Home » date » 2010 » Dec » 10 »

Workshop 8 (Double Smoothing model)

*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 10 Dec 2010 15:49:13 +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/Dec/10/t1291996060bx3guhifjctqmud.htm/, Retrieved Fri, 10 Dec 2010 16:47:41 +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/Dec/10/t1291996060bx3guhifjctqmud.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 «

37 30 47 35 30 43 82 40 47 19 52 136 80 42 54 66 81 63 137 72 107 58 36 52 79 77 54 84 48 96 83 66 61 53 30 74 69 59 42 65 70 100 63 105 82 81 75 102 121 98 76 77 63 37 35 23 40 29 37 51 20 28 13 22 25 13 16 13 16 17 9 17 25 14 8 7 10 7 10 3

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

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.458869668373879
beta	0.071121400333114
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	47	23	24
4	35	27.7961229222165	7.20387707778349
5	30	25.1201162837129	4.87988371628709
6	43	21.5369567996642	21.4630432003358
7	82	26.2637623545199	55.7362376454801
8	40	48.5364746640747	-8.53647466407467
9	47	41.0377970696815	5.96220293031854
10	19	40.3867020506924	-21.3867020506924
11	52	26.4880593548409	25.5119406451591
12	136	34.9423750297094	101.057624970291
13	80	81.3603752268598	-1.36037522685979
14	42	80.7374651757254	-38.7374651757254
15	54	61.6991275159735	-7.69912751597347
16	66	56.6520770478746	9.34792295212543
17	81	59.732474678577	21.267525321423
18	63	68.9764916268721	-5.97649162687212
19	137	65.5240100390352	71.4759899609648
20	72	99.944774330671	-27.944774330671
21	107	87.8323751022993	19.1676248977007
22	58	97.9639710130011	-39.9639710130011
23	36	79.657628804661	-43.657628804661
24	52	58.231592560615	-6.231592560615
25	79	53.775858307896	25.224141692104
26	77	64.577407700552	12.4225922994481
27	54	69.9101313006393	-15.9101313006393
28	84	61.7225930698122	22.2774069301878
29	48	71.7851911183916	-23.7851911183916
30	96	59.9348195799791	36.0651804200209
31	83	76.7249716958758	6.27502830412423
32	66	80.0501149832532	-14.0501149832532
33	61	73.5901346381083	-12.5901346381083
34	53	67.3892102376778	-14.3892102376778
35	30	59.8931462135325	-29.8931462135325
36	74	44.30721984987	29.69278015013
37	69	57.0325050989165	11.9674949010835
38	59	62.0147592058819	-3.01475920588188
39	42	60.0237233057599	-18.0237233057599
40	65	50.5573166447196	14.4426833552804
41	70	56.4601027609199	13.5398972390801
42	100	62.3905083965525	37.6094916034475
43	63	80.5931236261194	-17.5931236261194
44	105	72.8907735459248	32.1092264540752
45	82	89.0432235276064	-7.04322352760644
46	81	86.9999429770526	-5.99994297705263
47	75	85.2395813674112	-10.2395813674112
48	102	81.1996049151613	20.8003950848387
49	121	92.0817624880721	28.9182375119279
50	98	107.632711515714	-9.63271151571374
51	76	105.1794314399	-29.1794314398995
52	77	92.8044705001153	-15.8044705001153
53	63	86.0510873910001	-23.0510873910001
54	37	75.2201689043062	-38.2201689043062
55	35	56.1812864734165	-21.1812864734165
56	23	44.2697694857101	-21.2697694857101
57	40	31.6235017569322	8.37649824306778
58	29	32.8543778873243	-3.85437788732425
59	37	28.3470865739708	8.6529134260292
60	51	29.8614036305922	21.1385963694078
61	20	37.7948895553043	-17.7948895553043
62	28	27.2822354165287	0.717764583471265
63	13	25.2879013157388	-12.2879013157388
64	22	16.9246403862059	5.07535961379408
65	25	16.6944899033857	8.3055100966143
66	13	18.2176115890128	-5.21761158901281
67	16	13.3651037915816	2.63489620841841
68	13	12.2018646754455	0.79813532455454
69	16	10.2218392098281	5.77816079017186
70	17	10.7155692752316	6.28443072476838
71	9	11.6467065036014	-2.6467065036014
72	17	8.3932392870651	8.6067607129349
73	25	10.5845323782812	14.4154676217188
74	14	15.9117202040056	-1.91172020400564
75	8	13.6844669110586	-5.68446691105861
76	7	9.5404994328923	-2.54049943289231
77	10	6.7562929179933	3.2437070820067
78	7	6.73214317966192	0.267856820338082
79	10	5.35120764740237	4.64879235259763
80	3	6.13226599611851	-3.13226599611851

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
81	3.24060975985528	-43.5153135754196	49.9965330951302
82	1.78625538248973	-50.3120403951058	53.8845511600853
83	0.331901005124177	-57.2424823469809	57.9062843572292
84	-1.12245337224137	-64.3087232376746	62.0638164931919
85	-2.57680774960693	-71.5113739161083	66.3577584168945
86	-4.03116212697248	-78.850113628458	70.7877893745131
87	-5.48551650433803	-86.3240266303809	75.3529936217048
88	-6.93987088170358	-93.9318176678924	80.0520759044852
89	-8.39422525906913	-101.671953087191	84.8835025690531
90	-9.84857963643468	-109.542754867559	89.8455955946895
91	-11.3029340138002	-117.542464088998	94.9365960613978
92	-12.7572883911658	-125.669284130188	100.154707347857

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291996060bx3guhifjctqmud/1u3qj1291996149.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291996060bx3guhifjctqmud/1u3qj1291996149.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291996060bx3guhifjctqmud/2u3qj1291996149.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291996060bx3guhifjctqmud/2u3qj1291996149.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291996060bx3guhifjctqmud/3mcpm1291996149.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t1291996060bx3guhifjctqmud/3mcpm1291996149.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