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Tijdreeks A - Stap 32

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 19 Aug 2010 10:19:50 +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/19/t1282213237myxuen5b94f700a.htm/, Retrieved Thu, 19 Aug 2010 12:20:46 +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/19/t1282213237myxuen5b94f700a.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:

Quaglia Laura

Dataseries X:

» Textbox « » Textfile « » CSV «

239 238 237 235 255 254 239 229 230 230 231 233 239 236 231 235 253 257 236 226 226 221 217 219 225 226 225 229 242 252 233 232 225 218 209 211 220 225 215 222 238 246 226 230 222 214 208 203 208 212 199 200 223 225 203 207 195 198 193 189 184 188 180 186 215 212 191 190 180 190 189 181 174 179 165 185 211 209 183 178 170 182 195 188 175 176 162 193 211 207 179 176 167 175 190 173 159 159 147 181 196 199 171 170 156 164 178 155 138 142 113 148 156 158 141 139 119 120 125 102

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	0.318694192704481
beta	0.0303866885745872
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	239	239.501602564103	-0.501602564102598
14	236	236.306292784362	-0.306292784362086
15	231	231.211927605806	-0.211927605805784
16	235	235.395583741748	-0.395583741747743
17	253	253.933545543219	-0.933545543218514
18	257	258.499354863838	-1.49935486383822
19	236	235.786990862227	0.213009137773327
20	226	225.622410117248	0.377589882751977
21	226	226.763936903452	-0.763936903452105
22	221	226.450934387029	-5.45093438702912
23	217	225.424759142588	-8.42475914258767
24	219	224.244257335430	-5.24425733542958
25	225	227.726499201986	-2.72649920198592
26	226	223.709542806251	2.29045719374929
27	225	219.286534730157	5.71346526984334
28	229	225.070331460622	3.92966853937796
29	242	244.498973841876	-2.49897384187616
30	252	248.044005670487	3.95599432951349
31	233	228.153307841671	4.84669215832898
32	232	219.538892180577	12.4611078194228
33	225	223.831962056112	1.16803794388841
34	218	221.038424386372	-3.03842438637179
35	209	218.875415174319	-9.87541517431916
36	211	219.505841004978	-8.5058410049777
37	220	223.738761898307	-3.73876189830708
38	225	222.882245536837	2.11775446316290
39	215	220.799601670005	-5.79960167000496
40	222	221.650734796260	0.349265203740174
41	238	235.475574235803	2.52442576419671
42	246	244.985110752988	1.01488924701195
43	226	224.701224681404	1.29877531859557
44	230	220.046783156443	9.95321684355702
45	222	215.725211104072	6.27478889592774
46	214	211.621374631667	2.37862536833345
47	208	206.507221770145	1.49277822985491
48	203	211.784369516200	-8.78436951619969
49	208	219.264312243418	-11.2643122434177
50	212	220.014595981365	-8.01459598136529
51	199	209.225638539535	-10.2256385395351
52	200	212.72956449837	-12.7295644983699
53	223	223.615636569291	-0.615636569291297
54	225	230.813019087993	-5.81301908799298
55	203	208.197431256241	-5.19743125624066
56	207	206.956997774525	0.0430022254745381
57	195	196.462982511168	-1.46298251116784
58	198	186.655770296276	11.3442297037240
59	193	183.299280038599	9.70071996140123
60	189	183.773766284549	5.22623371545146
61	184	193.748282632906	-9.74828263290559
62	188	196.929523205335	-8.92952320533482
63	180	184.067483864448	-4.06748386444804
64	186	187.612570834901	-1.61257083490079
65	215	210.187043496449	4.8129565035513
66	212	215.518240859261	-3.51824085926091
67	191	194.020372509962	-3.02037250996233
68	190	197.032158964540	-7.03215896454046
69	180	183.176844669691	-3.17684466969106
70	190	181.452015348036	8.5479846519637
71	189	175.960519044008	13.0394809559917
72	181	174.358762076299	6.64123792370097
73	174	174.503916596795	-0.503916596795193
74	179	181.200540997147	-2.20054099714739
75	165	173.872121226677	-8.87212122667705
76	185	177.588612652598	7.41138734740161
77	211	207.534174013265	3.46582598673487
78	209	206.864366404783	2.13563359521675
79	183	187.666718920437	-4.66671892043723
80	178	187.563790918699	-9.56379091869866
81	170	175.647011754299	-5.64701175429934
82	182	181.217931099255	0.782068900745287
83	195	176.331141721468	18.6688582785322
84	188	172.238366376833	15.7616336231667
85	175	170.584517139283	4.41548286071702
86	176	177.903059653120	-1.90305965311964
87	162	166.33699406429	-4.33699406429005
88	193	182.849706542703	10.1502934572968
89	211	211.263384649236	-0.263384649236059
90	207	208.746094704912	-1.74609470491191
91	179	183.886553025488	-4.8865530254879
92	176	180.584705037044	-4.58470503704382
93	167	173.179017248116	-6.17901724811594
94	175	183.211168773218	-8.21116877321765
95	190	187.808178443866	2.1918215561341
96	173	176.487511702037	-3.48751170203701
97	159	160.786416888864	-1.78641688886418
98	159	161.581074342772	-2.58107434277193
99	147	147.891593907455	-0.891593907455132
100	181	175.156892140315	5.84310785968518
101	196	194.845568404345	1.15443159565464
102	199	191.52625207503	7.47374792496998
103	171	167.310996511065	3.68900348893504
104	170	166.876413887443	3.12358611255709
105	156	160.844381635660	-4.84438163566017
106	164	169.933563917539	-5.93356391753915
107	178	182.382313991437	-4.38231399143731
108	155	165.071744605154	-10.0717446051538
109	138	148.342095570001	-10.3420955700008
110	142	145.696686252288	-3.69668625228783
111	113	132.619899034861	-19.6198990348613
112	148	158.140799978916	-10.1407999789158
113	156	169.022099499516	-13.0220994995162
114	158	164.833929784938	-6.83392978493771
115	141	132.685513468153	8.31448653184705
116	139	132.589798155297	6.41020184470264
117	119	121.458371208245	-2.45837120824541
118	120	129.870803870640	-9.8708038706402
119	125	141.388434474232	-16.388434474232
120	102	115.525854545312	-13.5258545453119

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	96.6282716863822	83.194194931532	110.062348441232
122	101.023600250983	86.883749267713	115.163451234253
123	77.5293631944334	62.6780633034482	92.3806630854186
124	115.204192619366	99.635459970831	130.772925267901
125	126.895479596409	110.603081998895	143.187877193922
126	130.740739630246	113.718245447803	147.763233812690
127	110.824467549421	93.0652853445223	128.583649754320
128	106.434561943355	87.9319728591344	124.937151027575
129	86.808942279971	67.556126666479	106.061757893463
130	90.5694288770997	70.559488311789	110.579369442410
131	100.502635966407	79.7286115580843	121.27666037473
132	81.6822620583776	60.1371497292265	103.227374387529

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282213237myxuen5b94f700a/1jept1282213187.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282213237myxuen5b94f700a/1jept1282213187.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282213237myxuen5b94f700a/2c5ow1282213187.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282213237myxuen5b94f700a/2c5ow1282213187.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282213237myxuen5b94f700a/3c5ow1282213187.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/19/t1282213237myxuen5b94f700a/3c5ow1282213187.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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