
4838.7
6823.2
7767.3
7048.5
5748.6
3444.3
5168.1
4015.8
4089.3
5661.9
10739.4
11097
3806.1
7146.9
10894.2
7432.5
7243.5
5851.2
5562.3
3854.7
4398.3
6478.8
8766
9057.6
6097.5
4467.6
7311.3
6724.2
6065.1
5462.4
4256.1
3728.4
6192.9
8603.1
11808
7562.7
4309.5
5360.4
8452.5
5682
7342.8
5065.5
3253.5
4106.7
3375.3
10135.2
12551.4
6875.7
3291.6
5217
6253.8
5981.1
4576.5
4453.5
3896.7
4905
3596.4
7035.9
11962.8
8205.9
5713.2
5465.7
5896.2
4408.8
3602.7
3926.7
2018.1
2497.2
5327.1
9250.8
13317
10486.8
4709.7
6599.1
6536.7
7362
2150.1
1936.5
2772.3
5329.8
5593.2
6538.8
11617.8
12151.5
2936.7
4336.8
6644.1
6252.3
3869.7
3050.7
2227.8
3222.9
3013.2
4480.5
9028.2
14435.1
8109.9
3454.8
5867.7
5633.4
4391.1
2821.2
2640.9
2130.6
2944.8
3823.2
7311.9
8823.6
9800.7
5129.1
6377.4
7721.1
4753.5
3099.6




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298768&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298768&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298768&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0105482613594323
beta0.455433621753624
gamma0.502410055977054

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0105482613594323 \tabularnewline
beta & 0.455433621753624 \tabularnewline
gamma & 0.502410055977054 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298768&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]0.0105482613594323[/C][/ROW]
[ROW][C]beta[/C][C]0.455433621753624[/C][/ROW]
[ROW][C]gamma[/C][C]0.502410055977054[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298768&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298768&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
alpha0.0105482613594323
beta0.455433621753624
gamma0.502410055977054







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134838.74875.37838439777-36.6783843977692
146823.26925.88918677376-102.689186773765
157767.37984.84371180026-217.543711800257
167048.57470.22052097712-421.720520977125
175748.66319.99101818998-571.39101818998
183444.33797.41753277335-353.11753277335
195168.15226.53567109208-58.4356710920747
204015.86405.46507444684-2389.66507444684
214089.35033.58387863286-944.283878632857
225661.910267.5358606368-4605.63586063683
2310739.410983.8855452296-244.485545229607
24110979620.721872650281476.27812734972
253806.13893.63014108503-87.5301410850307
267146.95455.776577052971691.12342294703
2710894.26218.346566385684675.85343361432
287432.55750.334865093941682.16513490606
297243.54781.776828125072461.72317187493
305851.22886.417552411842964.78244758816
315562.34212.906354929521349.39364507048
323854.74269.62563770525-414.925637705254
334398.33780.57674892181617.723251078193
346478.86695.32364442265-216.523644422649
3587669288.52126265275-522.521262652754
369057.68968.2350792224389.364920777567
376097.53373.383649764212724.11635023579
384467.65660.69965993176-1193.09965993176
397311.37743.08616433384-431.786164333839
406724.25999.69603714074724.503962859262
416065.15517.67525743927547.424742560733
425462.44015.604190068491446.79580993151
434256.14508.10485422444-252.00485422444
443728.43753.90465388602-25.5046538860211
456192.93798.132408003192394.76759199681
468603.16196.368432267132406.73156773287
47118088609.750736549443198.24926345056
487562.78732.68311797146-1169.98311797146
494309.54612.43873931359-302.938739313594
505360.44942.45443415156417.945565848438
518452.57427.442463393271025.05753660673
5256826344.60356465299-662.603564652987
537342.85809.072004983721533.72799501628
545065.54798.80281907207266.697180927933
553253.54463.35020687058-1209.85020687058
564106.73825.86000785262280.839992147379
573375.35132.63705020331-1757.33705020331
5810135.27551.85223467772583.3477653223
5912551.410434.63009080912116.76990919094
606875.78337.57670007914-1461.87670007914
613291.64566.4495204939-1274.8495204939
6252175258.4102378522-41.4102378521957
636253.88090.86731170113-1837.06731170113
645981.16094.36141341515-113.261413415147
654576.56649.64758311146-2073.14758311146
664453.54938.25988276689-484.759882766891
673896.73838.6083546471958.0916453528107
6849053939.23116646663965.768833533372
693596.44221.97136720796-625.571367207963
707035.98759.19649037704-1723.29649037704
7111962.811271.2631906789691.536809321064
728205.97415.84098986306790.05901013694
735713.23826.164870813711887.03512918629
745465.75137.56646712288328.133532877124
755896.27042.51196164652-1146.31196164652
764408.85931.27152922205-1522.47152922205
773602.75497.16669398044-1894.46669398044
783926.74591.0985953089-664.398595308902
792018.13773.22421297325-1755.12421297325
802497.24272.61203821085-1775.41203821085
815327.13729.288523173281597.81147682672
829250.87548.42520635851702.3747936415
831331711121.66076070652195.33923929346
8410486.87475.556369373873011.24363062612
854709.74570.18349021057139.516509789433
866599.15053.146484037311545.95351596269
876536.76177.84734954118358.852650458818
8873624948.314745763542413.68525423646
892150.14404.10971330494-2254.00971330494
901936.54125.46737299013-2188.96737299013
912772.32795.47847859651-23.1784785965051
925329.83293.868643173322035.93135682668
935593.24480.967255828861112.23274417114
946538.88364.65129713321-1825.85129713321
9511617.812175.1569604801-557.356960480143
9612151.58952.49098732663199.0090126734
972936.74647.55490432139-1710.85490432139
984336.85815.33443806226-1478.53443806226
996644.16308.9759839141335.1240160859
1006252.36090.66233846669161.637661533314
1013869.73224.35237951241645.347620487592
1023050.73005.4681293557845.2318706442165
1032227.82784.54780619943-556.747806199426
1043222.94300.41486660382-1077.51486660382
1053013.24977.17787688527-1963.97787688527
1064480.57284.88613394183-2804.38613394183
1079028.211535.5450275685-2507.34502756853
10814435.110126.34971364324308.75028635682
1098109.93624.343118873124485.55688112688
1103454.84939.14263818503-1484.34263818503
1115867.76299.94560362087-432.245603620867
1125633.45997.33213101066-363.932131010658
1134391.13440.88355278406950.21644721594
1142821.22942.28241028282-121.082410282822
1152640.92434.56315406003206.336845939972
1162130.63669.96366234432-1539.36366234432
1172944.83892.40520057691-947.605200576907
1183823.25747.45826530657-1924.25826530657
1197311.910065.6407290743-2753.74072907432
1208823.612003.0695783988-3179.46957839883
1219800.75650.347191959794150.35280804021
1225129.14032.934968624571096.16503137543
1236377.45869.11698121585508.283018784148
1247721.15613.201738452892107.89826154711
1254753.53796.5481952006956.951804799403
1263099.62798.92967229691300.670327703093

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4838.7 & 4875.37838439777 & -36.6783843977692 \tabularnewline
14 & 6823.2 & 6925.88918677376 & -102.689186773765 \tabularnewline
15 & 7767.3 & 7984.84371180026 & -217.543711800257 \tabularnewline
16 & 7048.5 & 7470.22052097712 & -421.720520977125 \tabularnewline
17 & 5748.6 & 6319.99101818998 & -571.39101818998 \tabularnewline
18 & 3444.3 & 3797.41753277335 & -353.11753277335 \tabularnewline
19 & 5168.1 & 5226.53567109208 & -58.4356710920747 \tabularnewline
20 & 4015.8 & 6405.46507444684 & -2389.66507444684 \tabularnewline
21 & 4089.3 & 5033.58387863286 & -944.283878632857 \tabularnewline
22 & 5661.9 & 10267.5358606368 & -4605.63586063683 \tabularnewline
23 & 10739.4 & 10983.8855452296 & -244.485545229607 \tabularnewline
24 & 11097 & 9620.72187265028 & 1476.27812734972 \tabularnewline
25 & 3806.1 & 3893.63014108503 & -87.5301410850307 \tabularnewline
26 & 7146.9 & 5455.77657705297 & 1691.12342294703 \tabularnewline
27 & 10894.2 & 6218.34656638568 & 4675.85343361432 \tabularnewline
28 & 7432.5 & 5750.33486509394 & 1682.16513490606 \tabularnewline
29 & 7243.5 & 4781.77682812507 & 2461.72317187493 \tabularnewline
30 & 5851.2 & 2886.41755241184 & 2964.78244758816 \tabularnewline
31 & 5562.3 & 4212.90635492952 & 1349.39364507048 \tabularnewline
32 & 3854.7 & 4269.62563770525 & -414.925637705254 \tabularnewline
33 & 4398.3 & 3780.57674892181 & 617.723251078193 \tabularnewline
34 & 6478.8 & 6695.32364442265 & -216.523644422649 \tabularnewline
35 & 8766 & 9288.52126265275 & -522.521262652754 \tabularnewline
36 & 9057.6 & 8968.23507922243 & 89.364920777567 \tabularnewline
37 & 6097.5 & 3373.38364976421 & 2724.11635023579 \tabularnewline
38 & 4467.6 & 5660.69965993176 & -1193.09965993176 \tabularnewline
39 & 7311.3 & 7743.08616433384 & -431.786164333839 \tabularnewline
40 & 6724.2 & 5999.69603714074 & 724.503962859262 \tabularnewline
41 & 6065.1 & 5517.67525743927 & 547.424742560733 \tabularnewline
42 & 5462.4 & 4015.60419006849 & 1446.79580993151 \tabularnewline
43 & 4256.1 & 4508.10485422444 & -252.00485422444 \tabularnewline
44 & 3728.4 & 3753.90465388602 & -25.5046538860211 \tabularnewline
45 & 6192.9 & 3798.13240800319 & 2394.76759199681 \tabularnewline
46 & 8603.1 & 6196.36843226713 & 2406.73156773287 \tabularnewline
47 & 11808 & 8609.75073654944 & 3198.24926345056 \tabularnewline
48 & 7562.7 & 8732.68311797146 & -1169.98311797146 \tabularnewline
49 & 4309.5 & 4612.43873931359 & -302.938739313594 \tabularnewline
50 & 5360.4 & 4942.45443415156 & 417.945565848438 \tabularnewline
51 & 8452.5 & 7427.44246339327 & 1025.05753660673 \tabularnewline
52 & 5682 & 6344.60356465299 & -662.603564652987 \tabularnewline
53 & 7342.8 & 5809.07200498372 & 1533.72799501628 \tabularnewline
54 & 5065.5 & 4798.80281907207 & 266.697180927933 \tabularnewline
55 & 3253.5 & 4463.35020687058 & -1209.85020687058 \tabularnewline
56 & 4106.7 & 3825.86000785262 & 280.839992147379 \tabularnewline
57 & 3375.3 & 5132.63705020331 & -1757.33705020331 \tabularnewline
58 & 10135.2 & 7551.8522346777 & 2583.3477653223 \tabularnewline
59 & 12551.4 & 10434.6300908091 & 2116.76990919094 \tabularnewline
60 & 6875.7 & 8337.57670007914 & -1461.87670007914 \tabularnewline
61 & 3291.6 & 4566.4495204939 & -1274.8495204939 \tabularnewline
62 & 5217 & 5258.4102378522 & -41.4102378521957 \tabularnewline
63 & 6253.8 & 8090.86731170113 & -1837.06731170113 \tabularnewline
64 & 5981.1 & 6094.36141341515 & -113.261413415147 \tabularnewline
65 & 4576.5 & 6649.64758311146 & -2073.14758311146 \tabularnewline
66 & 4453.5 & 4938.25988276689 & -484.759882766891 \tabularnewline
67 & 3896.7 & 3838.60835464719 & 58.0916453528107 \tabularnewline
68 & 4905 & 3939.23116646663 & 965.768833533372 \tabularnewline
69 & 3596.4 & 4221.97136720796 & -625.571367207963 \tabularnewline
70 & 7035.9 & 8759.19649037704 & -1723.29649037704 \tabularnewline
71 & 11962.8 & 11271.2631906789 & 691.536809321064 \tabularnewline
72 & 8205.9 & 7415.84098986306 & 790.05901013694 \tabularnewline
73 & 5713.2 & 3826.16487081371 & 1887.03512918629 \tabularnewline
74 & 5465.7 & 5137.56646712288 & 328.133532877124 \tabularnewline
75 & 5896.2 & 7042.51196164652 & -1146.31196164652 \tabularnewline
76 & 4408.8 & 5931.27152922205 & -1522.47152922205 \tabularnewline
77 & 3602.7 & 5497.16669398044 & -1894.46669398044 \tabularnewline
78 & 3926.7 & 4591.0985953089 & -664.398595308902 \tabularnewline
79 & 2018.1 & 3773.22421297325 & -1755.12421297325 \tabularnewline
80 & 2497.2 & 4272.61203821085 & -1775.41203821085 \tabularnewline
81 & 5327.1 & 3729.28852317328 & 1597.81147682672 \tabularnewline
82 & 9250.8 & 7548.4252063585 & 1702.3747936415 \tabularnewline
83 & 13317 & 11121.6607607065 & 2195.33923929346 \tabularnewline
84 & 10486.8 & 7475.55636937387 & 3011.24363062612 \tabularnewline
85 & 4709.7 & 4570.18349021057 & 139.516509789433 \tabularnewline
86 & 6599.1 & 5053.14648403731 & 1545.95351596269 \tabularnewline
87 & 6536.7 & 6177.84734954118 & 358.852650458818 \tabularnewline
88 & 7362 & 4948.31474576354 & 2413.68525423646 \tabularnewline
89 & 2150.1 & 4404.10971330494 & -2254.00971330494 \tabularnewline
90 & 1936.5 & 4125.46737299013 & -2188.96737299013 \tabularnewline
91 & 2772.3 & 2795.47847859651 & -23.1784785965051 \tabularnewline
92 & 5329.8 & 3293.86864317332 & 2035.93135682668 \tabularnewline
93 & 5593.2 & 4480.96725582886 & 1112.23274417114 \tabularnewline
94 & 6538.8 & 8364.65129713321 & -1825.85129713321 \tabularnewline
95 & 11617.8 & 12175.1569604801 & -557.356960480143 \tabularnewline
96 & 12151.5 & 8952.4909873266 & 3199.0090126734 \tabularnewline
97 & 2936.7 & 4647.55490432139 & -1710.85490432139 \tabularnewline
98 & 4336.8 & 5815.33443806226 & -1478.53443806226 \tabularnewline
99 & 6644.1 & 6308.9759839141 & 335.1240160859 \tabularnewline
100 & 6252.3 & 6090.66233846669 & 161.637661533314 \tabularnewline
101 & 3869.7 & 3224.35237951241 & 645.347620487592 \tabularnewline
102 & 3050.7 & 3005.46812935578 & 45.2318706442165 \tabularnewline
103 & 2227.8 & 2784.54780619943 & -556.747806199426 \tabularnewline
104 & 3222.9 & 4300.41486660382 & -1077.51486660382 \tabularnewline
105 & 3013.2 & 4977.17787688527 & -1963.97787688527 \tabularnewline
106 & 4480.5 & 7284.88613394183 & -2804.38613394183 \tabularnewline
107 & 9028.2 & 11535.5450275685 & -2507.34502756853 \tabularnewline
108 & 14435.1 & 10126.3497136432 & 4308.75028635682 \tabularnewline
109 & 8109.9 & 3624.34311887312 & 4485.55688112688 \tabularnewline
110 & 3454.8 & 4939.14263818503 & -1484.34263818503 \tabularnewline
111 & 5867.7 & 6299.94560362087 & -432.245603620867 \tabularnewline
112 & 5633.4 & 5997.33213101066 & -363.932131010658 \tabularnewline
113 & 4391.1 & 3440.88355278406 & 950.21644721594 \tabularnewline
114 & 2821.2 & 2942.28241028282 & -121.082410282822 \tabularnewline
115 & 2640.9 & 2434.56315406003 & 206.336845939972 \tabularnewline
116 & 2130.6 & 3669.96366234432 & -1539.36366234432 \tabularnewline
117 & 2944.8 & 3892.40520057691 & -947.605200576907 \tabularnewline
118 & 3823.2 & 5747.45826530657 & -1924.25826530657 \tabularnewline
119 & 7311.9 & 10065.6407290743 & -2753.74072907432 \tabularnewline
120 & 8823.6 & 12003.0695783988 & -3179.46957839883 \tabularnewline
121 & 9800.7 & 5650.34719195979 & 4150.35280804021 \tabularnewline
122 & 5129.1 & 4032.93496862457 & 1096.16503137543 \tabularnewline
123 & 6377.4 & 5869.11698121585 & 508.283018784148 \tabularnewline
124 & 7721.1 & 5613.20173845289 & 2107.89826154711 \tabularnewline
125 & 4753.5 & 3796.5481952006 & 956.951804799403 \tabularnewline
126 & 3099.6 & 2798.92967229691 & 300.670327703093 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298768&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]4838.7[/C][C]4875.37838439777[/C][C]-36.6783843977692[/C][/ROW]
[ROW][C]14[/C][C]6823.2[/C][C]6925.88918677376[/C][C]-102.689186773765[/C][/ROW]
[ROW][C]15[/C][C]7767.3[/C][C]7984.84371180026[/C][C]-217.543711800257[/C][/ROW]
[ROW][C]16[/C][C]7048.5[/C][C]7470.22052097712[/C][C]-421.720520977125[/C][/ROW]
[ROW][C]17[/C][C]5748.6[/C][C]6319.99101818998[/C][C]-571.39101818998[/C][/ROW]
[ROW][C]18[/C][C]3444.3[/C][C]3797.41753277335[/C][C]-353.11753277335[/C][/ROW]
[ROW][C]19[/C][C]5168.1[/C][C]5226.53567109208[/C][C]-58.4356710920747[/C][/ROW]
[ROW][C]20[/C][C]4015.8[/C][C]6405.46507444684[/C][C]-2389.66507444684[/C][/ROW]
[ROW][C]21[/C][C]4089.3[/C][C]5033.58387863286[/C][C]-944.283878632857[/C][/ROW]
[ROW][C]22[/C][C]5661.9[/C][C]10267.5358606368[/C][C]-4605.63586063683[/C][/ROW]
[ROW][C]23[/C][C]10739.4[/C][C]10983.8855452296[/C][C]-244.485545229607[/C][/ROW]
[ROW][C]24[/C][C]11097[/C][C]9620.72187265028[/C][C]1476.27812734972[/C][/ROW]
[ROW][C]25[/C][C]3806.1[/C][C]3893.63014108503[/C][C]-87.5301410850307[/C][/ROW]
[ROW][C]26[/C][C]7146.9[/C][C]5455.77657705297[/C][C]1691.12342294703[/C][/ROW]
[ROW][C]27[/C][C]10894.2[/C][C]6218.34656638568[/C][C]4675.85343361432[/C][/ROW]
[ROW][C]28[/C][C]7432.5[/C][C]5750.33486509394[/C][C]1682.16513490606[/C][/ROW]
[ROW][C]29[/C][C]7243.5[/C][C]4781.77682812507[/C][C]2461.72317187493[/C][/ROW]
[ROW][C]30[/C][C]5851.2[/C][C]2886.41755241184[/C][C]2964.78244758816[/C][/ROW]
[ROW][C]31[/C][C]5562.3[/C][C]4212.90635492952[/C][C]1349.39364507048[/C][/ROW]
[ROW][C]32[/C][C]3854.7[/C][C]4269.62563770525[/C][C]-414.925637705254[/C][/ROW]
[ROW][C]33[/C][C]4398.3[/C][C]3780.57674892181[/C][C]617.723251078193[/C][/ROW]
[ROW][C]34[/C][C]6478.8[/C][C]6695.32364442265[/C][C]-216.523644422649[/C][/ROW]
[ROW][C]35[/C][C]8766[/C][C]9288.52126265275[/C][C]-522.521262652754[/C][/ROW]
[ROW][C]36[/C][C]9057.6[/C][C]8968.23507922243[/C][C]89.364920777567[/C][/ROW]
[ROW][C]37[/C][C]6097.5[/C][C]3373.38364976421[/C][C]2724.11635023579[/C][/ROW]
[ROW][C]38[/C][C]4467.6[/C][C]5660.69965993176[/C][C]-1193.09965993176[/C][/ROW]
[ROW][C]39[/C][C]7311.3[/C][C]7743.08616433384[/C][C]-431.786164333839[/C][/ROW]
[ROW][C]40[/C][C]6724.2[/C][C]5999.69603714074[/C][C]724.503962859262[/C][/ROW]
[ROW][C]41[/C][C]6065.1[/C][C]5517.67525743927[/C][C]547.424742560733[/C][/ROW]
[ROW][C]42[/C][C]5462.4[/C][C]4015.60419006849[/C][C]1446.79580993151[/C][/ROW]
[ROW][C]43[/C][C]4256.1[/C][C]4508.10485422444[/C][C]-252.00485422444[/C][/ROW]
[ROW][C]44[/C][C]3728.4[/C][C]3753.90465388602[/C][C]-25.5046538860211[/C][/ROW]
[ROW][C]45[/C][C]6192.9[/C][C]3798.13240800319[/C][C]2394.76759199681[/C][/ROW]
[ROW][C]46[/C][C]8603.1[/C][C]6196.36843226713[/C][C]2406.73156773287[/C][/ROW]
[ROW][C]47[/C][C]11808[/C][C]8609.75073654944[/C][C]3198.24926345056[/C][/ROW]
[ROW][C]48[/C][C]7562.7[/C][C]8732.68311797146[/C][C]-1169.98311797146[/C][/ROW]
[ROW][C]49[/C][C]4309.5[/C][C]4612.43873931359[/C][C]-302.938739313594[/C][/ROW]
[ROW][C]50[/C][C]5360.4[/C][C]4942.45443415156[/C][C]417.945565848438[/C][/ROW]
[ROW][C]51[/C][C]8452.5[/C][C]7427.44246339327[/C][C]1025.05753660673[/C][/ROW]
[ROW][C]52[/C][C]5682[/C][C]6344.60356465299[/C][C]-662.603564652987[/C][/ROW]
[ROW][C]53[/C][C]7342.8[/C][C]5809.07200498372[/C][C]1533.72799501628[/C][/ROW]
[ROW][C]54[/C][C]5065.5[/C][C]4798.80281907207[/C][C]266.697180927933[/C][/ROW]
[ROW][C]55[/C][C]3253.5[/C][C]4463.35020687058[/C][C]-1209.85020687058[/C][/ROW]
[ROW][C]56[/C][C]4106.7[/C][C]3825.86000785262[/C][C]280.839992147379[/C][/ROW]
[ROW][C]57[/C][C]3375.3[/C][C]5132.63705020331[/C][C]-1757.33705020331[/C][/ROW]
[ROW][C]58[/C][C]10135.2[/C][C]7551.8522346777[/C][C]2583.3477653223[/C][/ROW]
[ROW][C]59[/C][C]12551.4[/C][C]10434.6300908091[/C][C]2116.76990919094[/C][/ROW]
[ROW][C]60[/C][C]6875.7[/C][C]8337.57670007914[/C][C]-1461.87670007914[/C][/ROW]
[ROW][C]61[/C][C]3291.6[/C][C]4566.4495204939[/C][C]-1274.8495204939[/C][/ROW]
[ROW][C]62[/C][C]5217[/C][C]5258.4102378522[/C][C]-41.4102378521957[/C][/ROW]
[ROW][C]63[/C][C]6253.8[/C][C]8090.86731170113[/C][C]-1837.06731170113[/C][/ROW]
[ROW][C]64[/C][C]5981.1[/C][C]6094.36141341515[/C][C]-113.261413415147[/C][/ROW]
[ROW][C]65[/C][C]4576.5[/C][C]6649.64758311146[/C][C]-2073.14758311146[/C][/ROW]
[ROW][C]66[/C][C]4453.5[/C][C]4938.25988276689[/C][C]-484.759882766891[/C][/ROW]
[ROW][C]67[/C][C]3896.7[/C][C]3838.60835464719[/C][C]58.0916453528107[/C][/ROW]
[ROW][C]68[/C][C]4905[/C][C]3939.23116646663[/C][C]965.768833533372[/C][/ROW]
[ROW][C]69[/C][C]3596.4[/C][C]4221.97136720796[/C][C]-625.571367207963[/C][/ROW]
[ROW][C]70[/C][C]7035.9[/C][C]8759.19649037704[/C][C]-1723.29649037704[/C][/ROW]
[ROW][C]71[/C][C]11962.8[/C][C]11271.2631906789[/C][C]691.536809321064[/C][/ROW]
[ROW][C]72[/C][C]8205.9[/C][C]7415.84098986306[/C][C]790.05901013694[/C][/ROW]
[ROW][C]73[/C][C]5713.2[/C][C]3826.16487081371[/C][C]1887.03512918629[/C][/ROW]
[ROW][C]74[/C][C]5465.7[/C][C]5137.56646712288[/C][C]328.133532877124[/C][/ROW]
[ROW][C]75[/C][C]5896.2[/C][C]7042.51196164652[/C][C]-1146.31196164652[/C][/ROW]
[ROW][C]76[/C][C]4408.8[/C][C]5931.27152922205[/C][C]-1522.47152922205[/C][/ROW]
[ROW][C]77[/C][C]3602.7[/C][C]5497.16669398044[/C][C]-1894.46669398044[/C][/ROW]
[ROW][C]78[/C][C]3926.7[/C][C]4591.0985953089[/C][C]-664.398595308902[/C][/ROW]
[ROW][C]79[/C][C]2018.1[/C][C]3773.22421297325[/C][C]-1755.12421297325[/C][/ROW]
[ROW][C]80[/C][C]2497.2[/C][C]4272.61203821085[/C][C]-1775.41203821085[/C][/ROW]
[ROW][C]81[/C][C]5327.1[/C][C]3729.28852317328[/C][C]1597.81147682672[/C][/ROW]
[ROW][C]82[/C][C]9250.8[/C][C]7548.4252063585[/C][C]1702.3747936415[/C][/ROW]
[ROW][C]83[/C][C]13317[/C][C]11121.6607607065[/C][C]2195.33923929346[/C][/ROW]
[ROW][C]84[/C][C]10486.8[/C][C]7475.55636937387[/C][C]3011.24363062612[/C][/ROW]
[ROW][C]85[/C][C]4709.7[/C][C]4570.18349021057[/C][C]139.516509789433[/C][/ROW]
[ROW][C]86[/C][C]6599.1[/C][C]5053.14648403731[/C][C]1545.95351596269[/C][/ROW]
[ROW][C]87[/C][C]6536.7[/C][C]6177.84734954118[/C][C]358.852650458818[/C][/ROW]
[ROW][C]88[/C][C]7362[/C][C]4948.31474576354[/C][C]2413.68525423646[/C][/ROW]
[ROW][C]89[/C][C]2150.1[/C][C]4404.10971330494[/C][C]-2254.00971330494[/C][/ROW]
[ROW][C]90[/C][C]1936.5[/C][C]4125.46737299013[/C][C]-2188.96737299013[/C][/ROW]
[ROW][C]91[/C][C]2772.3[/C][C]2795.47847859651[/C][C]-23.1784785965051[/C][/ROW]
[ROW][C]92[/C][C]5329.8[/C][C]3293.86864317332[/C][C]2035.93135682668[/C][/ROW]
[ROW][C]93[/C][C]5593.2[/C][C]4480.96725582886[/C][C]1112.23274417114[/C][/ROW]
[ROW][C]94[/C][C]6538.8[/C][C]8364.65129713321[/C][C]-1825.85129713321[/C][/ROW]
[ROW][C]95[/C][C]11617.8[/C][C]12175.1569604801[/C][C]-557.356960480143[/C][/ROW]
[ROW][C]96[/C][C]12151.5[/C][C]8952.4909873266[/C][C]3199.0090126734[/C][/ROW]
[ROW][C]97[/C][C]2936.7[/C][C]4647.55490432139[/C][C]-1710.85490432139[/C][/ROW]
[ROW][C]98[/C][C]4336.8[/C][C]5815.33443806226[/C][C]-1478.53443806226[/C][/ROW]
[ROW][C]99[/C][C]6644.1[/C][C]6308.9759839141[/C][C]335.1240160859[/C][/ROW]
[ROW][C]100[/C][C]6252.3[/C][C]6090.66233846669[/C][C]161.637661533314[/C][/ROW]
[ROW][C]101[/C][C]3869.7[/C][C]3224.35237951241[/C][C]645.347620487592[/C][/ROW]
[ROW][C]102[/C][C]3050.7[/C][C]3005.46812935578[/C][C]45.2318706442165[/C][/ROW]
[ROW][C]103[/C][C]2227.8[/C][C]2784.54780619943[/C][C]-556.747806199426[/C][/ROW]
[ROW][C]104[/C][C]3222.9[/C][C]4300.41486660382[/C][C]-1077.51486660382[/C][/ROW]
[ROW][C]105[/C][C]3013.2[/C][C]4977.17787688527[/C][C]-1963.97787688527[/C][/ROW]
[ROW][C]106[/C][C]4480.5[/C][C]7284.88613394183[/C][C]-2804.38613394183[/C][/ROW]
[ROW][C]107[/C][C]9028.2[/C][C]11535.5450275685[/C][C]-2507.34502756853[/C][/ROW]
[ROW][C]108[/C][C]14435.1[/C][C]10126.3497136432[/C][C]4308.75028635682[/C][/ROW]
[ROW][C]109[/C][C]8109.9[/C][C]3624.34311887312[/C][C]4485.55688112688[/C][/ROW]
[ROW][C]110[/C][C]3454.8[/C][C]4939.14263818503[/C][C]-1484.34263818503[/C][/ROW]
[ROW][C]111[/C][C]5867.7[/C][C]6299.94560362087[/C][C]-432.245603620867[/C][/ROW]
[ROW][C]112[/C][C]5633.4[/C][C]5997.33213101066[/C][C]-363.932131010658[/C][/ROW]
[ROW][C]113[/C][C]4391.1[/C][C]3440.88355278406[/C][C]950.21644721594[/C][/ROW]
[ROW][C]114[/C][C]2821.2[/C][C]2942.28241028282[/C][C]-121.082410282822[/C][/ROW]
[ROW][C]115[/C][C]2640.9[/C][C]2434.56315406003[/C][C]206.336845939972[/C][/ROW]
[ROW][C]116[/C][C]2130.6[/C][C]3669.96366234432[/C][C]-1539.36366234432[/C][/ROW]
[ROW][C]117[/C][C]2944.8[/C][C]3892.40520057691[/C][C]-947.605200576907[/C][/ROW]
[ROW][C]118[/C][C]3823.2[/C][C]5747.45826530657[/C][C]-1924.25826530657[/C][/ROW]
[ROW][C]119[/C][C]7311.9[/C][C]10065.6407290743[/C][C]-2753.74072907432[/C][/ROW]
[ROW][C]120[/C][C]8823.6[/C][C]12003.0695783988[/C][C]-3179.46957839883[/C][/ROW]
[ROW][C]121[/C][C]9800.7[/C][C]5650.34719195979[/C][C]4150.35280804021[/C][/ROW]
[ROW][C]122[/C][C]5129.1[/C][C]4032.93496862457[/C][C]1096.16503137543[/C][/ROW]
[ROW][C]123[/C][C]6377.4[/C][C]5869.11698121585[/C][C]508.283018784148[/C][/ROW]
[ROW][C]124[/C][C]7721.1[/C][C]5613.20173845289[/C][C]2107.89826154711[/C][/ROW]
[ROW][C]125[/C][C]4753.5[/C][C]3796.5481952006[/C][C]956.951804799403[/C][/ROW]
[ROW][C]126[/C][C]3099.6[/C][C]2798.92967229691[/C][C]300.670327703093[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298768&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298768&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
134838.74875.37838439777-36.6783843977692
146823.26925.88918677376-102.689186773765
157767.37984.84371180026-217.543711800257
167048.57470.22052097712-421.720520977125
175748.66319.99101818998-571.39101818998
183444.33797.41753277335-353.11753277335
195168.15226.53567109208-58.4356710920747
204015.86405.46507444684-2389.66507444684
214089.35033.58387863286-944.283878632857
225661.910267.5358606368-4605.63586063683
2310739.410983.8855452296-244.485545229607
24110979620.721872650281476.27812734972
253806.13893.63014108503-87.5301410850307
267146.95455.776577052971691.12342294703
2710894.26218.346566385684675.85343361432
287432.55750.334865093941682.16513490606
297243.54781.776828125072461.72317187493
305851.22886.417552411842964.78244758816
315562.34212.906354929521349.39364507048
323854.74269.62563770525-414.925637705254
334398.33780.57674892181617.723251078193
346478.86695.32364442265-216.523644422649
3587669288.52126265275-522.521262652754
369057.68968.2350792224389.364920777567
376097.53373.383649764212724.11635023579
384467.65660.69965993176-1193.09965993176
397311.37743.08616433384-431.786164333839
406724.25999.69603714074724.503962859262
416065.15517.67525743927547.424742560733
425462.44015.604190068491446.79580993151
434256.14508.10485422444-252.00485422444
443728.43753.90465388602-25.5046538860211
456192.93798.132408003192394.76759199681
468603.16196.368432267132406.73156773287
47118088609.750736549443198.24926345056
487562.78732.68311797146-1169.98311797146
494309.54612.43873931359-302.938739313594
505360.44942.45443415156417.945565848438
518452.57427.442463393271025.05753660673
5256826344.60356465299-662.603564652987
537342.85809.072004983721533.72799501628
545065.54798.80281907207266.697180927933
553253.54463.35020687058-1209.85020687058
564106.73825.86000785262280.839992147379
573375.35132.63705020331-1757.33705020331
5810135.27551.85223467772583.3477653223
5912551.410434.63009080912116.76990919094
606875.78337.57670007914-1461.87670007914
613291.64566.4495204939-1274.8495204939
6252175258.4102378522-41.4102378521957
636253.88090.86731170113-1837.06731170113
645981.16094.36141341515-113.261413415147
654576.56649.64758311146-2073.14758311146
664453.54938.25988276689-484.759882766891
673896.73838.6083546471958.0916453528107
6849053939.23116646663965.768833533372
693596.44221.97136720796-625.571367207963
707035.98759.19649037704-1723.29649037704
7111962.811271.2631906789691.536809321064
728205.97415.84098986306790.05901013694
735713.23826.164870813711887.03512918629
745465.75137.56646712288328.133532877124
755896.27042.51196164652-1146.31196164652
764408.85931.27152922205-1522.47152922205
773602.75497.16669398044-1894.46669398044
783926.74591.0985953089-664.398595308902
792018.13773.22421297325-1755.12421297325
802497.24272.61203821085-1775.41203821085
815327.13729.288523173281597.81147682672
829250.87548.42520635851702.3747936415
831331711121.66076070652195.33923929346
8410486.87475.556369373873011.24363062612
854709.74570.18349021057139.516509789433
866599.15053.146484037311545.95351596269
876536.76177.84734954118358.852650458818
8873624948.314745763542413.68525423646
892150.14404.10971330494-2254.00971330494
901936.54125.46737299013-2188.96737299013
912772.32795.47847859651-23.1784785965051
925329.83293.868643173322035.93135682668
935593.24480.967255828861112.23274417114
946538.88364.65129713321-1825.85129713321
9511617.812175.1569604801-557.356960480143
9612151.58952.49098732663199.0090126734
972936.74647.55490432139-1710.85490432139
984336.85815.33443806226-1478.53443806226
996644.16308.9759839141335.1240160859
1006252.36090.66233846669161.637661533314
1013869.73224.35237951241645.347620487592
1023050.73005.4681293557845.2318706442165
1032227.82784.54780619943-556.747806199426
1043222.94300.41486660382-1077.51486660382
1053013.24977.17787688527-1963.97787688527
1064480.57284.88613394183-2804.38613394183
1079028.211535.5450275685-2507.34502756853
10814435.110126.34971364324308.75028635682
1098109.93624.343118873124485.55688112688
1103454.84939.14263818503-1484.34263818503
1115867.76299.94560362087-432.245603620867
1125633.45997.33213101066-363.932131010658
1134391.13440.88355278406950.21644721594
1142821.22942.28241028282-121.082410282822
1152640.92434.56315406003206.336845939972
1162130.63669.96366234432-1539.36366234432
1172944.83892.40520057691-947.605200576907
1183823.25747.45826530657-1924.25826530657
1197311.910065.6407290743-2753.74072907432
1208823.612003.0695783988-3179.46957839883
1219800.75650.347191959794150.35280804021
1225129.14032.934968624571096.16503137543
1236377.45869.11698121585508.283018784148
1247721.15613.201738452892107.89826154711
1254753.53796.5481952006956.951804799403
1263099.62798.92967229691300.670327703093







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1272471.7224244567754.2852078078334189.15964110556
1282827.523510757491109.06164457644545.98537693858
1293358.781369955631637.756287199285079.80645271197
1304734.592130402993004.315162804536464.86909800145
1318679.564784486996896.3452120180510462.7843569559
13210510.01814287868658.4802965218212361.5559892354
1337855.80318347536036.521716634189675.08465031641
1344658.682646666592893.905045241986423.46024809121
1356238.378096728114414.477637370588062.27855608564
1366801.592706042354928.978188682698674.20722340201
1374354.008939602082557.349323451316150.66855575285
1382999.039718348362568.241316045153429.83812065156
1392511.42364708508-74.3440446752025097.19133884536
1402872.87896155873272.898734870335472.85918824712
1413412.58664480373786.4150587434166038.75823086404
1424810.335796171012099.107239161197521.56435318082
1438818.234970558555710.5378639024111925.9320772147
14410677.70954114317245.0136049962414110.4054772901

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 2471.7224244567 & 754.285207807833 & 4189.15964110556 \tabularnewline
128 & 2827.52351075749 & 1109.0616445764 & 4545.98537693858 \tabularnewline
129 & 3358.78136995563 & 1637.75628719928 & 5079.80645271197 \tabularnewline
130 & 4734.59213040299 & 3004.31516280453 & 6464.86909800145 \tabularnewline
131 & 8679.56478448699 & 6896.34521201805 & 10462.7843569559 \tabularnewline
132 & 10510.0181428786 & 8658.48029652182 & 12361.5559892354 \tabularnewline
133 & 7855.8031834753 & 6036.52171663418 & 9675.08465031641 \tabularnewline
134 & 4658.68264666659 & 2893.90504524198 & 6423.46024809121 \tabularnewline
135 & 6238.37809672811 & 4414.47763737058 & 8062.27855608564 \tabularnewline
136 & 6801.59270604235 & 4928.97818868269 & 8674.20722340201 \tabularnewline
137 & 4354.00893960208 & 2557.34932345131 & 6150.66855575285 \tabularnewline
138 & 2999.03971834836 & 2568.24131604515 & 3429.83812065156 \tabularnewline
139 & 2511.42364708508 & -74.344044675202 & 5097.19133884536 \tabularnewline
140 & 2872.87896155873 & 272.89873487033 & 5472.85918824712 \tabularnewline
141 & 3412.58664480373 & 786.415058743416 & 6038.75823086404 \tabularnewline
142 & 4810.33579617101 & 2099.10723916119 & 7521.56435318082 \tabularnewline
143 & 8818.23497055855 & 5710.53786390241 & 11925.9320772147 \tabularnewline
144 & 10677.7095411431 & 7245.01360499624 & 14110.4054772901 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298768&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]127[/C][C]2471.7224244567[/C][C]754.285207807833[/C][C]4189.15964110556[/C][/ROW]
[ROW][C]128[/C][C]2827.52351075749[/C][C]1109.0616445764[/C][C]4545.98537693858[/C][/ROW]
[ROW][C]129[/C][C]3358.78136995563[/C][C]1637.75628719928[/C][C]5079.80645271197[/C][/ROW]
[ROW][C]130[/C][C]4734.59213040299[/C][C]3004.31516280453[/C][C]6464.86909800145[/C][/ROW]
[ROW][C]131[/C][C]8679.56478448699[/C][C]6896.34521201805[/C][C]10462.7843569559[/C][/ROW]
[ROW][C]132[/C][C]10510.0181428786[/C][C]8658.48029652182[/C][C]12361.5559892354[/C][/ROW]
[ROW][C]133[/C][C]7855.8031834753[/C][C]6036.52171663418[/C][C]9675.08465031641[/C][/ROW]
[ROW][C]134[/C][C]4658.68264666659[/C][C]2893.90504524198[/C][C]6423.46024809121[/C][/ROW]
[ROW][C]135[/C][C]6238.37809672811[/C][C]4414.47763737058[/C][C]8062.27855608564[/C][/ROW]
[ROW][C]136[/C][C]6801.59270604235[/C][C]4928.97818868269[/C][C]8674.20722340201[/C][/ROW]
[ROW][C]137[/C][C]4354.00893960208[/C][C]2557.34932345131[/C][C]6150.66855575285[/C][/ROW]
[ROW][C]138[/C][C]2999.03971834836[/C][C]2568.24131604515[/C][C]3429.83812065156[/C][/ROW]
[ROW][C]139[/C][C]2511.42364708508[/C][C]-74.344044675202[/C][C]5097.19133884536[/C][/ROW]
[ROW][C]140[/C][C]2872.87896155873[/C][C]272.89873487033[/C][C]5472.85918824712[/C][/ROW]
[ROW][C]141[/C][C]3412.58664480373[/C][C]786.415058743416[/C][C]6038.75823086404[/C][/ROW]
[ROW][C]142[/C][C]4810.33579617101[/C][C]2099.10723916119[/C][C]7521.56435318082[/C][/ROW]
[ROW][C]143[/C][C]8818.23497055855[/C][C]5710.53786390241[/C][C]11925.9320772147[/C][/ROW]
[ROW][C]144[/C][C]10677.7095411431[/C][C]7245.01360499624[/C][C]14110.4054772901[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298768&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298768&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
1272471.7224244567754.2852078078334189.15964110556
1282827.523510757491109.06164457644545.98537693858
1293358.781369955631637.756287199285079.80645271197
1304734.592130402993004.315162804536464.86909800145
1318679.564784486996896.3452120180510462.7843569559
13210510.01814287868658.4802965218212361.5559892354
1337855.80318347536036.521716634189675.08465031641
1344658.682646666592893.905045241986423.46024809121
1356238.378096728114414.477637370588062.27855608564
1366801.592706042354928.978188682698674.20722340201
1374354.008939602082557.349323451316150.66855575285
1382999.039718348362568.241316045153429.83812065156
1392511.42364708508-74.3440446752025097.19133884536
1402872.87896155873272.898734870335472.85918824712
1413412.58664480373786.4150587434166038.75823086404
1424810.335796171012099.107239161197521.56435318082
1438818.234970558555710.5378639024111925.9320772147
14410677.70954114317245.0136049962414110.4054772901



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 18 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 18 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'multiplicative'
par2 <- 'Triple'
par1 <- '12'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')