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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: Sun, 26 Dec 2010 11:47:47 +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/26/t12933639508e8dzsoc7ec3o0q.htm/, Retrieved Sun, 26 Dec 2010 12:45:51 +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/26/t12933639508e8dzsoc7ec3o0q.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 «

16896.2 16698 19691.6 15930.7 17444.6 17699.4 15189.8 15672.7 17180.8 17664.9 17862.9 16162.3 17463.6 16772.1 19106.9 16721.3 18161.3 18509.9 17802.7 16409.9 17967.7 20286.6 19537.3 18021.9 20194.3 19049.6 20244.7 21473.3 19673.6 21053.2 20159.5 18203.6 21289.5 20432.3 17180.4 15816.8 15076.6 14531.6 15761.3 14345.5 13916.8 15496.8 14285.6 13597.3 16263.1 16773.3 15986.9 16842.6 16014.6 15878.6 18664.9 17690.5 17107.6 19165.7 17203.6 16579 18885.1

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.356656	-2.669	0.004968
2	-0.207845	-1.5554	0.062746
3	0.308493	2.3085	0.012342
4	-0.144663	-1.0826	0.141822
5	-0.043731	-0.3273	0.372349
6	0.256487	1.9194	0.030019
7	-0.201225	-1.5058	0.068865
8	0.073588	0.5507	0.29202
9	0.063598	0.4759	0.317991
10	-0.232247	-1.738	0.043856
11	-0.15396	-1.1521	0.127081
12	0.46202	3.4574	0.000524
13	-0.21688	-1.623	0.055105
14	-0.144463	-1.0811	0.142152
15	0.083517	0.625	0.267259
16	-0.059798	-0.4475	0.328124
17	-0.018946	-0.1418	0.443881
18	0.062434	0.4672	0.32108
19	-0.075827	-0.5674	0.286342
20	0.119909	0.8973	0.186695
21	-0.065066	-0.4869	0.314112
22	-0.128275	-0.9599	0.170611
23	-0.020927	-0.1566	0.438059
24	0.204876	1.5332	0.065435
25	-0.032081	-0.2401	0.405575
26	-0.142709	-1.0679	0.145066
27	0.037148	0.278	0.391022
28	0.03391	0.2538	0.400305
29	-0.024027	-0.1798	0.428978
30	0.067152	0.5025	0.308635
31	0.005204	0.0389	0.484537
32	0.001738	0.013	0.494834
33	0.016397	0.1227	0.451389
34	-0.049908	-0.3735	0.355102
35	-0.085124	-0.637	0.263356
36	0.186009	1.392	0.084719
37	0.004052	0.0303	0.48796
38	-0.153795	-1.1509	0.127333
39	0.07936	0.5939	0.277494
40	0.026519	0.1985	0.421705
41	-0.100204	-0.7499	0.228239
42	0.069886	0.523	0.301527
43	0.041334	0.3093	0.379115
44	-0.07217	-0.5401	0.295645
45	0.044206	0.3308	0.371013
46	0.009149	0.0685	0.47283
47	-0.123561	-0.9246	0.179559
48	0.132308	0.9901	0.163191
49	0.026669	0.1996	0.421268
50	-0.122058	-0.9134	0.182475
51	0.088999	0.666	0.25407
52	-0.00349	-0.0261	0.489628
53	-0.067966	-0.5086	0.306511
54	0.046209	0.3458	0.365395
55	-0.003569	-0.0267	0.489394
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	-0.356656	-2.669	0.004968
2	-0.383879	-2.8727	0.002869
3	0.092712	0.6938	0.24534
4	-0.055016	-0.4117	0.341064
5	-0.00651	-0.0487	0.480659
6	0.204815	1.5327	0.065491
7	-0.009253	-0.0692	0.472522
8	0.125512	0.9392	0.17582
9	0.004064	0.0304	0.487924
10	-0.17344	-1.2979	0.09982
11	-0.489885	-3.666	0.000275
12	0.161769	1.2106	0.115573
13	0.062675	0.469	0.320439
14	0.025971	0.1944	0.423302
15	-0.2075	-1.5528	0.063054
16	-0.030218	-0.2261	0.410962
17	0.035414	0.265	0.395985
18	-0.102466	-0.7668	0.223215
19	-0.012398	-0.0928	0.463205
20	0.009639	0.0721	0.471377
21	-0.034191	-0.2559	0.399498
22	-0.117445	-0.8789	0.191612
23	-0.06061	-0.4536	0.325947
24	-0.07046	-0.5273	0.300043
25	0.005288	0.0396	0.484289
26	-0.134287	-1.0049	0.15963
27	-0.042132	-0.3153	0.376857
28	-0.063886	-0.4781	0.317227
29	0.020194	0.1511	0.440213
30	0.111847	0.837	0.20308
31	0.099487	0.7445	0.229845
32	-0.109082	-0.8163	0.208895
33	-0.079443	-0.5945	0.277286
34	0.04233	0.3168	0.376297
35	-0.130432	-0.9761	0.166615
36	-0.114448	-0.8565	0.197699
37	-0.126987	-0.9503	0.173025
38	0.012386	0.0927	0.46324
39	0.007274	0.0544	0.478391
40	0.093285	0.6981	0.244007
41	-0.018119	-0.1356	0.446315
42	-0.091338	-0.6835	0.248552
43	0.004842	0.0362	0.485612
44	-0.022299	-0.1669	0.434036
45	-0.033925	-0.2539	0.400263
46	-0.005511	-0.0412	0.483625
47	0.002208	0.0165	0.493438
48	-0.073901	-0.553	0.291223
49	-0.09393	-0.7029	0.242513
50	-0.047117	-0.3526	0.36286
51	0.050693	0.3794	0.352931
52	-0.022128	-0.1656	0.434539
53	0.010492	0.0785	0.468848
54	-0.040259	-0.3013	0.382161
55	-0.031491	-0.2357	0.407278
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/26/t12933639508e8dzsoc7ec3o0q/1alpl1293364063.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t12933639508e8dzsoc7ec3o0q/1alpl1293364063.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t12933639508e8dzsoc7ec3o0q/2lco61293364063.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t12933639508e8dzsoc7ec3o0q/2lco61293364063.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t12933639508e8dzsoc7ec3o0q/3lco61293364063.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t12933639508e8dzsoc7ec3o0q/3lco61293364063.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; 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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