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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 07 Dec 2016 11:50:47 +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/07/t1481108187rv9v4q9157gw279.htm/, Retrieved Tue, 07 May 2024 14:51:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298001, Retrieved Tue, 07 May 2024 14:51:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact50
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Expontential smoo...] [2016-12-07 10:50:47] [c0b73e623858a81821526bb2f691ccd9] [Current]
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Dataseries X:
7360
4820
2600
5520
3180
4080
3360
4960
4640
5420
4880
4780
4860
3780
4120
3980
3060
4420
3340
4220
5780
5440
4200
3720
4040
3920
3160
3500
2780
3340
3100
3100
4400
3480
5100
4260
3640
2900
3820
2980
2860
2420
2680
4420
3160
3160
4300
2820
3240
2520
3480
2740
2240
3700
2600
3160
3800
3440
2180
2300
3160
1800
2620
2820
2180
2300
2560
2860
2620
3960
3960
2320
3400
2640
2340
2340
1960
2100
2280
2320
2660
2520
2120
1800
2300
2420
1920
1720
2000
1960
2860
2160
2360
2300
2360
2260
2460
2200
1620
1740
1720
2460
1840
2160
2460
2860
2700
2420




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=298001&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=298001&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298001&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
alpha0.0895016584643743
beta0.129272807881799
gamma0.327804687160506

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0895016584643743 \tabularnewline
beta & 0.129272807881799 \tabularnewline
gamma & 0.327804687160506 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298001&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]0.0895016584643743[/C][/ROW]
[ROW][C]beta[/C][C]0.129272807881799[/C][/ROW]
[ROW][C]gamma[/C][C]0.327804687160506[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298001&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298001&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
alpha0.0895016584643743
beta0.129272807881799
gamma0.327804687160506







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
531803697.64685614159-517.64685614159
640804457.35479120993-377.354791209932
733602342.94919173591017.0508082641
849605728.07286637977-768.072866379768
946402979.48549630051660.5145036995
1054203900.488725950521519.51127404948
1148802495.733911492432384.26608850757
1247805542.82626055735-762.826260557347
1348603551.680085728991308.31991427101
1437804473.87208027805-693.872080278052
1541203131.79756115362988.202438846379
1639805015.8368944376-1035.8368944376
1730603695.28213065194-635.282130651935
1844203801.83322598568618.166774014321
1933403132.87264473423207.127355265772
2042204195.62026611524.3797338849972
2157803181.355605636332598.64439436367
2254403988.754478710341451.24552128966
2342003301.87636036596898.123639634044
2437204500.72400664649-780.724006646491
2540404178.02948626379-138.029486263789
2639204404.57708064004-484.577080640044
2731603410.89936051174-250.899360511739
2835003937.03045715906-437.030457159059
2927803823.05635822612-1043.05635822612
3033403819.8895454312-479.889545431205
3131002962.06040313348137.939596866522
3231003390.83425003228-290.834250032276
3344003106.614805527681293.38519447232
3434803469.8862656953910.1137343046094
3551002878.246890967732221.75310903227
3642603413.14194245316846.858057546837
3736403766.24034628318-126.240346283179
3829003655.91000630809-755.910006308093
3938203647.22219788111172.777802118888
4029803586.14749957272-606.147499572715
4128603503.05210621503-643.052106215026
4224203154.49689351003-734.496893510028
4326803372.73035453377-692.730354533767
4444203000.319888976251419.68011102375
4531603078.4130571665981.5869428334063
4631602778.78106368045381.218936319545
4743003113.818439613011186.18156038699
4828203577.0535529347-757.053552934697
4932403077.36889349136162.631106508643
5025202885.9463512132-365.946351213196
5134803372.07415721217107.925842787831
5227403155.81481434651-415.81481434651
5322402961.33950678803-721.339506788028
5437002543.748663727121156.25133627288
5526003286.56116725045-686.561167250446
5631602855.96872785125304.03127214875
5738002641.046029905451158.95397009455
5834402970.2994730643469.700526935695
5921803115.51820852747-935.518208527466
6023002970.74680381995-670.746803819952
6131602912.09168710513247.908312894873
6218002940.13346226433-1140.13346226433
6326202519.25340730495100.746592695049
6428202523.95523833079296.044761669214
6521802802.12840272653-622.128402726529
6623002346.9330458797-46.9330458797012
6725602386.2700313623173.729968637705
6828602447.74703615888412.252963841116
6926202457.68461018222162.315389817782
7039602258.51114802541701.4888519746
7139602554.656004161481405.34399583852
7223202856.61164104612-536.61164104612
7334002735.92098582944664.079014170562
7426403080.23433932592-440.234339325921
7523403094.06336709927-754.063367099273
7623402619.68561167629-279.685611676287
7719602861.74959624682-901.749596246818
7821002711.66476672423-611.664766724231
7922802587.15155054436-307.151550544364
8023202294.3755027736625.6244972263357
8126602344.40154943677315.598450563233
8225202378.44140649604141.558593503958
8321202412.07190524665-292.071905246651
8418002226.84332649562-426.843326495618
8523002310.5164363129-10.516436312902
8624202257.58911002446162.410889975537
8719202161.9551854797-241.955185479701
8817201945.43943923264-225.439439232637
8920002149.01771356684-149.017713566843
9019602126.94075030225-166.940750302252
9128601890.03030744637969.969692553626
9221601798.15133394921361.848666050795
9323602085.84216336012274.157836639879
9423002114.34395576964185.656044230362
9523602264.2649305964195.7350694035931
9622601920.00883743936339.991162560644
9724602191.16204216883268.837957831173
9822002203.09588430307-3.0958843030744
9916202319.15188289907-699.151882899072
10017401980.13251447601-240.132514476009
10117202158.95707679863-438.957076798634
10224602017.38611799845442.613882001553
10318401955.73909223056-115.739092230562
10421601807.75655814871352.243441851293
10524601977.15591791606482.844082083935
10628602196.46423282241663.535767177586
10727001995.25046446616704.749535533841
10824202084.88616246349335.11383753651

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
5 & 3180 & 3697.64685614159 & -517.64685614159 \tabularnewline
6 & 4080 & 4457.35479120993 & -377.354791209932 \tabularnewline
7 & 3360 & 2342.9491917359 & 1017.0508082641 \tabularnewline
8 & 4960 & 5728.07286637977 & -768.072866379768 \tabularnewline
9 & 4640 & 2979.4854963005 & 1660.5145036995 \tabularnewline
10 & 5420 & 3900.48872595052 & 1519.51127404948 \tabularnewline
11 & 4880 & 2495.73391149243 & 2384.26608850757 \tabularnewline
12 & 4780 & 5542.82626055735 & -762.826260557347 \tabularnewline
13 & 4860 & 3551.68008572899 & 1308.31991427101 \tabularnewline
14 & 3780 & 4473.87208027805 & -693.872080278052 \tabularnewline
15 & 4120 & 3131.79756115362 & 988.202438846379 \tabularnewline
16 & 3980 & 5015.8368944376 & -1035.8368944376 \tabularnewline
17 & 3060 & 3695.28213065194 & -635.282130651935 \tabularnewline
18 & 4420 & 3801.83322598568 & 618.166774014321 \tabularnewline
19 & 3340 & 3132.87264473423 & 207.127355265772 \tabularnewline
20 & 4220 & 4195.620266115 & 24.3797338849972 \tabularnewline
21 & 5780 & 3181.35560563633 & 2598.64439436367 \tabularnewline
22 & 5440 & 3988.75447871034 & 1451.24552128966 \tabularnewline
23 & 4200 & 3301.87636036596 & 898.123639634044 \tabularnewline
24 & 3720 & 4500.72400664649 & -780.724006646491 \tabularnewline
25 & 4040 & 4178.02948626379 & -138.029486263789 \tabularnewline
26 & 3920 & 4404.57708064004 & -484.577080640044 \tabularnewline
27 & 3160 & 3410.89936051174 & -250.899360511739 \tabularnewline
28 & 3500 & 3937.03045715906 & -437.030457159059 \tabularnewline
29 & 2780 & 3823.05635822612 & -1043.05635822612 \tabularnewline
30 & 3340 & 3819.8895454312 & -479.889545431205 \tabularnewline
31 & 3100 & 2962.06040313348 & 137.939596866522 \tabularnewline
32 & 3100 & 3390.83425003228 & -290.834250032276 \tabularnewline
33 & 4400 & 3106.61480552768 & 1293.38519447232 \tabularnewline
34 & 3480 & 3469.88626569539 & 10.1137343046094 \tabularnewline
35 & 5100 & 2878.24689096773 & 2221.75310903227 \tabularnewline
36 & 4260 & 3413.14194245316 & 846.858057546837 \tabularnewline
37 & 3640 & 3766.24034628318 & -126.240346283179 \tabularnewline
38 & 2900 & 3655.91000630809 & -755.910006308093 \tabularnewline
39 & 3820 & 3647.22219788111 & 172.777802118888 \tabularnewline
40 & 2980 & 3586.14749957272 & -606.147499572715 \tabularnewline
41 & 2860 & 3503.05210621503 & -643.052106215026 \tabularnewline
42 & 2420 & 3154.49689351003 & -734.496893510028 \tabularnewline
43 & 2680 & 3372.73035453377 & -692.730354533767 \tabularnewline
44 & 4420 & 3000.31988897625 & 1419.68011102375 \tabularnewline
45 & 3160 & 3078.41305716659 & 81.5869428334063 \tabularnewline
46 & 3160 & 2778.78106368045 & 381.218936319545 \tabularnewline
47 & 4300 & 3113.81843961301 & 1186.18156038699 \tabularnewline
48 & 2820 & 3577.0535529347 & -757.053552934697 \tabularnewline
49 & 3240 & 3077.36889349136 & 162.631106508643 \tabularnewline
50 & 2520 & 2885.9463512132 & -365.946351213196 \tabularnewline
51 & 3480 & 3372.07415721217 & 107.925842787831 \tabularnewline
52 & 2740 & 3155.81481434651 & -415.81481434651 \tabularnewline
53 & 2240 & 2961.33950678803 & -721.339506788028 \tabularnewline
54 & 3700 & 2543.74866372712 & 1156.25133627288 \tabularnewline
55 & 2600 & 3286.56116725045 & -686.561167250446 \tabularnewline
56 & 3160 & 2855.96872785125 & 304.03127214875 \tabularnewline
57 & 3800 & 2641.04602990545 & 1158.95397009455 \tabularnewline
58 & 3440 & 2970.2994730643 & 469.700526935695 \tabularnewline
59 & 2180 & 3115.51820852747 & -935.518208527466 \tabularnewline
60 & 2300 & 2970.74680381995 & -670.746803819952 \tabularnewline
61 & 3160 & 2912.09168710513 & 247.908312894873 \tabularnewline
62 & 1800 & 2940.13346226433 & -1140.13346226433 \tabularnewline
63 & 2620 & 2519.25340730495 & 100.746592695049 \tabularnewline
64 & 2820 & 2523.95523833079 & 296.044761669214 \tabularnewline
65 & 2180 & 2802.12840272653 & -622.128402726529 \tabularnewline
66 & 2300 & 2346.9330458797 & -46.9330458797012 \tabularnewline
67 & 2560 & 2386.2700313623 & 173.729968637705 \tabularnewline
68 & 2860 & 2447.74703615888 & 412.252963841116 \tabularnewline
69 & 2620 & 2457.68461018222 & 162.315389817782 \tabularnewline
70 & 3960 & 2258.5111480254 & 1701.4888519746 \tabularnewline
71 & 3960 & 2554.65600416148 & 1405.34399583852 \tabularnewline
72 & 2320 & 2856.61164104612 & -536.61164104612 \tabularnewline
73 & 3400 & 2735.92098582944 & 664.079014170562 \tabularnewline
74 & 2640 & 3080.23433932592 & -440.234339325921 \tabularnewline
75 & 2340 & 3094.06336709927 & -754.063367099273 \tabularnewline
76 & 2340 & 2619.68561167629 & -279.685611676287 \tabularnewline
77 & 1960 & 2861.74959624682 & -901.749596246818 \tabularnewline
78 & 2100 & 2711.66476672423 & -611.664766724231 \tabularnewline
79 & 2280 & 2587.15155054436 & -307.151550544364 \tabularnewline
80 & 2320 & 2294.37550277366 & 25.6244972263357 \tabularnewline
81 & 2660 & 2344.40154943677 & 315.598450563233 \tabularnewline
82 & 2520 & 2378.44140649604 & 141.558593503958 \tabularnewline
83 & 2120 & 2412.07190524665 & -292.071905246651 \tabularnewline
84 & 1800 & 2226.84332649562 & -426.843326495618 \tabularnewline
85 & 2300 & 2310.5164363129 & -10.516436312902 \tabularnewline
86 & 2420 & 2257.58911002446 & 162.410889975537 \tabularnewline
87 & 1920 & 2161.9551854797 & -241.955185479701 \tabularnewline
88 & 1720 & 1945.43943923264 & -225.439439232637 \tabularnewline
89 & 2000 & 2149.01771356684 & -149.017713566843 \tabularnewline
90 & 1960 & 2126.94075030225 & -166.940750302252 \tabularnewline
91 & 2860 & 1890.03030744637 & 969.969692553626 \tabularnewline
92 & 2160 & 1798.15133394921 & 361.848666050795 \tabularnewline
93 & 2360 & 2085.84216336012 & 274.157836639879 \tabularnewline
94 & 2300 & 2114.34395576964 & 185.656044230362 \tabularnewline
95 & 2360 & 2264.26493059641 & 95.7350694035931 \tabularnewline
96 & 2260 & 1920.00883743936 & 339.991162560644 \tabularnewline
97 & 2460 & 2191.16204216883 & 268.837957831173 \tabularnewline
98 & 2200 & 2203.09588430307 & -3.0958843030744 \tabularnewline
99 & 1620 & 2319.15188289907 & -699.151882899072 \tabularnewline
100 & 1740 & 1980.13251447601 & -240.132514476009 \tabularnewline
101 & 1720 & 2158.95707679863 & -438.957076798634 \tabularnewline
102 & 2460 & 2017.38611799845 & 442.613882001553 \tabularnewline
103 & 1840 & 1955.73909223056 & -115.739092230562 \tabularnewline
104 & 2160 & 1807.75655814871 & 352.243441851293 \tabularnewline
105 & 2460 & 1977.15591791606 & 482.844082083935 \tabularnewline
106 & 2860 & 2196.46423282241 & 663.535767177586 \tabularnewline
107 & 2700 & 1995.25046446616 & 704.749535533841 \tabularnewline
108 & 2420 & 2084.88616246349 & 335.11383753651 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298001&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]5[/C][C]3180[/C][C]3697.64685614159[/C][C]-517.64685614159[/C][/ROW]
[ROW][C]6[/C][C]4080[/C][C]4457.35479120993[/C][C]-377.354791209932[/C][/ROW]
[ROW][C]7[/C][C]3360[/C][C]2342.9491917359[/C][C]1017.0508082641[/C][/ROW]
[ROW][C]8[/C][C]4960[/C][C]5728.07286637977[/C][C]-768.072866379768[/C][/ROW]
[ROW][C]9[/C][C]4640[/C][C]2979.4854963005[/C][C]1660.5145036995[/C][/ROW]
[ROW][C]10[/C][C]5420[/C][C]3900.48872595052[/C][C]1519.51127404948[/C][/ROW]
[ROW][C]11[/C][C]4880[/C][C]2495.73391149243[/C][C]2384.26608850757[/C][/ROW]
[ROW][C]12[/C][C]4780[/C][C]5542.82626055735[/C][C]-762.826260557347[/C][/ROW]
[ROW][C]13[/C][C]4860[/C][C]3551.68008572899[/C][C]1308.31991427101[/C][/ROW]
[ROW][C]14[/C][C]3780[/C][C]4473.87208027805[/C][C]-693.872080278052[/C][/ROW]
[ROW][C]15[/C][C]4120[/C][C]3131.79756115362[/C][C]988.202438846379[/C][/ROW]
[ROW][C]16[/C][C]3980[/C][C]5015.8368944376[/C][C]-1035.8368944376[/C][/ROW]
[ROW][C]17[/C][C]3060[/C][C]3695.28213065194[/C][C]-635.282130651935[/C][/ROW]
[ROW][C]18[/C][C]4420[/C][C]3801.83322598568[/C][C]618.166774014321[/C][/ROW]
[ROW][C]19[/C][C]3340[/C][C]3132.87264473423[/C][C]207.127355265772[/C][/ROW]
[ROW][C]20[/C][C]4220[/C][C]4195.620266115[/C][C]24.3797338849972[/C][/ROW]
[ROW][C]21[/C][C]5780[/C][C]3181.35560563633[/C][C]2598.64439436367[/C][/ROW]
[ROW][C]22[/C][C]5440[/C][C]3988.75447871034[/C][C]1451.24552128966[/C][/ROW]
[ROW][C]23[/C][C]4200[/C][C]3301.87636036596[/C][C]898.123639634044[/C][/ROW]
[ROW][C]24[/C][C]3720[/C][C]4500.72400664649[/C][C]-780.724006646491[/C][/ROW]
[ROW][C]25[/C][C]4040[/C][C]4178.02948626379[/C][C]-138.029486263789[/C][/ROW]
[ROW][C]26[/C][C]3920[/C][C]4404.57708064004[/C][C]-484.577080640044[/C][/ROW]
[ROW][C]27[/C][C]3160[/C][C]3410.89936051174[/C][C]-250.899360511739[/C][/ROW]
[ROW][C]28[/C][C]3500[/C][C]3937.03045715906[/C][C]-437.030457159059[/C][/ROW]
[ROW][C]29[/C][C]2780[/C][C]3823.05635822612[/C][C]-1043.05635822612[/C][/ROW]
[ROW][C]30[/C][C]3340[/C][C]3819.8895454312[/C][C]-479.889545431205[/C][/ROW]
[ROW][C]31[/C][C]3100[/C][C]2962.06040313348[/C][C]137.939596866522[/C][/ROW]
[ROW][C]32[/C][C]3100[/C][C]3390.83425003228[/C][C]-290.834250032276[/C][/ROW]
[ROW][C]33[/C][C]4400[/C][C]3106.61480552768[/C][C]1293.38519447232[/C][/ROW]
[ROW][C]34[/C][C]3480[/C][C]3469.88626569539[/C][C]10.1137343046094[/C][/ROW]
[ROW][C]35[/C][C]5100[/C][C]2878.24689096773[/C][C]2221.75310903227[/C][/ROW]
[ROW][C]36[/C][C]4260[/C][C]3413.14194245316[/C][C]846.858057546837[/C][/ROW]
[ROW][C]37[/C][C]3640[/C][C]3766.24034628318[/C][C]-126.240346283179[/C][/ROW]
[ROW][C]38[/C][C]2900[/C][C]3655.91000630809[/C][C]-755.910006308093[/C][/ROW]
[ROW][C]39[/C][C]3820[/C][C]3647.22219788111[/C][C]172.777802118888[/C][/ROW]
[ROW][C]40[/C][C]2980[/C][C]3586.14749957272[/C][C]-606.147499572715[/C][/ROW]
[ROW][C]41[/C][C]2860[/C][C]3503.05210621503[/C][C]-643.052106215026[/C][/ROW]
[ROW][C]42[/C][C]2420[/C][C]3154.49689351003[/C][C]-734.496893510028[/C][/ROW]
[ROW][C]43[/C][C]2680[/C][C]3372.73035453377[/C][C]-692.730354533767[/C][/ROW]
[ROW][C]44[/C][C]4420[/C][C]3000.31988897625[/C][C]1419.68011102375[/C][/ROW]
[ROW][C]45[/C][C]3160[/C][C]3078.41305716659[/C][C]81.5869428334063[/C][/ROW]
[ROW][C]46[/C][C]3160[/C][C]2778.78106368045[/C][C]381.218936319545[/C][/ROW]
[ROW][C]47[/C][C]4300[/C][C]3113.81843961301[/C][C]1186.18156038699[/C][/ROW]
[ROW][C]48[/C][C]2820[/C][C]3577.0535529347[/C][C]-757.053552934697[/C][/ROW]
[ROW][C]49[/C][C]3240[/C][C]3077.36889349136[/C][C]162.631106508643[/C][/ROW]
[ROW][C]50[/C][C]2520[/C][C]2885.9463512132[/C][C]-365.946351213196[/C][/ROW]
[ROW][C]51[/C][C]3480[/C][C]3372.07415721217[/C][C]107.925842787831[/C][/ROW]
[ROW][C]52[/C][C]2740[/C][C]3155.81481434651[/C][C]-415.81481434651[/C][/ROW]
[ROW][C]53[/C][C]2240[/C][C]2961.33950678803[/C][C]-721.339506788028[/C][/ROW]
[ROW][C]54[/C][C]3700[/C][C]2543.74866372712[/C][C]1156.25133627288[/C][/ROW]
[ROW][C]55[/C][C]2600[/C][C]3286.56116725045[/C][C]-686.561167250446[/C][/ROW]
[ROW][C]56[/C][C]3160[/C][C]2855.96872785125[/C][C]304.03127214875[/C][/ROW]
[ROW][C]57[/C][C]3800[/C][C]2641.04602990545[/C][C]1158.95397009455[/C][/ROW]
[ROW][C]58[/C][C]3440[/C][C]2970.2994730643[/C][C]469.700526935695[/C][/ROW]
[ROW][C]59[/C][C]2180[/C][C]3115.51820852747[/C][C]-935.518208527466[/C][/ROW]
[ROW][C]60[/C][C]2300[/C][C]2970.74680381995[/C][C]-670.746803819952[/C][/ROW]
[ROW][C]61[/C][C]3160[/C][C]2912.09168710513[/C][C]247.908312894873[/C][/ROW]
[ROW][C]62[/C][C]1800[/C][C]2940.13346226433[/C][C]-1140.13346226433[/C][/ROW]
[ROW][C]63[/C][C]2620[/C][C]2519.25340730495[/C][C]100.746592695049[/C][/ROW]
[ROW][C]64[/C][C]2820[/C][C]2523.95523833079[/C][C]296.044761669214[/C][/ROW]
[ROW][C]65[/C][C]2180[/C][C]2802.12840272653[/C][C]-622.128402726529[/C][/ROW]
[ROW][C]66[/C][C]2300[/C][C]2346.9330458797[/C][C]-46.9330458797012[/C][/ROW]
[ROW][C]67[/C][C]2560[/C][C]2386.2700313623[/C][C]173.729968637705[/C][/ROW]
[ROW][C]68[/C][C]2860[/C][C]2447.74703615888[/C][C]412.252963841116[/C][/ROW]
[ROW][C]69[/C][C]2620[/C][C]2457.68461018222[/C][C]162.315389817782[/C][/ROW]
[ROW][C]70[/C][C]3960[/C][C]2258.5111480254[/C][C]1701.4888519746[/C][/ROW]
[ROW][C]71[/C][C]3960[/C][C]2554.65600416148[/C][C]1405.34399583852[/C][/ROW]
[ROW][C]72[/C][C]2320[/C][C]2856.61164104612[/C][C]-536.61164104612[/C][/ROW]
[ROW][C]73[/C][C]3400[/C][C]2735.92098582944[/C][C]664.079014170562[/C][/ROW]
[ROW][C]74[/C][C]2640[/C][C]3080.23433932592[/C][C]-440.234339325921[/C][/ROW]
[ROW][C]75[/C][C]2340[/C][C]3094.06336709927[/C][C]-754.063367099273[/C][/ROW]
[ROW][C]76[/C][C]2340[/C][C]2619.68561167629[/C][C]-279.685611676287[/C][/ROW]
[ROW][C]77[/C][C]1960[/C][C]2861.74959624682[/C][C]-901.749596246818[/C][/ROW]
[ROW][C]78[/C][C]2100[/C][C]2711.66476672423[/C][C]-611.664766724231[/C][/ROW]
[ROW][C]79[/C][C]2280[/C][C]2587.15155054436[/C][C]-307.151550544364[/C][/ROW]
[ROW][C]80[/C][C]2320[/C][C]2294.37550277366[/C][C]25.6244972263357[/C][/ROW]
[ROW][C]81[/C][C]2660[/C][C]2344.40154943677[/C][C]315.598450563233[/C][/ROW]
[ROW][C]82[/C][C]2520[/C][C]2378.44140649604[/C][C]141.558593503958[/C][/ROW]
[ROW][C]83[/C][C]2120[/C][C]2412.07190524665[/C][C]-292.071905246651[/C][/ROW]
[ROW][C]84[/C][C]1800[/C][C]2226.84332649562[/C][C]-426.843326495618[/C][/ROW]
[ROW][C]85[/C][C]2300[/C][C]2310.5164363129[/C][C]-10.516436312902[/C][/ROW]
[ROW][C]86[/C][C]2420[/C][C]2257.58911002446[/C][C]162.410889975537[/C][/ROW]
[ROW][C]87[/C][C]1920[/C][C]2161.9551854797[/C][C]-241.955185479701[/C][/ROW]
[ROW][C]88[/C][C]1720[/C][C]1945.43943923264[/C][C]-225.439439232637[/C][/ROW]
[ROW][C]89[/C][C]2000[/C][C]2149.01771356684[/C][C]-149.017713566843[/C][/ROW]
[ROW][C]90[/C][C]1960[/C][C]2126.94075030225[/C][C]-166.940750302252[/C][/ROW]
[ROW][C]91[/C][C]2860[/C][C]1890.03030744637[/C][C]969.969692553626[/C][/ROW]
[ROW][C]92[/C][C]2160[/C][C]1798.15133394921[/C][C]361.848666050795[/C][/ROW]
[ROW][C]93[/C][C]2360[/C][C]2085.84216336012[/C][C]274.157836639879[/C][/ROW]
[ROW][C]94[/C][C]2300[/C][C]2114.34395576964[/C][C]185.656044230362[/C][/ROW]
[ROW][C]95[/C][C]2360[/C][C]2264.26493059641[/C][C]95.7350694035931[/C][/ROW]
[ROW][C]96[/C][C]2260[/C][C]1920.00883743936[/C][C]339.991162560644[/C][/ROW]
[ROW][C]97[/C][C]2460[/C][C]2191.16204216883[/C][C]268.837957831173[/C][/ROW]
[ROW][C]98[/C][C]2200[/C][C]2203.09588430307[/C][C]-3.0958843030744[/C][/ROW]
[ROW][C]99[/C][C]1620[/C][C]2319.15188289907[/C][C]-699.151882899072[/C][/ROW]
[ROW][C]100[/C][C]1740[/C][C]1980.13251447601[/C][C]-240.132514476009[/C][/ROW]
[ROW][C]101[/C][C]1720[/C][C]2158.95707679863[/C][C]-438.957076798634[/C][/ROW]
[ROW][C]102[/C][C]2460[/C][C]2017.38611799845[/C][C]442.613882001553[/C][/ROW]
[ROW][C]103[/C][C]1840[/C][C]1955.73909223056[/C][C]-115.739092230562[/C][/ROW]
[ROW][C]104[/C][C]2160[/C][C]1807.75655814871[/C][C]352.243441851293[/C][/ROW]
[ROW][C]105[/C][C]2460[/C][C]1977.15591791606[/C][C]482.844082083935[/C][/ROW]
[ROW][C]106[/C][C]2860[/C][C]2196.46423282241[/C][C]663.535767177586[/C][/ROW]
[ROW][C]107[/C][C]2700[/C][C]1995.25046446616[/C][C]704.749535533841[/C][/ROW]
[ROW][C]108[/C][C]2420[/C][C]2084.88616246349[/C][C]335.11383753651[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298001&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298001&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
531803697.64685614159-517.64685614159
640804457.35479120993-377.354791209932
733602342.94919173591017.0508082641
849605728.07286637977-768.072866379768
946402979.48549630051660.5145036995
1054203900.488725950521519.51127404948
1148802495.733911492432384.26608850757
1247805542.82626055735-762.826260557347
1348603551.680085728991308.31991427101
1437804473.87208027805-693.872080278052
1541203131.79756115362988.202438846379
1639805015.8368944376-1035.8368944376
1730603695.28213065194-635.282130651935
1844203801.83322598568618.166774014321
1933403132.87264473423207.127355265772
2042204195.62026611524.3797338849972
2157803181.355605636332598.64439436367
2254403988.754478710341451.24552128966
2342003301.87636036596898.123639634044
2437204500.72400664649-780.724006646491
2540404178.02948626379-138.029486263789
2639204404.57708064004-484.577080640044
2731603410.89936051174-250.899360511739
2835003937.03045715906-437.030457159059
2927803823.05635822612-1043.05635822612
3033403819.8895454312-479.889545431205
3131002962.06040313348137.939596866522
3231003390.83425003228-290.834250032276
3344003106.614805527681293.38519447232
3434803469.8862656953910.1137343046094
3551002878.246890967732221.75310903227
3642603413.14194245316846.858057546837
3736403766.24034628318-126.240346283179
3829003655.91000630809-755.910006308093
3938203647.22219788111172.777802118888
4029803586.14749957272-606.147499572715
4128603503.05210621503-643.052106215026
4224203154.49689351003-734.496893510028
4326803372.73035453377-692.730354533767
4444203000.319888976251419.68011102375
4531603078.4130571665981.5869428334063
4631602778.78106368045381.218936319545
4743003113.818439613011186.18156038699
4828203577.0535529347-757.053552934697
4932403077.36889349136162.631106508643
5025202885.9463512132-365.946351213196
5134803372.07415721217107.925842787831
5227403155.81481434651-415.81481434651
5322402961.33950678803-721.339506788028
5437002543.748663727121156.25133627288
5526003286.56116725045-686.561167250446
5631602855.96872785125304.03127214875
5738002641.046029905451158.95397009455
5834402970.2994730643469.700526935695
5921803115.51820852747-935.518208527466
6023002970.74680381995-670.746803819952
6131602912.09168710513247.908312894873
6218002940.13346226433-1140.13346226433
6326202519.25340730495100.746592695049
6428202523.95523833079296.044761669214
6521802802.12840272653-622.128402726529
6623002346.9330458797-46.9330458797012
6725602386.2700313623173.729968637705
6828602447.74703615888412.252963841116
6926202457.68461018222162.315389817782
7039602258.51114802541701.4888519746
7139602554.656004161481405.34399583852
7223202856.61164104612-536.61164104612
7334002735.92098582944664.079014170562
7426403080.23433932592-440.234339325921
7523403094.06336709927-754.063367099273
7623402619.68561167629-279.685611676287
7719602861.74959624682-901.749596246818
7821002711.66476672423-611.664766724231
7922802587.15155054436-307.151550544364
8023202294.3755027736625.6244972263357
8126602344.40154943677315.598450563233
8225202378.44140649604141.558593503958
8321202412.07190524665-292.071905246651
8418002226.84332649562-426.843326495618
8523002310.5164363129-10.516436312902
8624202257.58911002446162.410889975537
8719202161.9551854797-241.955185479701
8817201945.43943923264-225.439439232637
8920002149.01771356684-149.017713566843
9019602126.94075030225-166.940750302252
9128601890.03030744637969.969692553626
9221601798.15133394921361.848666050795
9323602085.84216336012274.157836639879
9423002114.34395576964185.656044230362
9523602264.2649305964195.7350694035931
9622601920.00883743936339.991162560644
9724602191.16204216883268.837957831173
9822002203.09588430307-3.0958843030744
9916202319.15188289907-699.151882899072
10017401980.13251447601-240.132514476009
10117202158.95707679863-438.957076798634
10224602017.38611799845442.613882001553
10318401955.73909223056-115.739092230562
10421601807.75655814871352.243441851293
10524601977.15591791606482.844082083935
10628602196.46423282241663.535767177586
10727001995.25046446616704.749535533841
10824202084.88616246349335.11383753651







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1092332.058507178461737.378753383972926.73826097295
1102598.18543086781979.193248356813217.1776133788
1112341.800450201911707.413052184952976.18784821888
1122257.718525912281968.062390153782547.37466167078
1132376.925777364991451.284052887893302.56750184208
1142647.9335276841681.119692220343614.74736314767
1152386.425867138221413.804200144373359.04753413208
1162300.53768449341805.130455801642795.94491318516
1172421.793047551511190.562757351393653.02333775164
1182697.681624500211404.64686922293990.71637977751
1192431.051284074531143.157651113993718.94491703507
1202343.356843074521628.749726758763057.96395939027

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 2332.05850717846 & 1737.37875338397 & 2926.73826097295 \tabularnewline
110 & 2598.1854308678 & 1979.19324835681 & 3217.1776133788 \tabularnewline
111 & 2341.80045020191 & 1707.41305218495 & 2976.18784821888 \tabularnewline
112 & 2257.71852591228 & 1968.06239015378 & 2547.37466167078 \tabularnewline
113 & 2376.92577736499 & 1451.28405288789 & 3302.56750184208 \tabularnewline
114 & 2647.933527684 & 1681.11969222034 & 3614.74736314767 \tabularnewline
115 & 2386.42586713822 & 1413.80420014437 & 3359.04753413208 \tabularnewline
116 & 2300.5376844934 & 1805.13045580164 & 2795.94491318516 \tabularnewline
117 & 2421.79304755151 & 1190.56275735139 & 3653.02333775164 \tabularnewline
118 & 2697.68162450021 & 1404.6468692229 & 3990.71637977751 \tabularnewline
119 & 2431.05128407453 & 1143.15765111399 & 3718.94491703507 \tabularnewline
120 & 2343.35684307452 & 1628.74972675876 & 3057.96395939027 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298001&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]109[/C][C]2332.05850717846[/C][C]1737.37875338397[/C][C]2926.73826097295[/C][/ROW]
[ROW][C]110[/C][C]2598.1854308678[/C][C]1979.19324835681[/C][C]3217.1776133788[/C][/ROW]
[ROW][C]111[/C][C]2341.80045020191[/C][C]1707.41305218495[/C][C]2976.18784821888[/C][/ROW]
[ROW][C]112[/C][C]2257.71852591228[/C][C]1968.06239015378[/C][C]2547.37466167078[/C][/ROW]
[ROW][C]113[/C][C]2376.92577736499[/C][C]1451.28405288789[/C][C]3302.56750184208[/C][/ROW]
[ROW][C]114[/C][C]2647.933527684[/C][C]1681.11969222034[/C][C]3614.74736314767[/C][/ROW]
[ROW][C]115[/C][C]2386.42586713822[/C][C]1413.80420014437[/C][C]3359.04753413208[/C][/ROW]
[ROW][C]116[/C][C]2300.5376844934[/C][C]1805.13045580164[/C][C]2795.94491318516[/C][/ROW]
[ROW][C]117[/C][C]2421.79304755151[/C][C]1190.56275735139[/C][C]3653.02333775164[/C][/ROW]
[ROW][C]118[/C][C]2697.68162450021[/C][C]1404.6468692229[/C][C]3990.71637977751[/C][/ROW]
[ROW][C]119[/C][C]2431.05128407453[/C][C]1143.15765111399[/C][C]3718.94491703507[/C][/ROW]
[ROW][C]120[/C][C]2343.35684307452[/C][C]1628.74972675876[/C][C]3057.96395939027[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298001&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298001&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
1092332.058507178461737.378753383972926.73826097295
1102598.18543086781979.193248356813217.1776133788
1112341.800450201911707.413052184952976.18784821888
1122257.718525912281968.062390153782547.37466167078
1132376.925777364991451.284052887893302.56750184208
1142647.9335276841681.119692220343614.74736314767
1152386.425867138221413.804200144373359.04753413208
1162300.53768449341805.130455801642795.94491318516
1172421.793047551511190.562757351393653.02333775164
1182697.681624500211404.64686922293990.71637977751
1192431.051284074531143.157651113993718.94491703507
1202343.356843074521628.749726758763057.96395939027



Parameters (Session):
par1 = 4 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
Parameters (R input):
par1 = 4 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
R code (references can be found in the software module):
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')