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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 23 Apr 2016 14:32:39 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/23/t14614184860q1r5d2unaitns5.htm/, Retrieved Mon, 13 May 2024 01:50:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294601, Retrieved Mon, 13 May 2024 01:50:33 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

142

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Exponential Smoothing] [Exponential smoot...] [2016-04-23 13:32:39] [f41d2dc125a0429ac7ee523034b5d7c0] [Current]

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Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294601&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294601&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294601&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 Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.669691112865472
beta	0.12791578004407
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.669691112865472 \tabularnewline
beta & 0.12791578004407 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294601&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]0.669691112865472[/C][/ROW]
[ROW][C]beta[/C][C]0.12791578004407[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294601&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294601&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
Parameter	Value
alpha	0.669691112865472
beta	0.12791578004407
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.336	1.27502100314958	0.0609789968504164
14	1.3649	1.34594680884469	0.0189531911553134
15	1.3999	1.39995980401397	-5.98040139683231e-05
16	1.4442	1.45793319654295	-0.0137331965429452
17	1.4349	1.45534694789036	-0.0204469478903608
18	1.4388	1.45915390588882	-0.0203539058888187
19	1.4264	1.36021736093086	0.066182639069138
20	1.4343	1.43876789690378	-0.00446789690377525
21	1.377	1.4693858046344	-0.0923858046344042
22	1.3706	1.4988546980942	-0.128254698094199
23	1.3556	1.37446782318281	-0.0188678231828094
24	1.3179	1.29815387627764	0.0197461237223591
25	1.2905	1.32853007548978	-0.0380300754897842
26	1.3224	1.30027642416838	0.0221235758316156
27	1.3201	1.33054369269094	-0.0104436926909417
28	1.3162	1.35467265252761	-0.0384726525276116
29	1.2789	1.31179795164023	-0.032897951640229
30	1.2526	1.28336344371875	-0.0307634437187525
31	1.2288	1.19051641105198	0.0382835889480222
32	1.24	1.20230604932358	0.0376939506764236
33	1.2856	1.21085523210101	0.0747447678989905
34	1.2974	1.32408895646397	-0.0266889564639685
35	1.2828	1.30420829366888	-0.0214082936688764
36	1.3119	1.24134904132181	0.0705509586781925
37	1.3288	1.2909399535736	0.0378600464263978
38	1.3359	1.34491738907144	-0.00901738907143756
39	1.2964	1.35220439251578	-0.0558043925157805
40	1.3026	1.34110039140059	-0.0385003914005897
41	1.2982	1.30455912776911	-0.00635912776910597
42	1.3189	1.30147862698089	0.017421373019112
43	1.308	1.27239481458123	0.0356051854187702
44	1.331	1.29210454999986	0.0388954500001402
45	1.3348	1.32326906077429	0.011530939225709
46	1.3635	1.36665589009337	-0.00315589009337325
47	1.3493	1.37136957075273	-0.0220695707527347
48	1.3704	1.34364288811902	0.0267571118809802
49	1.361	1.3554957325408	0.00550426745919941
50	1.3658	1.37272756522751	-0.00692756522750848
51	1.3823	1.36567912750771	0.0166208724922923
52	1.3812	1.4172149587873	-0.0360149587872967
53	1.3732	1.40006036185903	-0.0268603618590268
54	1.3592	1.3970728867608	-0.0378728867607974
55	1.3539	1.33588491174926	0.0180150882507404
56	1.3316	1.34343951482301	-0.0118395148230064
57	1.2901	1.32612126986721	-0.0360212698672127
58	1.2673	1.32251719878946	-0.055217198789463
59	1.2472	1.27222950852532	-0.0250295085253223
60	1.2331	1.2442123530343	-0.0111123530342983
61	1.1621	1.20814322669564	-0.0460432266956425
62	1.135	1.16446147694818	-0.0294614769481751
63	1.0838	1.12632920492776	-0.0425292049277577
64	1.0779	1.08825230914676	-0.0103523091467574
65	1.115	1.06281100353954	0.0521889964604589
66	1.1213	1.0865180854813	0.0347819145186992
67	1.0996	1.08119279353566	0.0184072064643417
68	1.1139	1.06795959121441	0.0459404087855941
69	1.1221	1.07515475541703	0.0469452445829746
70	1.1235	1.11589635451617	0.00760364548383352
71	1.0736	1.12042405885687	-0.0468240588568676
72	1.0877	1.08346944053527	0.00423055946472517

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.336 & 1.27502100314958 & 0.0609789968504164 \tabularnewline
14 & 1.3649 & 1.34594680884469 & 0.0189531911553134 \tabularnewline
15 & 1.3999 & 1.39995980401397 & -5.98040139683231e-05 \tabularnewline
16 & 1.4442 & 1.45793319654295 & -0.0137331965429452 \tabularnewline
17 & 1.4349 & 1.45534694789036 & -0.0204469478903608 \tabularnewline
18 & 1.4388 & 1.45915390588882 & -0.0203539058888187 \tabularnewline
19 & 1.4264 & 1.36021736093086 & 0.066182639069138 \tabularnewline
20 & 1.4343 & 1.43876789690378 & -0.00446789690377525 \tabularnewline
21 & 1.377 & 1.4693858046344 & -0.0923858046344042 \tabularnewline
22 & 1.3706 & 1.4988546980942 & -0.128254698094199 \tabularnewline
23 & 1.3556 & 1.37446782318281 & -0.0188678231828094 \tabularnewline
24 & 1.3179 & 1.29815387627764 & 0.0197461237223591 \tabularnewline
25 & 1.2905 & 1.32853007548978 & -0.0380300754897842 \tabularnewline
26 & 1.3224 & 1.30027642416838 & 0.0221235758316156 \tabularnewline
27 & 1.3201 & 1.33054369269094 & -0.0104436926909417 \tabularnewline
28 & 1.3162 & 1.35467265252761 & -0.0384726525276116 \tabularnewline
29 & 1.2789 & 1.31179795164023 & -0.032897951640229 \tabularnewline
30 & 1.2526 & 1.28336344371875 & -0.0307634437187525 \tabularnewline
31 & 1.2288 & 1.19051641105198 & 0.0382835889480222 \tabularnewline
32 & 1.24 & 1.20230604932358 & 0.0376939506764236 \tabularnewline
33 & 1.2856 & 1.21085523210101 & 0.0747447678989905 \tabularnewline
34 & 1.2974 & 1.32408895646397 & -0.0266889564639685 \tabularnewline
35 & 1.2828 & 1.30420829366888 & -0.0214082936688764 \tabularnewline
36 & 1.3119 & 1.24134904132181 & 0.0705509586781925 \tabularnewline
37 & 1.3288 & 1.2909399535736 & 0.0378600464263978 \tabularnewline
38 & 1.3359 & 1.34491738907144 & -0.00901738907143756 \tabularnewline
39 & 1.2964 & 1.35220439251578 & -0.0558043925157805 \tabularnewline
40 & 1.3026 & 1.34110039140059 & -0.0385003914005897 \tabularnewline
41 & 1.2982 & 1.30455912776911 & -0.00635912776910597 \tabularnewline
42 & 1.3189 & 1.30147862698089 & 0.017421373019112 \tabularnewline
43 & 1.308 & 1.27239481458123 & 0.0356051854187702 \tabularnewline
44 & 1.331 & 1.29210454999986 & 0.0388954500001402 \tabularnewline
45 & 1.3348 & 1.32326906077429 & 0.011530939225709 \tabularnewline
46 & 1.3635 & 1.36665589009337 & -0.00315589009337325 \tabularnewline
47 & 1.3493 & 1.37136957075273 & -0.0220695707527347 \tabularnewline
48 & 1.3704 & 1.34364288811902 & 0.0267571118809802 \tabularnewline
49 & 1.361 & 1.3554957325408 & 0.00550426745919941 \tabularnewline
50 & 1.3658 & 1.37272756522751 & -0.00692756522750848 \tabularnewline
51 & 1.3823 & 1.36567912750771 & 0.0166208724922923 \tabularnewline
52 & 1.3812 & 1.4172149587873 & -0.0360149587872967 \tabularnewline
53 & 1.3732 & 1.40006036185903 & -0.0268603618590268 \tabularnewline
54 & 1.3592 & 1.3970728867608 & -0.0378728867607974 \tabularnewline
55 & 1.3539 & 1.33588491174926 & 0.0180150882507404 \tabularnewline
56 & 1.3316 & 1.34343951482301 & -0.0118395148230064 \tabularnewline
57 & 1.2901 & 1.32612126986721 & -0.0360212698672127 \tabularnewline
58 & 1.2673 & 1.32251719878946 & -0.055217198789463 \tabularnewline
59 & 1.2472 & 1.27222950852532 & -0.0250295085253223 \tabularnewline
60 & 1.2331 & 1.2442123530343 & -0.0111123530342983 \tabularnewline
61 & 1.1621 & 1.20814322669564 & -0.0460432266956425 \tabularnewline
62 & 1.135 & 1.16446147694818 & -0.0294614769481751 \tabularnewline
63 & 1.0838 & 1.12632920492776 & -0.0425292049277577 \tabularnewline
64 & 1.0779 & 1.08825230914676 & -0.0103523091467574 \tabularnewline
65 & 1.115 & 1.06281100353954 & 0.0521889964604589 \tabularnewline
66 & 1.1213 & 1.0865180854813 & 0.0347819145186992 \tabularnewline
67 & 1.0996 & 1.08119279353566 & 0.0184072064643417 \tabularnewline
68 & 1.1139 & 1.06795959121441 & 0.0459404087855941 \tabularnewline
69 & 1.1221 & 1.07515475541703 & 0.0469452445829746 \tabularnewline
70 & 1.1235 & 1.11589635451617 & 0.00760364548383352 \tabularnewline
71 & 1.0736 & 1.12042405885687 & -0.0468240588568676 \tabularnewline
72 & 1.0877 & 1.08346944053527 & 0.00423055946472517 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294601&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]1.336[/C][C]1.27502100314958[/C][C]0.0609789968504164[/C][/ROW]
[ROW][C]14[/C][C]1.3649[/C][C]1.34594680884469[/C][C]0.0189531911553134[/C][/ROW]
[ROW][C]15[/C][C]1.3999[/C][C]1.39995980401397[/C][C]-5.98040139683231e-05[/C][/ROW]
[ROW][C]16[/C][C]1.4442[/C][C]1.45793319654295[/C][C]-0.0137331965429452[/C][/ROW]
[ROW][C]17[/C][C]1.4349[/C][C]1.45534694789036[/C][C]-0.0204469478903608[/C][/ROW]
[ROW][C]18[/C][C]1.4388[/C][C]1.45915390588882[/C][C]-0.0203539058888187[/C][/ROW]
[ROW][C]19[/C][C]1.4264[/C][C]1.36021736093086[/C][C]0.066182639069138[/C][/ROW]
[ROW][C]20[/C][C]1.4343[/C][C]1.43876789690378[/C][C]-0.00446789690377525[/C][/ROW]
[ROW][C]21[/C][C]1.377[/C][C]1.4693858046344[/C][C]-0.0923858046344042[/C][/ROW]
[ROW][C]22[/C][C]1.3706[/C][C]1.4988546980942[/C][C]-0.128254698094199[/C][/ROW]
[ROW][C]23[/C][C]1.3556[/C][C]1.37446782318281[/C][C]-0.0188678231828094[/C][/ROW]
[ROW][C]24[/C][C]1.3179[/C][C]1.29815387627764[/C][C]0.0197461237223591[/C][/ROW]
[ROW][C]25[/C][C]1.2905[/C][C]1.32853007548978[/C][C]-0.0380300754897842[/C][/ROW]
[ROW][C]26[/C][C]1.3224[/C][C]1.30027642416838[/C][C]0.0221235758316156[/C][/ROW]
[ROW][C]27[/C][C]1.3201[/C][C]1.33054369269094[/C][C]-0.0104436926909417[/C][/ROW]
[ROW][C]28[/C][C]1.3162[/C][C]1.35467265252761[/C][C]-0.0384726525276116[/C][/ROW]
[ROW][C]29[/C][C]1.2789[/C][C]1.31179795164023[/C][C]-0.032897951640229[/C][/ROW]
[ROW][C]30[/C][C]1.2526[/C][C]1.28336344371875[/C][C]-0.0307634437187525[/C][/ROW]
[ROW][C]31[/C][C]1.2288[/C][C]1.19051641105198[/C][C]0.0382835889480222[/C][/ROW]
[ROW][C]32[/C][C]1.24[/C][C]1.20230604932358[/C][C]0.0376939506764236[/C][/ROW]
[ROW][C]33[/C][C]1.2856[/C][C]1.21085523210101[/C][C]0.0747447678989905[/C][/ROW]
[ROW][C]34[/C][C]1.2974[/C][C]1.32408895646397[/C][C]-0.0266889564639685[/C][/ROW]
[ROW][C]35[/C][C]1.2828[/C][C]1.30420829366888[/C][C]-0.0214082936688764[/C][/ROW]
[ROW][C]36[/C][C]1.3119[/C][C]1.24134904132181[/C][C]0.0705509586781925[/C][/ROW]
[ROW][C]37[/C][C]1.3288[/C][C]1.2909399535736[/C][C]0.0378600464263978[/C][/ROW]
[ROW][C]38[/C][C]1.3359[/C][C]1.34491738907144[/C][C]-0.00901738907143756[/C][/ROW]
[ROW][C]39[/C][C]1.2964[/C][C]1.35220439251578[/C][C]-0.0558043925157805[/C][/ROW]
[ROW][C]40[/C][C]1.3026[/C][C]1.34110039140059[/C][C]-0.0385003914005897[/C][/ROW]
[ROW][C]41[/C][C]1.2982[/C][C]1.30455912776911[/C][C]-0.00635912776910597[/C][/ROW]
[ROW][C]42[/C][C]1.3189[/C][C]1.30147862698089[/C][C]0.017421373019112[/C][/ROW]
[ROW][C]43[/C][C]1.308[/C][C]1.27239481458123[/C][C]0.0356051854187702[/C][/ROW]
[ROW][C]44[/C][C]1.331[/C][C]1.29210454999986[/C][C]0.0388954500001402[/C][/ROW]
[ROW][C]45[/C][C]1.3348[/C][C]1.32326906077429[/C][C]0.011530939225709[/C][/ROW]
[ROW][C]46[/C][C]1.3635[/C][C]1.36665589009337[/C][C]-0.00315589009337325[/C][/ROW]
[ROW][C]47[/C][C]1.3493[/C][C]1.37136957075273[/C][C]-0.0220695707527347[/C][/ROW]
[ROW][C]48[/C][C]1.3704[/C][C]1.34364288811902[/C][C]0.0267571118809802[/C][/ROW]
[ROW][C]49[/C][C]1.361[/C][C]1.3554957325408[/C][C]0.00550426745919941[/C][/ROW]
[ROW][C]50[/C][C]1.3658[/C][C]1.37272756522751[/C][C]-0.00692756522750848[/C][/ROW]
[ROW][C]51[/C][C]1.3823[/C][C]1.36567912750771[/C][C]0.0166208724922923[/C][/ROW]
[ROW][C]52[/C][C]1.3812[/C][C]1.4172149587873[/C][C]-0.0360149587872967[/C][/ROW]
[ROW][C]53[/C][C]1.3732[/C][C]1.40006036185903[/C][C]-0.0268603618590268[/C][/ROW]
[ROW][C]54[/C][C]1.3592[/C][C]1.3970728867608[/C][C]-0.0378728867607974[/C][/ROW]
[ROW][C]55[/C][C]1.3539[/C][C]1.33588491174926[/C][C]0.0180150882507404[/C][/ROW]
[ROW][C]56[/C][C]1.3316[/C][C]1.34343951482301[/C][C]-0.0118395148230064[/C][/ROW]
[ROW][C]57[/C][C]1.2901[/C][C]1.32612126986721[/C][C]-0.0360212698672127[/C][/ROW]
[ROW][C]58[/C][C]1.2673[/C][C]1.32251719878946[/C][C]-0.055217198789463[/C][/ROW]
[ROW][C]59[/C][C]1.2472[/C][C]1.27222950852532[/C][C]-0.0250295085253223[/C][/ROW]
[ROW][C]60[/C][C]1.2331[/C][C]1.2442123530343[/C][C]-0.0111123530342983[/C][/ROW]
[ROW][C]61[/C][C]1.1621[/C][C]1.20814322669564[/C][C]-0.0460432266956425[/C][/ROW]
[ROW][C]62[/C][C]1.135[/C][C]1.16446147694818[/C][C]-0.0294614769481751[/C][/ROW]
[ROW][C]63[/C][C]1.0838[/C][C]1.12632920492776[/C][C]-0.0425292049277577[/C][/ROW]
[ROW][C]64[/C][C]1.0779[/C][C]1.08825230914676[/C][C]-0.0103523091467574[/C][/ROW]
[ROW][C]65[/C][C]1.115[/C][C]1.06281100353954[/C][C]0.0521889964604589[/C][/ROW]
[ROW][C]66[/C][C]1.1213[/C][C]1.0865180854813[/C][C]0.0347819145186992[/C][/ROW]
[ROW][C]67[/C][C]1.0996[/C][C]1.08119279353566[/C][C]0.0184072064643417[/C][/ROW]
[ROW][C]68[/C][C]1.1139[/C][C]1.06795959121441[/C][C]0.0459404087855941[/C][/ROW]
[ROW][C]69[/C][C]1.1221[/C][C]1.07515475541703[/C][C]0.0469452445829746[/C][/ROW]
[ROW][C]70[/C][C]1.1235[/C][C]1.11589635451617[/C][C]0.00760364548383352[/C][/ROW]
[ROW][C]71[/C][C]1.0736[/C][C]1.12042405885687[/C][C]-0.0468240588568676[/C][/ROW]
[ROW][C]72[/C][C]1.0877[/C][C]1.08346944053527[/C][C]0.00423055946472517[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294601&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294601&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
t	Observed	Fitted	Residuals
13	1.336	1.27502100314958	0.0609789968504164
14	1.3649	1.34594680884469	0.0189531911553134
15	1.3999	1.39995980401397	-5.98040139683231e-05
16	1.4442	1.45793319654295	-0.0137331965429452
17	1.4349	1.45534694789036	-0.0204469478903608
18	1.4388	1.45915390588882	-0.0203539058888187
19	1.4264	1.36021736093086	0.066182639069138
20	1.4343	1.43876789690378	-0.00446789690377525
21	1.377	1.4693858046344	-0.0923858046344042
22	1.3706	1.4988546980942	-0.128254698094199
23	1.3556	1.37446782318281	-0.0188678231828094
24	1.3179	1.29815387627764	0.0197461237223591
25	1.2905	1.32853007548978	-0.0380300754897842
26	1.3224	1.30027642416838	0.0221235758316156
27	1.3201	1.33054369269094	-0.0104436926909417
28	1.3162	1.35467265252761	-0.0384726525276116
29	1.2789	1.31179795164023	-0.032897951640229
30	1.2526	1.28336344371875	-0.0307634437187525
31	1.2288	1.19051641105198	0.0382835889480222
32	1.24	1.20230604932358	0.0376939506764236
33	1.2856	1.21085523210101	0.0747447678989905
34	1.2974	1.32408895646397	-0.0266889564639685
35	1.2828	1.30420829366888	-0.0214082936688764
36	1.3119	1.24134904132181	0.0705509586781925
37	1.3288	1.2909399535736	0.0378600464263978
38	1.3359	1.34491738907144	-0.00901738907143756
39	1.2964	1.35220439251578	-0.0558043925157805
40	1.3026	1.34110039140059	-0.0385003914005897
41	1.2982	1.30455912776911	-0.00635912776910597
42	1.3189	1.30147862698089	0.017421373019112
43	1.308	1.27239481458123	0.0356051854187702
44	1.331	1.29210454999986	0.0388954500001402
45	1.3348	1.32326906077429	0.011530939225709
46	1.3635	1.36665589009337	-0.00315589009337325
47	1.3493	1.37136957075273	-0.0220695707527347
48	1.3704	1.34364288811902	0.0267571118809802
49	1.361	1.3554957325408	0.00550426745919941
50	1.3658	1.37272756522751	-0.00692756522750848
51	1.3823	1.36567912750771	0.0166208724922923
52	1.3812	1.4172149587873	-0.0360149587872967
53	1.3732	1.40006036185903	-0.0268603618590268
54	1.3592	1.3970728867608	-0.0378728867607974
55	1.3539	1.33588491174926	0.0180150882507404
56	1.3316	1.34343951482301	-0.0118395148230064
57	1.2901	1.32612126986721	-0.0360212698672127
58	1.2673	1.32251719878946	-0.055217198789463
59	1.2472	1.27222950852532	-0.0250295085253223
60	1.2331	1.2442123530343	-0.0111123530342983
61	1.1621	1.20814322669564	-0.0460432266956425
62	1.135	1.16446147694818	-0.0294614769481751
63	1.0838	1.12632920492776	-0.0425292049277577
64	1.0779	1.08825230914676	-0.0103523091467574
65	1.115	1.06281100353954	0.0521889964604589
66	1.1213	1.0865180854813	0.0347819145186992
67	1.0996	1.08119279353566	0.0184072064643417
68	1.1139	1.06795959121441	0.0459404087855941
69	1.1221	1.07515475541703	0.0469452445829746
70	1.1235	1.11589635451617	0.00760364548383352
71	1.0736	1.12042405885687	-0.0468240588568676
72	1.0877	1.08346944053527	0.00423055946472517

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.05205160413865	0.975393071616271	1.12871013666102
74	1.05055458623967	0.954242429732716	1.14686674274662
75	1.03711259485976	0.921457244906791	1.15276794481272
76	1.0502631214024	0.912569986854584	1.18795625595021
77	1.06556434807167	0.904325285985474	1.22680341015786
78	1.0580711636213	0.875117182058589	1.241025145184
79	1.03170888774815	0.829532157680271	1.23388561781603
80	1.02008917344876	0.795856487181324	1.24432185971621
81	0.998659014999971	0.754011882127097	1.24330614787284
82	0.991724723511147	0.722964250255602	1.26048519676669
83	0.970759107656163	0.681063519861096	1.26045469545123
84	0.980415091709844	-7.58733943892171	9.5481696223414

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.05205160413865 & 0.975393071616271 & 1.12871013666102 \tabularnewline
74 & 1.05055458623967 & 0.954242429732716 & 1.14686674274662 \tabularnewline
75 & 1.03711259485976 & 0.921457244906791 & 1.15276794481272 \tabularnewline
76 & 1.0502631214024 & 0.912569986854584 & 1.18795625595021 \tabularnewline
77 & 1.06556434807167 & 0.904325285985474 & 1.22680341015786 \tabularnewline
78 & 1.0580711636213 & 0.875117182058589 & 1.241025145184 \tabularnewline
79 & 1.03170888774815 & 0.829532157680271 & 1.23388561781603 \tabularnewline
80 & 1.02008917344876 & 0.795856487181324 & 1.24432185971621 \tabularnewline
81 & 0.998659014999971 & 0.754011882127097 & 1.24330614787284 \tabularnewline
82 & 0.991724723511147 & 0.722964250255602 & 1.26048519676669 \tabularnewline
83 & 0.970759107656163 & 0.681063519861096 & 1.26045469545123 \tabularnewline
84 & 0.980415091709844 & -7.58733943892171 & 9.5481696223414 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294601&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]73[/C][C]1.05205160413865[/C][C]0.975393071616271[/C][C]1.12871013666102[/C][/ROW]
[ROW][C]74[/C][C]1.05055458623967[/C][C]0.954242429732716[/C][C]1.14686674274662[/C][/ROW]
[ROW][C]75[/C][C]1.03711259485976[/C][C]0.921457244906791[/C][C]1.15276794481272[/C][/ROW]
[ROW][C]76[/C][C]1.0502631214024[/C][C]0.912569986854584[/C][C]1.18795625595021[/C][/ROW]
[ROW][C]77[/C][C]1.06556434807167[/C][C]0.904325285985474[/C][C]1.22680341015786[/C][/ROW]
[ROW][C]78[/C][C]1.0580711636213[/C][C]0.875117182058589[/C][C]1.241025145184[/C][/ROW]
[ROW][C]79[/C][C]1.03170888774815[/C][C]0.829532157680271[/C][C]1.23388561781603[/C][/ROW]
[ROW][C]80[/C][C]1.02008917344876[/C][C]0.795856487181324[/C][C]1.24432185971621[/C][/ROW]
[ROW][C]81[/C][C]0.998659014999971[/C][C]0.754011882127097[/C][C]1.24330614787284[/C][/ROW]
[ROW][C]82[/C][C]0.991724723511147[/C][C]0.722964250255602[/C][C]1.26048519676669[/C][/ROW]
[ROW][C]83[/C][C]0.970759107656163[/C][C]0.681063519861096[/C][C]1.26045469545123[/C][/ROW]
[ROW][C]84[/C][C]0.980415091709844[/C][C]-7.58733943892171[/C][C]9.5481696223414[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294601&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294601&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
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.05205160413865	0.975393071616271	1.12871013666102
74	1.05055458623967	0.954242429732716	1.14686674274662
75	1.03711259485976	0.921457244906791	1.15276794481272
76	1.0502631214024	0.912569986854584	1.18795625595021
77	1.06556434807167	0.904325285985474	1.22680341015786
78	1.0580711636213	0.875117182058589	1.241025145184
79	1.03170888774815	0.829532157680271	1.23388561781603
80	1.02008917344876	0.795856487181324	1.24432185971621
81	0.998659014999971	0.754011882127097	1.24330614787284
82	0.991724723511147	0.722964250255602	1.26048519676669
83	0.970759107656163	0.681063519861096	1.26045469545123
84	0.980415091709844	-7.58733943892171	9.5481696223414

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code