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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 computationFri, 16 Dec 2016 14:37:04 +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/16/t1481895507jpjv4qfq3odllev.htm/, Retrieved Fri, 01 Nov 2024 03:40:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300259, Retrieved Fri, 01 Nov 2024 03:40:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [forecast N2170: s...] [2016-12-16 13:37:04] [111362aa4cdbe055231fbc5cb9e916c4] [Current]
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Dataseries X:
4030
4320
4840
4410
4180
4240
3680
4270
4140
4470
4180
4510
4490
3960
3750
3670
3590
2840
3530
4320
3740
3710
3830
3490
4200
4280
4650
2100
2410
1230
2420
2360
1870
2250
1960
2550
3180
3330
3760
3930
3710
3250
3450
3480
3090
3690
3250
3300
4040
3630
3820
3400
2500
2380
2520
2340
2420
2430
2080
2420
2430
2400
2790
2370
2700
2640
2910
2420
2800
2830
2310
2540
2780
2820
3610
3270
3030
3250
3040
3630
3320
3440
3110
3180
3330
3100
3440
3320
3380
3610
3320
3860
3430
3510
3290
3010
3860
3530
3610
3370
3700
3500
4110
4590
3680
4220
3740
3550
4150
4110
4160
3780
3150
3260
4750
4110
3610
3890
2800
2610
3600
3400
3400
3120
3150
3240




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=300259&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=300259&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300259&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
alpha0.845601496093728
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.845601496093728 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300259&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]0.845601496093728[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300259&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300259&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
alpha0.845601496093728
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1344904912.96207264958-422.962072649576
1439603981.59696064344-21.5969606434392
1537503720.0434544961929.9565455038137
1636703665.833670275934.16632972407388
1735903587.732307674412.26769232559491
1828402848.85878778152-8.85878778152437
1935303127.66003299714402.339967002861
2043204005.83822711698314.161772883024
2137404154.03614169957-414.036141699568
2237104162.30214359212-452.302143592121
2338303497.37702370147332.622976298527
2434904143.68575951191-653.685759511905
2542003522.3323081512677.667691848801
2642803583.6315444641696.368455535902
2746503937.15045260191712.849547398089
2821004456.41404172358-2356.41404172358
2924102381.9092386026528.0907613973509
3012301663.15383266829-433.153832668294
3124201646.65902568933773.340974310668
3223602824.94164539167-464.94164539167
3318702201.89587531022-331.895875310224
3422502273.71159590846-23.7115959084585
3519602092.39454854031-132.394548540313
3625502193.1991764384356.800823561597
3731802631.87367256783548.126327432166
3833302586.5199072592743.480092740803
3937602982.42114222716777.578857772838
4039303082.53022678845847.469773211551
4137104085.39834504634-375.398345046337
4232502954.23647178709295.763528212913
4334503740.3962688662-290.396268866204
4434803827.99210039238-347.992100392381
4530903324.38110838145-234.381108381447
4636903526.23865345295163.761346547048
4732503486.6685214158-236.668521415801
4833003574.82995541715-274.829955417149
4940403508.93689142003531.063108579966
5036303479.31677181791150.683228182088
5138203379.21288954136440.787110458645
5234003205.32142148212194.678578517883
5325003467.37932093653-967.379320936531
5423801939.26383791567440.736162084333
5525202757.51051537009-237.510515370086
5623402880.93390895574-540.933908955745
5724202231.7124021584188.287597841604
5824302852.45183694664-422.451836946644
5920802255.35318738451-175.35318738451
6024202389.4708912594830.5291087405221
6124302706.21859214947-276.218592149467
6224001935.22977419197464.770225808032
6327902145.5099324124644.490067587602
6423702105.8712005299264.1287994701
6527002247.23630959732452.763690402679
6626402137.40680553762502.593194462376
6729102903.239609836476.76039016352797
6824203186.37072857373-766.370728573735
6928002459.11021949859340.88978050141
7028303114.59303324327-284.59303324327
7123102672.21965615205-362.219656152055
7225402680.11071296993-140.110712969928
7327802805.20373923429-25.2037392342904
7428202360.88102134753459.118978652473
7536102594.130951211461015.86904878854
7632702809.80363070901460.196369290995
7730303146.08871509695-116.08871509695
7832502562.93036676746687.069633232541
7930403408.20088051301-368.200880513009
8036303254.89389973257375.10610026743
8133203663.82727091754-343.827270917538
8234403643.73871092021-203.738710920206
8331103257.75043531061-147.750435310605
8431803481.29027466959-301.290274669588
8533303487.83108725417-157.831087254167
8631003006.1371885083993.8628114916123
8734403016.48733484236423.512665157644
8833202645.46753974494674.532460255065
8933803074.01798846598305.982011534019
9036102971.76972541491638.23027458509
9133203612.8094158812-292.809415881201
9238603638.0190561617221.980943838295
9334303806.46732906136-376.467329061359
9435103780.407751143-270.407751142998
9532903346.68854136829-56.6885413682853
9630103623.52413299499-613.524132994986
9738603388.18941175704471.810588242959
9835303477.7826172232852.2173827767219
9936103503.81477094943106.185229050573
10033702903.21950194218466.780498057819
10137003099.19094271631600.809057283687
10235003297.5475053806202.452494619401
10341103426.34171785815683.658282141854
10445904356.73676584021233.263234159795
10536804442.32584231409-762.325842314085
10642204106.35916846424113.640831535757
10737404030.38994102061-290.389941020608
10835504023.63269719318-473.63269719318
10941504074.1644405566175.8355594433879
11041103764.13600608095345.863993919049
11141604046.80872823563113.191271764369
11237803507.81314947927272.186850520734
11331503559.92971979089-409.92971979089
11432602842.09840310436417.901596895642
11547503227.374152463251522.62584753675
11641104797.66110734212-687.661107342122
11736103950.79771893986-340.797718939856
11838904106.52380077501-216.523800775012
11928003688.98511947736-888.985119477356
12026103147.7624897877-537.762489787702
12136003228.9030613577371.0969386423
12234003210.24007716653189.759922833469
12334003324.9866430644475.0133569355589
12431202778.25644189879341.743558101211
12531502783.87249025803366.127509741973
12632402850.092244702389.907755298003

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4490 & 4912.96207264958 & -422.962072649576 \tabularnewline
14 & 3960 & 3981.59696064344 & -21.5969606434392 \tabularnewline
15 & 3750 & 3720.04345449619 & 29.9565455038137 \tabularnewline
16 & 3670 & 3665.83367027593 & 4.16632972407388 \tabularnewline
17 & 3590 & 3587.73230767441 & 2.26769232559491 \tabularnewline
18 & 2840 & 2848.85878778152 & -8.85878778152437 \tabularnewline
19 & 3530 & 3127.66003299714 & 402.339967002861 \tabularnewline
20 & 4320 & 4005.83822711698 & 314.161772883024 \tabularnewline
21 & 3740 & 4154.03614169957 & -414.036141699568 \tabularnewline
22 & 3710 & 4162.30214359212 & -452.302143592121 \tabularnewline
23 & 3830 & 3497.37702370147 & 332.622976298527 \tabularnewline
24 & 3490 & 4143.68575951191 & -653.685759511905 \tabularnewline
25 & 4200 & 3522.3323081512 & 677.667691848801 \tabularnewline
26 & 4280 & 3583.6315444641 & 696.368455535902 \tabularnewline
27 & 4650 & 3937.15045260191 & 712.849547398089 \tabularnewline
28 & 2100 & 4456.41404172358 & -2356.41404172358 \tabularnewline
29 & 2410 & 2381.90923860265 & 28.0907613973509 \tabularnewline
30 & 1230 & 1663.15383266829 & -433.153832668294 \tabularnewline
31 & 2420 & 1646.65902568933 & 773.340974310668 \tabularnewline
32 & 2360 & 2824.94164539167 & -464.94164539167 \tabularnewline
33 & 1870 & 2201.89587531022 & -331.895875310224 \tabularnewline
34 & 2250 & 2273.71159590846 & -23.7115959084585 \tabularnewline
35 & 1960 & 2092.39454854031 & -132.394548540313 \tabularnewline
36 & 2550 & 2193.1991764384 & 356.800823561597 \tabularnewline
37 & 3180 & 2631.87367256783 & 548.126327432166 \tabularnewline
38 & 3330 & 2586.5199072592 & 743.480092740803 \tabularnewline
39 & 3760 & 2982.42114222716 & 777.578857772838 \tabularnewline
40 & 3930 & 3082.53022678845 & 847.469773211551 \tabularnewline
41 & 3710 & 4085.39834504634 & -375.398345046337 \tabularnewline
42 & 3250 & 2954.23647178709 & 295.763528212913 \tabularnewline
43 & 3450 & 3740.3962688662 & -290.396268866204 \tabularnewline
44 & 3480 & 3827.99210039238 & -347.992100392381 \tabularnewline
45 & 3090 & 3324.38110838145 & -234.381108381447 \tabularnewline
46 & 3690 & 3526.23865345295 & 163.761346547048 \tabularnewline
47 & 3250 & 3486.6685214158 & -236.668521415801 \tabularnewline
48 & 3300 & 3574.82995541715 & -274.829955417149 \tabularnewline
49 & 4040 & 3508.93689142003 & 531.063108579966 \tabularnewline
50 & 3630 & 3479.31677181791 & 150.683228182088 \tabularnewline
51 & 3820 & 3379.21288954136 & 440.787110458645 \tabularnewline
52 & 3400 & 3205.32142148212 & 194.678578517883 \tabularnewline
53 & 2500 & 3467.37932093653 & -967.379320936531 \tabularnewline
54 & 2380 & 1939.26383791567 & 440.736162084333 \tabularnewline
55 & 2520 & 2757.51051537009 & -237.510515370086 \tabularnewline
56 & 2340 & 2880.93390895574 & -540.933908955745 \tabularnewline
57 & 2420 & 2231.7124021584 & 188.287597841604 \tabularnewline
58 & 2430 & 2852.45183694664 & -422.451836946644 \tabularnewline
59 & 2080 & 2255.35318738451 & -175.35318738451 \tabularnewline
60 & 2420 & 2389.47089125948 & 30.5291087405221 \tabularnewline
61 & 2430 & 2706.21859214947 & -276.218592149467 \tabularnewline
62 & 2400 & 1935.22977419197 & 464.770225808032 \tabularnewline
63 & 2790 & 2145.5099324124 & 644.490067587602 \tabularnewline
64 & 2370 & 2105.8712005299 & 264.1287994701 \tabularnewline
65 & 2700 & 2247.23630959732 & 452.763690402679 \tabularnewline
66 & 2640 & 2137.40680553762 & 502.593194462376 \tabularnewline
67 & 2910 & 2903.23960983647 & 6.76039016352797 \tabularnewline
68 & 2420 & 3186.37072857373 & -766.370728573735 \tabularnewline
69 & 2800 & 2459.11021949859 & 340.88978050141 \tabularnewline
70 & 2830 & 3114.59303324327 & -284.59303324327 \tabularnewline
71 & 2310 & 2672.21965615205 & -362.219656152055 \tabularnewline
72 & 2540 & 2680.11071296993 & -140.110712969928 \tabularnewline
73 & 2780 & 2805.20373923429 & -25.2037392342904 \tabularnewline
74 & 2820 & 2360.88102134753 & 459.118978652473 \tabularnewline
75 & 3610 & 2594.13095121146 & 1015.86904878854 \tabularnewline
76 & 3270 & 2809.80363070901 & 460.196369290995 \tabularnewline
77 & 3030 & 3146.08871509695 & -116.08871509695 \tabularnewline
78 & 3250 & 2562.93036676746 & 687.069633232541 \tabularnewline
79 & 3040 & 3408.20088051301 & -368.200880513009 \tabularnewline
80 & 3630 & 3254.89389973257 & 375.10610026743 \tabularnewline
81 & 3320 & 3663.82727091754 & -343.827270917538 \tabularnewline
82 & 3440 & 3643.73871092021 & -203.738710920206 \tabularnewline
83 & 3110 & 3257.75043531061 & -147.750435310605 \tabularnewline
84 & 3180 & 3481.29027466959 & -301.290274669588 \tabularnewline
85 & 3330 & 3487.83108725417 & -157.831087254167 \tabularnewline
86 & 3100 & 3006.13718850839 & 93.8628114916123 \tabularnewline
87 & 3440 & 3016.48733484236 & 423.512665157644 \tabularnewline
88 & 3320 & 2645.46753974494 & 674.532460255065 \tabularnewline
89 & 3380 & 3074.01798846598 & 305.982011534019 \tabularnewline
90 & 3610 & 2971.76972541491 & 638.23027458509 \tabularnewline
91 & 3320 & 3612.8094158812 & -292.809415881201 \tabularnewline
92 & 3860 & 3638.0190561617 & 221.980943838295 \tabularnewline
93 & 3430 & 3806.46732906136 & -376.467329061359 \tabularnewline
94 & 3510 & 3780.407751143 & -270.407751142998 \tabularnewline
95 & 3290 & 3346.68854136829 & -56.6885413682853 \tabularnewline
96 & 3010 & 3623.52413299499 & -613.524132994986 \tabularnewline
97 & 3860 & 3388.18941175704 & 471.810588242959 \tabularnewline
98 & 3530 & 3477.78261722328 & 52.2173827767219 \tabularnewline
99 & 3610 & 3503.81477094943 & 106.185229050573 \tabularnewline
100 & 3370 & 2903.21950194218 & 466.780498057819 \tabularnewline
101 & 3700 & 3099.19094271631 & 600.809057283687 \tabularnewline
102 & 3500 & 3297.5475053806 & 202.452494619401 \tabularnewline
103 & 4110 & 3426.34171785815 & 683.658282141854 \tabularnewline
104 & 4590 & 4356.73676584021 & 233.263234159795 \tabularnewline
105 & 3680 & 4442.32584231409 & -762.325842314085 \tabularnewline
106 & 4220 & 4106.35916846424 & 113.640831535757 \tabularnewline
107 & 3740 & 4030.38994102061 & -290.389941020608 \tabularnewline
108 & 3550 & 4023.63269719318 & -473.63269719318 \tabularnewline
109 & 4150 & 4074.16444055661 & 75.8355594433879 \tabularnewline
110 & 4110 & 3764.13600608095 & 345.863993919049 \tabularnewline
111 & 4160 & 4046.80872823563 & 113.191271764369 \tabularnewline
112 & 3780 & 3507.81314947927 & 272.186850520734 \tabularnewline
113 & 3150 & 3559.92971979089 & -409.92971979089 \tabularnewline
114 & 3260 & 2842.09840310436 & 417.901596895642 \tabularnewline
115 & 4750 & 3227.37415246325 & 1522.62584753675 \tabularnewline
116 & 4110 & 4797.66110734212 & -687.661107342122 \tabularnewline
117 & 3610 & 3950.79771893986 & -340.797718939856 \tabularnewline
118 & 3890 & 4106.52380077501 & -216.523800775012 \tabularnewline
119 & 2800 & 3688.98511947736 & -888.985119477356 \tabularnewline
120 & 2610 & 3147.7624897877 & -537.762489787702 \tabularnewline
121 & 3600 & 3228.9030613577 & 371.0969386423 \tabularnewline
122 & 3400 & 3210.24007716653 & 189.759922833469 \tabularnewline
123 & 3400 & 3324.98664306444 & 75.0133569355589 \tabularnewline
124 & 3120 & 2778.25644189879 & 341.743558101211 \tabularnewline
125 & 3150 & 2783.87249025803 & 366.127509741973 \tabularnewline
126 & 3240 & 2850.092244702 & 389.907755298003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300259&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]4490[/C][C]4912.96207264958[/C][C]-422.962072649576[/C][/ROW]
[ROW][C]14[/C][C]3960[/C][C]3981.59696064344[/C][C]-21.5969606434392[/C][/ROW]
[ROW][C]15[/C][C]3750[/C][C]3720.04345449619[/C][C]29.9565455038137[/C][/ROW]
[ROW][C]16[/C][C]3670[/C][C]3665.83367027593[/C][C]4.16632972407388[/C][/ROW]
[ROW][C]17[/C][C]3590[/C][C]3587.73230767441[/C][C]2.26769232559491[/C][/ROW]
[ROW][C]18[/C][C]2840[/C][C]2848.85878778152[/C][C]-8.85878778152437[/C][/ROW]
[ROW][C]19[/C][C]3530[/C][C]3127.66003299714[/C][C]402.339967002861[/C][/ROW]
[ROW][C]20[/C][C]4320[/C][C]4005.83822711698[/C][C]314.161772883024[/C][/ROW]
[ROW][C]21[/C][C]3740[/C][C]4154.03614169957[/C][C]-414.036141699568[/C][/ROW]
[ROW][C]22[/C][C]3710[/C][C]4162.30214359212[/C][C]-452.302143592121[/C][/ROW]
[ROW][C]23[/C][C]3830[/C][C]3497.37702370147[/C][C]332.622976298527[/C][/ROW]
[ROW][C]24[/C][C]3490[/C][C]4143.68575951191[/C][C]-653.685759511905[/C][/ROW]
[ROW][C]25[/C][C]4200[/C][C]3522.3323081512[/C][C]677.667691848801[/C][/ROW]
[ROW][C]26[/C][C]4280[/C][C]3583.6315444641[/C][C]696.368455535902[/C][/ROW]
[ROW][C]27[/C][C]4650[/C][C]3937.15045260191[/C][C]712.849547398089[/C][/ROW]
[ROW][C]28[/C][C]2100[/C][C]4456.41404172358[/C][C]-2356.41404172358[/C][/ROW]
[ROW][C]29[/C][C]2410[/C][C]2381.90923860265[/C][C]28.0907613973509[/C][/ROW]
[ROW][C]30[/C][C]1230[/C][C]1663.15383266829[/C][C]-433.153832668294[/C][/ROW]
[ROW][C]31[/C][C]2420[/C][C]1646.65902568933[/C][C]773.340974310668[/C][/ROW]
[ROW][C]32[/C][C]2360[/C][C]2824.94164539167[/C][C]-464.94164539167[/C][/ROW]
[ROW][C]33[/C][C]1870[/C][C]2201.89587531022[/C][C]-331.895875310224[/C][/ROW]
[ROW][C]34[/C][C]2250[/C][C]2273.71159590846[/C][C]-23.7115959084585[/C][/ROW]
[ROW][C]35[/C][C]1960[/C][C]2092.39454854031[/C][C]-132.394548540313[/C][/ROW]
[ROW][C]36[/C][C]2550[/C][C]2193.1991764384[/C][C]356.800823561597[/C][/ROW]
[ROW][C]37[/C][C]3180[/C][C]2631.87367256783[/C][C]548.126327432166[/C][/ROW]
[ROW][C]38[/C][C]3330[/C][C]2586.5199072592[/C][C]743.480092740803[/C][/ROW]
[ROW][C]39[/C][C]3760[/C][C]2982.42114222716[/C][C]777.578857772838[/C][/ROW]
[ROW][C]40[/C][C]3930[/C][C]3082.53022678845[/C][C]847.469773211551[/C][/ROW]
[ROW][C]41[/C][C]3710[/C][C]4085.39834504634[/C][C]-375.398345046337[/C][/ROW]
[ROW][C]42[/C][C]3250[/C][C]2954.23647178709[/C][C]295.763528212913[/C][/ROW]
[ROW][C]43[/C][C]3450[/C][C]3740.3962688662[/C][C]-290.396268866204[/C][/ROW]
[ROW][C]44[/C][C]3480[/C][C]3827.99210039238[/C][C]-347.992100392381[/C][/ROW]
[ROW][C]45[/C][C]3090[/C][C]3324.38110838145[/C][C]-234.381108381447[/C][/ROW]
[ROW][C]46[/C][C]3690[/C][C]3526.23865345295[/C][C]163.761346547048[/C][/ROW]
[ROW][C]47[/C][C]3250[/C][C]3486.6685214158[/C][C]-236.668521415801[/C][/ROW]
[ROW][C]48[/C][C]3300[/C][C]3574.82995541715[/C][C]-274.829955417149[/C][/ROW]
[ROW][C]49[/C][C]4040[/C][C]3508.93689142003[/C][C]531.063108579966[/C][/ROW]
[ROW][C]50[/C][C]3630[/C][C]3479.31677181791[/C][C]150.683228182088[/C][/ROW]
[ROW][C]51[/C][C]3820[/C][C]3379.21288954136[/C][C]440.787110458645[/C][/ROW]
[ROW][C]52[/C][C]3400[/C][C]3205.32142148212[/C][C]194.678578517883[/C][/ROW]
[ROW][C]53[/C][C]2500[/C][C]3467.37932093653[/C][C]-967.379320936531[/C][/ROW]
[ROW][C]54[/C][C]2380[/C][C]1939.26383791567[/C][C]440.736162084333[/C][/ROW]
[ROW][C]55[/C][C]2520[/C][C]2757.51051537009[/C][C]-237.510515370086[/C][/ROW]
[ROW][C]56[/C][C]2340[/C][C]2880.93390895574[/C][C]-540.933908955745[/C][/ROW]
[ROW][C]57[/C][C]2420[/C][C]2231.7124021584[/C][C]188.287597841604[/C][/ROW]
[ROW][C]58[/C][C]2430[/C][C]2852.45183694664[/C][C]-422.451836946644[/C][/ROW]
[ROW][C]59[/C][C]2080[/C][C]2255.35318738451[/C][C]-175.35318738451[/C][/ROW]
[ROW][C]60[/C][C]2420[/C][C]2389.47089125948[/C][C]30.5291087405221[/C][/ROW]
[ROW][C]61[/C][C]2430[/C][C]2706.21859214947[/C][C]-276.218592149467[/C][/ROW]
[ROW][C]62[/C][C]2400[/C][C]1935.22977419197[/C][C]464.770225808032[/C][/ROW]
[ROW][C]63[/C][C]2790[/C][C]2145.5099324124[/C][C]644.490067587602[/C][/ROW]
[ROW][C]64[/C][C]2370[/C][C]2105.8712005299[/C][C]264.1287994701[/C][/ROW]
[ROW][C]65[/C][C]2700[/C][C]2247.23630959732[/C][C]452.763690402679[/C][/ROW]
[ROW][C]66[/C][C]2640[/C][C]2137.40680553762[/C][C]502.593194462376[/C][/ROW]
[ROW][C]67[/C][C]2910[/C][C]2903.23960983647[/C][C]6.76039016352797[/C][/ROW]
[ROW][C]68[/C][C]2420[/C][C]3186.37072857373[/C][C]-766.370728573735[/C][/ROW]
[ROW][C]69[/C][C]2800[/C][C]2459.11021949859[/C][C]340.88978050141[/C][/ROW]
[ROW][C]70[/C][C]2830[/C][C]3114.59303324327[/C][C]-284.59303324327[/C][/ROW]
[ROW][C]71[/C][C]2310[/C][C]2672.21965615205[/C][C]-362.219656152055[/C][/ROW]
[ROW][C]72[/C][C]2540[/C][C]2680.11071296993[/C][C]-140.110712969928[/C][/ROW]
[ROW][C]73[/C][C]2780[/C][C]2805.20373923429[/C][C]-25.2037392342904[/C][/ROW]
[ROW][C]74[/C][C]2820[/C][C]2360.88102134753[/C][C]459.118978652473[/C][/ROW]
[ROW][C]75[/C][C]3610[/C][C]2594.13095121146[/C][C]1015.86904878854[/C][/ROW]
[ROW][C]76[/C][C]3270[/C][C]2809.80363070901[/C][C]460.196369290995[/C][/ROW]
[ROW][C]77[/C][C]3030[/C][C]3146.08871509695[/C][C]-116.08871509695[/C][/ROW]
[ROW][C]78[/C][C]3250[/C][C]2562.93036676746[/C][C]687.069633232541[/C][/ROW]
[ROW][C]79[/C][C]3040[/C][C]3408.20088051301[/C][C]-368.200880513009[/C][/ROW]
[ROW][C]80[/C][C]3630[/C][C]3254.89389973257[/C][C]375.10610026743[/C][/ROW]
[ROW][C]81[/C][C]3320[/C][C]3663.82727091754[/C][C]-343.827270917538[/C][/ROW]
[ROW][C]82[/C][C]3440[/C][C]3643.73871092021[/C][C]-203.738710920206[/C][/ROW]
[ROW][C]83[/C][C]3110[/C][C]3257.75043531061[/C][C]-147.750435310605[/C][/ROW]
[ROW][C]84[/C][C]3180[/C][C]3481.29027466959[/C][C]-301.290274669588[/C][/ROW]
[ROW][C]85[/C][C]3330[/C][C]3487.83108725417[/C][C]-157.831087254167[/C][/ROW]
[ROW][C]86[/C][C]3100[/C][C]3006.13718850839[/C][C]93.8628114916123[/C][/ROW]
[ROW][C]87[/C][C]3440[/C][C]3016.48733484236[/C][C]423.512665157644[/C][/ROW]
[ROW][C]88[/C][C]3320[/C][C]2645.46753974494[/C][C]674.532460255065[/C][/ROW]
[ROW][C]89[/C][C]3380[/C][C]3074.01798846598[/C][C]305.982011534019[/C][/ROW]
[ROW][C]90[/C][C]3610[/C][C]2971.76972541491[/C][C]638.23027458509[/C][/ROW]
[ROW][C]91[/C][C]3320[/C][C]3612.8094158812[/C][C]-292.809415881201[/C][/ROW]
[ROW][C]92[/C][C]3860[/C][C]3638.0190561617[/C][C]221.980943838295[/C][/ROW]
[ROW][C]93[/C][C]3430[/C][C]3806.46732906136[/C][C]-376.467329061359[/C][/ROW]
[ROW][C]94[/C][C]3510[/C][C]3780.407751143[/C][C]-270.407751142998[/C][/ROW]
[ROW][C]95[/C][C]3290[/C][C]3346.68854136829[/C][C]-56.6885413682853[/C][/ROW]
[ROW][C]96[/C][C]3010[/C][C]3623.52413299499[/C][C]-613.524132994986[/C][/ROW]
[ROW][C]97[/C][C]3860[/C][C]3388.18941175704[/C][C]471.810588242959[/C][/ROW]
[ROW][C]98[/C][C]3530[/C][C]3477.78261722328[/C][C]52.2173827767219[/C][/ROW]
[ROW][C]99[/C][C]3610[/C][C]3503.81477094943[/C][C]106.185229050573[/C][/ROW]
[ROW][C]100[/C][C]3370[/C][C]2903.21950194218[/C][C]466.780498057819[/C][/ROW]
[ROW][C]101[/C][C]3700[/C][C]3099.19094271631[/C][C]600.809057283687[/C][/ROW]
[ROW][C]102[/C][C]3500[/C][C]3297.5475053806[/C][C]202.452494619401[/C][/ROW]
[ROW][C]103[/C][C]4110[/C][C]3426.34171785815[/C][C]683.658282141854[/C][/ROW]
[ROW][C]104[/C][C]4590[/C][C]4356.73676584021[/C][C]233.263234159795[/C][/ROW]
[ROW][C]105[/C][C]3680[/C][C]4442.32584231409[/C][C]-762.325842314085[/C][/ROW]
[ROW][C]106[/C][C]4220[/C][C]4106.35916846424[/C][C]113.640831535757[/C][/ROW]
[ROW][C]107[/C][C]3740[/C][C]4030.38994102061[/C][C]-290.389941020608[/C][/ROW]
[ROW][C]108[/C][C]3550[/C][C]4023.63269719318[/C][C]-473.63269719318[/C][/ROW]
[ROW][C]109[/C][C]4150[/C][C]4074.16444055661[/C][C]75.8355594433879[/C][/ROW]
[ROW][C]110[/C][C]4110[/C][C]3764.13600608095[/C][C]345.863993919049[/C][/ROW]
[ROW][C]111[/C][C]4160[/C][C]4046.80872823563[/C][C]113.191271764369[/C][/ROW]
[ROW][C]112[/C][C]3780[/C][C]3507.81314947927[/C][C]272.186850520734[/C][/ROW]
[ROW][C]113[/C][C]3150[/C][C]3559.92971979089[/C][C]-409.92971979089[/C][/ROW]
[ROW][C]114[/C][C]3260[/C][C]2842.09840310436[/C][C]417.901596895642[/C][/ROW]
[ROW][C]115[/C][C]4750[/C][C]3227.37415246325[/C][C]1522.62584753675[/C][/ROW]
[ROW][C]116[/C][C]4110[/C][C]4797.66110734212[/C][C]-687.661107342122[/C][/ROW]
[ROW][C]117[/C][C]3610[/C][C]3950.79771893986[/C][C]-340.797718939856[/C][/ROW]
[ROW][C]118[/C][C]3890[/C][C]4106.52380077501[/C][C]-216.523800775012[/C][/ROW]
[ROW][C]119[/C][C]2800[/C][C]3688.98511947736[/C][C]-888.985119477356[/C][/ROW]
[ROW][C]120[/C][C]2610[/C][C]3147.7624897877[/C][C]-537.762489787702[/C][/ROW]
[ROW][C]121[/C][C]3600[/C][C]3228.9030613577[/C][C]371.0969386423[/C][/ROW]
[ROW][C]122[/C][C]3400[/C][C]3210.24007716653[/C][C]189.759922833469[/C][/ROW]
[ROW][C]123[/C][C]3400[/C][C]3324.98664306444[/C][C]75.0133569355589[/C][/ROW]
[ROW][C]124[/C][C]3120[/C][C]2778.25644189879[/C][C]341.743558101211[/C][/ROW]
[ROW][C]125[/C][C]3150[/C][C]2783.87249025803[/C][C]366.127509741973[/C][/ROW]
[ROW][C]126[/C][C]3240[/C][C]2850.092244702[/C][C]389.907755298003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300259&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300259&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
1344904912.96207264958-422.962072649576
1439603981.59696064344-21.5969606434392
1537503720.0434544961929.9565455038137
1636703665.833670275934.16632972407388
1735903587.732307674412.26769232559491
1828402848.85878778152-8.85878778152437
1935303127.66003299714402.339967002861
2043204005.83822711698314.161772883024
2137404154.03614169957-414.036141699568
2237104162.30214359212-452.302143592121
2338303497.37702370147332.622976298527
2434904143.68575951191-653.685759511905
2542003522.3323081512677.667691848801
2642803583.6315444641696.368455535902
2746503937.15045260191712.849547398089
2821004456.41404172358-2356.41404172358
2924102381.9092386026528.0907613973509
3012301663.15383266829-433.153832668294
3124201646.65902568933773.340974310668
3223602824.94164539167-464.94164539167
3318702201.89587531022-331.895875310224
3422502273.71159590846-23.7115959084585
3519602092.39454854031-132.394548540313
3625502193.1991764384356.800823561597
3731802631.87367256783548.126327432166
3833302586.5199072592743.480092740803
3937602982.42114222716777.578857772838
4039303082.53022678845847.469773211551
4137104085.39834504634-375.398345046337
4232502954.23647178709295.763528212913
4334503740.3962688662-290.396268866204
4434803827.99210039238-347.992100392381
4530903324.38110838145-234.381108381447
4636903526.23865345295163.761346547048
4732503486.6685214158-236.668521415801
4833003574.82995541715-274.829955417149
4940403508.93689142003531.063108579966
5036303479.31677181791150.683228182088
5138203379.21288954136440.787110458645
5234003205.32142148212194.678578517883
5325003467.37932093653-967.379320936531
5423801939.26383791567440.736162084333
5525202757.51051537009-237.510515370086
5623402880.93390895574-540.933908955745
5724202231.7124021584188.287597841604
5824302852.45183694664-422.451836946644
5920802255.35318738451-175.35318738451
6024202389.4708912594830.5291087405221
6124302706.21859214947-276.218592149467
6224001935.22977419197464.770225808032
6327902145.5099324124644.490067587602
6423702105.8712005299264.1287994701
6527002247.23630959732452.763690402679
6626402137.40680553762502.593194462376
6729102903.239609836476.76039016352797
6824203186.37072857373-766.370728573735
6928002459.11021949859340.88978050141
7028303114.59303324327-284.59303324327
7123102672.21965615205-362.219656152055
7225402680.11071296993-140.110712969928
7327802805.20373923429-25.2037392342904
7428202360.88102134753459.118978652473
7536102594.130951211461015.86904878854
7632702809.80363070901460.196369290995
7730303146.08871509695-116.08871509695
7832502562.93036676746687.069633232541
7930403408.20088051301-368.200880513009
8036303254.89389973257375.10610026743
8133203663.82727091754-343.827270917538
8234403643.73871092021-203.738710920206
8331103257.75043531061-147.750435310605
8431803481.29027466959-301.290274669588
8533303487.83108725417-157.831087254167
8631003006.1371885083993.8628114916123
8734403016.48733484236423.512665157644
8833202645.46753974494674.532460255065
8933803074.01798846598305.982011534019
9036102971.76972541491638.23027458509
9133203612.8094158812-292.809415881201
9238603638.0190561617221.980943838295
9334303806.46732906136-376.467329061359
9435103780.407751143-270.407751142998
9532903346.68854136829-56.6885413682853
9630103623.52413299499-613.524132994986
9738603388.18941175704471.810588242959
9835303477.7826172232852.2173827767219
9936103503.81477094943106.185229050573
10033702903.21950194218466.780498057819
10137003099.19094271631600.809057283687
10235003297.5475053806202.452494619401
10341103426.34171785815683.658282141854
10445904356.73676584021233.263234159795
10536804442.32584231409-762.325842314085
10642204106.35916846424113.640831535757
10737404030.38994102061-290.389941020608
10835504023.63269719318-473.63269719318
10941504074.1644405566175.8355594433879
11041103764.13600608095345.863993919049
11141604046.80872823563113.191271764369
11237803507.81314947927272.186850520734
11331503559.92971979089-409.92971979089
11432602842.09840310436417.901596895642
11547503227.374152463251522.62584753675
11641104797.66110734212-687.661107342122
11736103950.79771893986-340.797718939856
11838904106.52380077501-216.523800775012
11928003688.98511947736-888.985119477356
12026103147.7624897877-537.762489787702
12136003228.9030613577371.0969386423
12234003210.24007716653189.759922833469
12334003324.9866430644475.0133569355589
12431202778.25644189879341.743558101211
12531502783.87249025803366.127509741973
12632402850.092244702389.907755298003







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1273382.264131252482399.021710701674365.50655180329
1283323.751392426452036.100973742694611.4018111102
1293111.930453427321579.18078570524644.68012114944
1303575.023303302571831.291819653755318.75478695139
1313236.750450337681304.9436716375168.55722903837
1323501.483216245251398.353316928585604.61311556193
1334177.683089733521916.171799342616439.19438012444
1343817.221815086911407.71745532096226.72617485292
1353753.790408235191204.8711857226302.70963074838
1363184.81154422441503.7171508724985865.90593757632
1372905.2135742255398.16083349747215712.26631495358
1382665.50699300699-262.0898085342885593.10379454827

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 3382.26413125248 & 2399.02171070167 & 4365.50655180329 \tabularnewline
128 & 3323.75139242645 & 2036.10097374269 & 4611.4018111102 \tabularnewline
129 & 3111.93045342732 & 1579.1807857052 & 4644.68012114944 \tabularnewline
130 & 3575.02330330257 & 1831.29181965375 & 5318.75478695139 \tabularnewline
131 & 3236.75045033768 & 1304.943671637 & 5168.55722903837 \tabularnewline
132 & 3501.48321624525 & 1398.35331692858 & 5604.61311556193 \tabularnewline
133 & 4177.68308973352 & 1916.17179934261 & 6439.19438012444 \tabularnewline
134 & 3817.22181508691 & 1407.7174553209 & 6226.72617485292 \tabularnewline
135 & 3753.79040823519 & 1204.871185722 & 6302.70963074838 \tabularnewline
136 & 3184.81154422441 & 503.717150872498 & 5865.90593757632 \tabularnewline
137 & 2905.21357422553 & 98.1608334974721 & 5712.26631495358 \tabularnewline
138 & 2665.50699300699 & -262.089808534288 & 5593.10379454827 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300259&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]3382.26413125248[/C][C]2399.02171070167[/C][C]4365.50655180329[/C][/ROW]
[ROW][C]128[/C][C]3323.75139242645[/C][C]2036.10097374269[/C][C]4611.4018111102[/C][/ROW]
[ROW][C]129[/C][C]3111.93045342732[/C][C]1579.1807857052[/C][C]4644.68012114944[/C][/ROW]
[ROW][C]130[/C][C]3575.02330330257[/C][C]1831.29181965375[/C][C]5318.75478695139[/C][/ROW]
[ROW][C]131[/C][C]3236.75045033768[/C][C]1304.943671637[/C][C]5168.55722903837[/C][/ROW]
[ROW][C]132[/C][C]3501.48321624525[/C][C]1398.35331692858[/C][C]5604.61311556193[/C][/ROW]
[ROW][C]133[/C][C]4177.68308973352[/C][C]1916.17179934261[/C][C]6439.19438012444[/C][/ROW]
[ROW][C]134[/C][C]3817.22181508691[/C][C]1407.7174553209[/C][C]6226.72617485292[/C][/ROW]
[ROW][C]135[/C][C]3753.79040823519[/C][C]1204.871185722[/C][C]6302.70963074838[/C][/ROW]
[ROW][C]136[/C][C]3184.81154422441[/C][C]503.717150872498[/C][C]5865.90593757632[/C][/ROW]
[ROW][C]137[/C][C]2905.21357422553[/C][C]98.1608334974721[/C][C]5712.26631495358[/C][/ROW]
[ROW][C]138[/C][C]2665.50699300699[/C][C]-262.089808534288[/C][C]5593.10379454827[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300259&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300259&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
1273382.264131252482399.021710701674365.50655180329
1283323.751392426452036.100973742694611.4018111102
1293111.930453427321579.18078570524644.68012114944
1303575.023303302571831.291819653755318.75478695139
1313236.750450337681304.9436716375168.55722903837
1323501.483216245251398.353316928585604.61311556193
1334177.683089733521916.171799342616439.19438012444
1343817.221815086911407.71745532096226.72617485292
1353753.790408235191204.8711857226302.70963074838
1363184.81154422441503.7171508724985865.90593757632
1372905.2135742255398.16083349747215712.26631495358
1382665.50699300699-262.0898085342885593.10379454827



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