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exponential smoothing - sigaretten - caroline thys

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 05 Jun 2009 02:29:38 -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/05/t124419069619ayydqkrf0g03b.htm/, Retrieved Fri, 05 Jun 2009 10:31:40 +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/05/t124419069619ayydqkrf0g03b.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 «

106.07 106.07 106.07 106.07 106.07 106.2 107.5 108.31 108.53 108.61 108.62 108.62 108.62 108.62 110.1 110.74 110.77 110.77 110.78 110.78 110.78 110.84 110.84 110.84 110.84 110.84 111.01 112.66 114.04 114.16 114.2 114.2 114.23 114.23 114.23 114.23 114.23 114.23 115.97 116.96 117.08 117.08 117.08 117.63 119.12 119.47 119.5 119.52 119.49 119.49 119.5 119.5 119.56 122.35 122.92 122.92 123.04 123.04 123.04 123.06 123.33 128.21 129.57 129.79 131.66 135.01 136.01 136.31 136.37 136.4 136.4 136.4 137.34 142.18 143.79 144.08 144.08 144.09 144.09 144.11 144.11 144.15 144.15 144.16 144.2 144.38 144.38 144.28 144.46 144.53 144.53 145.34 147.98 150.42 150.53 150.64

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	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0252584287655884
gamma	0.160169143914703

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	108.62	106.501159188034	2.11884081196575
14	108.62	108.716653787850	-0.0966537878498599
15	110.1	110.237129131701	-0.137129131701201
16	110.74	110.883665465296	-0.143665465296408
17	110.77	110.911286701375	-0.141286701375165
18	110.77	110.908134687960	-0.138134687959607
19	110.78	110.765895622784	0.0141043772162561
20	110.78	111.697501877191	-0.917501877190944
21	110.78	111.022660554717	-0.242660554716934
22	110.84	110.788197997048	0.0518020029519022
23	110.84	110.751589767583	0.0884102324170897
24	110.84	110.747989537807	0.092010462192789
25	110.84	110.809480244179	0.0305197558211461
26	110.84	110.897751125257	-0.0577511252572123
27	111.01	112.419209089240	-1.40920908924043
28	112.66	111.723614681844	0.93638531815597
29	114.04	112.788516303700	1.25148369630018
30	114.16	114.170543482161	-0.0105434821607844
31	114.2	114.151527170368	0.0484728296323169
32	114.2	115.114001517882	-0.914001517882028
33	114.23	114.439248608984	-0.209248608984282
34	114.23	114.235629984567	-0.00562998456663877
35	114.23	114.137571113336	0.0924288866641518
36	114.23	114.134072388452	0.0959276115478076
37	114.23	114.195662035862	0.0343379641382313
38	114.23	114.284029358883	-0.0540293588829286
39	115.97	115.805581328837	0.164418671162991
40	116.96	116.719734286130	0.240265713869704
41	117.08	117.107053020549	-0.027053020548891
42	117.08	117.196786370423	-0.116786370423114
43	117.08	117.055086530205	0.0249134697949813
44	117.63	117.976965805307	-0.34696580530715
45	119.12	117.866535327563	1.25346467243699
46	119.47	119.159862542369	0.310137457631356
47	119.5	119.419779460583	0.0802205394169135
48	119.52	119.445972372030	0.0740276279698548
49	119.49	119.527008860265	-0.0370088602645495
50	119.49	119.583574074604	-0.093574074603879
51	119.5	121.104127207173	-1.60412720717285
52	119.5	120.243609474380	-0.743609474379525
53	119.56	119.616077067442	-0.0560770674415068
54	122.35	119.645077315495	2.70492268450519
55	122.92	122.364649412438	0.555350587562174
56	122.92	123.869926695694	-0.94992669569369
57	123.04	123.194266373251	-0.154266373251303
58	123.04	123.082036513718	-0.0420365137183012
59	123.04	122.983058070764	0.056941929235677
60	123.06	122.978663001094	0.0813369989056554
61	123.33	123.059884112554	0.270115887446124
62	128.21	123.424206815455	4.78579318454462
63	129.57	129.948005098361	-0.378005098360745
64	129.79	130.468457283511	-0.678457283510738
65	131.66	130.062570518545	1.59742948145532
66	135.01	131.943335743977	3.06666425602324
67	136.01	135.232044864635	0.777955135364493
68	136.31	137.172944789005	-0.8629447890049
69	136.37	136.799481492857	-0.429481492856524
70	136.4	136.620300131830	-0.220300131829788
71	136.4	136.546819029976	-0.1468190299762
72	136.4	136.537277278633	-0.137277278632808
73	137.34	136.592976536936	0.747023463064039
74	142.18	137.639345175864	4.540654824136
75	143.79	144.116951648955	-0.326951648955259
76	144.08	144.888693364020	-0.808693364020257
77	144.08	144.549517040292	-0.469517040292004
78	144.09	144.508074444242	-0.418074444242222
79	144.09	144.368764540674	-0.27876454067362
80	144.11	145.282973386381	-1.17297338638062
81	144.11	144.62167925499	-0.511679254990128
82	144.15	144.380421707644	-0.230421707643842
83	144.15	144.316684950689	-0.166684950688591
84	144.16	144.306641417402	-0.146641417402009
85	144.2	144.372104152273	-0.172104152273107
86	144.38	144.495257071803	-0.115257071802631
87	144.38	146.195262525931	-1.81526252593147
88	144.28	145.319411846729	-1.03941184672937
89	144.46	144.584407936641	-0.124407936640665
90	144.53	144.731682254302	-0.201682254301829
91	144.53	144.657838077448	-0.127838077448274
92	145.34	145.575859088475	-0.235859088475479
93	147.98	145.728234991824	2.25176500817614
94	150.42	148.196777704546	2.22322229545358
95	150.53	150.595016139859	-0.0650161398594946
96	150.64	150.697540600989	-0.0575406009889434

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	150.865253882484	148.725181116073	153.005326648896
98	151.178007764969	148.113026924141	154.242988605796
99	153.013678314120	149.212568977828	156.814787650412
100	154.019348863271	149.575394633073	158.463303093468
101	154.416269412422	149.386275132633	159.446263692211
102	154.783606628240	149.205917518094	160.361295738385
103	155.012193844057	148.914334127451	161.110053560664
104	156.162031059875	149.564568043247	162.759494076503
105	156.660201609026	149.578935121621	163.741468096431
106	156.930038824844	149.377344774892	164.482732874795
107	157.101959373995	149.087664697949	165.116254050040
108	157.268046589812	148.800025914841	165.736067264783

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t124419069619ayydqkrf0g03b/14znh1244190576.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t124419069619ayydqkrf0g03b/14znh1244190576.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t124419069619ayydqkrf0g03b/2900t1244190576.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t124419069619ayydqkrf0g03b/2900t1244190576.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t124419069619ayydqkrf0g03b/3li0j1244190576.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t124419069619ayydqkrf0g03b/3li0j1244190576.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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