Blog & Share Statistical Computations at FreeStatistics.org

Home » date » 2010 » Aug » 19 »

*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 01:56:37 +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/t12821832871yjbeeh8t8kpnj7.htm/, Retrieved Thu, 19 Aug 2010 04:01:28 +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/t12821832871yjbeeh8t8kpnj7.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

94 93 92 90 110 109 94 84 85 85 86 88 93 94 90 91 104 103 88 79 82 88 93 89 94 96 94 92 113 122 107 98 103 110 113 110 123 124 118 117 139 146 134 121 123 122 127 122 139 136 127 123 140 146 138 120 122 115 115 102 119 114 108 102 121 109 102 95 98 92 94 90 113 111 103 90 108 99 95 91 85 72 90 90 114 115 104 93 101 90 79 75 71 61 84 87 107 99 93 74 87 71 67 61 63 52 80 84 102 93 87 72 83 72 66 64 64 47 77 79

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

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.365777387991424
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	93	94.5619658119659	-1.56196581196586
14	94	95.2432564147555	-1.24325641475546
15	90	90.916123708385	-0.916123708385001
16	91	91.375315415544	-0.375315415543952
17	104	103.615655900796	0.384344099204228
18	103	102.217195992448	0.782804007551704
19	88	91.9644837085955	-3.96448370859548
20	79	80.3086542572199	-1.30865425721991
21	82	80.6659338321859	1.33406616781413
22	88	80.9898607814124	7.01013921858764
23	93	84.556633571866	8.44336642813403
24	89	89.9393151340924	-0.939315134092354
25	94	93.8993899049992	0.100610095000818
26	96	95.390945886747	0.609054113253023
27	94	91.9488214465682	2.05117855343181
28	92	93.836378072517	-1.83637807251708
29	113	106.02408811709	6.97591188290978
30	122	107.289386939288	14.7106130607122
31	107	99.1203150560522	7.87968494394775
32	98	93.4812017690346	4.51879823096544
33	103	97.6461047445466	5.35389525545341
34	110	103.040288153835	6.9597118461652
35	113	107.497600856161	5.50239914383927
36	110	105.85383427893	4.14616572107037
37	123	112.333607048807	10.6663929511926
38	124	118.012354179094	5.98764582090638
39	118	117.452224894104	0.547775105895795
40	117	116.324294216276	0.675705783724482
41	139	135.019821285508	3.98017871449213
42	146	140.094871038334	5.90512896166598
43	134	124.372623108692	9.62737689130783
44	121	117.241225667421	3.75877433257907
45	123	121.657766502721	1.34223349727851
46	122	126.603019945167	-4.60301994516733
47	127	125.906686146232	1.09331385376818
48	122	121.790021964285	0.209978035714713
49	139	130.965301828747	8.03469817125278
50	136	132.714067290539	3.28593270946135
51	127	127.71562342668	-0.715623426679713
52	123	126.206706662262	-3.20670666226191
53	140	145.577906501359	-5.57790650135905
54	146	148.377671783481	-2.37767178348088
55	138	131.986496436507	6.01350356349326
56	120	119.811225405218	0.188774594781549
57	122	121.389316220708	0.61068377929233
58	115	122.296371150802	-7.29637115080169
59	115	124.227614083759	-9.22761408375929
60	102	115.77555628937	-13.7755562893696
61	119	124.797858381335	-5.79785838133486
62	114	118.475213003084	-4.47521300308364
63	108	108.100040147907	-0.100040147906824
64	102	105.236388510888	-3.23638851088805
65	121	123.092862845377	-2.09286284537745
66	109	129.197039514834	-20.1970395148335
67	102	111.609815529806	-9.60981552980647
68	95	90.025712828036	4.97428717196391
69	98	93.621820279238	4.37817972076198
70	92	90.8921070030116	1.10789299698841
71	94	94.6726017865744	-0.672601786574361
72	90	86.4653662595773	3.53463374042272
73	113	106.878980851324	6.12101914867569
74	111	105.754842970346	5.24515702965442
75	103	101.709995232253	1.29000476774694
76	90	97.3656475427341	-7.36564754273411
77	108	114.436982128694	-6.43698212869384
78	99	107.470099978008	-8.47009997800812
79	95	100.886982155598	-5.88698215559813
80	91	89.9141754306911	1.08582456930888
81	85	91.7099063630525	-6.7099063630525
82	72	82.8503321332957	-10.8503321332957
83	90	81.127548511391	8.87245148860907
84	90	79.0800015448968	10.9199984551032
85	114	103.835359660627	10.1646403393732
86	115	103.634795415923	11.3652045840769
87	104	99.320075688232	4.67992431176805
88	93	90.7260734980348	2.27392650196524
89	101	111.912326903989	-10.9123269039892
90	90	102.019015518122	-12.0190155181215
91	79	95.7760563717014	-16.7760563717014
92	75	85.2425842164849	-10.2425842164849
93	71	77.9504105386412	-6.95041053864122
94	61	66.3769136729053	-5.37691367290529
95	84	79.1648181035906	4.83518189640944
96	87	76.9391297963446	10.0608702036554
97	107	100.90117302715	6.09882697284978
98	99	99.974851180339	-0.974851180339058
99	93	86.9064621711582	6.0935378288418
100	74	77.3035896254456	-3.30358962544555
101	87	88.0866936731042	-1.08669367310422
102	71	81.0854898022562	-10.0854898022562
103	67	72.5327477662106	-5.53274776621065
104	61	70.2554994408588	-9.25549944085876
105	63	65.4123500431176	-2.4123500431176
106	52	56.4967203841557	-4.49672038415572
107	80	76.0833215429794	3.91667845702062
108	84	76.8359151345768	7.16408486542316
109	102	97.2255623840596	4.77443761594043
110	93	91.328522222771	1.67147777722896
111	87	83.7110326475509	3.28896735244912
112	72	67.1224409191098	4.87755908089017
113	83	82.3040297127866	0.695970287213441
114	72	70.2476440230466	1.75235597695344
115	66	68.9123702414677	-2.91237024146766
116	64	65.2325434717131	-1.23254347171307
117	64	67.6640900377365	-3.66409003773653
118	47	56.9686473910121	-9.96864739101214
119	77	79.889709170909	-2.88970917090892
120	79	80.2122586488956	-1.21225864889561

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	96.0224605264459	83.4407450070382	108.604176045854
122	86.4110717510053	73.0140961739951	99.8080473280155
123	79.2080418636374	65.0426493942877	93.3734343329872
124	62.4239410432556	47.52972293654	77.3181591499711
125	73.169370849479	57.5803643958875	88.7583773030705
126	61.5283986573978	45.2742757524294	77.7825215623662
127	56.5936778371858	39.7006052744599	73.4867503999117
128	55.0445143688549	37.5357939755987	72.5532347621111
129	56.3847556522236	38.2813118083322	74.488199496115
130	43.0310614567155	24.3518198177027	61.7103030957283
131	74.0880517293054	54.8502385113658	93.3258649472451
132	76.5314685314685	56.7508505783297	96.3120864846073

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/19/t12821832871yjbeeh8t8kpnj7/1c4yr1282182992.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t12821832871yjbeeh8t8kpnj7/1c4yr1282182992.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t12821832871yjbeeh8t8kpnj7/2nvft1282182992.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t12821832871yjbeeh8t8kpnj7/2nvft1282182992.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t12821832871yjbeeh8t8kpnj7/3nvft1282182992.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t12821832871yjbeeh8t8kpnj7/3nvft1282182992.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