Home » date » 2010 » Aug » 19 »

Tijdreeks A - Stap 32

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 19 Aug 2010 19:38:01 +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/19/t128224665197029ilybhzuzc5.htm/, Retrieved Thu, 19 Aug 2010 21:37:34 +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/19/t128224665197029ilybhzuzc5.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:

Gregory Goris

Dataseries X:

» Textbox « » Textfile « » CSV «

159 158 157 155 175 174 159 149 150 150 151 153 146 156 154 151 171 167 144 138 138 132 132 132 125 131 129 131 145 156 126 123 127 116 114 114 109 110 113 114 138 155 126 123 124 124 134 131 126 128 128 124 148 174 146 137 152 159 170 166 165 168 175 180 199 228 206 193 201 214 225 224 215 222 238 248 262 288 261 240 248 260 266 268 256 261 287 295 304 331 299 275 293 309 311 311 289 298 319 325 331 348 320 305 322 337 346 343 321 331 343 345 347 363 322 304 323 340 352 351

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	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.9999492214626
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	158	159	-1
3	157	158.000050778537	-1.0000507785374
4	155	157.000050781116	-2.00005078111585
5	175	155.000101559653	19.9998984403466
6	174	174.998984434409	-0.998984434409039
7	159	174.000050726968	-15.0000507269685
8	149	159.000761680637	-10.0007616806368
9	150	149.000507824051	0.999492175948973
10	150	149.999949247249	5.07527508375460e-05
11	151	149.999999997423	1.00000000257717
12	153	150.999949221462	2.00005077853754
13	146	152.999898440347	-6.99989844034673
14	156	146.000355444605	9.99964455539526
15	154	155.999492232675	-1.99949223267495
16	151	154.000101531291	-3.00010153129111
17	171	151.000152340768	19.9998476592322
18	167	170.998984436988	-3.99898443698766
19	144	167.000203062581	-23.0002030625808
20	138	144.001167916671	-6.00116791667142
21	138	138.000304730530	-0.000304730529506969
22	132	138.000000015474	-6.00000001547377
23	132	132.000304671225	-0.000304671225194397
24	132	132.000000015471	-1.54707606725424e-08
25	125	132.000000000001	-7.0000000000008
26	131	125.000355449762	5.9996445502382
27	129	130.999695346825	-1.99969534682481
28	131	129.000101541605	1.99989845839505
29	145	130.999898448081	14.0001015519187
30	156	144.999289095320	11.0007109046803
31	126	155.99944139999	-29.9994413999899
32	123	126.001523327757	-3.0015233277571
33	127	123.000152412965	3.99984758703545
34	116	126.999796893590	-10.9997968935897
35	114	116.000558553598	-2.00055855359795
36	114	114.000101585437	-0.000101585437334961
37	109	114.000000005158	-5.00000000515837
38	110	109.000253892687	0.999746107312731
39	113	109.999949234355	3.0000507656451
40	114	112.99984766181	1.00015233819001
41	138	113.999949213727	24.0000507862729
42	155	137.998781312524	17.0012186874764
43	126	154.999136702981	-28.9991367029810
44	123	126.001472533748	-3.00147253374763
45	124	123.000152410385	0.999847589614689
46	124	123.999949229202	5.07707982251304e-05
47	134	123.999999997422	10.0000000025781
48	131	133.999492214626	-2.99949221462586
49	126	131.000152309828	-5.0001523098276
50	128	126.000253900421	1.99974609957893
51	128	127.999898455818	0.000101544182101065
52	124	127.999999994844	-3.99999999484373
53	148	124.000203114149	23.9997968858507
54	174	147.998781325416	26.0012186745838
55	146	173.998679696145	-27.9986796961451
56	137	146.001421732004	-9.00142173200408
57	152	137.00045707903	14.9995429209699
58	159	151.999238345149	7.0007616548512
59	170	158.999644511562	11.0003554884375
60	166	169.999441418037	-3.99944141803741
61	165	166.000203085786	-1.00020308578561
62	168	165.000050788850	2.99994921115021
63	175	167.999847666967	7.00015233303321
64	180	174.999644542503	5.00035545749705
65	199	179.999746089263	19.0002539107366
66	228	198.999035194896	29.0009648051038
67	206	227.998527373424	-21.9985273734240
68	193	206.001117053045	-13.0011170530450
69	201	193.000660177709	7.99933982229146
70	214	200.999593805224	13.0004061947763
71	225	213.999339858388	11.0006601416122
72	224	224.999441402568	-0.999441402567584
73	215	224.000050750173	-9.00005075017265
74	222	215.000457009414	6.99954299058638
75	238	221.999644573444	16.0003554265555
76	248	237.999187525354	10.0008124746464
77	262	247.99949217337	14.0005078266303
78	288	261.999289074690	26.0007109253103
79	261	287.998679721928	-26.9986797219279
80	240	261.001370953468	-21.001370953468
81	248	240.001066418900	7.9989335810996
82	260	247.999593825852	12.000406174148
83	266	259.999390636926	6.00060936307375
84	268	265.999695297833	2.00030470216694
85	256	267.999898427453	-11.9998984274529
86	261	256.000609337291	4.99939066270889
87	287	260.999746138254	26.0002538617458
88	295	286.998679745137	8.00132025486312
89	304	294.99959370466	9.00040629533981
90	331	303.999542972532	27.0004570274677
91	299	330.998628956283	-31.998628956283
92	275	299.001624843577	-24.0016248435772
93	293	275.001218767405	17.9987812325953
94	309	292.999086048214	16.0009139517859
95	311	308.999187496992	2.00081250300752
96	311	310.999898401667	0.000101598332548747
97	289	310.999999994841	-21.9999999948409
98	298	289.001117127823	8.99888287217749
99	319	297.999543049889	21.0004569501105
100	325	318.998933627511	6.00106637248865
101	331	324.999695274627	6.00030472537327
102	348	330.999695313302	17.0003046866979
103	320	347.999136749393	-27.9991367493926
104	305	320.001421755213	-15.0014217552126
105	322	305.000761750256	16.9992382497444
106	337	321.999136803545	15.0008631964553
107	346	336.999238278107	9.00076172189284
108	343	345.999542954484	-2.99954295448424
109	321	343.000152312404	-22.0001523124041
110	331	321.001117135557	9.99888286444303
111	343	330.999492271352	12.0005077286475
112	345	342.999390631769	2.00060936823053
113	347	344.999898411982	2.00010158801763
114	363	346.999898437767	16.0001015622333
115	322	362.999187538244	-40.9991875382444
116	304	322.002081878778	-18.0020818787777
117	323	304.000914119388	18.9990858806121
118	340	322.999035254207	17.0009647457929
119	352	339.999136715876	12.0008632841242
120	351	351.999390613715	-0.999390613714866

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	351.000050747594	323.490412931058	378.509688564129
122	351.000050747594	312.096535595816	389.903565899372
123	351.000050747594	303.353573338111	398.646528157076
124	351.000050747594	295.982870449981	406.017231045206
125	351.000050747594	289.489129389938	412.510972105249
126	351.000050747594	283.618326484739	418.381775010448
127	351.000050747594	278.219558285650	423.780543209537
128	351.000050747594	273.194502093461	428.805599401727
129	351.000050747594	268.474862351939	433.525239143249
130	351.000050747594	264.010913275688	437.989188219499
131	351.000050747594	259.76511579133	442.234985703857
132	351.000050747594	255.708305696717	446.291795798471

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/19/t128224665197029ilybhzuzc5/16fcp1282246679.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t128224665197029ilybhzuzc5/16fcp1282246679.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t128224665197029ilybhzuzc5/26fcp1282246679.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t128224665197029ilybhzuzc5/26fcp1282246679.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t128224665197029ilybhzuzc5/349jg1282246679.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t128224665197029ilybhzuzc5/349jg1282246679.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

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