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*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: Mon, 27 Dec 2010 06:47:49 +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/27/t1293432453cmufimf03wl7pmo.htm/, Retrieved Mon, 27 Dec 2010 07:47:36 +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/27/t1293432453cmufimf03wl7pmo.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 «

313737 312276 309391 302950 300316 304035 333476 337698 335932 323931 313927 314485 313218 309664 302963 298989 298423 301631 329765 335083 327616 309119 295916 291413 291542 284678 276475 272566 264981 263290 296806 303598 286994 276427 266424 267153 268381 262522 255542 253158 243803 250741 280445 285257 270976 261076 255603 260376 263903 264291 263276 262572 256167 264221 293860 300713 287224 275902 271115 277509 279681

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	'Gwilym Jenkins' @ 72.249.127.135
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.519991743636534
beta	0.543769083912884
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	313218	314937.831730769	-1719.83173076925
14	309664	309777.65862079	-113.658620789764
15	302963	302465.419674192	497.580325807736
16	298989	298846.921807561	142.078192438872
17	298423	298895.697481043	-472.697481042531
18	301631	302609.303765351	-978.303765351186
19	329765	326328.711583789	3436.28841621149
20	335083	332202.633444242	2880.36655575765
21	327616	332860.128156268	-5244.1281562678
22	309119	317631.355296961	-8512.35529696062
23	295916	300104.2582578	-4188.25825779984
24	291413	294138.528195965	-2725.52819596475
25	291542	285587.964350982	5954.03564901819
26	284678	282552.53942915	2125.46057084994
27	276475	274694.570990146	1780.42900985375
28	272566	269931.779598843	2634.22040115687
29	264981	270045.297708218	-5064.29770821839
30	263290	268894.261140499	-5604.2611404988
31	296806	288784.881974550	8021.11802545033
32	303598	294530.047742695	9067.95225730474
33	286994	294008.802320778	-7014.8023207782
34	276427	275293.440690815	1133.55930918502
35	266424	266588.099845105	-164.099845105084
36	267153	266285.232056573	867.767943427025
37	268381	267653.649470515	727.350529485324
38	262522	262469.004799314	52.9952006864478
39	255542	255188.113642516	353.886357483512
40	253158	251510.356241818	1647.64375818230
41	243803	248553.547955925	-4750.54795592546
42	250741	248533.223778547	2207.77622145310
43	280445	282461.982068065	-2016.98206806486
44	285257	284087.228421378	1169.77157862228
45	270976	270103.206449268	872.793550731905
46	261076	259994.938177361	1081.06182263902
47	255603	251218.895783996	4384.10421600423
48	260376	255641.874847082	4734.12515291807
49	263903	261912.111314452	1990.88868554833
50	264291	260376.818950993	3914.18104900717
51	263276	259655.933100468	3620.06689953234
52	262572	263628.897450846	-1056.89745084598
53	256167	260761.16209574	-4594.16209574009
54	264221	268773.026160229	-4552.02616022911
55	293860	299858.269135979	-5998.26913597935
56	300713	302516.661566683	-1803.66156668309
57	287224	287576.887044053	-352.887044053408
58	275902	277317.637664595	-1415.63766459492
59	271115	268509.2566162	2605.74338380009
60	277509	271353.111324632	6155.88867536822
61	279681	276625.483949213	3055.51605078712

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
62	276447.621430008	268944.816224921	283950.426635096
63	272324.096759681	262702.928599385	281945.264919978
64	269919.961349259	257314.536413130	282525.386285388
65	263953.017846731	247696.239408473	280209.796284989
66	273722.188303240	253283.832817304	294160.543789175
67	307115.503299307	282051.016405556	332179.990193059
68	317237.700184815	287157.966041817	347317.434327813
69	306773.501405897	271327.581194132	342219.421617662
70	299128.704904528	257993.583171717	340263.826637338
71	296328.102702328	249202.244374373	343453.961030284
72	302125.666158217	248724.736528957	355526.595787477
73	303572.786806536	243626.663475406	363518.910137667

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293432453cmufimf03wl7pmo/1uwfg1293432466.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293432453cmufimf03wl7pmo/1uwfg1293432466.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293432453cmufimf03wl7pmo/2uwfg1293432466.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293432453cmufimf03wl7pmo/2uwfg1293432466.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293432453cmufimf03wl7pmo/35nej1293432466.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293432453cmufimf03wl7pmo/35nej1293432466.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=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

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