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opdracht 10 oef 2

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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: Wed, 22 Dec 2010 19:47:55 +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/22/t1293047333rlj2jcaytkoyald.htm/, Retrieved Wed, 22 Dec 2010 20:48:57 +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/22/t1293047333rlj2jcaytkoyald.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:

KDGP2W82

Dataseries X:

» Textbox « » Textfile « » CSV «

7.08 7.08 7.09 7.07 7.06 6.99 6.99 6.99 6.98 6.96 6.95 6.91 6.91 6.87 6.91 6.89 6.88 6.9 6.91 6.85 6.86 6.82 6.8 6.83 6.84 6.89 7.14 7.21 7.25 7.31 7.3 7.48 7.49 7.4 7.44 7.42 7.14 7.24 7.33 7.61 7.66 7.69 7.7 7.68 7.71 7.71 7.72 7.68 7.72 7.74 7.76 7.9 7.97 7.96 7.95 7.97 7.93 7.99 7.96 7.92 7.97 7.98 8 8.04 8.17 8.29 8.26 8.3 8.32 8.28 8.27 8.32 8.31 8.34 8.32 8.36 8.33 8.35 8.34 8.37 8.31 8.33 8.34 8.25

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	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.99993142291123
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	7.08	7.08	0
3	7.09	7.08	0.00999999999999979
4	7.07	7.08999931422911	-0.0199993142291124
5	7.06	7.07000137149475	-0.0100013714947478
6	6.99	7.06000068586494	-0.0700006858649402
7	6.99	6.99000480044325	-4.80044324824291e-06
8	6.99	6.9900000003292	-3.29200666726592e-10
9	6.98	6.99000000000002	-0.010000000000022
10	6.96	6.98000068577089	-0.0200006857708885
11	6.95	6.9600013715888	-0.0100013715888032
12	6.91	6.95000068586495	-0.0400006858649471
13	6.91	6.91000274313059	-2.74313058579168e-06
14	6.87	6.91000000018812	-0.0400000001881162
15	6.91	6.87000274308356	0.0399972569164362
16	6.89	6.90999725710456	-0.0199972571045626
17	6.88	6.89000137135368	-0.0100013713536757
18	6.9	6.88000068586493	0.0199993141350694
19	6.91	6.89999862850526	0.0100013714947407
20	6.85	6.90999931413506	-0.0599993141350597
21	6.86	6.85000411457829	0.00999588542170926
22	6.82	6.85999931451128	-0.0399993145112782
23	6.8	6.82000274303654	-0.0200027430365424
24	6.83	6.80000137172989	0.029998628270115
25	6.84	6.8299979427814	0.0100020572185935
26	6.89	6.83999931408803	0.0500006859119653
27	7.14	6.88999657109852	0.250003428901477
28	7.21	7.13998285549266	0.0700171445073368
29	7.25	7.20999519842807	0.0400048015719339
30	7.31	7.24999725658717	0.060002743412829
31	7.3	7.30999588518654	-0.00999588518653827
32	7.48	7.3000006854887	0.179999314511295
33	7.49	7.47998765617103	0.0100123438289694
34	7.4	7.48999931338261	-0.0899993133826085
35	7.44	7.4000061718909	0.0399938281090968
36	7.42	7.4399972573397	-0.0199972573397007
37	7.14	7.42000137135369	-0.280001371353692
38	7.24	7.1400192016789	0.0999807983211012
39	7.33	7.23999314360792	0.0900068563920815
40	7.61	7.32999382759182	0.28000617240818
41	7.66	7.60998079799186	0.0500192020081407
42	7.69	7.65999656982874	0.0300034301712566
43	7.7	7.6899979424521	0.0100020575478936
44	7.68	7.69999931408801	-0.0199993140880119
45	7.71	7.68000137149474	0.0299986285052629
46	7.71	7.70999794278139	2.05721861057384e-06
47	7.72	7.70999999985892	0.0100000001410780
48	7.68	7.7199993142291	-0.0399993142291031
49	7.72	7.68000274303652	0.0399972569634777
50	7.74	7.71999725710456	0.0200027428954419
51	7.76	7.73999862827013	0.0200013717298742
52	7.9	7.75999862836416	0.140001371635845
53	7.97	7.89999039911351	0.0700096008864897
54	7.96	7.96999519894539	-0.00999519894538548
55	7.95	7.96000068544164	-0.0100006854416446
56	7.97	7.9500006858179	0.0199993141821064
57	7.93	7.96999862850526	-0.0399986285052565
58	7.99	7.9300027429895	0.0599972570105027
59	7.96	7.98999588556278	-0.0299958855627809
60	7.92	7.9600020570305	-0.0400020570305069
61	7.97	7.92000274322462	0.0499972567753835
62	7.98	7.96999657133368	0.0100034286663169
63	8	7.97999931399398	0.0200006860060151
64	8.04	7.99999862841118	0.0400013715888186
65	8.17	8.03999725682239	0.130002743177611
66	8.29	8.16999108479034	0.120008915209658
67	8.26	8.28999177013797	-0.0299917701379666
68	8.3	8.26000205674828	0.0399979432517181
69	8.32	8.2999972570575	0.0200027429425038
70	8.28	8.31999862827012	-0.039998628270121
71	8.27	8.28000274298948	-0.0100027429894816
72	8.32	8.270000685959	0.0499993140410062
73	8.31	8.3199965711926	-0.00999657119260178
74	8.34	8.31000068553575	0.0299993144642485
75	8.32	8.33999794273435	-0.0199979427343493
76	8.36	8.3200013714007	0.0399986285993066
77	8.33	8.3599972570105	-0.0299972570104945
78	8.35	8.33000205712456	0.0199979428754435
79	8.34	8.3499986285993	-0.00999862859929657
80	8.37	8.34000068567684	0.0299993143231578
81	8.31	8.36999794273436	-0.0599979427343573
82	8.33	8.31000411448425	0.0199958855157547
83	8.34	8.32999862874038	0.0100013712596159
84	8.25	8.33999931413508	-0.089999314135076

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	8.25000617189095	8.11362819862611	8.3863841451558
86	8.25000617189095	8.05714520552604	8.44286713825587
87	8.25000617189095	8.01380339226592	8.48620895151599
88	8.25000617189095	7.97726425384758	8.52274808993433
89	8.25000617189095	7.94507248301194	8.55493986076997
90	8.25000617189095	7.91596881564356	8.58404352813834
91	8.25000617189095	7.88920517948083	8.61080716430108
92	8.25000617189095	7.8642941590115	8.6357181847704
93	8.25000617189095	7.84089719174642	8.65911515203548
94	8.25000617189095	7.81876777101473	8.68124457276718
95	8.25000617189095	7.79771980337465	8.70229254040726
96	8.25000617189095	7.77760871222267	8.72240363155924

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293047333rlj2jcaytkoyald/1pxn11293047272.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293047333rlj2jcaytkoyald/1pxn11293047272.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293047333rlj2jcaytkoyald/2pxn11293047272.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293047333rlj2jcaytkoyald/2pxn11293047272.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293047333rlj2jcaytkoyald/3pxn11293047272.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293047333rlj2jcaytkoyald/3pxn11293047272.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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