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*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: Thu, 26 Nov 2009 04:02:29 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/26/t1259233404wnoiygemw0qgdid.htm/, Retrieved Thu, 26 Nov 2009 12:03:26 +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/2009/Nov/26/t1259233404wnoiygemw0qgdid.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

785.8 819.3 849.4 880.4 900.1 937.2 948.9 952.6 947.3 974.2 1000.8 1032.8 1050.7 1057.3 1075.4 1118.4 1179.8 1227 1257.8 1251.5 1236.3 1170.6 1213.1 1265.5 1300.8 1348.4 1371.9 1403.3 1451.8 1474.2 1438.2 1513.6 1562.2 1546.2 1527.5 1418.7 1448.5 1492.1 1395.4 1403.7 1316.6 1274.5 1264.4 1323.9 1332.1 1250.2 1096.7 1080.8 1039.2 792 746.6 688.8 715.8 672.9 629.5 681.2 755.4 760.6 765.9 836.8 904.9

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' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.182451	1.2641	0.106156
2	0.103207	0.715	0.239024
3	0.097444	0.6751	0.251422
4	-0.01643	-0.1138	0.454922
5	0.249572	1.7291	0.045111
6	0.112672	0.7806	0.219432
7	-0.146039	-1.0118	0.158357
8	0.095642	0.6626	0.255369
9	-0.080604	-0.5584	0.28957
10	-0.048993	-0.3394	0.367882
11	0.035825	0.2482	0.402518
12	-0.273742	-1.8965	0.031958
13	-0.077179	-0.5347	0.297658
14	0.045553	0.3156	0.376838
15	-0.048115	-0.3333	0.370162
16	-0.037904	-0.2626	0.39699
17	-0.189707	-1.3143	0.097491
18	-0.237971	-1.6487	0.052869
19	-0.01486	-0.1029	0.459216
20	-0.116356	-0.8061	0.212069
21	-0.065111	-0.4511	0.326975
22	-0.150085	-1.0398	0.151817
23	-0.146793	-1.017	0.157123
24	-0.092271	-0.6393	0.262842
25	0.012148	0.0842	0.466637
26	-0.005236	-0.0363	0.485605
27	0.092578	0.6414	0.262157
28	0.089485	0.62	0.269106
29	-0.018277	-0.1266	0.449882
30	-0.026187	-0.1814	0.428398
31	-0.04827	-0.3344	0.369758
32	0.012075	0.0837	0.466838
33	0.005788	0.0401	0.48409
34	0.043602	0.3021	0.381947
35	0.040692	0.2819	0.389607
36	0.037132	0.2573	0.399039
37	-0.02394	-0.1659	0.434482
38	-0.013435	-0.0931	0.463112
39	-0.030745	-0.213	0.416111
40	0.032398	0.2245	0.411675
41	0.040972	0.2839	0.388868
42	0.05025	0.3481	0.364629
43	0.028786	0.1994	0.421382
44	0.018244	0.1264	0.449971
45	-0.003545	-0.0246	0.490254
46	-0.007377	-0.0511	0.479725
47	-0.007346	-0.0509	0.479809
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.182451	1.2641	0.106156
2	0.072326	0.5011	0.309299
3	0.069442	0.4811	0.316312
4	-0.053662	-0.3718	0.355846
5	0.259705	1.7993	0.03913
6	0.027685	0.1918	0.424352
7	-0.222673	-1.5427	0.064733
8	0.127206	0.8813	0.19127
9	-0.081253	-0.5629	0.288048
10	-0.085419	-0.5918	0.27838
11	0.008956	0.0621	0.47539
12	-0.199607	-1.3829	0.086545
13	-0.018983	-0.1315	0.447958
14	0.109233	0.7568	0.226438
15	0.03044	0.2109	0.41693
16	-0.135454	-0.9385	0.176356
17	-0.076655	-0.5311	0.298906
18	-0.110735	-0.7672	0.223362
19	-0.059325	-0.411	0.341445
20	-0.056605	-0.3922	0.348335
21	-0.001286	-0.0089	0.496464
22	-0.156554	-1.0846	0.14175
23	0.012774	0.0885	0.464923
24	-0.102787	-0.7121	0.239917
25	0.036794	0.2549	0.399937
26	0.072252	0.5006	0.309479
27	0.125084	0.8666	0.195234
28	0.067568	0.4681	0.320908
29	-0.151629	-1.0505	0.149371
30	-0.131619	-0.9119	0.183194
31	-0.090022	-0.6237	0.267891
32	0.00245	0.017	0.493265
33	-0.091248	-0.6322	0.265132
34	0.018131	0.1256	0.450281
35	0.042299	0.2931	0.385371
36	-0.027864	-0.193	0.423868
37	-0.025153	-0.1743	0.431196
38	-0.009573	-0.0663	0.473698
39	-0.062657	-0.4341	0.333081
40	-0.021866	-0.1515	0.440113
41	-0.04448	-0.3082	0.379646
42	-0.094767	-0.6566	0.257297
43	-0.002715	-0.0188	0.492536
44	0.070359	0.4875	0.314075
45	0.022795	0.1579	0.437587
46	-0.053577	-0.3712	0.356064
47	-0.001999	-0.0139	0.494503
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259233404wnoiygemw0qgdid/1zucf1259233346.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259233404wnoiygemw0qgdid/1zucf1259233346.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259233404wnoiygemw0qgdid/2nu481259233346.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259233404wnoiygemw0qgdid/2nu481259233346.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; 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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