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Opgave 10

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 16 Jan 2011 23:28:57 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/17/t129522040124mqzywgaa8rq7j.htm/, Retrieved Mon, 17 Jan 2011 00:26:44 +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/2011/Jan/17/t129522040124mqzywgaa8rq7j.htm/},
    year = {2011},
}
@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 = {2011},
    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:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

96,1 96,5 96,9 97,8 98,9 100,2 101,2 101 101,6 102,4 103,7 103,7 104,6 104,5 104,5 105,6 106,1 107,6 107,7 108,3 108,1 108,1 108 108,2 108,9 109,8 109,9 109,8 110,9 111,1 112,2 112,7 114,6 114,2 114,7 114,7 116 116,3 116,4 116,6 118,1 117,2 108,3 109,5 110,5 110,6 111,2 111,1 111 112,4 112,5 112,4 111,8 111,6 112,9 112,8 113,7 113,8 114 113,8 113,9 114,4 114,4 114,5 113,8 114,3 115 115,4 115,3 114,9 114,3 114,5 115,5 115,8 115,8 116 114,9 114,1 114,1 113,5 115 114,7 115,4 116,1 116,6 117,2 118,2 118 117,7 118,5 117,5 118 117,7 116,3 115 115,7 113,6 114,8 114,9 117,3 117,3 117,7 120 119,6 119,2 117,3 117,5 119 112,5 118,9 118,4 119,4 120,6 118,6 122 122,6 120,6 117,4 116,4 122,2 121 122,4 124,9 126,1 124,5 123,2 126,4 123,9 116 126,6 125,9 126,6 116,7 126,4 129 128,7 128,4 129,2 133,3 128,9 132,7 127,7 131,8 133,9

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' @ www.wessa.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.488347465828906
beta	0.0122883696409223
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	96.9	96.9	0
4	97.8	97.3	0.499999999999986
5	98.9	97.947174230001	0.952825769998881
6	100.2	98.8212026791372	1.37879732086284
7	101.2	99.9115274103415	1.28847258965851
8	101	100.965474404464	0.0345255955364649
9	101.6	101.40726674962	0.192733250380044
10	102.4	101.927475993206	0.47252400679352
11	103.7	102.587155957461	1.11284404253858
12	103.7	103.566212759107	0.133787240893
13	104.6	104.067952509219	0.532047490780513
14	104.5	104.767374456997	-0.267374456997018
15	104.5	105.074796209891	-0.574796209890849
16	105.6	105.228639980112	0.371360019888101
17	106.1	105.846765276739	0.253234723260718
18	107.6	106.408724044207	1.19127595579283
19	107.7	107.435921710495	0.264078289505349
20	108.3	108.011909478405	0.288090521595208
21	108.1	108.601352388546	-0.50135238854638
22	108.1	108.802264241341	-0.702264241341297
23	108	108.900847016348	-0.900847016348393
24	108.2	108.897046418727	-0.697046418727368
25	108.9	108.988588354992	-0.0885883549916713
26	109.8	109.376737626542	0.423262373457661
27	109.9	110.017387899251	-0.117387899250801
28	109.8	110.393308537283	-0.593308537282994
29	110.9	110.533254096721	0.366745903278769
30	111.1	111.144240649294	-0.0442406492942808
31	112.2	111.55425747255	0.645742527450125
32	112.7	112.305100928778	0.394899071222127
33	114.6	112.935815405863	1.66418459413738
34	114.2	114.196369013529	0.00363098647093807
35	114.7	114.646017264547	0.0539827354527631
36	114.7	115.120578614662	-0.420578614661636
37	116	115.360865242251	0.639134757748678
38	116.3	116.12249565372	0.177504346280202
39	116.4	116.659755226146	-0.259755226145828
40	116.6	116.98192140487	-0.38192140486963
41	118.1	117.242136131678	0.857863868321644
42	117.2	118.112944890897	-0.912944890897322
43	108.3	118.113505103113	-9.81350510311326
44	109.5	113.708608504292	-4.20860850429239
45	110.5	112.015593120627	-1.51559312062675
46	110.6	111.628609909526	-1.02860990952648
47	111.2	111.473271033395	-0.273271033394565
48	111.1	111.685160085385	-0.585160085384587
49	111	111.741227366953	-0.741227366952657
50	112.4	111.716631485958	0.683368514042044
51	112.5	112.391834283748	0.108165716251676
52	112.4	112.786787354733	-0.38678735473303
53	111.8	112.937710239136	-1.13771023913608
54	111.6	112.715094443392	-1.115094443392
55	112.9	112.49683133893	0.403168661070282
56	112.8	113.022427586779	-0.222427586779091
57	113.7	113.241180705707	0.458819294293107
58	113.8	113.795372384522	0.00462761547819923
59	114	114.12778847828	-0.127788478280394
60	113.8	114.394772650303	-0.594772650303454
61	113.9	114.430137058128	-0.53013705812792
62	114.4	114.493884744197	-0.093884744196771
63	114.4	114.770111740433	-0.370111740433018
64	114.5	114.909222944666	-0.409222944665942
65	113.8	115.02677854692	-1.22677854691968
66	114.3	114.737721051727	-0.437721051726569
67	115	114.831371023223	0.168628976776645
68	115.4	115.222142436052	0.177857563947953
69	115.3	115.618487928244	-0.318487928243982
70	114.9	115.770533112947	-0.870533112946703
71	114.3	115.647764366538	-1.34776436653837
72	114.5	115.283853020714	-0.783853020713565
73	115.5	115.190622454164	0.309377545835559
74	115.8	115.633124837206	0.166875162793801
75	115.8	116.007037959495	-0.207037959494542
76	116	116.197109122485	-0.197109122484605
77	114.9	116.390846157172	-1.49084615717156
78	114.1	115.943843430418	-1.84384343041766
79	114.1	115.313390486147	-1.21339048614706
80	113.5	114.983536090298	-1.48353609029806
81	115	114.512854081823	0.48714591817668
82	114.7	115.007472997958	-0.307472997958371
83	115.4	115.11219663643	0.287803363570049
84	116.1	115.50934908383	0.590650916170347
85	116.6	116.057940858781	0.542059141219426
86	117.2	116.586055857322	0.613944142677866
87	118.2	117.15295998938	1.04704001062001
88	118	117.937648672011	0.0623513279886794
89	117.7	118.241841301805	-0.541841301805192
90	118.5	118.247726405472	0.252273594528262
91	117.5	118.642929398711	-1.14292939871055
92	118	118.349929833222	-0.349929833222106
93	117.7	118.442089669053	-0.742089669053144
94	116.3	118.338285967076	-2.03828596707615
95	115	117.589256345531	-2.58925634553084
96	115.7	116.555623623678	-0.85562362367763
97	113.6	116.363471455839	-2.76347145583928
98	114.8	115.223043057873	-0.423043057872988
99	114.9	115.223018258082	-0.3230182580822
100	117.3	115.269901885105	2.03009811489532
101	117.3	116.47810653663	0.821893463370031
102	117.7	117.101219686265	0.598780313735062
103	120	117.618969371856	2.38103062814361
104	119.6	119.021365032888	0.578634967111981
105	119.2	119.5470377255	-0.347037725499931
106	117.3	119.618577933119	-2.31857793311916
107	117.5	118.713407703901	-1.21340770390071
108	119	118.34066290287	0.659337097130319
109	112.5	118.886424957645	-6.38642495764455
110	118.9	115.953082069178	2.94691793082249
111	118.4	117.595337965338	0.804662034662314
112	119.4	118.196257395633	1.20374260436749
113	120.6	118.999290463159	1.6007095368406
114	118.6	120.005787174781	-1.40578717478114
115	122	119.535632715615	2.46436728438532
116	122.6	120.970247032663	1.62975296733688
117	120.6	122.007059701097	-1.40705970109735
118	117.4	121.552408841637	-4.1524088416368
119	116.4	119.732155105314	-3.33215510531437
120	122.2	118.29247395909	3.90752604090986
121	121	120.411721795037	0.588278204962606
122	122.4	120.913553615922	1.48644638407802
123	124.9	121.862923747056	3.03707625294446
124	126.1	123.587765521986	2.51223447801353
125	124.5	125.071378050633	-0.571378050633271
126	123.2	125.045687378965	-1.84568737896456
127	126.4	124.386615016916	2.01338498308382
128	123.9	125.624193174877	-1.72419317487663
129	116	125.026187637864	-9.02618763786352
130	126.6	120.808105509932	5.79189449006797
131	125.9	123.861153362708	2.03884663729221
132	126.6	125.093644914237	1.50635508576342
133	116.7	126.075135194094	-9.37513519409357
134	126.4	121.686417139667	4.71358286033323
135	129	124.206175027178	4.79382497282245
136	128.7	126.793886662705	1.906113337295
137	128.4	127.982830214009	0.417169785991277
138	129.2	128.447155388726	0.752844611273986
139	133.3	129.079924329838	4.22007567016166
140	128.9	131.431231421509	-2.53123142150932
141	132.7	130.470364898918	2.22963510108173
142	127.7	131.847835505034	-4.14783550503442
143	131.8	130.085993365558	1.71400663444214
144	133.9	131.19705272381	2.70294727618992

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
145	132.80727910917	128.599004755087	137.015553463254
146	133.097528041934	128.403122266893	137.791933816975
147	133.387776974698	128.242776519163	138.532777430232
148	133.678025907461	128.109219853087	139.246831961835
149	133.968274840225	127.996638997015	139.939910683435
150	134.258523772988	127.900945105182	140.616102440795
151	134.548772705752	127.819137351337	141.278408060167
152	134.839021638516	127.748939367211	141.929103909821
153	135.129270571279	127.688578005351	142.569963137208
154	135.419519504043	127.636641806457	143.202397201629
155	135.709768436807	127.591986700982	143.827550172632
156	136.00001736957	127.553671027083	144.446363712058

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/17/t129522040124mqzywgaa8rq7j/1llv61295220535.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/17/t129522040124mqzywgaa8rq7j/1llv61295220535.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/17/t129522040124mqzywgaa8rq7j/2568r1295220535.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/17/t129522040124mqzywgaa8rq7j/2568r1295220535.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/17/t129522040124mqzywgaa8rq7j/3uzyg1295220535.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/17/t129522040124mqzywgaa8rq7j/3uzyg1295220535.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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