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stationarity in the mean

*The author of this computation has been verified*

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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Tue, 07 Dec 2010 13:34:00 +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/Dec/07/t1291728758bh8oyatkj5mgf7b.htm/, Retrieved Tue, 07 Dec 2010 14:32:46 +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/2010/Dec/07/t1291728758bh8oyatkj5mgf7b.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

31806 34571 37121 40438 43635 48064 50846 53668 58465 58618 55826 60412 62714 63332 66050 62948 59535 57298 56599 57686 57472 60463 60784 63154 64042 65460 65268 65774 66028 67104 68102 69897 72185 73538 72325 74820 74813 74533 76916 80371 81261 81557 81446 81995 79948

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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.379564	-2.489	0.00838
2	-0.171433	-1.1242	0.133591
3	0.234813	1.5398	0.065472
4	-0.129013	-0.846	0.201119
5	-0.169799	-1.1134	0.135851
6	0.140483	0.9212	0.18104
7	0.030391	0.1993	0.421489
8	0.016657	0.1092	0.456764
9	-0.100238	-0.6573	0.257244
10	0.121008	0.7935	0.215921
11	-0.075545	-0.4954	0.311427
12	0.032367	0.2122	0.416459
13	-0.081919	-0.5372	0.296956
14	0.082848	0.5433	0.294874
15	-0.107506	-0.705	0.242317
16	0.056169	0.3683	0.35722
17	-0.043345	-0.2842	0.388799
18	0.109926	0.7208	0.237456
19	-0.030445	-0.1996	0.421351
20	-0.023669	-0.1552	0.438691
21	0.087889	0.5763	0.2837
22	-0.042018	-0.2755	0.392114
23	-0.240475	-1.5769	0.061074
24	0.226567	1.4857	0.072327
25	-0.052499	-0.3443	0.366164
26	-0.129949	-0.8521	0.199431
27	0.177343	1.1629	0.125639
28	0.010148	0.0665	0.473626
29	-0.116052	-0.761	0.225403
30	0.025172	0.1651	0.434832
31	0.045527	0.2985	0.383363
32	0.037088	0.2432	0.404504
33	-0.094417	-0.6191	0.269547
34	0.036547	0.2397	0.405869
35	0.056052	0.3676	0.357503
36	-0.019784	-0.1297	0.448691
37	-0.018663	-0.1224	0.451583
38	0.020643	0.1354	0.446476
39	-0.01567	-0.1028	0.459316
40	0.003214	0.0211	0.491642
41	-0.009977	-0.0654	0.474071
42	0.001129	0.0074	0.497063
43	NA	NA	NA
44	NA	NA	NA
45	NA	NA	NA
46	NA	NA	NA
47	NA	NA	NA
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.379564	-2.489	0.00838
2	-0.368606	-2.4171	0.009979
3	0.007907	0.0518	0.479444
4	-0.090867	-0.5959	0.277197
5	-0.251082	-1.6465	0.05348
6	-0.151356	-0.9925	0.163251
7	-0.048116	-0.3155	0.376946
8	0.098298	0.6446	0.261311
9	-0.113279	-0.7428	0.230815
10	0.013224	0.0867	0.46565
11	-0.061774	-0.4051	0.343714
12	0.10173	0.6671	0.25414
13	-0.108911	-0.7142	0.239489
14	-0.001988	-0.013	0.49483
15	-0.161464	-1.0588	0.147804
16	-0.017305	-0.1135	0.45509
17	-0.141994	-0.9311	0.178495
18	0.042388	0.278	0.391188
19	0.011547	0.0757	0.469996
20	-0.009006	-0.0591	0.47659
21	0.123332	0.8087	0.211558
22	0.04056	0.266	0.395768
23	-0.195395	-1.2813	0.103479
24	-0.071067	-0.466	0.321777
25	-0.043622	-0.286	0.388108
26	-0.181921	-1.1929	0.119717
27	-0.040906	-0.2682	0.394899
28	-0.123535	-0.8101	0.21118
29	-0.018583	-0.1219	0.451791
30	-0.1486	-0.9744	0.167645
31	-0.011811	-0.0775	0.469312
32	0.049382	0.3238	0.373821
33	0.047418	0.3109	0.378673
34	-0.060863	-0.3991	0.345895
35	0.011101	0.0728	0.471155
36	0.063811	0.4184	0.338855
37	0.035437	0.2324	0.408675
38	-0.07803	-0.5117	0.305746
39	-0.116654	-0.765	0.224239
40	-0.004351	-0.0285	0.488684
41	0.013906	0.0912	0.463882
42	-0.003241	-0.0213	0.49157
43	NA	NA	NA
44	NA	NA	NA
45	NA	NA	NA
46	NA	NA	NA
47	NA	NA	NA
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291728758bh8oyatkj5mgf7b/19c4d1291728838.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291728758bh8oyatkj5mgf7b/19c4d1291728838.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291728758bh8oyatkj5mgf7b/29c4d1291728838.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291728758bh8oyatkj5mgf7b/29c4d1291728838.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 1 ; 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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