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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Thu, 16 Dec 2010 17:59:52 +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/16/t12925222728jxq3v1or8lpn9p.htm/, Retrieved Thu, 16 Dec 2010 18:57:55 +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/16/t12925222728jxq3v1or8lpn9p.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 «

655362 873127 1107897 1555964 1671159 1493308 2957796 2638691 1305669 1280496 921900 867888 652586 913831 1108544 1555827 1699283 1509458 3268975 2425016 1312703 1365498 934453 775019 651142 843192 1146766 1652601 1465906 1652734 2922334 2702805 1458956 1410363 1019279 936574 708917 885295 1099663 1576220 1487870 1488635 2882530 2677026 1404398 1344370 936865 872705 628151 953712 1160384 1400618 1661511 1495347 2918786 2775677 1407026 1370199 964526 850851 683118 847224 1073256 1514326 1503734 1507712 2865698 2788128 1391596 1366378 946295 859626

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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.011205	-0.0776	0.469222
2	0.176534	1.2231	0.113638
3	0.248128	1.7191	0.046022
4	-0.05295	-0.3669	0.357671
5	0.117348	0.813	0.210114
6	-0.124443	-0.8622	0.196442
7	-0.192801	-1.3358	0.093963
8	-0.02975	-0.2061	0.418788
9	-0.207338	-1.4365	0.078676
10	-0.211551	-1.4657	0.07463
11	-0.174225	-1.2071	0.116661
12	-0.487314	-3.3762	0.000732
13	-0.031793	-0.2203	0.413299
14	-0.06605	-0.4576	0.324649
15	-0.048555	-0.3364	0.369019
16	-0.003329	-0.0231	0.490846
17	0.041029	0.2843	0.388719
18	0.259956	1.801	0.038991
19	0.010906	0.0756	0.470043
20	0.102044	0.707	0.241498
21	0.1408	0.9755	0.167104
22	-0.00836	-0.0579	0.477027
23	0.285402	1.9773	0.026882
24	-0.044415	-0.3077	0.379816
25	0.029817	0.2066	0.418606
26	0.034994	0.2424	0.404734
27	-0.08759	-0.6068	0.273409
28	0.043515	0.3015	0.382176
29	-0.029072	-0.2014	0.420611
30	-0.185874	-1.2878	0.102
31	0.072704	0.5037	0.308385
32	-0.025888	-0.1794	0.429207
33	-0.095169	-0.6594	0.256411
34	0.083394	0.5778	0.28306
35	-0.14093	-0.9764	0.166883
36	0.095185	0.6595	0.256376
37	0.01456	0.1009	0.460034
38	-0.048312	-0.3347	0.369648
39	0.035334	0.2448	0.403826
40	0.014979	0.1038	0.458889
41	-0.009657	-0.0669	0.473466
42	0.015373	0.1065	0.457812
43	-0.011564	-0.0801	0.468239
44	0.003827	0.0265	0.489478
45	0.008552	0.0592	0.4765
46	-0.006583	-0.0456	0.481907
47	0.000336	0.0023	0.499077
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.011205	-0.0776	0.469222
2	0.176431	1.2223	0.113772
3	0.259854	1.8003	0.039048
4	-0.075213	-0.5211	0.30235
5	0.024239	0.1679	0.433672
6	-0.17771	-1.2312	0.112122
7	-0.225523	-1.5625	0.062373
8	-0.045526	-0.3154	0.376907
9	-0.069272	-0.4799	0.316728
10	-0.148366	-1.0279	0.154573
11	-0.145255	-1.0064	0.159645
12	-0.474895	-3.2902	0.00094
13	-0.116389	-0.8064	0.212004
14	0.092658	0.642	0.261979
15	0.231488	1.6038	0.05766
16	-0.079663	-0.5519	0.291781
17	-0.115617	-0.801	0.213535
18	0.047058	0.326	0.372911
19	-0.169492	-1.1743	0.12304
20	-0.058713	-0.4068	0.34299
21	-0.016671	-0.1155	0.454264
22	-0.256665	-1.7782	0.04085
23	0.033565	0.2325	0.408551
24	-0.287442	-1.9915	0.026069
25	-0.023915	-0.1657	0.434549
26	-0.041654	-0.2886	0.387071
27	0.054441	0.3772	0.353851
28	-0.015162	-0.105	0.458388
29	0.086315	0.598	0.276324
30	-0.020063	-0.139	0.445016
31	-0.11073	-0.7672	0.223372
32	-0.07592	-0.526	0.300658
33	-0.08714	-0.6037	0.274435
34	-0.056529	-0.3916	0.348527
35	0.01064	0.0737	0.47077
36	-0.131981	-0.9144	0.182541
37	-0.030525	-0.2115	0.416704
38	-0.113786	-0.7883	0.217189
39	0.001773	0.0123	0.495126
40	0.123426	0.8551	0.198367
41	0.038567	0.2672	0.395231
42	-0.032132	-0.2226	0.412389
43	-0.102387	-0.7094	0.240768
44	-0.012613	-0.0874	0.465364
45	-0.000217	-0.0015	0.499404
46	-0.075382	-0.5223	0.301945
47	0.004064	0.0282	0.488827
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925222728jxq3v1or8lpn9p/1t3ak1292522389.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925222728jxq3v1or8lpn9p/1t3ak1292522389.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925222728jxq3v1or8lpn9p/24c9n1292522389.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925222728jxq3v1or8lpn9p/24c9n1292522389.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925222728jxq3v1or8lpn9p/34c9n1292522389.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t12925222728jxq3v1or8lpn9p/34c9n1292522389.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 0.0 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 0.0 ; par3 = 0 ; par4 = 2 ; 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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