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Partial Correlation

*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: Wed, 09 Dec 2009 03:12:59 -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/Dec/09/t1260353638qsh6inw849s54zs.htm/, Retrieved Wed, 09 Dec 2009 11:14:00 +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/Dec/09/t1260353638qsh6inw849s54zs.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 «

121.6 118.8 114.0 111.5 97.2 102.5 113.4 109.8 104.9 126.1 80.0 96.8 117.2 112.3 117.3 111.1 102.2 104.3 122.9 107.6 121.3 131.5 89.0 104.4 128.9 135.9 133.3 121.3 120.5 120.4 137.9 126.1 133.2 151.1 105.0 119.0 140.4 156.6 137.1 122.7 125.8 139.3 134.9 149.2 132.3 149.0 117.2 119.6 152.0 149.4 127.3 114.1 102.1 107.7 104.4 102.1 96.0 109.3 90.0 83.9

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.596547	-4.0897	8.4e-05
2	0.266575	1.8275	0.036985
3	-0.00403	-0.0276	0.489037
4	-0.064801	-0.4443	0.32945
5	0.079668	0.5462	0.293763
6	0.035751	0.2451	0.403725
7	-0.113756	-0.7799	0.219689
8	0.156442	1.0725	0.144482
9	-0.174541	-1.1966	0.118733
10	0.105707	0.7247	0.236118
11	0.055632	0.3814	0.352314
12	-0.11349	-0.778	0.220221
13	0.157714	1.0812	0.142555
14	-0.245964	-1.6862	0.049188
15	0.270298	1.8531	0.035078
16	-0.202591	-1.3889	0.085706
17	0.180302	1.2361	0.111284
18	-0.070749	-0.485	0.314954
19	0.006992	0.0479	0.480984
20	-0.115693	-0.7932	0.215838
21	0.189401	1.2985	0.100231
22	-0.269097	-1.8448	0.035684
23	0.322242	2.2092	0.016036
24	-0.282677	-1.9379	0.029326
25	0.090252	0.6187	0.269539
26	0.021904	0.1502	0.440637
27	-0.062682	-0.4297	0.33468
28	0.030104	0.2064	0.418691
29	-0.036055	-0.2472	0.402924
30	-0.020153	-0.1382	0.44535
31	-0.026258	-0.18	0.428957
32	0.010435	0.0715	0.471635
33	-0.024155	-0.1656	0.434592
34	0.065514	0.4491	0.327697
35	-0.134455	-0.9218	0.180676
36	0.081123	0.5562	0.290372
37	-0.087067	-0.5969	0.276719
38	0.071269	0.4886	0.313699
39	-0.094743	-0.6495	0.259581
40	0.065693	0.4504	0.327257
41	-0.059936	-0.4109	0.341506
42	0.04705	0.3226	0.374231
43	-0.024855	-0.1704	0.432715
44	0.031037	0.2128	0.416211
45	-0.018919	-0.1297	0.448679
46	0.002107	0.0144	0.494268
47	NA	NA	NA
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	-0.596547	-4.0897	8.4e-05
2	-0.138625	-0.9504	0.173393
3	0.149334	1.0238	0.155589
4	0.05107	0.3501	0.363907
5	0.029298	0.2009	0.420838
6	0.139248	0.9546	0.172324
7	-0.04088	-0.2803	0.390255
8	0.035006	0.24	0.405691
9	-0.090927	-0.6234	0.26803
10	-0.058486	-0.401	0.345132
11	0.14391	0.9866	0.164446
12	0.040111	0.275	0.392266
13	0.09384	0.6433	0.261567
14	-0.218245	-1.4962	0.070642
15	0.076252	0.5228	0.3018
16	-0.023239	-0.1593	0.437051
17	0.133199	0.9132	0.182909
18	0.093981	0.6443	0.261257
19	0.007279	0.0499	0.480205
20	-0.22429	-1.5377	0.065419
21	-0.03706	-0.2541	0.400273
22	-0.156683	-1.0742	0.144116
23	0.140375	0.9624	0.170396
24	0.052319	0.3587	0.36072
25	-0.054785	-0.3756	0.354457
26	-0.064822	-0.4444	0.329398
27	-0.014774	-0.1013	0.459878
28	-0.114886	-0.7876	0.217437
29	-0.090604	-0.6211	0.268752
30	0.007745	0.0531	0.478939
31	0.005146	0.0353	0.486004
32	-0.039143	-0.2684	0.394801
33	-0.038879	-0.2665	0.395495
34	-0.051895	-0.3558	0.361801
35	-0.016351	-0.1121	0.455611
36	-0.08865	-0.6078	0.273137
37	0.072081	0.4942	0.311748
38	-0.04197	-0.2877	0.387408
39	-0.03566	-0.2445	0.403965
40	-0.090882	-0.6231	0.26813
41	-0.012463	-0.0854	0.466135
42	0.051071	0.3501	0.363903
43	0.148973	1.0213	0.156169
44	-0.012093	-0.0829	0.467141
45	0.031708	0.2174	0.414428
46	-0.051623	-0.3539	0.362495
47	NA	NA	NA
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/Dec/09/t1260353638qsh6inw849s54zs/1nmf61260353577.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260353638qsh6inw849s54zs/1nmf61260353577.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260353638qsh6inw849s54zs/2qicx1260353577.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260353638qsh6inw849s54zs/2qicx1260353577.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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