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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 09:17:21 +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/t1282209525sdow2xutdrlvce6.htm/, Retrieved Thu, 19 Aug 2010 11:18:45 +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/t1282209525sdow2xutdrlvce6.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:

DeGroodtOlivierREEKSBStap27

Dataseries X:

» Textbox « » Textfile « » CSV «

80 79 78 76 74 73 74 76 77 77 78 80 90 90 89 82 78 76 74 78 81 82 88 99 117 113 106 100 97 96 100 104 104 111 117 118 140 147 134 126 116 114 120 122 117 119 132 134 154 152 132 130 123 129 124 128 128 129 141 138 155 160 142 133 131 140 134 134 134 136 145 137 152 168 160 157 147 161 159 164 163 158 175 163

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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.635975324827265
beta	0.008138384857576
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	90	87.0365918803419	2.9634081196581
14	90	89.2796787706	0.720321229399957
15	89	88.9332793277732	0.0667206722267792
16	82	82.0465513919437	-0.046551391943737
17	78	77.8375442770587	0.162455722941317
18	76	75.1789680368932	0.821031963106776
19	74	80.0268128753726	-6.0268128753726
20	78	77.7384037182123	0.261596281787732
21	81	78.4089549239193	2.59104507608068
22	82	79.7827221786551	2.21727782134488
23	88	82.2219255618689	5.77807443813114
24	99	88.0806139568314	10.9193860431686
25	117	106.510986703481	10.4890132965191
26	113	112.868316175076	0.131683824924238
27	106	112.051266821771	-6.05126682177128
28	100	101.342386107546	-1.34238610754639
29	97	96.4886069705327	0.511393029467314
30	96	94.3967534179586	1.60324658204138
31	100	97.35840072444	2.64159927555993
32	104	103.026007737323	0.973992262677044
33	104	105.155273112518	-1.15527311251789
34	111	104.148694761859	6.85130523814149
35	117	110.993508748006	6.00649125199371
36	118	119.032476809319	-1.03247680931877
37	140	129.806680724120	10.1933192758804
38	147	132.305689469044	14.6943105309564
39	134	138.67479505276	-4.67479505275992
40	126	130.738019838492	-4.73801983849214
41	116	124.564502270107	-8.56450227010698
42	114	117.216069249189	-3.21606924918862
43	120	117.583797092034	2.41620290796637
44	122	122.592901352030	-0.592901352029642
45	117	123.034339844768	-6.03433984476798
46	119	121.897918325330	-2.89791832532987
47	132	122.243004201915	9.75699579808528
48	134	130.132325104302	3.86767489569758
49	154	148.162216184821	5.83778381517891
50	152	149.559985117360	2.44001488264047
51	132	141.051704134660	-9.05170413465979
52	130	130.252528762407	-0.252528762407167
53	123	125.506176271455	-2.50617627145536
54	129	123.956444902216	5.04355509778377
55	124	131.668920540651	-7.66892054065073
56	128	129.158092712267	-1.15809271226669
57	128	127.245686015682	0.754313984317804
58	129	131.589972890176	-2.58997289017583
59	141	136.760756580712	4.23924341928804
60	138	138.991657257165	-0.991657257165173
61	155	154.617742527317	0.382257472682511
62	160	151.250264086173	8.74973591382664
63	142	142.545403129008	-0.545403129007838
64	133	140.377031698605	-7.37703169860461
65	131	130.260302188707	0.739697811293041
66	140	133.520969539368	6.47903046063232
67	134	137.523961410038	-3.52396141003754
68	134	140.046024962477	-6.04602496247716
69	134	135.722575839689	-1.72257583968891
70	136	137.262797692503	-1.26279769250345
71	145	145.759083250348	-0.759083250348198
72	137	142.876572122086	-5.87657212208572
73	152	155.840405078971	-3.8404050789712
74	168	152.755824505602	15.2441754943977
75	160	144.753659331667	15.2463406683333
76	157	150.179353449887	6.82064655011268
77	147	152.157958840575	-5.15795884057499
78	161	153.837867669192	7.16213233080845
79	159	154.718242093449	4.28175790655095
80	164	161.411140579956	2.58885942004358
81	163	164.322482979171	-1.32248297917127
82	158	166.45597137444	-8.45597137443994
83	175	170.695156700081	4.30484329991936
84	163	169.330711862381	-6.33071186238058

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	182.905013837075	171.820819075086	193.989208599064
86	189.388047230008	176.221279840589	202.554814619426
87	171.79080264	156.801244376908	186.780360903092
88	164.473179411447	147.834813013414	181.111545809480
89	157.738351253270	139.577528461572	175.899174044969
90	167.194945735493	147.608364009266	186.781527461721
91	162.446317427679	141.510751595773	183.381883259585
92	165.752169210966	143.530259617282	187.974078804650
93	165.532138797572	142.076077445583	188.988200149562
94	165.855675906723	141.209679401325	190.501672412121
95	180.107416276005	154.309454392476	205.905378159534
96	172.100826234940	145.183871029814	199.017781440066

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282209525sdow2xutdrlvce6/1b5an1282209437.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282209525sdow2xutdrlvce6/1b5an1282209437.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282209525sdow2xutdrlvce6/24eaq1282209437.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282209525sdow2xutdrlvce6/24eaq1282209437.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282209525sdow2xutdrlvce6/34eaq1282209437.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282209525sdow2xutdrlvce6/34eaq1282209437.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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