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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 computationMon, 19 Dec 2016 21:42:23 +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/19/t1482180162qovoh5hlcdsmacb.htm/, Retrieved Tue, 21 May 2024 03:35:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301489, Retrieved Tue, 21 May 2024 03:35:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [N2044 exponential] [2016-12-19 20:42:23] [2e11ca31a00cf8de75c33c1af2d59434] [Current]
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Dataseries X:
3880
3740
3990
3970
4100
3920
3850
4190
3990
4140
4080
3900
4070
3930
4210
4020
4120
4020
3910
4110
4130
4340
4200
4200
4160
3920
4280
3940
4190
4150
4070
4130
3960
4320
4110
4100
4280
3990
4360
4240
4450
4190
3950
4300
4150
4540
4240
4210
4390
4140
4460
4290
4430
4390
4340
4570
4470
4550
4420
4490
4480
4400
4770
4450
4610
4540
4520
4710
4580
4760
4450
4500
4660
4370
5030
4510
4740
4690
4580
4850
4730
4890
4740
4600
4740
4520
5000
4670
4940
4790
4820
5010
4870
5070
4770
4840
4850
4590
5050
4770
4720
4740
4400
4840
4650
4860
4580
4640
4800
4660
5020
4700
4800
4700
4560




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=301489&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=301489&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301489&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
alpha0.31885602393952
beta0
gamma0.267706015357322

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.31885602393952 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.267706015357322 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301489&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]0.31885602393952[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.267706015357322[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301489&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301489&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
alpha0.31885602393952
beta0
gamma0.267706015357322







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1340704018.1578815827151.8421184172898
1439303904.2423137980925.7576862019096
1542104196.6855228118413.3144771881607
1640204005.0270330198214.9729669801836
1741204103.9443769592316.0556230407674
1840203999.805000832420.1949991676029
1939103945.76074965814-35.7607496581441
2041104272.99165353869-162.991653538695
2141304010.1583362277119.841663772303
2243404196.8092508831143.190749116898
2342004185.804315152514.1956848474956
2442004007.99513448677192.00486551323
2541604257.35116210409-97.3511621040852
2639204084.66760331693-164.667603316929
2742804322.16258639573-42.162586395727
2839404108.01852122457-168.018521224573
2941904149.6851175012740.3148824987311
3041504052.6021735428797.3978264571256
3140704011.5146973044558.4853026955548
3241304353.22839788228-223.228397882275
3339604118.9345539907-158.934553990697
3443204220.6028685733999.3971314266073
3541104172.44527827611-62.4452782761136
3641004003.6165217694696.3834782305398
3742804167.41968630427112.580313695726
3839904049.20966902004-59.2096690200406
3943604344.7883401970315.2116598029688
4042404122.96587273931117.034127260693
4144504297.74064656794152.259353432059
4241904242.08555536233-52.0855553623251
4339504143.56438511204-193.564385112044
4443004355.53444102319-55.5344410231874
4541504182.44667046541-32.4466704654133
4645404377.70662279506162.293377204942
4742404315.67157825282-75.671578252819
4842104166.8165878762143.1834121237916
4943904320.4998047463369.5001952536695
5041404151.74990092141-11.7499009214062
5144604486.25515569786-26.2551556978633
5242904263.3605507739226.6394492260806
5344304418.3527258562711.6472741437328
5443904278.92660570522111.073394294779
5543404203.39892425598136.60107574402
5645704560.176479094999.82352090501354
5744704403.4751366065866.5248633934234
5845504679.89360158137-129.893601581367
5944204474.58163938793-54.581639387935
6044904349.45551458531140.544485414688
6144804545.63884268143-65.6388426814274
6244004310.6904774945289.3095225054785
6347704690.037313866879.9626861331981
6444504499.12579554713-49.1257955471328
6546104633.79141813853-23.7914181385258
6645404494.9628227234245.0371772765793
6745204398.18233650235121.817663497649
6847104738.03538956945-28.0353895694516
6945804573.894651351576.10534864842703
7047604801.63546399007-41.6354639900737
7144504632.21701401605-182.217014016045
7245004499.428740698150.571259301846112
7346604615.2383510571944.7616489428128
7443704438.63576703583-68.6357670358329
7550304770.63688368901259.363116310988
7645104606.90714203637-96.9071420363716
7747404734.285346283625.71465371637987
7846904614.2648818000275.7351181999766
7945804538.2733063940641.7266936059414
8048504830.7563691621419.2436308378628
8147304684.1711041674345.8288958325747
8248904921.41523465862-31.4152346586234
8347404724.0093260685115.9906739314856
8446004685.72037858506-85.7203785850634
8547404786.132213723-46.1322137230009
8645204553.48951308461-33.4895130846135
8750004968.4352632101931.5647367898137
8846704661.915677748238.08432225176512
8949404845.420928333394.5790716666979
9047904763.016556267526.9834437325035
9148204662.33371837621157.666281623789
9250104996.6689663908613.3310336091427
9348704847.8597613459122.1402386540931
9450705069.74818248930.251817510703404
9547704884.84038575446-114.840385754458
9648404784.48658018555.5134198150017
9748504941.48931037793-91.4893103779295
9845904689.68152424164-99.6815242416351
9950505106.84075068138-56.8407506813846
10047704760.965445912899.03455408710761
10147204964.39642814522-244.39642814522
10247404761.74524164888-21.7452416488832
10344004669.4724102952-269.472410295197
10448404832.977744409727.02225559028466
10546504689.10644204506-39.1064420450648
10648604879.86528826983-19.8652882698298
10745804675.67947563658-95.6794756365771
10846404613.9834245733526.0165754266473
10948004730.5461377889869.4538622110213
11046604535.20300425536124.79699574464
11150205025.45585894713-5.45585894713076
11247004711.45509486299-11.4550948629912
11348004859.66533873962-59.6653387396191
11447004756.53459067408-56.5345906740813
11545604607.43649455193-47.4364945519301

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4070 & 4018.15788158271 & 51.8421184172898 \tabularnewline
14 & 3930 & 3904.24231379809 & 25.7576862019096 \tabularnewline
15 & 4210 & 4196.68552281184 & 13.3144771881607 \tabularnewline
16 & 4020 & 4005.02703301982 & 14.9729669801836 \tabularnewline
17 & 4120 & 4103.94437695923 & 16.0556230407674 \tabularnewline
18 & 4020 & 3999.8050008324 & 20.1949991676029 \tabularnewline
19 & 3910 & 3945.76074965814 & -35.7607496581441 \tabularnewline
20 & 4110 & 4272.99165353869 & -162.991653538695 \tabularnewline
21 & 4130 & 4010.1583362277 & 119.841663772303 \tabularnewline
22 & 4340 & 4196.8092508831 & 143.190749116898 \tabularnewline
23 & 4200 & 4185.8043151525 & 14.1956848474956 \tabularnewline
24 & 4200 & 4007.99513448677 & 192.00486551323 \tabularnewline
25 & 4160 & 4257.35116210409 & -97.3511621040852 \tabularnewline
26 & 3920 & 4084.66760331693 & -164.667603316929 \tabularnewline
27 & 4280 & 4322.16258639573 & -42.162586395727 \tabularnewline
28 & 3940 & 4108.01852122457 & -168.018521224573 \tabularnewline
29 & 4190 & 4149.68511750127 & 40.3148824987311 \tabularnewline
30 & 4150 & 4052.60217354287 & 97.3978264571256 \tabularnewline
31 & 4070 & 4011.51469730445 & 58.4853026955548 \tabularnewline
32 & 4130 & 4353.22839788228 & -223.228397882275 \tabularnewline
33 & 3960 & 4118.9345539907 & -158.934553990697 \tabularnewline
34 & 4320 & 4220.60286857339 & 99.3971314266073 \tabularnewline
35 & 4110 & 4172.44527827611 & -62.4452782761136 \tabularnewline
36 & 4100 & 4003.61652176946 & 96.3834782305398 \tabularnewline
37 & 4280 & 4167.41968630427 & 112.580313695726 \tabularnewline
38 & 3990 & 4049.20966902004 & -59.2096690200406 \tabularnewline
39 & 4360 & 4344.78834019703 & 15.2116598029688 \tabularnewline
40 & 4240 & 4122.96587273931 & 117.034127260693 \tabularnewline
41 & 4450 & 4297.74064656794 & 152.259353432059 \tabularnewline
42 & 4190 & 4242.08555536233 & -52.0855553623251 \tabularnewline
43 & 3950 & 4143.56438511204 & -193.564385112044 \tabularnewline
44 & 4300 & 4355.53444102319 & -55.5344410231874 \tabularnewline
45 & 4150 & 4182.44667046541 & -32.4466704654133 \tabularnewline
46 & 4540 & 4377.70662279506 & 162.293377204942 \tabularnewline
47 & 4240 & 4315.67157825282 & -75.671578252819 \tabularnewline
48 & 4210 & 4166.81658787621 & 43.1834121237916 \tabularnewline
49 & 4390 & 4320.49980474633 & 69.5001952536695 \tabularnewline
50 & 4140 & 4151.74990092141 & -11.7499009214062 \tabularnewline
51 & 4460 & 4486.25515569786 & -26.2551556978633 \tabularnewline
52 & 4290 & 4263.36055077392 & 26.6394492260806 \tabularnewline
53 & 4430 & 4418.35272585627 & 11.6472741437328 \tabularnewline
54 & 4390 & 4278.92660570522 & 111.073394294779 \tabularnewline
55 & 4340 & 4203.39892425598 & 136.60107574402 \tabularnewline
56 & 4570 & 4560.17647909499 & 9.82352090501354 \tabularnewline
57 & 4470 & 4403.47513660658 & 66.5248633934234 \tabularnewline
58 & 4550 & 4679.89360158137 & -129.893601581367 \tabularnewline
59 & 4420 & 4474.58163938793 & -54.581639387935 \tabularnewline
60 & 4490 & 4349.45551458531 & 140.544485414688 \tabularnewline
61 & 4480 & 4545.63884268143 & -65.6388426814274 \tabularnewline
62 & 4400 & 4310.69047749452 & 89.3095225054785 \tabularnewline
63 & 4770 & 4690.0373138668 & 79.9626861331981 \tabularnewline
64 & 4450 & 4499.12579554713 & -49.1257955471328 \tabularnewline
65 & 4610 & 4633.79141813853 & -23.7914181385258 \tabularnewline
66 & 4540 & 4494.96282272342 & 45.0371772765793 \tabularnewline
67 & 4520 & 4398.18233650235 & 121.817663497649 \tabularnewline
68 & 4710 & 4738.03538956945 & -28.0353895694516 \tabularnewline
69 & 4580 & 4573.89465135157 & 6.10534864842703 \tabularnewline
70 & 4760 & 4801.63546399007 & -41.6354639900737 \tabularnewline
71 & 4450 & 4632.21701401605 & -182.217014016045 \tabularnewline
72 & 4500 & 4499.42874069815 & 0.571259301846112 \tabularnewline
73 & 4660 & 4615.23835105719 & 44.7616489428128 \tabularnewline
74 & 4370 & 4438.63576703583 & -68.6357670358329 \tabularnewline
75 & 5030 & 4770.63688368901 & 259.363116310988 \tabularnewline
76 & 4510 & 4606.90714203637 & -96.9071420363716 \tabularnewline
77 & 4740 & 4734.28534628362 & 5.71465371637987 \tabularnewline
78 & 4690 & 4614.26488180002 & 75.7351181999766 \tabularnewline
79 & 4580 & 4538.27330639406 & 41.7266936059414 \tabularnewline
80 & 4850 & 4830.75636916214 & 19.2436308378628 \tabularnewline
81 & 4730 & 4684.17110416743 & 45.8288958325747 \tabularnewline
82 & 4890 & 4921.41523465862 & -31.4152346586234 \tabularnewline
83 & 4740 & 4724.00932606851 & 15.9906739314856 \tabularnewline
84 & 4600 & 4685.72037858506 & -85.7203785850634 \tabularnewline
85 & 4740 & 4786.132213723 & -46.1322137230009 \tabularnewline
86 & 4520 & 4553.48951308461 & -33.4895130846135 \tabularnewline
87 & 5000 & 4968.43526321019 & 31.5647367898137 \tabularnewline
88 & 4670 & 4661.91567774823 & 8.08432225176512 \tabularnewline
89 & 4940 & 4845.4209283333 & 94.5790716666979 \tabularnewline
90 & 4790 & 4763.0165562675 & 26.9834437325035 \tabularnewline
91 & 4820 & 4662.33371837621 & 157.666281623789 \tabularnewline
92 & 5010 & 4996.66896639086 & 13.3310336091427 \tabularnewline
93 & 4870 & 4847.85976134591 & 22.1402386540931 \tabularnewline
94 & 5070 & 5069.7481824893 & 0.251817510703404 \tabularnewline
95 & 4770 & 4884.84038575446 & -114.840385754458 \tabularnewline
96 & 4840 & 4784.486580185 & 55.5134198150017 \tabularnewline
97 & 4850 & 4941.48931037793 & -91.4893103779295 \tabularnewline
98 & 4590 & 4689.68152424164 & -99.6815242416351 \tabularnewline
99 & 5050 & 5106.84075068138 & -56.8407506813846 \tabularnewline
100 & 4770 & 4760.96544591289 & 9.03455408710761 \tabularnewline
101 & 4720 & 4964.39642814522 & -244.39642814522 \tabularnewline
102 & 4740 & 4761.74524164888 & -21.7452416488832 \tabularnewline
103 & 4400 & 4669.4724102952 & -269.472410295197 \tabularnewline
104 & 4840 & 4832.97774440972 & 7.02225559028466 \tabularnewline
105 & 4650 & 4689.10644204506 & -39.1064420450648 \tabularnewline
106 & 4860 & 4879.86528826983 & -19.8652882698298 \tabularnewline
107 & 4580 & 4675.67947563658 & -95.6794756365771 \tabularnewline
108 & 4640 & 4613.98342457335 & 26.0165754266473 \tabularnewline
109 & 4800 & 4730.54613778898 & 69.4538622110213 \tabularnewline
110 & 4660 & 4535.20300425536 & 124.79699574464 \tabularnewline
111 & 5020 & 5025.45585894713 & -5.45585894713076 \tabularnewline
112 & 4700 & 4711.45509486299 & -11.4550948629912 \tabularnewline
113 & 4800 & 4859.66533873962 & -59.6653387396191 \tabularnewline
114 & 4700 & 4756.53459067408 & -56.5345906740813 \tabularnewline
115 & 4560 & 4607.43649455193 & -47.4364945519301 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301489&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]4070[/C][C]4018.15788158271[/C][C]51.8421184172898[/C][/ROW]
[ROW][C]14[/C][C]3930[/C][C]3904.24231379809[/C][C]25.7576862019096[/C][/ROW]
[ROW][C]15[/C][C]4210[/C][C]4196.68552281184[/C][C]13.3144771881607[/C][/ROW]
[ROW][C]16[/C][C]4020[/C][C]4005.02703301982[/C][C]14.9729669801836[/C][/ROW]
[ROW][C]17[/C][C]4120[/C][C]4103.94437695923[/C][C]16.0556230407674[/C][/ROW]
[ROW][C]18[/C][C]4020[/C][C]3999.8050008324[/C][C]20.1949991676029[/C][/ROW]
[ROW][C]19[/C][C]3910[/C][C]3945.76074965814[/C][C]-35.7607496581441[/C][/ROW]
[ROW][C]20[/C][C]4110[/C][C]4272.99165353869[/C][C]-162.991653538695[/C][/ROW]
[ROW][C]21[/C][C]4130[/C][C]4010.1583362277[/C][C]119.841663772303[/C][/ROW]
[ROW][C]22[/C][C]4340[/C][C]4196.8092508831[/C][C]143.190749116898[/C][/ROW]
[ROW][C]23[/C][C]4200[/C][C]4185.8043151525[/C][C]14.1956848474956[/C][/ROW]
[ROW][C]24[/C][C]4200[/C][C]4007.99513448677[/C][C]192.00486551323[/C][/ROW]
[ROW][C]25[/C][C]4160[/C][C]4257.35116210409[/C][C]-97.3511621040852[/C][/ROW]
[ROW][C]26[/C][C]3920[/C][C]4084.66760331693[/C][C]-164.667603316929[/C][/ROW]
[ROW][C]27[/C][C]4280[/C][C]4322.16258639573[/C][C]-42.162586395727[/C][/ROW]
[ROW][C]28[/C][C]3940[/C][C]4108.01852122457[/C][C]-168.018521224573[/C][/ROW]
[ROW][C]29[/C][C]4190[/C][C]4149.68511750127[/C][C]40.3148824987311[/C][/ROW]
[ROW][C]30[/C][C]4150[/C][C]4052.60217354287[/C][C]97.3978264571256[/C][/ROW]
[ROW][C]31[/C][C]4070[/C][C]4011.51469730445[/C][C]58.4853026955548[/C][/ROW]
[ROW][C]32[/C][C]4130[/C][C]4353.22839788228[/C][C]-223.228397882275[/C][/ROW]
[ROW][C]33[/C][C]3960[/C][C]4118.9345539907[/C][C]-158.934553990697[/C][/ROW]
[ROW][C]34[/C][C]4320[/C][C]4220.60286857339[/C][C]99.3971314266073[/C][/ROW]
[ROW][C]35[/C][C]4110[/C][C]4172.44527827611[/C][C]-62.4452782761136[/C][/ROW]
[ROW][C]36[/C][C]4100[/C][C]4003.61652176946[/C][C]96.3834782305398[/C][/ROW]
[ROW][C]37[/C][C]4280[/C][C]4167.41968630427[/C][C]112.580313695726[/C][/ROW]
[ROW][C]38[/C][C]3990[/C][C]4049.20966902004[/C][C]-59.2096690200406[/C][/ROW]
[ROW][C]39[/C][C]4360[/C][C]4344.78834019703[/C][C]15.2116598029688[/C][/ROW]
[ROW][C]40[/C][C]4240[/C][C]4122.96587273931[/C][C]117.034127260693[/C][/ROW]
[ROW][C]41[/C][C]4450[/C][C]4297.74064656794[/C][C]152.259353432059[/C][/ROW]
[ROW][C]42[/C][C]4190[/C][C]4242.08555536233[/C][C]-52.0855553623251[/C][/ROW]
[ROW][C]43[/C][C]3950[/C][C]4143.56438511204[/C][C]-193.564385112044[/C][/ROW]
[ROW][C]44[/C][C]4300[/C][C]4355.53444102319[/C][C]-55.5344410231874[/C][/ROW]
[ROW][C]45[/C][C]4150[/C][C]4182.44667046541[/C][C]-32.4466704654133[/C][/ROW]
[ROW][C]46[/C][C]4540[/C][C]4377.70662279506[/C][C]162.293377204942[/C][/ROW]
[ROW][C]47[/C][C]4240[/C][C]4315.67157825282[/C][C]-75.671578252819[/C][/ROW]
[ROW][C]48[/C][C]4210[/C][C]4166.81658787621[/C][C]43.1834121237916[/C][/ROW]
[ROW][C]49[/C][C]4390[/C][C]4320.49980474633[/C][C]69.5001952536695[/C][/ROW]
[ROW][C]50[/C][C]4140[/C][C]4151.74990092141[/C][C]-11.7499009214062[/C][/ROW]
[ROW][C]51[/C][C]4460[/C][C]4486.25515569786[/C][C]-26.2551556978633[/C][/ROW]
[ROW][C]52[/C][C]4290[/C][C]4263.36055077392[/C][C]26.6394492260806[/C][/ROW]
[ROW][C]53[/C][C]4430[/C][C]4418.35272585627[/C][C]11.6472741437328[/C][/ROW]
[ROW][C]54[/C][C]4390[/C][C]4278.92660570522[/C][C]111.073394294779[/C][/ROW]
[ROW][C]55[/C][C]4340[/C][C]4203.39892425598[/C][C]136.60107574402[/C][/ROW]
[ROW][C]56[/C][C]4570[/C][C]4560.17647909499[/C][C]9.82352090501354[/C][/ROW]
[ROW][C]57[/C][C]4470[/C][C]4403.47513660658[/C][C]66.5248633934234[/C][/ROW]
[ROW][C]58[/C][C]4550[/C][C]4679.89360158137[/C][C]-129.893601581367[/C][/ROW]
[ROW][C]59[/C][C]4420[/C][C]4474.58163938793[/C][C]-54.581639387935[/C][/ROW]
[ROW][C]60[/C][C]4490[/C][C]4349.45551458531[/C][C]140.544485414688[/C][/ROW]
[ROW][C]61[/C][C]4480[/C][C]4545.63884268143[/C][C]-65.6388426814274[/C][/ROW]
[ROW][C]62[/C][C]4400[/C][C]4310.69047749452[/C][C]89.3095225054785[/C][/ROW]
[ROW][C]63[/C][C]4770[/C][C]4690.0373138668[/C][C]79.9626861331981[/C][/ROW]
[ROW][C]64[/C][C]4450[/C][C]4499.12579554713[/C][C]-49.1257955471328[/C][/ROW]
[ROW][C]65[/C][C]4610[/C][C]4633.79141813853[/C][C]-23.7914181385258[/C][/ROW]
[ROW][C]66[/C][C]4540[/C][C]4494.96282272342[/C][C]45.0371772765793[/C][/ROW]
[ROW][C]67[/C][C]4520[/C][C]4398.18233650235[/C][C]121.817663497649[/C][/ROW]
[ROW][C]68[/C][C]4710[/C][C]4738.03538956945[/C][C]-28.0353895694516[/C][/ROW]
[ROW][C]69[/C][C]4580[/C][C]4573.89465135157[/C][C]6.10534864842703[/C][/ROW]
[ROW][C]70[/C][C]4760[/C][C]4801.63546399007[/C][C]-41.6354639900737[/C][/ROW]
[ROW][C]71[/C][C]4450[/C][C]4632.21701401605[/C][C]-182.217014016045[/C][/ROW]
[ROW][C]72[/C][C]4500[/C][C]4499.42874069815[/C][C]0.571259301846112[/C][/ROW]
[ROW][C]73[/C][C]4660[/C][C]4615.23835105719[/C][C]44.7616489428128[/C][/ROW]
[ROW][C]74[/C][C]4370[/C][C]4438.63576703583[/C][C]-68.6357670358329[/C][/ROW]
[ROW][C]75[/C][C]5030[/C][C]4770.63688368901[/C][C]259.363116310988[/C][/ROW]
[ROW][C]76[/C][C]4510[/C][C]4606.90714203637[/C][C]-96.9071420363716[/C][/ROW]
[ROW][C]77[/C][C]4740[/C][C]4734.28534628362[/C][C]5.71465371637987[/C][/ROW]
[ROW][C]78[/C][C]4690[/C][C]4614.26488180002[/C][C]75.7351181999766[/C][/ROW]
[ROW][C]79[/C][C]4580[/C][C]4538.27330639406[/C][C]41.7266936059414[/C][/ROW]
[ROW][C]80[/C][C]4850[/C][C]4830.75636916214[/C][C]19.2436308378628[/C][/ROW]
[ROW][C]81[/C][C]4730[/C][C]4684.17110416743[/C][C]45.8288958325747[/C][/ROW]
[ROW][C]82[/C][C]4890[/C][C]4921.41523465862[/C][C]-31.4152346586234[/C][/ROW]
[ROW][C]83[/C][C]4740[/C][C]4724.00932606851[/C][C]15.9906739314856[/C][/ROW]
[ROW][C]84[/C][C]4600[/C][C]4685.72037858506[/C][C]-85.7203785850634[/C][/ROW]
[ROW][C]85[/C][C]4740[/C][C]4786.132213723[/C][C]-46.1322137230009[/C][/ROW]
[ROW][C]86[/C][C]4520[/C][C]4553.48951308461[/C][C]-33.4895130846135[/C][/ROW]
[ROW][C]87[/C][C]5000[/C][C]4968.43526321019[/C][C]31.5647367898137[/C][/ROW]
[ROW][C]88[/C][C]4670[/C][C]4661.91567774823[/C][C]8.08432225176512[/C][/ROW]
[ROW][C]89[/C][C]4940[/C][C]4845.4209283333[/C][C]94.5790716666979[/C][/ROW]
[ROW][C]90[/C][C]4790[/C][C]4763.0165562675[/C][C]26.9834437325035[/C][/ROW]
[ROW][C]91[/C][C]4820[/C][C]4662.33371837621[/C][C]157.666281623789[/C][/ROW]
[ROW][C]92[/C][C]5010[/C][C]4996.66896639086[/C][C]13.3310336091427[/C][/ROW]
[ROW][C]93[/C][C]4870[/C][C]4847.85976134591[/C][C]22.1402386540931[/C][/ROW]
[ROW][C]94[/C][C]5070[/C][C]5069.7481824893[/C][C]0.251817510703404[/C][/ROW]
[ROW][C]95[/C][C]4770[/C][C]4884.84038575446[/C][C]-114.840385754458[/C][/ROW]
[ROW][C]96[/C][C]4840[/C][C]4784.486580185[/C][C]55.5134198150017[/C][/ROW]
[ROW][C]97[/C][C]4850[/C][C]4941.48931037793[/C][C]-91.4893103779295[/C][/ROW]
[ROW][C]98[/C][C]4590[/C][C]4689.68152424164[/C][C]-99.6815242416351[/C][/ROW]
[ROW][C]99[/C][C]5050[/C][C]5106.84075068138[/C][C]-56.8407506813846[/C][/ROW]
[ROW][C]100[/C][C]4770[/C][C]4760.96544591289[/C][C]9.03455408710761[/C][/ROW]
[ROW][C]101[/C][C]4720[/C][C]4964.39642814522[/C][C]-244.39642814522[/C][/ROW]
[ROW][C]102[/C][C]4740[/C][C]4761.74524164888[/C][C]-21.7452416488832[/C][/ROW]
[ROW][C]103[/C][C]4400[/C][C]4669.4724102952[/C][C]-269.472410295197[/C][/ROW]
[ROW][C]104[/C][C]4840[/C][C]4832.97774440972[/C][C]7.02225559028466[/C][/ROW]
[ROW][C]105[/C][C]4650[/C][C]4689.10644204506[/C][C]-39.1064420450648[/C][/ROW]
[ROW][C]106[/C][C]4860[/C][C]4879.86528826983[/C][C]-19.8652882698298[/C][/ROW]
[ROW][C]107[/C][C]4580[/C][C]4675.67947563658[/C][C]-95.6794756365771[/C][/ROW]
[ROW][C]108[/C][C]4640[/C][C]4613.98342457335[/C][C]26.0165754266473[/C][/ROW]
[ROW][C]109[/C][C]4800[/C][C]4730.54613778898[/C][C]69.4538622110213[/C][/ROW]
[ROW][C]110[/C][C]4660[/C][C]4535.20300425536[/C][C]124.79699574464[/C][/ROW]
[ROW][C]111[/C][C]5020[/C][C]5025.45585894713[/C][C]-5.45585894713076[/C][/ROW]
[ROW][C]112[/C][C]4700[/C][C]4711.45509486299[/C][C]-11.4550948629912[/C][/ROW]
[ROW][C]113[/C][C]4800[/C][C]4859.66533873962[/C][C]-59.6653387396191[/C][/ROW]
[ROW][C]114[/C][C]4700[/C][C]4756.53459067408[/C][C]-56.5345906740813[/C][/ROW]
[ROW][C]115[/C][C]4560[/C][C]4607.43649455193[/C][C]-47.4364945519301[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301489&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301489&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
1340704018.1578815827151.8421184172898
1439303904.2423137980925.7576862019096
1542104196.6855228118413.3144771881607
1640204005.0270330198214.9729669801836
1741204103.9443769592316.0556230407674
1840203999.805000832420.1949991676029
1939103945.76074965814-35.7607496581441
2041104272.99165353869-162.991653538695
2141304010.1583362277119.841663772303
2243404196.8092508831143.190749116898
2342004185.804315152514.1956848474956
2442004007.99513448677192.00486551323
2541604257.35116210409-97.3511621040852
2639204084.66760331693-164.667603316929
2742804322.16258639573-42.162586395727
2839404108.01852122457-168.018521224573
2941904149.6851175012740.3148824987311
3041504052.6021735428797.3978264571256
3140704011.5146973044558.4853026955548
3241304353.22839788228-223.228397882275
3339604118.9345539907-158.934553990697
3443204220.6028685733999.3971314266073
3541104172.44527827611-62.4452782761136
3641004003.6165217694696.3834782305398
3742804167.41968630427112.580313695726
3839904049.20966902004-59.2096690200406
3943604344.7883401970315.2116598029688
4042404122.96587273931117.034127260693
4144504297.74064656794152.259353432059
4241904242.08555536233-52.0855553623251
4339504143.56438511204-193.564385112044
4443004355.53444102319-55.5344410231874
4541504182.44667046541-32.4466704654133
4645404377.70662279506162.293377204942
4742404315.67157825282-75.671578252819
4842104166.8165878762143.1834121237916
4943904320.4998047463369.5001952536695
5041404151.74990092141-11.7499009214062
5144604486.25515569786-26.2551556978633
5242904263.3605507739226.6394492260806
5344304418.3527258562711.6472741437328
5443904278.92660570522111.073394294779
5543404203.39892425598136.60107574402
5645704560.176479094999.82352090501354
5744704403.4751366065866.5248633934234
5845504679.89360158137-129.893601581367
5944204474.58163938793-54.581639387935
6044904349.45551458531140.544485414688
6144804545.63884268143-65.6388426814274
6244004310.6904774945289.3095225054785
6347704690.037313866879.9626861331981
6444504499.12579554713-49.1257955471328
6546104633.79141813853-23.7914181385258
6645404494.9628227234245.0371772765793
6745204398.18233650235121.817663497649
6847104738.03538956945-28.0353895694516
6945804573.894651351576.10534864842703
7047604801.63546399007-41.6354639900737
7144504632.21701401605-182.217014016045
7245004499.428740698150.571259301846112
7346604615.2383510571944.7616489428128
7443704438.63576703583-68.6357670358329
7550304770.63688368901259.363116310988
7645104606.90714203637-96.9071420363716
7747404734.285346283625.71465371637987
7846904614.2648818000275.7351181999766
7945804538.2733063940641.7266936059414
8048504830.7563691621419.2436308378628
8147304684.1711041674345.8288958325747
8248904921.41523465862-31.4152346586234
8347404724.0093260685115.9906739314856
8446004685.72037858506-85.7203785850634
8547404786.132213723-46.1322137230009
8645204553.48951308461-33.4895130846135
8750004968.4352632101931.5647367898137
8846704661.915677748238.08432225176512
8949404845.420928333394.5790716666979
9047904763.016556267526.9834437325035
9148204662.33371837621157.666281623789
9250104996.6689663908613.3310336091427
9348704847.8597613459122.1402386540931
9450705069.74818248930.251817510703404
9547704884.84038575446-114.840385754458
9648404784.48658018555.5134198150017
9748504941.48931037793-91.4893103779295
9845904689.68152424164-99.6815242416351
9950505106.84075068138-56.8407506813846
10047704760.965445912899.03455408710761
10147204964.39642814522-244.39642814522
10247404761.74524164888-21.7452416488832
10344004669.4724102952-269.472410295197
10448404832.977744409727.02225559028466
10546504689.10644204506-39.1064420450648
10648604879.86528826983-19.8652882698298
10745804675.67947563658-95.6794756365771
10846404613.9834245733526.0165754266473
10948004730.5461377889869.4538622110213
11046604535.20300425536124.79699574464
11150205025.45585894713-5.45585894713076
11247004711.45509486299-11.4550948629912
11348004859.66533873962-59.6653387396191
11447004756.53459067408-56.5345906740813
11545604607.43649455193-47.4364945519301







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1164895.88335667214802.369227058854989.39748628535
1174739.350363944394629.574616792114849.12611109667
1184949.054402451664821.834278324135076.27452657919
1194733.697025734664596.740879794214870.65317167511
1204724.309982032844575.316870239694873.30309382599
1214842.715977459544679.795477427775005.63647749132
1224631.629436475344463.701232012664799.55764093801
1235061.422630828184871.379636664425251.46562499194
1244745.592664485664556.301712318224934.8836166531
1254889.767306755794686.899903813855092.63470969773
1264805.058847028134596.855723482715013.26197057355
1274673.391969760084483.390809558444863.39312996171

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
116 & 4895.8833566721 & 4802.36922705885 & 4989.39748628535 \tabularnewline
117 & 4739.35036394439 & 4629.57461679211 & 4849.12611109667 \tabularnewline
118 & 4949.05440245166 & 4821.83427832413 & 5076.27452657919 \tabularnewline
119 & 4733.69702573466 & 4596.74087979421 & 4870.65317167511 \tabularnewline
120 & 4724.30998203284 & 4575.31687023969 & 4873.30309382599 \tabularnewline
121 & 4842.71597745954 & 4679.79547742777 & 5005.63647749132 \tabularnewline
122 & 4631.62943647534 & 4463.70123201266 & 4799.55764093801 \tabularnewline
123 & 5061.42263082818 & 4871.37963666442 & 5251.46562499194 \tabularnewline
124 & 4745.59266448566 & 4556.30171231822 & 4934.8836166531 \tabularnewline
125 & 4889.76730675579 & 4686.89990381385 & 5092.63470969773 \tabularnewline
126 & 4805.05884702813 & 4596.85572348271 & 5013.26197057355 \tabularnewline
127 & 4673.39196976008 & 4483.39080955844 & 4863.39312996171 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301489&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]116[/C][C]4895.8833566721[/C][C]4802.36922705885[/C][C]4989.39748628535[/C][/ROW]
[ROW][C]117[/C][C]4739.35036394439[/C][C]4629.57461679211[/C][C]4849.12611109667[/C][/ROW]
[ROW][C]118[/C][C]4949.05440245166[/C][C]4821.83427832413[/C][C]5076.27452657919[/C][/ROW]
[ROW][C]119[/C][C]4733.69702573466[/C][C]4596.74087979421[/C][C]4870.65317167511[/C][/ROW]
[ROW][C]120[/C][C]4724.30998203284[/C][C]4575.31687023969[/C][C]4873.30309382599[/C][/ROW]
[ROW][C]121[/C][C]4842.71597745954[/C][C]4679.79547742777[/C][C]5005.63647749132[/C][/ROW]
[ROW][C]122[/C][C]4631.62943647534[/C][C]4463.70123201266[/C][C]4799.55764093801[/C][/ROW]
[ROW][C]123[/C][C]5061.42263082818[/C][C]4871.37963666442[/C][C]5251.46562499194[/C][/ROW]
[ROW][C]124[/C][C]4745.59266448566[/C][C]4556.30171231822[/C][C]4934.8836166531[/C][/ROW]
[ROW][C]125[/C][C]4889.76730675579[/C][C]4686.89990381385[/C][C]5092.63470969773[/C][/ROW]
[ROW][C]126[/C][C]4805.05884702813[/C][C]4596.85572348271[/C][C]5013.26197057355[/C][/ROW]
[ROW][C]127[/C][C]4673.39196976008[/C][C]4483.39080955844[/C][C]4863.39312996171[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301489&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301489&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
1164895.88335667214802.369227058854989.39748628535
1174739.350363944394629.574616792114849.12611109667
1184949.054402451664821.834278324135076.27452657919
1194733.697025734664596.740879794214870.65317167511
1204724.309982032844575.316870239694873.30309382599
1214842.715977459544679.795477427775005.63647749132
1224631.629436475344463.701232012664799.55764093801
1235061.422630828184871.379636664425251.46562499194
1244745.592664485664556.301712318224934.8836166531
1254889.767306755794686.899903813855092.63470969773
1264805.058847028134596.855723482715013.26197057355
1274673.391969760084483.390809558444863.39312996171



Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
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')