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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Wed, 05 May 2010 16:27:58 +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/May/05/t1273076967f039g7jg7wus2iv.htm/, Retrieved Wed, 05 May 2010 18:29:29 +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/May/05/t1273076967f039g7jg7wus2iv.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:

KDGP2W21

Dataseries X:

» Textbox « » Textfile « » CSV «

8027.7 8059.6 8059.5 7988.9 7950.2 8003.8 8037.5 8069 8157.6 8244.3 8329.4 8417 8432.5 8486.4 8531.1 8643.8 8727.9 8847.3 8904.3 9003.2 9025.3 9044.7 9120.7 9184.3 9247.2 9407.1 9488.9 9592.5 9666.2 9809.6 9932.7 10008.9 10103.4 10194.3 10328.8 10507.6 10601.2 10684 10819.9 11014.3 11043 11258.5 11267.9 11334.5 11297.2 11371.3 11340.1 11380.1 11477.9 11538.8 11596.4 11598.8 11645.8 11738.7 11935.5 12042.8 12127.6 12213.8 12303.5 12410.3 12534.1 12587.5 12683.2 12748.7 12915.9 12962.5 12965.9 13060.7 13099.9 13204 13321.1 13391.2 13366.9 13415.3 13324.6 13141.9 12925.4 12901.5 12973 13155

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	4 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.467303	4.1535	4.1e-05
2	0.345271	3.0688	0.001472
3	0.047389	0.4212	0.337376
4	0.070365	0.6254	0.266751
5	-0.045368	-0.4032	0.34393
6	0.045359	0.4032	0.343961
7	-0.029667	-0.2637	0.396355
8	-0.012729	-0.1131	0.455105
9	0.080976	0.7197	0.236907
10	0.046593	0.4141	0.339952
11	-0.072319	-0.6428	0.261113
12	-0.141771	-1.2601	0.105674
13	-0.095138	-0.8456	0.200164
14	-0.05066	-0.4503	0.326871
15	-0.014235	-0.1265	0.449821
16	-0.022847	-0.2031	0.419803
17	-0.073743	-0.6554	0.257043
18	-0.09362	-0.8321	0.203928
19	0.027895	0.2479	0.402414
20	-0.053559	-0.476	0.31768
21	-0.098334	-0.874	0.19238
22	-0.089094	-0.7919	0.215401
23	0.016319	0.145	0.442523
24	0.100835	0.8962	0.186424
25	0.108472	0.9641	0.168963
26	0.056329	0.5007	0.309
27	-0.097228	-0.8642	0.195052
28	0.050185	0.4461	0.328388
29	0.085722	0.7619	0.22419
30	0.151106	1.3431	0.091549
31	0.029208	0.2596	0.397922
32	0.050055	0.4449	0.328804
33	-0.09409	-0.8363	0.202757
34	-0.097489	-0.8665	0.19442
35	-0.17798	-1.5819	0.058831
36	-0.18856	-1.676	0.04885
37	-0.18368	-1.6326	0.053268
38	-0.091802	-0.816	0.208491
39	-0.060987	-0.5421	0.294649
40	-0.046507	-0.4134	0.340231
41	-0.090965	-0.8085	0.210611
42	-0.073367	-0.6521	0.258113
43	-0.017899	-0.1591	0.437003
44	0.005998	0.0533	0.47881
45	-0.012153	-0.108	0.457129
46	-0.084575	-0.7517	0.227227
47	-0.082265	-0.7312	0.233414
48	-0.036233	-0.322	0.374134

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.467303	4.1535	4.1e-05
2	0.162353	1.443	0.076484
3	-0.215013	-1.9111	0.029811
4	0.09027	0.8023	0.212382
5	-0.058365	-0.5188	0.30269
6	0.069128	0.6144	0.27035
7	-0.044302	-0.3938	0.347408
8	-0.04324	-0.3843	0.350886
9	0.193411	1.7191	0.044758
10	-0.084032	-0.7469	0.228672
11	-0.187485	-1.6664	0.049797
12	-0.035512	-0.3156	0.376554
13	0.070227	0.6242	0.26715
14	0.042175	0.3749	0.354384
15	-0.062696	-0.5573	0.289464
16	-0.030224	-0.2686	0.394454
17	-0.030772	-0.2735	0.39259
18	-0.062683	-0.5571	0.289503
19	0.135875	1.2077	0.115387
20	-0.11723	-1.042	0.150303
21	-0.095919	-0.8525	0.198244
22	0.077545	0.6892	0.246348
23	0.063107	0.5609	0.288223
24	0.109723	0.9752	0.16621
25	-0.078485	-0.6976	0.243742
26	-0.023775	-0.2113	0.416591
27	-0.097065	-0.8627	0.195447
28	0.165014	1.4667	0.073217
29	0.099875	0.8877	0.188696
30	0.006657	0.0592	0.476484
31	-0.072013	-0.6401	0.261991
32	-0.041939	-0.3728	0.355161
33	-0.147449	-1.3106	0.096902
34	-0.074653	-0.6635	0.25446
35	-0.041809	-0.3716	0.355591
36	0.01218	0.1083	0.457031
37	-0.006247	-0.0555	0.477931
38	-0.125118	-1.1121	0.13474
39	-0.043285	-0.3847	0.350736
40	0.063819	0.5672	0.28608
41	-0.027746	-0.2466	0.402923
42	0.000773	0.0069	0.497267
43	0.069664	0.6192	0.268787
44	-0.022209	-0.1974	0.422012
45	-0.056379	-0.5011	0.308846
46	-0.050838	-0.4519	0.326303
47	-0.053293	-0.4737	0.318517
48	0.011366	0.101	0.459894

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/05/t1273076967f039g7jg7wus2iv/1xyre1273076874.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/05/t1273076967f039g7jg7wus2iv/1xyre1273076874.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/05/t1273076967f039g7jg7wus2iv/2xyre1273076874.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/05/t1273076967f039g7jg7wus2iv/2xyre1273076874.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

R code (references can be found in the software module):

if (par1 == 'Default') {

par1 = 10*log10(length(x))

} else {

par1 <- as.numeric(par1)

}

par2 <- as.numeric(par2)

par3 <- as.numeric(par3)

par4 <- as.numeric(par4)

par5 <- as.numeric(par5)

if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'

par7 <- as.numeric(par7)

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')

dev.off()

(myacf <- c(racf$acf))

(mypacf <- c(rpacf$acf))

lengthx <- length(x)

sqrtn <- sqrt(lengthx)

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Autocorrelation Function',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Time lag k',header=TRUE)

a<-table.element(a,hyperlink('http://www.xycoon.com/basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)

a<-table.element(a,'T-STAT',header=TRUE)

a<-table.element(a,'P-value',header=TRUE)

a<-table.row.end(a)

for (i in 2:(par1+1)) {

a<-table.row.start(a)

a<-table.element(a,i-1,header=TRUE)

a<-table.element(a,round(myacf[i],6))

mytstat <- myacf[i]*sqrtn

a<-table.element(a,round(mytstat,4))

a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))

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,'Partial Autocorrelation Function',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Time lag k',header=TRUE)

a<-table.element(a,hyperlink('http://www.xycoon.com/basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)

a<-table.element(a,'T-STAT',header=TRUE)

a<-table.element(a,'P-value',header=TRUE)

a<-table.row.end(a)

for (i in 1:par1) {

a<-table.row.start(a)

a<-table.element(a,i,header=TRUE)

a<-table.element(a,round(mypacf[i],6))

mytstat <- mypacf[i]*sqrtn

a<-table.element(a,round(mytstat,4))

a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable1.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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