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TIJDREEKS B - STAP 27

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 03 Aug 2010 18:02:49 +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/03/t1280858593fyuq29dl7o6t8em.htm/, Retrieved Tue, 03 Aug 2010 20:03:13 +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/03/t1280858593fyuq29dl7o6t8em.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:

Lisa Bruggeman

Dataseries X:

» Textbox « » Textfile « » CSV «

162 161 160 158 156 155 156 158 159 159 160 162 152 157 149 150 144 146 151 148 151 151 145 140 139 144 140 134 130 132 136 137 146 139 132 131 137 145 142 142 137 139 139 139 150 146 138 134 137 143 136 138 129 132 124 132 154 145 136 132 135 148 142 139 126 124 115 126 147 136 127 123 132 156 153 147 129 119 108 121 138 128 123 125

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	1
beta	0
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	160	161	-1
4	158	160	-2
5	156	158	-2
6	155	156	-1
7	156	155	1
8	158	156	2
9	159	158	1
10	159	159	0
11	160	159	1
12	162	160	2
13	152	162	-10
14	157	152	5
15	149	157	-8
16	150	149	1
17	144	150	-6
18	146	144	2
19	151	146	5
20	148	151	-3
21	151	148	3
22	151	151	0
23	145	151	-6
24	140	145	-5
25	139	140	-1
26	144	139	5
27	140	144	-4
28	134	140	-6
29	130	134	-4
30	132	130	2
31	136	132	4
32	137	136	1
33	146	137	9
34	139	146	-7
35	132	139	-7
36	131	132	-1
37	137	131	6
38	145	137	8
39	142	145	-3
40	142	142	0
41	137	142	-5
42	139	137	2
43	139	139	0
44	139	139	0
45	150	139	11
46	146	150	-4
47	138	146	-8
48	134	138	-4
49	137	134	3
50	143	137	6
51	136	143	-7
52	138	136	2
53	129	138	-9
54	132	129	3
55	124	132	-8
56	132	124	8
57	154	132	22
58	145	154	-9
59	136	145	-9
60	132	136	-4
61	135	132	3
62	148	135	13
63	142	148	-6
64	139	142	-3
65	126	139	-13
66	124	126	-2
67	115	124	-9
68	126	115	11
69	147	126	21
70	136	147	-11
71	127	136	-9
72	123	127	-4
73	132	123	9
74	156	132	24
75	153	156	-3
76	147	153	-6
77	129	147	-18
78	119	129	-10
79	108	119	-11
80	121	108	13
81	138	121	17
82	128	138	-10
83	123	128	-5
84	125	123	2

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	125	109.511713598514	140.488286401486
86	125	103.096255313099	146.903744686901
87	125	98.1735010304477	151.826498969552
88	125	94.0234271970276	155.976572802972
89	125	90.3671387512912	159.632861248709
90	125	87.0616013262713	162.938398673729
91	125	84.021845947124	165.978154052876
92	125	81.1925106261988	168.807489373801
93	125	78.5351407955413	171.464859204459
94	125	76.0217379182904	173.978262081710
95	125	73.6311653607064	176.368834639294
96	125	71.3470020608955	178.652997939105

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/03/t1280858593fyuq29dl7o6t8em/1toh81280858564.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/03/t1280858593fyuq29dl7o6t8em/1toh81280858564.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/03/t1280858593fyuq29dl7o6t8em/2toh81280858564.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/03/t1280858593fyuq29dl7o6t8em/2toh81280858564.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/03/t1280858593fyuq29dl7o6t8em/3toh81280858564.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/03/t1280858593fyuq29dl7o6t8em/3toh81280858564.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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