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(Partial) Autocorrelation Function

*Unverified author*

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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Sun, 21 Dec 2008 09:20:20 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/21/t12298764663s1rhlo2t9onzzc.htm/, Retrieved Sun, 21 Dec 2008 17:21:08 +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/2008/Dec/21/t12298764663s1rhlo2t9onzzc.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

67.8 66.9 71.5 75.9 71.9 70.7 73.5 76.1 82.5 87.1 83.2 86.1 85.9 77.4 74.4 69.9 73.8 69.2 69.7 71 71.2 75.8 73 66.4 58.6 55.5 52.6 54.9 54.6 51.2 50.9 49.6 53.4 52 47.5 42.1 44.5 43.2 51.4 59.4 60.3 61.4 68.8 73.6 81.8 79.6 85.8 88.1 89.1 95 96.2 84.2 96.9 103.1 99.3 103.5 112.4 111.1 113.7 92 93 98.4 92.6 94.6 99.5 97.6 91.3 93.6 93.1 78.4 70.2 69.3 71.1 73.5 85.9 91.5 91.8 88.3 91.3 94 99.3 96.7 88 96.7 106.8 114.3 105.7 90.1 91.6 97.7 100.8 104.6 95.9 102.7 104 107.9 113.8 113.8 123.1 125.1 137.6 134 140.3 152.1 150.6 167.3 153.2 142 154.4 158.5 180.9 181.3 172.4 192 199.3 215.4 214.3 201.5 190.5 196 215.7 209.4 214.1 237.8 239 237.8 251.5 248.8 215.4 201.2 203.1 214.2 188.9 203 213.3 228.5 228.2 240.9 258.8 248.5 269.2 289.6 323.4 317.2 322.8 340.9 368.2 388.5 441.2 474.3 483.9 417.9 365.9 263 199.4

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.984478	12.2567	0
2	0.960731	11.961	0
3	0.933499	11.622	0
4	0.905049	11.2678	0
5	0.874918	10.8926	0
6	0.844231	10.5106	0
7	0.814837	10.1446	0
8	0.787923	9.8096	0
9	0.763248	9.5024	0
10	0.740828	9.2232	0
11	0.715762	8.9112	0
12	0.688516	8.5719	0
13	0.661741	8.2386	0
14	0.638161	7.945	0
15	0.615999	7.6691	0
16	0.595294	7.4114	0
17	0.576818	7.1813	0
18	0.559202	6.962	0
19	0.543309	6.7641	0
20	0.528657	6.5817	0
21	0.514891	6.4103	0
22	0.503458	6.268	0
23	0.49066	6.1087	0
24	0.476849	5.9367	0
25	0.462054	5.7525	0
26	0.443876	5.5262	0
27	0.424605	5.2863	0
28	0.40586	5.0529	1e-06
29	0.387282	4.8216	2e-06
30	0.369902	4.6052	4e-06
31	0.352364	4.3869	1.1e-05
32	0.335006	4.1708	2.5e-05
33	0.320327	3.988	5.1e-05
34	0.305842	3.8077	0.000101
35	0.290543	3.6172	0.000201
36	0.2716	3.3814	0.000456

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.984478	12.2567	0
2	-0.274865	-3.422	0.000397
3	-0.05949	-0.7406	0.230016
4	-0.013909	-0.1732	0.431374
5	-0.05851	-0.7284	0.233719
6	-0.008858	-0.1103	0.456165
7	0.038961	0.4851	0.31416
8	0.047668	0.5935	0.276867
9	0.021469	0.2673	0.394801
10	0.026812	0.3338	0.369488
11	-0.149691	-1.8636	0.032132
12	-0.054142	-0.6741	0.250638
13	0.041396	0.5154	0.303512
14	0.091458	1.1386	0.128304
15	-0.002324	-0.0289	0.488479
16	0.027896	0.3473	0.364418
17	0.03757	0.4677	0.320313
18	-0.049303	-0.6138	0.270119
19	0.019124	0.2381	0.406063
20	-0.00421	-0.0524	0.479131
21	0.017795	0.2215	0.412481
22	0.093363	1.1624	0.123437
23	-0.084841	-1.0563	0.146247
24	-0.051507	-0.6413	0.261153
25	-0.031657	-0.3941	0.347013
26	-0.119158	-1.4835	0.069985
27	0.011172	0.1391	0.444779
28	0.05862	0.7298	0.233305
29	-0.001012	-0.0126	0.494981
30	0.041749	0.5198	0.301984
31	-0.045132	-0.5619	0.2875
32	-0.057408	-0.7147	0.237929
33	0.07681	0.9563	0.170211
34	-0.037805	-0.4707	0.319269
35	-0.025584	-0.3185	0.37526
36	-0.100674	-1.2534	0.105978

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t12298764663s1rhlo2t9onzzc/1px6s1229876419.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t12298764663s1rhlo2t9onzzc/1px6s1229876419.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t12298764663s1rhlo2t9onzzc/2iayz1229876419.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t12298764663s1rhlo2t9onzzc/2iayz1229876419.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = -0.1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 36 ; par2 = -0.1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')

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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