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Paper

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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: Wed, 29 Dec 2010 15:48:19 +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/t1293637592o4ntavat4smui1r.htm/, Retrieved Wed, 29 Dec 2010 16:46:32 +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/t1293637592o4ntavat4smui1r.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 «

235243 230354 227184 221678 217142 219452 256446 265845 248624 241114 229245 231805 219277 219313 212610 214771 211142 211457 240048 240636 230580 208795 197922 194596 194581 185686 178106 172608 167302 168053 202300 202388 182516 173476 166444 171297 169701 164182 161914 159612 151001 158114 186530 187069 174330 169362 166827 178037 186413 189226 191563 188906 186005 195309 223532 226899 214126 206903 204442 220375 214320 212588 205816 202196 195722 198563 229139 229527 211868 203555 195770

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.882365	7.4349	0
2	0.720361	6.0699	0
3	0.623894	5.257	1e-06
4	0.599759	5.0537	2e-06
5	0.603858	5.0882	1e-06
6	0.580181	4.8887	3e-06
7	0.510958	4.3054	2.6e-05
8	0.408719	3.4439	0.000483
9	0.340676	2.8706	0.002698
10	0.327366	2.7584	0.00369
11	0.378203	3.1868	0.00107
12	0.379415	3.197	0.001037
13	0.241104	2.0316	0.02297
14	0.069258	0.5836	0.280678
15	-0.034361	-0.2895	0.38651
16	-0.078234	-0.6592	0.255946
17	-0.092147	-0.7764	0.220032
18	-0.131146	-1.1051	0.136434
19	-0.212034	-1.7866	0.039133
20	-0.303359	-2.5562	0.006362
21	-0.363251	-3.0608	0.001558
22	-0.355993	-2.9996	0.001863
23	-0.292497	-2.4646	0.008069
24	-0.262421	-2.2112	0.015122
25	-0.353188	-2.976	0.001995
26	-0.451397	-3.8035	0.00015
27	-0.484167	-4.0797	5.8e-05
28	-0.464335	-3.9126	0.000103
29	-0.42383	-3.5713	0.000321
30	-0.404106	-3.4051	0.000546
31	-0.418912	-3.5298	0.000367
32	-0.440879	-3.7149	0.000201
33	-0.431894	-3.6392	0.000258
34	-0.377632	-3.182	0.001085
35	-0.282249	-2.3783	0.010044
36	-0.222944	-1.8786	0.032205
37	-0.249397	-2.1015	0.019576
38	-0.279163	-2.3523	0.010718
39	-0.263085	-2.2168	0.014921
40	-0.215864	-1.8189	0.036571
41	-0.148134	-1.2482	0.10803
42	-0.106779	-0.8997	0.185651
43	-0.095097	-0.8013	0.212816
44	-0.091762	-0.7732	0.220986
45	-0.068068	-0.5735	0.284043
46	-0.011348	-0.0956	0.462047
47	0.063118	0.5318	0.298247
48	0.107046	0.902	0.185057

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.882365	7.4349	0
2	-0.262859	-2.2149	0.014989
3	0.257753	2.1719	0.016604
4	0.161619	1.3618	0.088779
5	0.090467	0.7623	0.224206
6	-0.048401	-0.4078	0.342313
7	-0.089355	-0.7529	0.226994
8	-0.143375	-1.2081	0.115509
9	0.080289	0.6765	0.250452
10	0.047702	0.4019	0.344466
11	0.261518	2.2036	0.015399
12	-0.250191	-2.1081	0.019275
13	-0.4659	-3.9257	9.9e-05
14	-0.07514	-0.6331	0.264338
15	0.020036	0.1688	0.433207
16	-0.165762	-1.3967	0.083422
17	0.032285	0.272	0.393192
18	-0.13004	-1.0957	0.138449
19	-0.017417	-0.1468	0.441868
20	0.012916	0.1088	0.456822
21	-0.035307	-0.2975	0.383475
22	0.069495	0.5856	0.280009
23	0.073131	0.6162	0.269862
24	0.009642	0.0812	0.467738
25	-0.170334	-1.4353	0.077802
26	0.120295	1.0136	0.157101
27	0.002691	0.0227	0.490986
28	-0.041212	-0.3473	0.364712
29	-0.010906	-0.0919	0.46352
30	0.038912	0.3279	0.371984
31	-0.015845	-0.1335	0.447083
32	0.055151	0.4647	0.32178
33	-0.035743	-0.3012	0.382081
34	-0.046113	-0.3886	0.349386
35	-0.053059	-0.4471	0.328088
36	0.021706	0.1829	0.4277
37	-0.009641	-0.0812	0.467742
38	0.025459	0.2145	0.415379
39	-0.106917	-0.9009	0.185344
40	-0.029742	-0.2506	0.401421
41	0.063687	0.5366	0.296599
42	-0.054867	-0.4623	0.322635
43	0.044657	0.3763	0.353912
44	-0.026451	-0.2229	0.412136
45	0.002861	0.0241	0.490418
46	8.2e-05	7e-04	0.499727
47	-0.068944	-0.5809	0.281563
48	0.031994	0.2696	0.39413

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637592o4ntavat4smui1r/1ztbz1293637696.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637592o4ntavat4smui1r/1ztbz1293637696.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637592o4ntavat4smui1r/292sk1293637696.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637592o4ntavat4smui1r/292sk1293637696.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637592o4ntavat4smui1r/392sk1293637696.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293637592o4ntavat4smui1r/392sk1293637696.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 0 ; 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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