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TIJDREEKS B - STAP 27

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 16 Aug 2010 19:54:13 +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/Aug/16/t1281988470340uuhfym87m2a1.htm/, Retrieved Mon, 16 Aug 2010 21:54:35 +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/16/t1281988470340uuhfym87m2a1.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:

De Cock Nicola

Dataseries X:

» Textbox « » Textfile « » CSV «

76 75 74 72 70 69 70 72 73 73 74 76 74 67 66 58 55 58 64 68 66 76 75 88 85 83 77 66 65 65 63 62 57 68 69 79 74 76 82 75 75 76 78 77 67 74 68 87 76 88 95 96 96 105 108 113 101 107 102 116 105 121 134 140 131 141 131 128 123 129 125 144 135 141 156 159 146 154 145 133 126 127 122 148

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

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.796773318034331
beta	0.0131562838165992
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	74	79.5803952991453	-5.58039529914534
14	67	67.9006174409027	-0.900617440902664
15	66	65.9817875904125	0.0182124095874769
16	58	57.5035810949057	0.496418905094266
17	55	54.0782671910517	0.921732808948285
18	58	56.6264941917157	1.3735058082843
19	64	63.7574130762899	0.242586923710114
20	68	65.7397889046167	2.26021109538333
21	66	68.6034466731327	-2.60344667313272
22	76	66.8145808762672	9.18541912373277
23	75	75.806722316124	-0.806722316123938
24	88	77.703935538761	10.296064461239
25	85	83.0463970780077	1.95360292199234
26	83	78.5557609274844	4.44423907251557
27	77	81.3735259620734	-4.37352596207342
28	66	69.7384721854195	-3.73847218541947
29	65	63.2261409758154	1.77385902418457
30	65	66.7548600002482	-1.75486000024823
31	63	71.3402825192019	-8.3402825192019
32	62	66.9810564008034	-4.98105640080344
33	57	63.0976976245827	-6.09769762458272
34	68	60.8949464477619	7.10505355223808
35	69	66.1514592325584	2.84854076744156
36	79	73.2084085152728	5.79159148472721
37	74	73.2101343644327	0.789865635567338
38	76	68.229947118747	7.77005288125302
39	82	71.8720098252749	10.1279901747251
40	75	72.0388333917923	2.96116660820775
41	75	72.1734742096893	2.8265257903107
42	76	76.0234606411593	-0.0234606411592608
43	78	80.8678924035702	-2.86789240357020
44	77	81.8267798371326	-4.82677983713259
45	67	78.116205179314	-11.116205179314
46	74	74.822177474344	-0.822177474343988
47	68	73.0385343936094	-5.03853439360944
48	87	74.4677894710597	12.5322105289403
49	76	78.9528460323263	-2.95284603232629
50	88	72.4989624859111	15.5010375140889
51	95	82.9509400756249	12.0490599243751
52	96	83.3829455797412	12.6170544202588
53	96	91.4760107311506	4.52398926884938
54	105	96.4093244439262	8.5906755560738
55	108	107.939530953019	0.060469046980586
56	113	111.264582529636	1.73541747036437
57	101	112.004223348916	-11.0042233489161
58	107	111.392425529664	-4.39242552966425
59	102	106.370787093354	-4.37078709335414
60	116	112.373488565228	3.62651143477159
61	105	106.992949350156	-1.99294935015591
62	121	105.441473885853	15.5585261141473
63	134	115.625592030191	18.3744079698090
64	140	121.667072785788	18.3329272142123
65	131	133.183758226321	-2.18375822632143
66	141	134.042754534558	6.95724546544227
67	131	142.964577073295	-11.9645770732949
68	128	137.349388612978	-9.34938861297812
69	123	126.852321104405	-3.85232110440545
70	129	133.542036585655	-4.54203658565527
71	125	128.663395936463	-3.66339593646279
72	144	137.120213910621	6.87978608937868
73	135	133.489097123842	1.51090287615850
74	141	138.632379499973	2.36762050002744
75	156	139.076377421148	16.9236225788518
76	159	144.136052207265	14.8639477927345
77	146	148.865416773383	-2.86541677338283
78	154	151.1780433284	2.82195667159999
79	145	153.055272142834	-8.0552721428335
80	133	151.223082462648	-18.2230824626477
81	126	134.816516929158	-8.8165169291583
82	127	137.402361160027	-10.4023611600268
83	122	127.963138298558	-5.96313829855828
84	148	136.636336416663	11.3636635833369

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	135.439853439265	120.095201830217	150.784505048313
86	139.490658625666	119.770171825321	159.211145426010
87	140.918810976790	117.544729318343	164.292892635238
88	131.810654082974	105.205008806137	158.416299359810
89	120.672969360090	91.1181499950518	150.227788725129
90	126.033774175387	93.733922765828	158.333625584945
91	123.031683309154	88.141981861168	157.921384757140
92	125.215472410293	87.8581211625884	162.572823657998
93	125.095385925227	85.3691550088904	164.821616841564
94	134.331277617844	92.3176107314006	176.344944504287
95	134.139158522133	89.906277246782	178.372039797484
96	151.204015049935	104.809792228174	197.598237871695

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281988470340uuhfym87m2a1/1y79g1281988451.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281988470340uuhfym87m2a1/1y79g1281988451.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281988470340uuhfym87m2a1/2y79g1281988451.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281988470340uuhfym87m2a1/2y79g1281988451.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281988470340uuhfym87m2a1/3ry8j1281988451.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281988470340uuhfym87m2a1/3ry8j1281988451.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

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