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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: Tue, 01 Dec 2009 10:46:53 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/01/t1259689660xx9clo2z1sfzo3q.htm/, Retrieved Tue, 01 Dec 2009 18:47:42 +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/2009/Dec/01/t1259689660xx9clo2z1sfzo3q.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

116222 110924 103753 99983 93302 91496 119321 139261 133739 123913 113438 109416 109406 105645 101328 97686 93093 91382 122257 139183 139887 131822 116805 113706 113012 110452 107005 102841 98173 98181 137277 147579 146571 138920 130340 128140 127059 122860 117702 113537 108366 111078 150739 159129 157928 147768 137507 136919 136151 133001 125554 119647 114158 116193 152803 161761 160942 149470 139208 134588 130322 126611 122401 117352 112135 112879 148729 157230 157221 146681 136524 132111

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.883938	6.847	0
2	0.783503	6.069	0
3	0.719577	5.5738	0
4	0.680146	5.2684	1e-06
5	0.637002	4.9342	3e-06
6	0.571851	4.4295	2e-05
7	0.507404	3.9303	0.000111
8	0.407944	3.1599	0.001236
9	0.354414	2.7453	0.003983
10	0.285005	2.2076	0.015552
11	0.182516	1.4138	0.0813
12	0.113981	0.8829	0.190409
13	0.050388	0.3903	0.348847
14	0.003816	0.0296	0.48826
15	-0.081568	-0.6318	0.264952
16	-0.164798	-1.2765	0.103345
17	-0.253852	-1.9663	0.026946
18	-0.324682	-2.515	0.007301
19	-0.333596	-2.584	0.006109
20	-0.370451	-2.8695	0.002835
21	-0.409137	-3.1692	0.001203
22	-0.461267	-3.573	0.000352
23	-0.48033	-3.7206	0.00022
24	-0.503006	-3.8963	0.000124
25	-0.510137	-3.9515	0.000104
26	-0.497172	-3.8511	0.000144
27	-0.479026	-3.7105	0.000227
28	-0.455573	-3.5289	0.000404
29	-0.461364	-3.5737	0.000351
30	-0.449062	-3.4784	0.000473
31	-0.409352	-3.1708	0.001197
32	-0.363908	-2.8188	0.00326
33	-0.324201	-2.5113	0.007371
34	-0.295326	-2.2876	0.012851
35	-0.265101	-2.0535	0.022197
36	-0.22894	-1.7734	0.040622

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.883938	6.847	0
2	0.009864	0.0764	0.469676
3	0.114902	0.89	0.188503
4	0.095817	0.7422	0.230432
5	-0.000494	-0.0038	0.498479
6	-0.091446	-0.7083	0.240738
7	-0.033482	-0.2594	0.398126
8	-0.230502	-1.7855	0.03962
9	0.11058	0.8565	0.197551
10	-0.156011	-1.2085	0.115806
11	-0.203194	-1.5739	0.060381
12	0.087883	0.6807	0.249327
13	-0.067238	-0.5208	0.302203
14	0.012303	0.0953	0.462196
15	-0.15629	-1.2106	0.115394
16	-0.112422	-0.8708	0.193662
17	-0.113519	-0.8793	0.191369
18	-0.038032	-0.2946	0.384661
19	0.120988	0.9372	0.176214
20	-0.073639	-0.5704	0.285267
21	-0.009644	-0.0747	0.47035
22	-0.074965	-0.5807	0.281818
23	0.029171	0.226	0.411001
24	-0.106022	-0.8212	0.20738
25	0.071502	0.5539	0.290869
26	-0.023406	-0.1813	0.42837
27	0.12666	0.9811	0.165241
28	-0.078259	-0.6062	0.273337
29	-0.160367	-1.2422	0.109499
30	0.073874	0.5722	0.284653
31	0.096424	0.7469	0.229021
32	-0.012975	-0.1005	0.460141
33	-0.096786	-0.7497	0.228183
34	-0.013365	-0.1035	0.458946
35	-0.089777	-0.6954	0.244742
36	0.080362	0.6225	0.267991

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259689660xx9clo2z1sfzo3q/1gitl1259689611.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259689660xx9clo2z1sfzo3q/1gitl1259689611.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259689660xx9clo2z1sfzo3q/2kpzh1259689611.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259689660xx9clo2z1sfzo3q/2kpzh1259689611.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; 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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

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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