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Tijdreeks 1 - 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: Wed, 18 Aug 2010 08:58:58 +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/18/t1282121916ckqvrf9em3p9e51.htm/, Retrieved Wed, 18 Aug 2010 10:58:52 +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/18/t1282121916ckqvrf9em3p9e51.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:

Patrick Fieremans

Dataseries X:

» Textbox « » Textfile « » CSV «

136 135 134 132 152 151 136 126 127 127 128 130 125 118 111 104 126 131 122 116 115 115 113 122 114 106 93 89 114 122 115 116 120 120 120 121 118 112 99 96 120 135 128 134 134 132 130 125 124 114 101 101 123 143 133 136 137 135 141 136 133 124 110 104 130 160 142 142 137 135 139 135 134 120 103 101 127 159 141 140 135 127 130 128 126 110 101 102 129 169 146 145 138 123 124 137 132 112 105 106 137 175 151 142 140 122 127 135 128 117 107 108 134 171 154 146 148 122 124 135

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	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999933893038648
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	135	136	-1
3	134	135.000066106961	-1.00006610696136
4	132	134.000066111331	-2.00006611133148
5	152	132.000132218293	19.9998677817069
6	151	151.998677869514	-0.9986778695135
7	136	151.000066019559	-15.0000660195593
8	126	136.000991608785	-10.0009916087846
9	127	126.000661135166	0.999338864834243
10	127	126.999933936744	6.60632557156760e-05
11	128	126.999999995633	1.00000000436724
12	130	127.999933893038	2.00006610696164
13	125	129.999867781707	-4.99986778170717
14	118	125.000330526066	-7.00033052606621
15	111	118.000462770580	-7.00046277057953
16	104	111.000462779322	-7.00046277932181
17	126	104.000462779322	21.9995372206776
18	131	125.998545677443	5.00145432255681
19	122	130.999669369052	-8.99966936905238
20	116	122.000594940795	-6.00059494079515
21	115	116.000396681098	-1.00039668109784
22	115	115.000066133185	-6.61331847453539e-05
23	113	115.000000004372	-2.00000000437187
24	122	113.000132213923	8.999867786077
25	114	121.999405046088	-7.99940504608809
26	106	114.000528816360	-8.00052881636022
27	93	106.000528890649	-13.0005288906492
28	89	93.000859425461	-4.00085942546093
29	114	89.0002644846594	24.9997355153406
30	122	113.998347343450	8.00165265654952
31	115	121.999471035057	-6.99947103505707
32	116	115.000462713761	0.999537286238791
33	120	115.999933923627	4.00006607637275
34	120	119.999735567786	0.000264432213512578
35	120	119.999999982519	1.74808150177341e-08
36	121	119.999999999999	1.00000000000115
37	118	120.999933893039	-2.99993389303864
38	112	118.000198316514	-6.00019831651392
39	99	112.000396654878	-13.0003966548782
40	96	99.0008594167192	-3.00085941671922
41	120	96.0001983776975	23.9998016223025
42	135	119.998413446042	15.0015865539583
43	128	134.999008290697	-6.99900829069747
44	134	128.000462683171	5.99953731682942
45	134	133.999603388818	0.000396611181514572
46	132	133.999999973781	-1.99999997378126
47	130	132.000132213921	-2.00013221392098
48	125	130.000132222663	-5.00013222266296
49	124	125.000330543548	-1.00033054354759
50	114	124.000066128813	-10.0000661288126
51	101	114.000661073985	-13.0006610739851
52	101	101.000859434199	-0.000859434199171005
53	123	101.000000056815	21.9999999431854
54	143	122.998545646854	20.001454353146
55	133	142.99867776463	-9.99867776463009
56	136	133.000660982205	2.99933901779542
57	137	135.999801722811	1.00019827718853
58	135	136.999933879931	-1.99993387993115
59	141	135.000132209552	5.99986779044829
60	136	140.999603366972	-4.99960336697185
61	133	136.000330508587	-3.00033050858656
62	124	133.000198342733	-9.00019834273297
63	110	124.000594975764	-14.000594975764
64	104	110.000925536791	-6.00092553679096
65	130	104.000396702953	25.9996032970475
66	160	129.998281245230	30.0017187547703
67	142	159.998016677538	-17.9980166775378
68	142	142.001189794193	-0.00118979419292486
69	137	142.000000078654	-5.00000007865367
70	135	137.000330534812	-2.00033053481195
71	139	135.000132235773	3.99986776422665
72	135	138.999735580896	-3.99973558089627
73	134	135.000264410365	-1.00026441036547
74	120	134.000066124441	-14.0000661244407
75	103	120.000925501830	-17.0009255018302
76	101	103.001123879525	-2.00112387952510
77	127	101.000132288219	25.9998677117810
78	159	126.99828122775	32.00171877225
79	141	158.997884463614	-17.9978844636139
80	140	141.001189785453	-1.00118978545265
81	135	140.000066185614	-5.00006618561446
82	127	135.000330539182	-8.0003305391821
83	130	127.000528877542	2.99947112245825
84	128	129.999801714078	-1.99980171407842
85	126	128.000132200815	-2.00013220081462
86	110	126.000132222662	-16.0001322226621
87	101	110.001057720122	-9.00105772012246
88	102	101.000595032575	0.999404967425164
89	129	101.999933932374	27.0000660676256
90	169	128.998215107676	40.001784892324
91	146	168.997355603552	-22.9973556035521
92	145	146.001520285298	-1.00152028529806
93	138	145.000066207463	-7.00006620746279
94	123	138.000462753106	-15.0004627531062
95	124	123.000991635011	0.999008364988512
96	137	123.999933958593	13.0000660414074
97	132	136.999140605137	-4.99914060513663
98	112	132.000330477995	-20.0003304779948
99	105	112.001322161074	-7.00132216107394
100	106	105.000462836134	0.999537163866478
101	137	105.999933923635	31.0000660763647
102	175	136.99795067983	38.00204932017
103	151	174.997487799994	-23.9974877999943
104	142	151.001586400999	-9.00158640099855
105	140	142.000595067524	-2.00059506752433
106	122	140.000132253261	-18.0001322532608
107	127	122.001189934047	4.99881006595281
108	135	126.999669543856	8.00033045614383
109	128	134.999471122464	-6.99947112246375
110	117	128.000462713767	-11.0004627137670
111	107	117.000727207163	-10.0007272071635
112	108	107.000661117687	0.999338882313026
113	134	107.999933936743	26.0000660632569
114	171	133.998281214638	37.0017187853624
115	154	170.997553928806	-16.9975539288063
116	146	154.001123656641	-8.00112365664063
117	148	146.000528929972	1.99947107002768
118	122	147.999867821043	-25.9998678210433
119	124	122.001718772257	1.99828122774281
120	135	123.9998678997	11.0001321002999

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	134.999272814692	108.768390807580	161.230154821805
122	134.999272814692	97.904429861163	172.094115768222
123	134.999272814692	89.5680547303954	180.430490898989
124	134.999272814692	82.540109844827	187.458435784558
125	134.999272814692	76.3483394685398	193.650206160845
126	134.999272814692	70.7505359769087	199.248009652476
127	134.999272814692	65.6028147773637	204.395730852021
128	134.999272814692	60.8114261617354	209.187119467649
129	134.999272814692	56.3112508934456	213.687294735939
130	134.999272814692	52.0548757962406	217.943669833144
131	134.999272814692	48.0065076003914	221.992038028993
132	134.999272814692	44.1383384011259	225.860207228259

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/18/t1282121916ckqvrf9em3p9e51/1a74t1282121935.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/18/t1282121916ckqvrf9em3p9e51/1a74t1282121935.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/18/t1282121916ckqvrf9em3p9e51/2a74t1282121935.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/18/t1282121916ckqvrf9em3p9e51/2a74t1282121935.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/18/t1282121916ckqvrf9em3p9e51/3lglw1282121935.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/18/t1282121916ckqvrf9em3p9e51/3lglw1282121935.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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