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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, 17 Aug 2010 14:49:25 +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/17/t1282056551x95rzg3b4t7z7c1.htm/, Retrieved Tue, 17 Aug 2010 16:49:12 +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/17/t1282056551x95rzg3b4t7z7c1.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:

Quaglia Laura

Dataseries X:

» Textbox « » Textfile « » CSV «

93 92 91 89 87 86 87 89 90 90 91 93 93 87 89 92 98 92 92 87 92 98 101 102 102 90 87 92 105 90 88 83 98 109 118 118 115 107 101 111 128 115 111 105 120 132 135 142 139 127 113 130 143 139 137 134 139 157 152 153 147 132 117 123 139 134 134 128 118 144 140 151 144 135 122 124 146 146 147 148 132 161 159 173

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

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.975824090716957
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	92	93	-1
3	91	92.024175909283	-1.02417590928304
4	89	91.0247603838727	-2.0247603838727
5	87	89.0489504233604	-2.04895042336041
6	86	87.0495352395606	-1.04953523956061
7	87	86.025373468741	0.97462653125902
8	89	86.9764375173954	2.02356248260456
9	90	88.951078536992	1.04892146300801
10	90	89.9746413698653	0.0253586301347184
11	91	89.9993869320583	1.00061306794169
12	93	90.975809269242	2.02419073075798
13	93	92.9510633485216	0.0489366514783853
14	87	92.9988169119532	-5.99881691195324
15	89	87.145026853469	1.85497314653104
16	92	88.955154337487	3.04484566251301
17	98	91.9263880874822	6.07361191251778
18	92	97.8531649093826	-5.85316490938256
19	92	92.141505583868	-0.141505583867925
20	87	92.0034210261586	-5.00342102615863
21	92	87.1209622528333	4.87903774716672
22	98	91.882044826036	6.11795517396405
23	101	97.8520928707165	3.14790712928348
24	102	100.923896482811	1.076103517189
25	102	101.973984218989	0.0260157810107273
26	90	101.999371044838	-11.9993710448384
27	87	90.2900957058336	-3.29009570583359
28	92	87.0795410553168	4.92045894468323
29	105	91.8810434309224	13.1189565690776
30	90	104.682837296098	-14.6828372960978
31	88	90.3549709424881	-2.35497094248814
32	83	88.0569335638698	-5.05693356386979
33	98	83.1222559670905	14.8777440329095
34	109	97.640317009924	11.359682990076
35	118	108.725369334548	9.2746306654522
36	118	117.775777370398	0.224222629601698
37	115	117.994579214048	-2.99457921404755
38	107	115.07239667542	-8.0723966754197
39	101	107.195157529722	-6.19515752972168
40	111	101.149773566433	9.85022643356729
41	128	110.761861819325	17.2381381806753
42	115	127.583252335135	-12.5832523351354
43	111	115.30421156694	-4.30421156693987
44	105	111.104058228377	-6.10405822837737
45	120	105.147571157988	14.8524288420123
46	132	119.640929027683	12.3590709723173
47	135	131.701208221351	3.29879177864944
48	142	134.920248709216	7.07975129078429
49	139	141.828840575047	-2.82884057504748
50	127	139.068389793119	-12.0683897931185
51	113	127.291764296831	-14.2917642968308
52	130	113.345516397135	16.6544836028652
53	143	129.597362715261	13.4026372847388
54	139	142.675979056851	-3.67597905685062
55	137	139.088870136205	-2.08887013620478
56	134	137.050500334917	-3.05050033491693
57	139	134.073748619365	4.92625138063516
58	157	138.880903393516	18.1190966064837
59	152	156.561954364151	-4.56195436415095
60	153	152.110289394861	0.889710605138902
61	147	152.978490437122	-5.97849043712199
62	132	147.144535442457	-15.1445354424574
63	117	132.366132914991	-15.3661329149907
64	123	117.371490235384	5.628509764616
65	139	122.863925658532	16.1360743414681
66	134	138.609895730536	-4.60989573053624
67	134	134.111448420986	-0.111448420985738
68	128	134.002694366915	-6.00269436691548
69	118	128.145120594468	-10.1451205944684
70	144	118.245267515157	25.7547324848426
71	140	143.377355923837	-3.3773559238374
72	151	140.081650650431	10.9183493495688
73	144	150.736038976604	-6.73603897660425
74	135	144.162849867225	-9.16284986722542
75	122	135.221520227164	-13.2215202271642
76	124	122.319642273596	1.68035772640415
77	146	123.959375824043	22.0406241759566
78	146	145.46714786938	0.532852130619574
79	147	145.987117815229	1.01288218477114
80	148	146.975512652187	1.02448734781345
81	132	147.975232086818	-15.9752320868176
82	161	132.386215761706	28.6137842382935
83	159	160.30823574801	-1.30823574801045
84	173	159.031627788765	13.9683722112353

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	172.662301900589	154.070183847756	191.254419953423
86	172.662301900589	146.684963317133	198.639640484045
87	172.662301900589	140.976699711764	204.347904089415
88	172.662301900589	136.150212775787	209.174391025392
89	172.662301900589	131.891136618658	213.433467182521
90	172.662301900589	128.036713000995	217.287890800183
91	172.662301900589	124.489711656504	220.834892144675
92	172.662301900589	121.186543363064	224.138060438115
93	172.662301900589	118.082919500249	227.24168430093
94	172.662301900589	115.146527982545	230.178075818634
95	172.662301900589	112.35293682699	232.971666974188
96	172.662301900589	109.683140412287	235.641463388892

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282056551x95rzg3b4t7z7c1/1g41y1282056560.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282056551x95rzg3b4t7z7c1/1g41y1282056560.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282056551x95rzg3b4t7z7c1/2rdi01282056560.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282056551x95rzg3b4t7z7c1/2rdi01282056560.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282056551x95rzg3b4t7z7c1/3rdi01282056560.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282056551x95rzg3b4t7z7c1/3rdi01282056560.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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