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stap 33 exponential smoothing

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 19 Aug 2010 13:26:45 +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/Aug/19/t1282224442g50s7apxf1e6kqa.htm/, Retrieved Thu, 19 Aug 2010 15:28:20 +0200

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/Aug/19/t1282224442g50s7apxf1e6kqa.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:

Philippe De Vocht

Dataseries X:

» Textbox « » Textfile « » CSV «

73 72 71 69 89 88 73 63 64 64 65 67 69 71 70 72 88 83 76 70 75 71 75 81 87 90 80 85 105 104 98 94 107 112 121 118 120 122 109 112 132 127 116 113 123 125 137 127 123 128 114 120 143 135 119 117 132 139 158 141 139 150 142 149 166 150 139 140 158 169 186 177 175 187 176 185 204 188 171 171 182 185 200 192 185 195 190 195 213 194 171 171 186 182 193 185 172 185 179 182 193 173 155 164 188 186 200 185 173 190 190 193 195 178 163 165 188 182 200 177

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.666695305515088
beta	0.0185297170665319
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	71	71	0
4	69	70	-1
5	89	68.3209510191041	20.6790489808959
6	88	81.3506844800964	6.64931551990357
7	73	85.1090039904545	-12.1090039904545
8	63	76.2116492394221	-13.2116492394221
9	64	66.4159536513059	-2.41595365130593
10	64	63.7878517244135	0.212148275586472
11	65	62.9145138255246	2.08548617447537
12	67	63.315884928679	3.68411507132097
13	69	64.8285667742777	4.1714332257223
14	71	66.7176738776512	4.28232612234882
15	70	68.7336152214107	1.26638477858934
16	72	68.7544871360387	3.24551286396132
17	88	70.1349284665628	17.8650715334372
18	83	81.4828602251074	1.51713977489263
19	76	81.9504448776355	-5.95044487763555
20	70	77.3659160343971	-7.36591603439715
21	75	71.7467030802828	3.25329691971724
22	71	73.2474597250049	-2.2474597250049
23	75	71.0531233500358	3.94687664996421
24	81	73.0372803899416	7.96271961005844
25	87	77.7971499322388	9.20285006776119
26	90	83.4974976512279	6.50250234877214
27	80	87.477866025888	-7.47786602588803
28	85	82.0452093063659	2.95479069363412
29	105	83.6044583708469	21.3955416291531
30	104	97.722383090094	6.2776169099061
31	98	101.838810011358	-3.83881001135829
32	94	99.1632391829005	-5.16323918290045
33	107	95.5408926625093	11.4591073374907
34	112	103.142148626109	8.8578513738911
35	121	109.118586470778	11.8814135292222
36	118	117.257598136144	0.742401863856216
37	120	117.979454407761	2.02054559223934
38	122	119.578404267203	2.42159573279731
39	109	121.474647980217	-12.4746479802173
40	112	113.285528188319	-1.28552818831938
41	132	112.540261036594	19.4597389634056
42	127	125.866165404729	1.13383459527054
43	116	126.988282385836	-10.9882823858359
44	113	119.892895209147	-6.89289520914699
45	123	115.442730847576	7.55726915242428
46	125	120.71978327966	4.28021672034031
47	137	123.864916647269	13.1350833527311
48	127	133.075814585494	-6.07581458549441
49	123	129.403838412512	-6.40383841251247
50	128	125.434059353021	2.56594064697863
51	114	127.4760886818	-13.4760886817996
52	120	118.656493141169	1.34350685883147
53	143	119.733649624714	23.2663503752856
54	135	135.714087904054	-0.714087904053855
55	119	135.698058948203	-16.6980589482034
56	117	124.819309133994	-7.81930913399405
57	132	119.763382933018	12.2366170669823
58	139	128.229815772994	10.7701842270062
59	158	135.851636082436	22.1483639175637
60	141	151.332849074934	-10.3328490749335
61	139	145.031341184667	-6.03134118466684
62	150	141.523119180371	8.47688081962903
63	142	147.792181311597	-5.79218131159712
64	149	144.476571978162	4.52342802183841
65	166	148.094211922245	17.9057880777547
66	150	160.855010785671	-10.8550107856706
67	139	154.307020784486	-15.3070207844856
68	140	144.601798651166	-4.60179865116598
69	158	141.976848731923	16.0231512680775
70	169	153.300400909665	15.6995990903345
71	186	164.602190120188	21.3978098798116
72	177	179.967291311006	-2.96729131100591
73	175	179.051636965889	-4.05163696588895
74	187	177.363001855268	9.63699814473156
75	176	184.919567858533	-8.91956785853279
76	185	179.994368975079	5.00563102492123
77	204	184.414872756345	19.5851272436547
78	188	198.797406527676	-10.7974065276758
79	171	192.790660008809	-21.7906600088094
80	171	179.185568261652	-8.1855682616521
81	182	174.549805460315	7.45019453968504
82	185	180.430369601644	4.56963039835631
83	200	184.446926883265	15.5530731167351
84	192	195.978231480081	-3.97823148008075
85	185	194.43896121132	-9.43896121131974
86	195	189.142442203319	5.85755779668142
87	190	194.116402976218	-4.11640297621847
88	195	192.38991821833	2.61008178167032
89	213	195.180193374192	17.8198066258078
90	194	208.330860788221	-14.3308607882209
91	171	199.869790366035	-28.8697903660349
92	171	181.359035828613	-10.3590358286127
93	186	175.061342276947	10.9386577230526
94	182	183.097853661088	-1.09785366108844
95	193	183.096116882899	9.903883117101
96	185	190.551535724279	-5.551535724279
97	172	187.634317509139	-15.634317509139
98	185	177.801814728192	7.19818527180817
99	179	183.280558408641	-4.28055840864096
100	182	181.053596935095	0.946403064905155
101	193	182.323117694313	10.6768823056866
102	173	190.211802021856	-17.2118020218562
103	155	179.294602416338	-24.2946024163377
104	164	163.355205406161	0.644794593838554
105	188	164.050752888146	23.9492471118537
106	186	180.579130685925	5.42086931407496
107	200	184.821693646902	15.1783063530976
108	185	195.757001945171	-10.7570019451714
109	173	189.268473443797	-16.2684734437969
110	190	178.904497327943	11.0955026720569
111	190	186.921025866953	3.07897413304687
112	193	189.631009109423	3.36899089057707
113	195	192.575964582482	2.42403541751816
114	178	194.920868424391	-16.9208684243911
115	163	184.159580773583	-21.1595807735828
116	165	170.310964906069	-5.31096490606942
117	188	166.962936899931	21.0370631000692
118	182	181.440900523568	0.559099476431896
119	200	182.273208866255	17.7267911337449
120	177	194.770127666612	-17.7701276666124

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	183.381890953853	161.11375555955	205.650026348156
122	183.840914934828	156.924021136214	210.757808733441
123	184.299938915802	153.290849553622	215.309028277982
124	184.758962896777	150.014833025366	219.503092768189
125	185.217986877752	146.989158269221	223.446815486282
126	185.677010858727	144.148932351368	227.205089366085
127	186.136034839701	141.45136390676	230.820705772643
128	186.595058820676	138.866553448505	234.323564192847
129	187.054082801651	136.372686972348	237.735478630953
130	187.513106782625	133.953307086532	241.072906478719
131	187.9721307636	131.595660862018	244.348600665182
132	188.431154744575	129.289647483546	247.572662005604

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282224442g50s7apxf1e6kqa/1yxqy1282224400.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282224442g50s7apxf1e6kqa/1yxqy1282224400.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282224442g50s7apxf1e6kqa/2qo711282224400.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282224442g50s7apxf1e6kqa/2qo711282224400.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282224442g50s7apxf1e6kqa/3qo711282224400.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282224442g50s7apxf1e6kqa/3qo711282224400.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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')

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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