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ACF, PACF

*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, 22 Dec 2009 06:29:08 -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/22/t1261488939qvuce064kimb654.htm/, Retrieved Thu, 23 May 2013 12:22:44 +0000

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

System-generated keywords (parent):

(pk = 0)

Estimated Impact

Dataseries X:

» Textfile « » CSV « » Stem and Leaf « » Histogram « » Kernel Density « » Harrell-Davis Quantiles « » Central Tendency « » Variability «

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	0.982319	12.6944	0
2	0.964762	12.4675	0
3	0.947616	12.2459	0
4	0.930547	12.0253	0
5	0.913998	11.8115	0
6	0.896418	11.5843	0
7	0.878241	11.3494	0
8	0.860001	11.1137	0
9	0.84238	10.886	0
10	0.825131	10.663	0
11	0.808437	10.4473	0
12	0.790618	10.217	0
13	0.77173	9.9729	0
14	0.752125	9.7196	0
15	0.732503	9.466	0
16	0.713083	9.2151	0
17	0.693698	8.9646	0
18	0.673886	8.7085	0
19	0.653929	8.4506	0
20	0.634777	8.2031	0
21	0.616265	7.9639	0
22	0.598896	7.7394	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.982319	12.6944	0
2	-0.005398	-0.0698	0.472234
3	0.002808	0.0363	0.485546
4	-0.006538	-0.0845	0.466382
5	0.00618	0.0799	0.468223
6	-0.037943	-0.4903	0.312272
7	-0.026175	-0.3383	0.3678
8	-0.012203	-0.1577	0.437441
9	0.007579	0.0979	0.461048
10	0.000192	0.0025	0.499009
11	0.007246	0.0936	0.462753
12	-0.040126	-0.5185	0.302383
13	-0.039455	-0.5099	0.305409
14	-0.032781	-0.4236	0.33619
15	-0.013366	-0.1727	0.431536
16	-0.008441	-0.1091	0.456634
17	-0.009745	-0.1259	0.449967
18	-0.021268	-0.2748	0.391886
19	-0.013224	-0.1709	0.432258
20	0.010898	0.1408	0.444087
21	0.005301	0.0685	0.472732
22	0.019276	0.2491	0.401796

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/22/t1261488939qvuce064kimb654/1p6ny1261488546.png (opens in new window)

http://www.freestatistics.org/blog/date/2009/Dec/22/t1261488939qvuce064kimb654/1p6ny1261488546.ps (opens in new window)

Click here to open pdf file.

http://www.freestatistics.org/blog/date/2009/Dec/22/t1261488939qvuce064kimb654/2jekx1261488546.png (opens in new window)

http://www.freestatistics.org/blog/date/2009/Dec/22/t1261488939qvuce064kimb654/2jekx1261488546.ps (opens in new window)

Click here to open pdf file.

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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')