Home » date » 2010 » Aug » 12 »

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: Thu, 12 Aug 2010 10:59:46 +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/12/t12816107728yhhb92ajyv9j1b.htm/, Retrieved Thu, 12 Aug 2010 12:59:36 +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/12/t12816107728yhhb92ajyv9j1b.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:

Hoes Isabelle

Dataseries X:

» Textbox « » Textfile « » CSV «

158 157 156 154 152 151 152 154 155 155 156 158 156 152 145 141 140 145 143 141 144 139 141 142 141 132 122 122 127 128 122 123 128 128 128 129 124 121 109 110 107 107 104 110 114 118 117 122 113 106 102 111 106 110 105 104 106 110 107 111 101 105 108 124 122 128 124 121 125 134 126 126 111 117 118 128 127 129 124 113 120 127 114 107

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.651858880178058
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	156	160.703792735043	-4.70379273504273
14	152	153.644722364827	-1.64472236482683
15	145	145.663067513859	-0.663067513859033
16	141	141.446313094764	-0.446313094764434
17	140	140.537518635241	-0.537518635241184
18	145	145.569271034237	-0.569271034236692
19	143	141.288658683313	1.7113413166866
20	141	143.78635041225	-2.7863504122499
21	144	142.727181847376	1.27281815262432
22	139	143.647351690988	-4.64735169098773
23	141	141.750072916546	-0.75007291654552
24	142	143.101603253086	-1.10160325308632
25	141	138.461401747913	2.53859825208713
26	132	137.188336440680	-5.18833644068019
27	122	127.238499705538	-5.23849970553798
28	122	120.114670307835	1.88532969216513
29	127	120.694025505379	6.30597449462076
30	128	130.175715356769	-2.17571535676947
31	122	125.641902946422	-3.64190294642171
32	123	123.084203429563	-0.0842034295629617
33	128	125.199616860621	2.80038313937911
34	128	125.054488947007	2.94551105299306
35	128	129.463488174994	-1.46348817499435
36	129	130.227590275046	-1.22759027504605
37	124	126.772566839210	-2.77256683920956
38	121	119.347307706392	1.65269229360759
39	109	113.839392406047	-4.83939240604742
40	110	109.455822589598	0.544177410402057
41	107	110.699943994466	-3.69994399446594
42	107	110.706362021562	-3.7063620215618
43	104	104.664343801024	-0.664343801023676
44	110	105.286174148137	4.71382585186279
45	114	111.533468771982	2.46653122801831
46	118	111.221241519646	6.77875848035424
47	117	116.594023194553	0.405976805447352
48	122	118.658878402339	3.34112159766116
49	113	117.644140500555	-4.64414050055491
50	106	110.539494126684	-4.53949412668369
51	102	98.734985483237	3.26501451676295
52	111	101.508587312536	9.49141268746362
53	106	107.107490307248	-1.10749030724834
54	110	108.801587912667	1.19841208733287
55	105	107.015841880096	-2.01584188009632
56	104	108.629048208371	-4.62904820837105
57	106	108.003731742752	-2.00373174275182
58	110	106.278787500743	3.72121249925684
59	107	107.439853327636	-0.439853327636115
60	111	109.975191246851	1.02480875314947
61	101	104.670546159156	-3.67054615915649
62	105	98.2369776082018	6.76302239179823
63	108	96.5171851044763	11.4828148955237
64	124	106.815298317806	17.1847016821935
65	122	113.739226104046	8.26077389595392
66	128	122.342889364026	5.65711063597391
67	124	122.344571598811	1.65542840118896
68	121	125.441163484024	-4.441163484024
69	125	125.852301958648	-0.852301958647857
70	134	126.87101594564	7.12898405436003
71	126	128.804829805718	-2.80482980571782
72	126	130.308445903248	-4.30844590324787
73	111	119.892625290399	-8.8926252903986
74	117	113.687352323820	3.31264767618043
75	118	111.361556269351	6.63844373064903
76	128	120.486884370988	7.51311562901176
77	127	117.999516690343	9.00048330965656
78	129	126.178923857428	2.82107614257187
79	124	122.938761688808	1.06123831119189
80	113	123.525551161327	-10.5255511613273
81	120	121.219957768385	-1.21995776838538
82	127	124.777625901139	2.22237409886121
83	114	120.054653408804	-6.05465340880444
84	107	118.916372539674	-11.9163725396738

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	101.945316043820	92.080500692086	111.810131395554
86	105.785937239200	94.0103058742817	117.561568604119
87	102.458608742814	89.0415894702222	115.875628015407
88	107.561117602239	92.6826997334002	122.439535471077
89	100.694072630945	84.4854875477726	116.902657714116
90	100.855129095751	83.417550636656	118.292707554845
91	95.163351478615	76.5778718066847	113.748831150545
92	91.0245254718946	71.3580319676019	110.691018976187
93	98.8197657766589	78.1286595019078	119.51087205141
94	104.371091485238	82.703770677356	126.038412293121
95	95.317871076168	72.7164617592613	117.919280393075
96	96.0856643356643	72.5872683217018	119.584060349627

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/12/t12816107728yhhb92ajyv9j1b/1aglo1281610784.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/12/t12816107728yhhb92ajyv9j1b/1aglo1281610784.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/12/t12816107728yhhb92ajyv9j1b/28tsx1281610784.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/12/t12816107728yhhb92ajyv9j1b/28tsx1281610784.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/12/t12816107728yhhb92ajyv9j1b/38tsx1281610784.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/12/t12816107728yhhb92ajyv9j1b/38tsx1281610784.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

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