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Partial Autocorrelation

*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, 24 Dec 2008 06:11:56 -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/24/t1230124388850rb7124gph7xv.htm/, Retrieved Wed, 24 Dec 2008 14:13:10 +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/24/t1230124388850rb7124gph7xv.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 «

97.5 97.1 97.5 98.5 100.5 102.8 105.2 107.4 108.0 107.6 107.0 105.8 104.3 103.8 104.4 106.2 108.5 109.8 110.3 109.7 108.7 108.9 109.7 110.4 111.4 112.6 113.6 113.8 113.2 113.6 113.9 113.4 113.8 116.0 118.3 120.5 121.9 121.2 120.2 120.6 110.2 109.2 108.7 109.9 112.2 114.5 114.7 113.2 112.1 112.6 113.6 114.0 114.5 115.0 114.9 114.8 114.3 113.7 114.5 116.0 116.6 116.2 115.7 115.6 115.2 115.0 115.7 115.9 115.6 115.9 117.0 117.9 118.8 119.9

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.327604	2.799	0.003276
2	0.143526	1.2263	0.112016
3	-0.101203	-0.8647	0.195025
4	-0.327629	-2.7993	0.003274
5	-0.366684	-3.133	0.001246
6	-0.208404	-1.7806	0.039569
7	-0.047452	-0.4054	0.343173
8	0.110695	0.9458	0.17369
9	0.167985	1.4353	0.077741
10	0.126819	1.0835	0.141067
11	0.070983	0.6065	0.273039
12	0.000306	0.0026	0.498961
13	-0.093286	-0.797	0.214007
14	-0.090291	-0.7714	0.221465
15	-0.07684	-0.6565	0.256777
16	-0.005384	-0.046	0.481716
17	0.065881	0.5629	0.287618
18	0.027411	0.2342	0.407742
19	0.041711	0.3564	0.361293
20	0.117138	1.0008	0.160109
21	0.063303	0.5409	0.295125
22	-0.046904	-0.4007	0.344888
23	-0.122427	-1.046	0.149503
24	-0.156495	-1.3371	0.092672
25	-0.102148	-0.8728	0.192829
26	-0.009731	-0.0831	0.466983
27	0.145089	1.2396	0.109539
28	0.254763	2.1767	0.016369
29	0.192914	1.6483	0.051799
30	0.051922	0.4436	0.329315
31	-0.037648	-0.3217	0.374312
32	-0.141593	-1.2098	0.115135
33	-0.226294	-1.9335	0.028529
34	-0.161029	-1.3758	0.08654
35	-0.121831	-1.0409	0.150672
36	-0.05428	-0.4638	0.322095
37	0.03063	0.2617	0.397143
38	0.043561	0.3722	0.355418
39	0.05777	0.4936	0.311541
40	-0.004048	-0.0346	0.486251
41	-0.023799	-0.2033	0.419718
42	-0.023042	-0.1969	0.422239
43	-0.003527	-0.0301	0.48802
44	0.014594	0.1247	0.450554
45	0.021764	0.186	0.426499
46	0.009208	0.0787	0.468755
47	-0.008181	-0.0699	0.472234
48	-0.014414	-0.1232	0.451163

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.327604	2.799	0.003276
2	0.040554	0.3465	0.364984
3	-0.179084	-1.5301	0.065158
4	-0.290178	-2.4793	0.007737
5	-0.200424	-1.7124	0.045532
6	-0.002844	-0.0243	0.49034
7	0.028427	0.2429	0.404388
8	0.025157	0.2149	0.415205
9	-0.029849	-0.255	0.399709
10	-0.059635	-0.5095	0.305962
11	-0.004196	-0.0359	0.48575
12	0.023026	0.1967	0.422292
13	-0.038162	-0.3261	0.372658
14	-0.01467	-0.1253	0.4503
15	-0.024078	-0.2057	0.418789
16	0.030775	0.2629	0.396669
17	0.050501	0.4315	0.333696
18	-0.064482	-0.5509	0.291682
19	-0.014871	-0.1271	0.449622
20	0.13763	1.1759	0.121725
21	0.067573	0.5773	0.282743
22	-0.093485	-0.7987	0.213518
23	-0.141019	-1.2049	0.116073
24	-0.061192	-0.5228	0.301339
25	0.066452	0.5678	0.285967
26	0.072686	0.621	0.268257
27	0.097395	0.8321	0.204021
28	0.09265	0.7916	0.215579
29	-0.01154	-0.0986	0.460863
30	-0.056709	-0.4845	0.314734
31	0.033653	0.2875	0.387262
32	0.038551	0.3294	0.371407
33	-0.063491	-0.5425	0.294576
34	-0.035322	-0.3018	0.381834
35	-0.08442	-0.7213	0.236519
36	-0.113492	-0.9697	0.167705
37	-0.089832	-0.7675	0.222622
38	-0.060197	-0.5143	0.304291
39	0.005389	0.046	0.481702
40	-0.096982	-0.8286	0.205013
41	-0.097227	-0.8307	0.204423
42	-0.042363	-0.3619	0.359218
43	0.016525	0.1412	0.444053
44	0.017646	0.1508	0.440289
45	-0.019133	-0.1635	0.435299
46	-0.029102	-0.2486	0.402167
47	-0.045916	-0.3923	0.347987
48	-0.072431	-0.6189	0.26897

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230124388850rb7124gph7xv/1mjo31230124315.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230124388850rb7124gph7xv/1mjo31230124315.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230124388850rb7124gph7xv/240231230124315.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/24/t1230124388850rb7124gph7xv/240231230124315.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; 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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