Home » date » 2010 » Jan » 16 »

Opgave 10 Oefening 2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 16 Jan 2010 02:07:27 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/16/t126363305215b807spmz61u2h.htm/, Retrieved Sat, 16 Jan 2010 10:10:56 +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/Jan/16/t126363305215b807spmz61u2h.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

5.2100 5.2300 5.2300 5.2300 5.2200 5.2100 5.2300 5.2500 5.2300 5.2300 5.2500 5.2400 5.2600 5.2700 5.2600 5.2900 5.2900 5.2900 5.2900 5.3100 5.3300 5.3400 5.3400 5.3700 5.4100 5.4100 5.3800 5.4400 5.4400 5.4600 5.4600 5.4500 5.4600 5.4600 5.4800 5.4700 5.4800 5.5100 5.5500 5.5800 5.5900 5.6000 5.6000 5.6700 5.7100 5.7000 5.7300 5.7300 5.7200 5.7500 5.7500 5.7700 5.8300 5.8500 5.8700 5.8600 5.8700 5.9300 5.9700 5.9800 5.9900 5.9900 6.0300 6.0600 6.0700 6.0800 6.0800 6.1000 6.1300 6.1400 6.1400 6.1600 6.2000 6.1900 6.3200 6.3200 6.3300 6.3200 6.3300 6.3800 6.4200 6.4600 6.4700 6.4200 6.4800 6.4700 6.4900 6.4800 6.5100 6.5100 6.5200 6.5700 6.5900 6.6200 6.6300 6.6100 6.6400 6.6900 6.6900 6.7500 6.7700 6.8100 6.8100 6.8100 6.8700 6.8600 6.8800 6.8800 6.9200 6.9200 6.9900 7.0200 7.0500 7.0600 7.0600 7.0900 7.1200 7.2300 7.3100 7.4500 7.4900 7.5400 7.5500 7.5800 7.6000 7.6300 7.6400 7.6300 etc...

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	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	5.23	5.25	-0.0200000000000005
4	5.23	5.25	-0.0200000000000005
5	5.22	5.25	-0.0300000000000011
6	5.21	5.24	-0.0300000000000002
7	5.23	5.23	0
8	5.25	5.25	-8.88178419700125e-16
9	5.23	5.27	-0.04
10	5.23	5.25	-0.0200000000000005
11	5.25	5.25	-8.88178419700125e-16
12	5.24	5.27	-0.0300000000000002
13	5.26	5.26	-8.88178419700125e-16
14	5.27	5.28	-0.0100000000000007
15	5.26	5.29	-0.0300000000000002
16	5.29	5.28	0.00999999999999979
17	5.29	5.31	-0.0200000000000005
18	5.29	5.31	-0.0200000000000005
19	5.29	5.31	-0.0200000000000005
20	5.31	5.31	-8.88178419700125e-16
21	5.33	5.33	0
22	5.34	5.35	-0.0100000000000007
23	5.34	5.36	-0.0200000000000005
24	5.37	5.36	0.00999999999999979
25	5.41	5.39	0.0199999999999996
26	5.41	5.43	-0.0200000000000005
27	5.38	5.43	-0.0500000000000007
28	5.44	5.4	0.04
29	5.44	5.46	-0.0200000000000005
30	5.46	5.46	-8.88178419700125e-16
31	5.46	5.48	-0.0200000000000005
32	5.45	5.48	-0.0300000000000002
33	5.46	5.47	-0.0100000000000007
34	5.46	5.48	-0.0200000000000005
35	5.48	5.48	0
36	5.47	5.5	-0.0300000000000011
37	5.48	5.49	-0.00999999999999979
38	5.51	5.5	0.0099999999999989
39	5.55	5.53	0.0199999999999996
40	5.58	5.57	0.00999999999999979
41	5.59	5.6	-0.0100000000000007
42	5.6	5.61	-0.0100000000000007
43	5.6	5.62	-0.0200000000000005
44	5.67	5.62	0.0499999999999998
45	5.71	5.69	0.0199999999999996
46	5.7	5.73	-0.0300000000000002
47	5.73	5.72	0.00999999999999979
48	5.73	5.75	-0.0200000000000005
49	5.72	5.75	-0.0300000000000011
50	5.75	5.74	0.00999999999999979
51	5.75	5.77	-0.0200000000000005
52	5.77	5.77	-8.88178419700125e-16
53	5.83	5.79	0.04
54	5.85	5.85	-8.88178419700125e-16
55	5.87	5.87	0
56	5.86	5.89	-0.0300000000000002
57	5.87	5.88	-0.0100000000000007
58	5.93	5.89	0.0399999999999991
59	5.97	5.95	0.0199999999999996
60	5.98	5.99	-0.00999999999999979
61	5.99	6	-0.0100000000000007
62	5.99	6.01	-0.0200000000000005
63	6.03	6.01	0.0199999999999996
64	6.06	6.05	0.0099999999999989
65	6.07	6.08	-0.00999999999999979
66	6.08	6.09	-0.0100000000000007
67	6.08	6.1	-0.0200000000000005
68	6.1	6.1	-8.88178419700125e-16
69	6.13	6.12	0.00999999999999979
70	6.14	6.15	-0.0100000000000007
71	6.14	6.16	-0.0200000000000005
72	6.16	6.16	0
73	6.2	6.18	0.0199999999999996
74	6.19	6.22	-0.0300000000000002
75	6.32	6.21	0.109999999999999
76	6.32	6.34	-0.0200000000000005
77	6.33	6.34	-0.0100000000000007
78	6.32	6.35	-0.0300000000000002
79	6.33	6.34	-0.0100000000000007
80	6.38	6.35	0.0299999999999994
81	6.42	6.4	0.0199999999999996
82	6.46	6.44	0.0199999999999996
83	6.47	6.48	-0.0100000000000007
84	6.42	6.49	-0.0700000000000003
85	6.48	6.44	0.04
86	6.47	6.5	-0.0300000000000011
87	6.49	6.49	0
88	6.48	6.51	-0.0300000000000002
89	6.51	6.5	0.0099999999999989
90	6.51	6.53	-0.0200000000000005
91	6.52	6.53	-0.0100000000000007
92	6.57	6.54	0.0300000000000002
93	6.59	6.59	-8.88178419700125e-16
94	6.62	6.61	0.00999999999999979
95	6.63	6.64	-0.0100000000000007
96	6.61	6.65	-0.04
97	6.64	6.63	0.0099999999999989
98	6.69	6.66	0.0300000000000002
99	6.69	6.71	-0.0200000000000005
100	6.75	6.71	0.0399999999999991
101	6.77	6.77	-8.88178419700125e-16
102	6.81	6.79	0.0199999999999996
103	6.81	6.83	-0.0200000000000005
104	6.81	6.83	-0.0200000000000005
105	6.87	6.83	0.04
106	6.86	6.89	-0.0300000000000002
107	6.88	6.88	-8.88178419700125e-16
108	6.88	6.9	-0.0200000000000005
109	6.92	6.9	0.0199999999999996
110	6.92	6.94	-0.0200000000000005
111	6.99	6.94	0.0499999999999998
112	7.02	7.01	0.0099999999999989
113	7.05	7.04	0.00999999999999979
114	7.06	7.07	-0.0100000000000007
115	7.06	7.08	-0.0200000000000005
116	7.09	7.08	0.00999999999999979
117	7.12	7.11	0.00999999999999979
118	7.23	7.14	0.0899999999999999
119	7.31	7.25	0.0599999999999987
120	7.45	7.33	0.12
121	7.49	7.47	0.0199999999999996
122	7.54	7.51	0.0299999999999994
123	7.55	7.56	-0.0100000000000007
124	7.58	7.57	0.00999999999999979
125	7.6	7.6	-8.88178419700125e-16
126	7.63	7.62	0.00999999999999979
127	7.64	7.65	-0.0100000000000007
128	7.63	7.66	-0.0300000000000002
129	7.66	7.65	0.00999999999999979
130	7.64	7.68	-0.0400000000000009
131	7.69	7.66	0.0300000000000002
132	7.7	7.71	-0.0100000000000007
133	7.68	7.72	-0.0400000000000009

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
134	7.7	7.64491694063439	7.75508305936561
135	7.72	7.64210079038815	7.79789920961185
136	7.74	7.64459334254243	7.83540665745757
137	7.76	7.64983388126878	7.87016611873123
138	7.78	7.65683053484984	7.90316946515017
139	7.8	7.66507461108282	7.93492538891719
140	7.82	7.67426392346599	7.96573607653402
141	7.84	7.6842015807763	7.9957984192237
142	7.86	7.69475082190317	8.02524917809684
143	7.88	7.7058120719144	8.05418792808561
144	7.9	7.7173101597794	8.08268984022061
145	7.92	7.72918668508486	8.11081331491515

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/16/t126363305215b807spmz61u2h/1vuqd1263632845.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/16/t126363305215b807spmz61u2h/1vuqd1263632845.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/16/t126363305215b807spmz61u2h/2f8ns1263632845.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/16/t126363305215b807spmz61u2h/2f8ns1263632845.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/16/t126363305215b807spmz61u2h/37zs81263632845.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/16/t126363305215b807spmz61u2h/37zs81263632845.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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

We may request personal information to be submitted to our servers in order to be able to:

personalize online software applications according to your needs
enforce strict security rules with respect to the data that you upload (e.g. statistical data)
manage user sessions of online applications
alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by