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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: Thu, 19 Aug 2010 23:27:41 +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/20/t1282260487n4w4f5bb7oxnsdh.htm/, Retrieved Fri, 20 Aug 2010 01:28:10 +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/20/t1282260487n4w4f5bb7oxnsdh.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:

Vanhille Olivier

Dataseries X:

» Textbox « » Textfile « » CSV «

31 30 29 27 25 24 25 27 28 28 29 31 31 27 25 16 20 21 25 24 28 27 23 36 37 30 27 22 22 25 33 35 35 29 25 34 31 29 21 19 18 25 23 22 20 15 17 25 26 26 23 24 24 42 40 45 47 40 39 49 55 54 48 44 48 62 57 60 56 57 54 62 65 68 69 67 72 82 72 77 79 78 76 79

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	0.915448264006933
beta	0.0348360292320682
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	29	29	0
4	27	28	-1
5	25	26.0526611535077	-1.05266115350767
6	24	24.0235437681110	-0.0235437681110433
7	25	22.9357792821562	2.06422071784385
8	27	23.8250843715944	3.17491562840556
9	28	25.8324230974796	2.16757690252039
10	28	26.9867206254895	1.01327937451050
11	29	27.1166325548088	1.88336744519118
12	31	28.1031267828271	2.89687321717292
13	31	30.109816084649	0.890183915350995
14	27	30.3078736322964	-3.30787363229643
15	25	26.5573366688268	-1.55733666882682
16	16	24.3596613561507	-8.35966135615068
17	20	15.6682152472242	4.33178475277585
18	21	18.7332745854193	2.26672541458069
19	25	19.9801661311978	5.01983386880217
20	24	23.9074714580722	0.0925285419277877
21	28	23.3270344663259	4.67296553367407
22	27	27.0887741598699	-0.088774159869942
23	23	26.4885564576383	-3.48855645763829
24	36	22.6647618554458	13.3352381445542
25	37	34.6675493278509	2.33245067214909
26	30	36.6722373199588	-6.67223731995882
27	27	30.2208177871532	-3.22081778715321
28	22	26.8262805187025	-4.82628051870249
29	22	21.8081122827478	0.191887717252165
30	25	21.3899368579676	3.61006314203244
31	33	24.216051208282	8.783948791718
32	35	32.0587154382612	2.94128456173879
33	35	34.6465221196597	0.353477880340307
34	29	34.8765982824861	-5.87659828248615
35	25	29.215953895161	-4.21595389516102
36	34	24.9410943038973	9.05890569610271
37	31	33.1075756597207	-2.10757565972067
38	29	30.9845092278692	-1.98450922786923
39	21	28.9108165921893	-7.91081659218934
40	19	21.1596156188111	-2.15961561881108
41	18	18.6044701924385	-0.604470192438495
42	25	17.4537030403851	7.5462969596149
43	23	24.0051973336536	-1.00519733365357
44	22	22.6961846930013	-0.696184693001253
45	20	21.6478554024131	-1.64785540241308
46	15	19.6757697443529	-4.67576974435294
47	17	14.7826721376873	2.21732786231272
48	25	16.2705606457643	8.72943935423572
49	26	23.9983372199193	2.00166278008074
50	26	25.6310166006337	0.368983399366336
51	23	25.7808295721264	-2.78082957212639
52	24	22.9584694520719	1.04153054792814
53	24	23.6684972841803	0.331502715819653
54	42	23.7391031846915	18.2608968153085
55	40	40.8054924244217	-0.805492424421665
56	45	40.391901111158	4.60809888884199
57	47	45.0811275253800	1.91887247461996
58	40	47.3697002481117	-7.36970024811174
59	39	40.9200411630615	-1.92004116306153
60	49	39.3980317957642	9.6019682042358
61	55	48.7300382606701	6.2699617393299
62	54	55.2117179236464	-1.21171792364638
63	48	54.805664536902	-6.80566453690197
64	44	49.0616058278233	-5.0616058278233
65	48	44.7527250781361	3.24727492186387
66	62	48.1537522753391	13.8462477246609
67	57	61.6991556302958	-4.69915563029581
68	60	58.1173428684094	1.88265713159058
69	56	60.6208782059573	-4.6208782059573
70	57	57.0234009112572	-0.0234009112572053
71	54	57.6339299561109	-3.63392995611092
72	62	54.8233183116952	7.1766816883048
73	65	62.1381308893653	2.86186911063474
74	68	65.594222456227	2.40577754377293
75	69	68.7095074371782	0.290492562821754
76	67	69.8976224314738	-2.89762243147378
77	72	68.0747762216246	3.92522377837544
78	82	72.623070402846	9.376929597154
79	72	82.4611549585225	-10.4611549585225
80	77	73.804887121385	3.19511287861501
81	79	77.7521199793743	1.24788002062567
82	78	79.9565575186297	-1.95655751862971
83	76	79.1651025165198	-3.16510251651981
84	79	77.1663501312394	1.83364986876062

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	79.8021731016535	69.8142732611922	89.7900729421147
86	80.7593844829141	67.00125315447	94.5175158113582
87	81.7165958641747	64.8363325073105	98.596859221039
88	82.6738072454354	63.0032100717013	102.344404419169
89	83.631018626696	61.3721688342546	105.889868419137
90	84.5882300079567	59.875516606963	109.300943408950
91	85.5454413892173	58.4729326072083	112.617950171226
92	86.502652770478	57.1382714841564	115.867034056799
93	87.4598641517386	55.8535422638901	119.066186039587
94	88.4170755329992	54.605809266997	122.228341799001
95	89.3742869142599	53.3854521465961	125.363121681924
96	90.3314982955205	52.1851223541746	128.477874236866

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282260487n4w4f5bb7oxnsdh/112r11282260459.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282260487n4w4f5bb7oxnsdh/112r11282260459.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282260487n4w4f5bb7oxnsdh/2pqjg1282260459.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282260487n4w4f5bb7oxnsdh/2pqjg1282260459.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282260487n4w4f5bb7oxnsdh/3pqjg1282260459.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282260487n4w4f5bb7oxnsdh/3pqjg1282260459.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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