Home » date » 2009 » Jun » 08 »

Opgave 10 OEFENING 2 - Tabakprijs - Quincy Cabral MAR201a

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 07 Jun 2009 19:29:27 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/08/t12444251274657v0lwc7tzy3y.htm/, Retrieved Mon, 08 Jun 2009 03:38:47 +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/2009/Jun/08/t12444251274657v0lwc7tzy3y.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

3.27 3.27 3.27 3.27 3.27 3.28 3.32 3.34 3.34 3.35 3.35 3.35 3.35 3.35 3.4 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.42 3.43 3.47 3.51 3.52 3.52 3.52 3.52 3.52 3.52 3.52 3.52 3.52 3.58 3.6 3.61 3.61 3.61 3.63 3.68 3.69 3.69 3.69 3.69 3.69 3.69 3.69 3.69 3.78 3.79 3.79 3.8 3.8 3.8 3.8 3.81 3.95 3.99 4 4.06 4.16 4.19 4.2 4.2 4.2 4.2 4.2 4.23 4.38 4.43 4.44 4.44 4.44 4.44 4.44 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.46 4.46 4.46 4.48 4.58 4.67 4.68 4.68 4.69 4.69 4.69 4.69 4.69 4.69 4.69 4.73 4.78 4.79 4.79 4.8 4.8 4.81 5.16 5.26 5.29 5.29 5.29 5.3 5.3 5.3 5.3 5.3 5.3 5.3 5.3 5.35 5.44 5.47 5.47 5.48 5.48 5.48 5.48

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0339940381487946
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	3.27	3.27	0
4	3.27	3.27	0
5	3.27	3.27	0
6	3.28	3.27	0.00999999999999979
7	3.32	3.28033994038149	0.0396600596185119
8	3.34	3.32168814596114	0.0183118540388567
9	3.34	3.34231063982591	-0.00231063982591495
10	3.35	3.34223209184752	0.0077679081524753
11	3.35	3.35249615441360	-0.00249615441359641
12	3.35	3.35241130004524	-0.00241130004523527
13	3.35	3.35232933021951	-0.00232933021950954
14	3.35	3.35225014687917	-0.00225014687916625
15	3.4	3.35217365530032	0.0478263446996841
16	3.42	3.40379946588655	0.0162005341134459
17	3.42	3.42435018746124	-0.00435018746123728
18	3.42	3.42420230702273	-0.00420230702272573
19	3.42	3.42405945363748	-0.00405945363748206
20	3.42	3.42392145641567	-0.00392145641566621
21	3.42	3.42378815027667	-0.00378815027667345
22	3.42	3.42365937575165	-0.00365937575165454
23	3.42	3.42353497879275	-0.00353497879275233
24	3.42	3.42341481058882	-0.00341481058881632
25	3.42	3.42329872738739	-0.00329872738738901
26	3.42	3.42318659032274	-0.00318659032273949
27	3.43	3.42307826524974	0.00692173475025637
28	3.47	3.4333135629649	0.0366864370351001
29	3.51	3.47456068310501	0.0354393168949851
30	3.52	3.51576540859551	0.00423459140449056
31	3.52	3.52590935945726	-0.00590935945725857
32	3.52	3.52570847646643	-0.00570847646643369
33	3.52	3.52551442229966	-0.00551442229966215
34	3.52	3.52532696481764	-0.00532696481763884
35	3.52	3.52514587977241	-0.00514587977241066
36	3.52	3.52497095053912	-0.00497095053911822
37	3.52	3.52480196785686	-0.00480196785685605
38	3.52	3.52463872957834	-0.00463872957834077
39	3.58	3.52448104042809	0.0555189595719074
40	3.6	3.58636835405776	0.0136316459422385
41	3.61	3.60683174874995	0.00316825125004705
42	3.61	3.61693945040381	-0.00693945040381161
43	3.61	3.61670355046205	-0.00670355046205273
44	3.63	3.61647566971191	0.0135243302880865
45	3.68	3.63693541631166	0.0430645836883365
46	3.69	3.68839935541243	0.00160064458757292
47	3.69	3.6984537677856	-0.00845376778559936
48	3.69	3.69816639008099	-0.00816639008099473
49	3.69	3.69788878150504	-0.00788878150504368
50	3.69	3.69762060996561	-0.00762060996561376
51	3.69	3.69736155465973	-0.00736155465972521
52	3.69	3.69711130568979	-0.00711130568978824
53	3.69	3.69686956369288	-0.00686956369288172
54	3.78	3.69663603948264	0.0833639605173593
55	3.79	3.7894699171367	0.00053008286329792
56	3.79	3.79948793679378	-0.00948793679377902
57	3.8	3.79916540350846	0.000834596491541717
58	3.8	3.80919377481343	-0.00919377481343053
59	3.8	3.80888124128169	-0.00888124128169121
60	3.8	3.80857933202675	-0.00857933202675287
61	3.81	3.80828768588654	0.00171231411345607
62	3.95	3.81834589435784	0.131654105642161
63	3.99	3.96282134904749	0.0271786509525151
64	4	4.0037452611448	-0.00374526114479767
65	4.06	4.01361794459456	0.0463820554054362
66	4.16	4.07519465795544	0.0848053420445645
67	4.19	4.17807753398812	0.0119224660118800
68	4.2	4.20848282675256	-0.00848282675255607
69	4.2	4.21819446121632	-0.0181944612163196
70	4.2	4.21757595800764	-0.0175759580076358
71	4.2	4.21697848022062	-0.0169784802206223
72	4.2	4.21640131311629	-0.0164013131162939
73	4.23	4.21584376625253	0.0141562337474719
74	4.38	4.24632499380258	0.133675006197416
75	4.43	4.4008691470628	0.0291308529372012
76	4.44	4.45185942238885	-0.0118594223888522
77	4.44	4.46145627273174	-0.0214562727317436
78	4.44	4.46072688737797	-0.0207268873779691
79	4.44	4.46002229677774	-0.0200222967777366
80	4.44	4.45934165805725	-0.0193416580572485
81	4.45	4.45868415699539	-0.00868415699538971
82	4.45	4.4683889474312	-0.0183889474311973
83	4.45	4.46776383285071	-0.0177638328507053
84	4.45	4.46715996843911	-0.0171599684391097
85	4.45	4.46657663181736	-0.0165766318173581
86	4.45	4.46601312516298	-0.0160131251629805
87	4.45	4.46546877437531	-0.0154687743753090
88	4.45	4.46494292826908	-0.0149429282690798
89	4.46	4.46443495779545	-0.00443495779544634
90	4.46	4.47428419567096	-0.0142841956709594
91	4.46	4.4737986181784	-0.013798618178396
92	4.48	4.47332954742564	0.00667045257436172
93	4.58	4.49355630304492	0.0864436969550786
94	4.67	4.59649487337694	0.0735051266230649
95	4.68	4.68899360945549	-0.00899360945549166
96	4.68	4.69868788035257	-0.0186878803525659
97	4.69	4.69805260383494	-0.00805260383494044
98	4.69	4.70777886331298	-0.0177788633129792
99	4.69	4.70717448795528	-0.0171744879552751
100	4.69	4.70659065775654	-0.0165906577565371
101	4.69	4.70602667430385	-0.0160266743038484
102	4.69	4.70548186292616	-0.0154818629261646
103	4.69	4.70495557188724	-0.0149555718872385
104	4.73	4.70444717160597	0.0255528283940336
105	4.78	4.7453158154292	0.0346841845707972
106	4.79	4.79649487092266	-0.00649487092266288
107	4.79	4.80627408403275	-0.0162740840327462
108	4.8	4.8057208621993	-0.00572086219930057
109	4.8	4.81552638699145	-0.0155263869914535
110	4.81	4.81499858239975	-0.00499858239975293
111	5.16	4.82482866039896	0.335171339601035
112	5.26	5.18622248770375	0.073777512296254
113	5.29	5.28873048327127	0.00126951672873243
114	5.29	5.31877363927137	-0.0287736392713747
115	5.29	5.3177955070803	-0.0277955070803042
116	5.3	5.31685062555225	-0.0168506255522516
117	5.3	5.3262778047444	-0.0262778047443968
118	5.3	5.32538451604745	-0.0253845160474491
119	5.3	5.32452159384054	-0.0245215938405439
120	5.3	5.32368800584406	-0.0236880058440585
121	5.3	5.32288275486973	-0.0228827548697268
122	5.3	5.32210487762774	-0.0221048776277364
123	5.3	5.32135344357438	-0.0213534435743847
124	5.35	5.32062755379891	0.0293724462010916
125	5.44	5.37162604185559	0.0683739581444085
126	5.47	5.46395034879714	0.00604965120286227
127	5.47	5.49415600087091	-0.0241560008709136
128	5.48	5.49333484085579	-0.0133348408557854
129	5.48	5.50288153576703	-0.0228815357670262
130	5.48	5.50210369996726	-0.0221036999672588
131	5.48	5.50135230594734	-0.0213523059473424

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
132	5.5006264548444	5.41958471087874	5.58166819881007
133	5.52125290968881	5.40467826467087	5.63782755470675
134	5.54187936453321	5.39668697446261	5.68707175460381
135	5.56250581937762	5.39204617479483	5.7329654639604
136	5.58313227422202	5.3894009961642	5.77686355227984
137	5.60375872906642	5.38806922426724	5.8194482338656
138	5.62438518391083	5.38765298727227	5.86111738054938
139	5.64501163875523	5.38789785309109	5.90212542441937
140	5.66563809359963	5.38863044138325	5.94264574581601
141	5.68626454844404	5.38972697224972	5.98280212463835
142	5.70689100328844	5.39109587626607	6.02268613031081
143	5.72751745813285	5.39266748695128	6.06236742931441

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/08/t12444251274657v0lwc7tzy3y/1egds1244424562.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/08/t12444251274657v0lwc7tzy3y/1egds1244424562.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/08/t12444251274657v0lwc7tzy3y/29rcm1244424562.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/08/t12444251274657v0lwc7tzy3y/29rcm1244424562.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/08/t12444251274657v0lwc7tzy3y/3icoy1244424562.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/08/t12444251274657v0lwc7tzy3y/3icoy1244424562.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=0, beta=0)

if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)

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