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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: Wed, 29 Dec 2010 20:01:15 +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/29/t1293652743f99lxcope2uce0t.htm/, Retrieved Wed, 29 Dec 2010 20:59:06 +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/29/t1293652743f99lxcope2uce0t.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 «

16198.90 16554.20 19554.20 15903.80 18003.80 18329.60 16260.70 14851.90 18174.10 18406.60 18466.50 16016.50 17428.50 17167.20 19630.00 17183.60 18344.70 19301.40 18147.50 16192.90 18374.40 20515.20 18957.20 16471.50 18746.80 19009.50 19211.20 20547.70 19325.80 20605.50 20056.90 16141.40 20359.80 19711.60 15638.60 14384.50 13721.40 14134.30 15021.70 14212.60 13635.00 15446.90 14762.10 12521.00 16236.80 16065.00 16032.10 15794.30 15160.00 15692.10 18908.90 17424.50 17014.20 19790.40 17681.20 16006.90 19601.70

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' @ www.wessa.org

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.84615	5.6761	0
2	0.790051	5.2998	2e-06
3	0.726753	4.8752	7e-06
4	0.523484	3.5116	0.000513
5	0.402536	2.7003	0.004864
6	0.238577	1.6004	0.058251
7	0.023368	0.1568	0.438068
8	-0.087652	-0.588	0.279741
9	-0.24011	-1.6107	0.057119
10	-0.36673	-2.4601	0.008898
11	-0.442218	-2.9665	0.002404
12	-0.500995	-3.3608	0.000796
13	-0.513656	-3.4457	0.000622
14	-0.492758	-3.3055	0.000934
15	-0.466606	-3.1301	0.001533
16	-0.434039	-2.9116	0.002788
17	-0.370522	-2.4855	0.008359
18	-0.302841	-2.0315	0.024067
19	-0.248033	-1.6639	0.051545
20	-0.174608	-1.1713	0.123821
21	-0.130029	-0.8723	0.193849
22	-0.0923	-0.6192	0.269463
23	-0.025673	-0.1722	0.432018
24	-0.030544	-0.2049	0.419288
25	-0.000171	-0.0011	0.499544
26	0.022959	0.154	0.439143
27	0.006715	0.045	0.482136
28	0.042137	0.2827	0.389365
29	0.056633	0.3799	0.3529
30	0.034874	0.2339	0.408046
31	0.067895	0.4555	0.325487
32	0.068468	0.4593	0.324115
33	0.062053	0.4163	0.339598
34	0.079833	0.5355	0.297458
35	0.085678	0.5747	0.284164
36	0.063185	0.4239	0.336844
37	0.065388	0.4386	0.331512
38	0.062615	0.42	0.33823
39	0.039618	0.2658	0.395818
40	0.03437	0.2306	0.409349
41	0.031607	0.212	0.416523
42	0.016411	0.1101	0.456415
43	0.017088	0.1146	0.454626
44	0.01104	0.0741	0.470646
45	NA	NA	NA
46	NA	NA	NA
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	0.84615	5.6761	0
2	0.260822	1.7496	0.043498
3	0.04502	0.302	0.382022
4	-0.546779	-3.6679	0.000322
5	-0.168405	-1.1297	0.132295
6	-0.190826	-1.2801	0.103535
7	-0.222761	-1.4943	0.071035
8	0.066227	0.4443	0.32949
9	0.027588	0.1851	0.427004
10	0.066769	0.4479	0.328188
11	-0.119499	-0.8016	0.213492
12	0.080983	0.5432	0.29482
13	0.074515	0.4999	0.309804
14	0.052785	0.3541	0.362462
15	-0.065774	-0.4412	0.330581
16	-0.264218	-1.7724	0.041547
17	-0.140762	-0.9443	0.175039
18	-0.069739	-0.4678	0.321085
19	0.008909	0.0598	0.476303
20	0.045857	0.3076	0.379897
21	-0.052665	-0.3533	0.36276
22	-0.084221	-0.565	0.28745
23	0.051904	0.3482	0.364662
24	-0.108962	-0.7309	0.234302
25	0.068721	0.461	0.323512
26	-0.043205	-0.2898	0.386641
27	-0.065536	-0.4396	0.331154
28	-0.030002	-0.2013	0.420701
29	0.05409	0.3628	0.359208
30	-0.040202	-0.2697	0.394318
31	-0.060076	-0.403	0.344427
32	-0.034284	-0.23	0.409572
33	-0.100382	-0.6734	0.252075
34	-0.075162	-0.5042	0.30829
35	0.078933	0.5295	0.299531
36	-0.103781	-0.6962	0.244947
37	-0.116682	-0.7827	0.218943
38	-0.011759	-0.0789	0.468739
39	0.067469	0.4526	0.326507
40	0.048459	0.3251	0.373317
41	0.053479	0.3587	0.360731
42	0.033135	0.2223	0.412553
43	-0.142286	-0.9545	0.172469
44	-0.114723	-0.7696	0.222784
45	NA	NA	NA
46	NA	NA	NA
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/2010/Dec/29/t1293652743f99lxcope2uce0t/1k2t81293652874.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293652743f99lxcope2uce0t/1k2t81293652874.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293652743f99lxcope2uce0t/2ctsc1293652874.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293652743f99lxcope2uce0t/2ctsc1293652874.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293652743f99lxcope2uce0t/3ctsc1293652874.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293652743f99lxcope2uce0t/3ctsc1293652874.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; 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 (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

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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