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*The author of this computation has been verified*

R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Wed, 29 Dec 2010 22:36:06 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t1293662182462hd8k0dbciot2.htm/, Retrieved Wed, 29 Dec 2010 23:36:26 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t1293662182462hd8k0dbciot2.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

20503 22885 26217 26583 27751 28158 27373 28367 26851 26733 26849 26733 27951 29781 32914 33488 35652 36488 35387 35676 34844 32447 31068 29010 29812 30951 32974 32936 34012 32946 31948 30599 27691 25073 23406 22248 22896 25317 26558 26471 27543 26198 24725 25005 23462 20780 19815 19761 21454 23899 24939 23580 24562 24696 23785 23812 21917 19713 19282 18788 21453 24482 27474 27264 27349 30632 29429 30084 26290 24379 23335 21346 21106 24514 28353 30805 31348 34556 33855 34787 32529 29998 29257 28155 30466 35704 39327 39351 42234 43630 43722 43121 37985 37135 34646 33026 35087 38846 42013 43908 42868 44423 44167 43636 44382 42142 43452 36912 42413 45344 44873 47510 49554 47369 45998 48140 48441 44928 40454 38661 37246 36843 36424 37594 38144 38737 34560 36080 33508 35462 33374 32110 35533 35532 37903 36763 40399 44164 44496 43110 43880 43930 44327

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.957106985347542
beta	0.0213231419809285
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	27951	24203.1065705128	3747.89342948717
14	29781	29654.6202551849	126.379744815073
15	32914	32946.4121193040	-32.4121193039537
16	33488	33593.0200307428	-105.020030742766
17	35652	35915.2410986994	-263.241098699371
18	36488	36895.8636472486	-407.86364724861
19	35387	34286.1180476207	1100.88195237935
20	35676	36417.4957808124	-741.495780812395
21	34844	34291.6797450762	552.32025492382
22	32447	34813.0811183624	-2366.08111836240
23	31068	32676.8052514774	-1608.80525147740
24	29010	30941.1150593774	-1931.11505937738
25	29812	30347.5787971139	-535.578797113856
26	30951	31417.2352441558	-466.23524415584
27	32974	33996.1472928091	-1022.14729280914
28	32936	33533.2865375479	-597.286537547945
29	34012	35208.4510334614	-1196.45103346142
30	32946	35101.5248152055	-2155.52481520546
31	31948	30659.9642363377	1288.03576366226
32	30599	32671.4316738823	-2072.43167388231
33	27691	29080.0894447366	-1389.08944473662
34	25073	27331.3798624235	-2258.37986242351
35	23406	25046.0703511283	-1640.07035112833
36	22248	22981.3960861217	-733.396086121684
37	22896	23333.2722700384	-437.272270038433
38	25317	24241.2077194554	1075.79228054459
39	26558	28044.8456366518	-1486.84563665182
40	26471	26918.6438964958	-447.643896495847
41	27543	28477.5879114903	-934.58791149029
42	26198	28351.7548651247	-2153.75486512472
43	24725	23831.2288487051	893.771151294939
44	25005	25084.7917687	-79.791768699979
45	23462	23234.1860439709	227.813956029069
46	20780	22832.9944567301	-2052.99445673013
47	19815	20612.2284668622	-797.228466862165
48	19761	19251.7817676982	509.218232301817
49	21454	20689.6820866713	764.317913328661
50	23899	22721.0981287399	1177.90187126014
51	24939	26423.1608238929	-1484.16082389287
52	23580	25254.77226647	-1674.77226646998
53	24562	25503.9618002243	-941.961800224315
54	24696	25204.2520675708	-508.252067570837
55	23785	22308.4228014571	1476.57719854289
56	23812	24008.9855756807	-196.985575680679
57	21917	21987.9663872987	-70.9663872986566
58	19713	21125.4410414518	-1412.44104145183
59	19282	19507.1512849844	-225.151284984386
60	18788	18697.4908395737	90.5091604262525
61	21453	19684.2482889172	1768.75171108282
62	24482	22653.9183268633	1828.08167313667
63	27474	26836.521499678	637.478500321988
64	27264	27706.3251380426	-442.325138042648
65	27349	29207.4155870462	-1858.41558704625
66	30632	28071.3458877918	2560.65411220821
67	29429	28282.7365692393	1146.26343076072
68	30084	29673.4414532652	410.558546734756
69	26290	28329.7832894657	-2039.7832894657
70	24379	25575.6399447567	-1196.63994475665
71	23335	24269.5158481258	-934.51584812579
72	21346	22834.6746514598	-1488.67465145977
73	21106	22389.9577075278	-1283.95770752776
74	24514	22386.0903534585	2127.90964654151
75	28353	26756.3987381583	1596.60126184173
76	30805	28469.2500454384	2335.74995456163
77	31348	32596.5922140575	-1248.59221405754
78	34556	32274.2585747892	2281.74142521078
79	33855	32192.8629260748	1662.13707392518
80	34787	34091.1161300118	695.883869988247
81	32529	32966.6240006515	-437.624000651507
82	29998	31865.9628984149	-1867.96289841495
83	29257	29998.7329284109	-741.732928410947
84	28155	28798.7492071101	-643.749207110133
85	30466	29262.8540575671	1203.14594243286
86	35704	31927.8712040234	3776.12879597661
87	39327	38028.664906047	1298.33509395298
88	39351	39657.4133971206	-306.413397120552
89	42234	41217.9221600109	1016.07783998913
90	43630	43376.5081197733	253.491880226655
91	43722	41447.8517953736	2274.14820462636
92	43121	44023.4776915287	-902.477691528664
93	37985	41421.0008466682	-3436.00084666823
94	37135	37428.4661847129	-293.466184712888
95	34646	37187.8839885004	-2541.88398850036
96	33026	34303.8060686305	-1277.80606863050
97	35087	34261.9695397592	825.030460240792
98	38846	36689.4358989501	2156.56410104987
99	42013	41114.7831357914	898.216864208553
100	43908	42264.5076086407	1643.49239135929
101	42868	45760.5696005895	-2892.5696005895
102	44423	44078.2415818128	344.758418187201
103	44167	42258.2611563071	1908.73884369290
104	43636	44275.0906888206	-639.090688820557
105	44382	41748.6028286708	2633.39717132920
106	42142	43756.3615625213	-1614.36156252131
107	43452	42184.5795956299	1267.42040437010
108	36912	43107.8557682616	-6195.85576826164
109	42413	38455.9684959766	3957.03150402343
110	45344	44008.9799360331	1335.02006396691
111	44873	47648.0523369253	-2775.05233692529
112	47510	45293.0713017396	2216.92869826043
113	49554	49134.1497955218	419.850204478171
114	47369	50819.3642618563	-3450.36426185632
115	45998	45415.0199694621	582.980030537889
116	48140	46007.506330629	2132.49366937105
117	48441	46284.4859863651	2156.51401363491
118	44928	47654.2827542829	-2726.28275428293
119	40454	45119.8543019029	-4665.85430190287
120	38661	39901.1127273158	-1240.11272731575
121	37246	40385.9124353145	-3139.91243531455
122	36843	38847.1078568753	-2004.10785687529
123	36424	38859.0220934941	-2435.02209349412
124	37594	36795.584901452	798.415098547994
125	38144	38924.9396374968	-780.939637496784
126	38737	38993.3858705737	-256.385870573657
127	34560	36582.7285794763	-2022.72857947634
128	36080	34458.2633380612	1621.73666193877
129	33508	33947.5273990168	-439.527399016821
130	35462	32270.3187389711	3191.68126102889
131	33374	35084.7196646531	-1710.71966465309
132	32110	32669.5071767581	-559.507176758118
133	35533	33566.3299314641	1966.67006853594
134	35532	36910.1059105796	-1378.10591057956
135	37903	37461.7802399509	441.219760049113
136	36763	38307.698416921	-1544.69841692103
137	40399	38096.6723864801	2302.32761351993
138	44164	41171.5327145295	2992.46728547053
139	44496	41893.813799733	2602.18620026704
140	43110	44545.7986950497	-1435.79869504966
141	43880	41151.4504753467	2728.54952465331
142	43930	42858.0296394016	1071.97036059837
143	44327	43585.9473051438	741.052694856175

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
144	43769.3449128364	40271.3686085046	47267.3212171682
145	45524.0726400356	40632.4850422983	50415.6602377729
146	47015.9719798341	41006.5861541469	53025.3578055213
147	49166.7071249071	42180.9145999255	56152.4996498887
148	49698.1737835982	41823.9398858644	57572.407681332
149	51355.1499768492	42652.8688118967	60057.4311418018
150	52433.601551324	42947.3006998531	61919.9024027949
151	50391.522025894	40154.6098333462	60628.4342184417
152	50443.119260207	39481.6735387997	61404.5649816143
153	48694.2922620933	37029.0936058157	60359.490918371
154	47755.3030739239	35403.1669813833	60107.4391664646
155	47458.1601579423	34432.8500262197	60483.4702896649

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293662182462hd8k0dbciot2/1kxbm1293662163.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293662182462hd8k0dbciot2/1kxbm1293662163.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293662182462hd8k0dbciot2/2kxbm1293662163.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293662182462hd8k0dbciot2/2kxbm1293662163.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293662182462hd8k0dbciot2/3kxbm1293662163.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293662182462hd8k0dbciot2/3kxbm1293662163.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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