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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 21 Dec 2012 09:14:08 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/21/t1356099272nria3xaczsxapon.htm/, Retrieved Thu, 25 Apr 2024 16:27:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203697, Retrieved Thu, 25 Apr 2024 16:27:52 +0000

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [ARIMA Backward Selection] [Arima Backward Se...] [2012-12-21 13:27:11] [1655ef4f70a4add09e51daeee7c8dd65]
- RMP     [(Partial) Autocorrelation Function] [Autocorrelation F...] [2012-12-21 14:14:08] [e5cf4d544f75f57c12196ef0ffd71d75] [Current]

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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	'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203697&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203697&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203697&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.259253	-2.8043	0.002953
2	-0.137102	-1.483	0.070383
3	0.155542	1.6824	0.047575
4	-0.238261	-2.5772	0.005602
5	0.112669	1.2187	0.112705
6	-0.054618	-0.5908	0.277903
7	-0.214965	-2.3252	0.010892
8	0.177499	1.9199	0.02865
9	-0.092417	-0.9996	0.159774
10	-0.205148	-2.219	0.014207
11	0.113445	1.2271	0.111125
12	0.190279	2.0582	0.020897
13	0.040097	0.4337	0.332645
14	0.07634	0.8257	0.205316
15	-0.08202	-0.8872	0.188401
16	-0.082416	-0.8915	0.187254
17	0.135171	1.4621	0.073197
18	-0.162871	-1.7617	0.040365
19	0.023279	0.2518	0.400819
20	0.114264	1.236	0.109476

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.259253 & -2.8043 & 0.002953 \tabularnewline
2 & -0.137102 & -1.483 & 0.070383 \tabularnewline
3 & 0.155542 & 1.6824 & 0.047575 \tabularnewline
4 & -0.238261 & -2.5772 & 0.005602 \tabularnewline
5 & 0.112669 & 1.2187 & 0.112705 \tabularnewline
6 & -0.054618 & -0.5908 & 0.277903 \tabularnewline
7 & -0.214965 & -2.3252 & 0.010892 \tabularnewline
8 & 0.177499 & 1.9199 & 0.02865 \tabularnewline
9 & -0.092417 & -0.9996 & 0.159774 \tabularnewline
10 & -0.205148 & -2.219 & 0.014207 \tabularnewline
11 & 0.113445 & 1.2271 & 0.111125 \tabularnewline
12 & 0.190279 & 2.0582 & 0.020897 \tabularnewline
13 & 0.040097 & 0.4337 & 0.332645 \tabularnewline
14 & 0.07634 & 0.8257 & 0.205316 \tabularnewline
15 & -0.08202 & -0.8872 & 0.188401 \tabularnewline
16 & -0.082416 & -0.8915 & 0.187254 \tabularnewline
17 & 0.135171 & 1.4621 & 0.073197 \tabularnewline
18 & -0.162871 & -1.7617 & 0.040365 \tabularnewline
19 & 0.023279 & 0.2518 & 0.400819 \tabularnewline
20 & 0.114264 & 1.236 & 0.109476 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203697&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]-0.259253[/C][C]-2.8043[/C][C]0.002953[/C][/ROW]
[ROW][C]2[/C][C]-0.137102[/C][C]-1.483[/C][C]0.070383[/C][/ROW]
[ROW][C]3[/C][C]0.155542[/C][C]1.6824[/C][C]0.047575[/C][/ROW]
[ROW][C]4[/C][C]-0.238261[/C][C]-2.5772[/C][C]0.005602[/C][/ROW]
[ROW][C]5[/C][C]0.112669[/C][C]1.2187[/C][C]0.112705[/C][/ROW]
[ROW][C]6[/C][C]-0.054618[/C][C]-0.5908[/C][C]0.277903[/C][/ROW]
[ROW][C]7[/C][C]-0.214965[/C][C]-2.3252[/C][C]0.010892[/C][/ROW]
[ROW][C]8[/C][C]0.177499[/C][C]1.9199[/C][C]0.02865[/C][/ROW]
[ROW][C]9[/C][C]-0.092417[/C][C]-0.9996[/C][C]0.159774[/C][/ROW]
[ROW][C]10[/C][C]-0.205148[/C][C]-2.219[/C][C]0.014207[/C][/ROW]
[ROW][C]11[/C][C]0.113445[/C][C]1.2271[/C][C]0.111125[/C][/ROW]
[ROW][C]12[/C][C]0.190279[/C][C]2.0582[/C][C]0.020897[/C][/ROW]
[ROW][C]13[/C][C]0.040097[/C][C]0.4337[/C][C]0.332645[/C][/ROW]
[ROW][C]14[/C][C]0.07634[/C][C]0.8257[/C][C]0.205316[/C][/ROW]
[ROW][C]15[/C][C]-0.08202[/C][C]-0.8872[/C][C]0.188401[/C][/ROW]
[ROW][C]16[/C][C]-0.082416[/C][C]-0.8915[/C][C]0.187254[/C][/ROW]
[ROW][C]17[/C][C]0.135171[/C][C]1.4621[/C][C]0.073197[/C][/ROW]
[ROW][C]18[/C][C]-0.162871[/C][C]-1.7617[/C][C]0.040365[/C][/ROW]
[ROW][C]19[/C][C]0.023279[/C][C]0.2518[/C][C]0.400819[/C][/ROW]
[ROW][C]20[/C][C]0.114264[/C][C]1.236[/C][C]0.109476[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203697&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203697&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.259253	-2.8043	0.002953
2	-0.137102	-1.483	0.070383
3	0.155542	1.6824	0.047575
4	-0.238261	-2.5772	0.005602
5	0.112669	1.2187	0.112705
6	-0.054618	-0.5908	0.277903
7	-0.214965	-2.3252	0.010892
8	0.177499	1.9199	0.02865
9	-0.092417	-0.9996	0.159774
10	-0.205148	-2.219	0.014207
11	0.113445	1.2271	0.111125
12	0.190279	2.0582	0.020897
13	0.040097	0.4337	0.332645
14	0.07634	0.8257	0.205316
15	-0.08202	-0.8872	0.188401
16	-0.082416	-0.8915	0.187254
17	0.135171	1.4621	0.073197
18	-0.162871	-1.7617	0.040365
19	0.023279	0.2518	0.400819
20	0.114264	1.236	0.109476

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.259253	-2.8043	0.002953
2	-0.219036	-2.3692	0.009731
3	0.062415	0.6751	0.250466
4	-0.228782	-2.4747	0.007385
5	0.026104	0.2824	0.389083
6	-0.124928	-1.3513	0.089602
7	-0.235349	-2.5457	0.006103
8	-0.042119	-0.4556	0.324765
9	-0.131315	-1.4204	0.079077
10	-0.329843	-3.5678	0.000261
11	-0.253441	-2.7414	0.00354
12	0.097533	1.055	0.146804
13	0.058209	0.6296	0.265083
14	0.083416	0.9023	0.184381
15	-0.001447	-0.0157	0.49377
16	-0.130377	-1.4102	0.080561
17	-0.011346	-0.1227	0.451268
18	-0.094448	-1.0216	0.154536
19	0.02399	0.2595	0.397856
20	0.050554	0.5468	0.29277

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.259253 & -2.8043 & 0.002953 \tabularnewline
2 & -0.219036 & -2.3692 & 0.009731 \tabularnewline
3 & 0.062415 & 0.6751 & 0.250466 \tabularnewline
4 & -0.228782 & -2.4747 & 0.007385 \tabularnewline
5 & 0.026104 & 0.2824 & 0.389083 \tabularnewline
6 & -0.124928 & -1.3513 & 0.089602 \tabularnewline
7 & -0.235349 & -2.5457 & 0.006103 \tabularnewline
8 & -0.042119 & -0.4556 & 0.324765 \tabularnewline
9 & -0.131315 & -1.4204 & 0.079077 \tabularnewline
10 & -0.329843 & -3.5678 & 0.000261 \tabularnewline
11 & -0.253441 & -2.7414 & 0.00354 \tabularnewline
12 & 0.097533 & 1.055 & 0.146804 \tabularnewline
13 & 0.058209 & 0.6296 & 0.265083 \tabularnewline
14 & 0.083416 & 0.9023 & 0.184381 \tabularnewline
15 & -0.001447 & -0.0157 & 0.49377 \tabularnewline
16 & -0.130377 & -1.4102 & 0.080561 \tabularnewline
17 & -0.011346 & -0.1227 & 0.451268 \tabularnewline
18 & -0.094448 & -1.0216 & 0.154536 \tabularnewline
19 & 0.02399 & 0.2595 & 0.397856 \tabularnewline
20 & 0.050554 & 0.5468 & 0.29277 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203697&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]-0.259253[/C][C]-2.8043[/C][C]0.002953[/C][/ROW]
[ROW][C]2[/C][C]-0.219036[/C][C]-2.3692[/C][C]0.009731[/C][/ROW]
[ROW][C]3[/C][C]0.062415[/C][C]0.6751[/C][C]0.250466[/C][/ROW]
[ROW][C]4[/C][C]-0.228782[/C][C]-2.4747[/C][C]0.007385[/C][/ROW]
[ROW][C]5[/C][C]0.026104[/C][C]0.2824[/C][C]0.389083[/C][/ROW]
[ROW][C]6[/C][C]-0.124928[/C][C]-1.3513[/C][C]0.089602[/C][/ROW]
[ROW][C]7[/C][C]-0.235349[/C][C]-2.5457[/C][C]0.006103[/C][/ROW]
[ROW][C]8[/C][C]-0.042119[/C][C]-0.4556[/C][C]0.324765[/C][/ROW]
[ROW][C]9[/C][C]-0.131315[/C][C]-1.4204[/C][C]0.079077[/C][/ROW]
[ROW][C]10[/C][C]-0.329843[/C][C]-3.5678[/C][C]0.000261[/C][/ROW]
[ROW][C]11[/C][C]-0.253441[/C][C]-2.7414[/C][C]0.00354[/C][/ROW]
[ROW][C]12[/C][C]0.097533[/C][C]1.055[/C][C]0.146804[/C][/ROW]
[ROW][C]13[/C][C]0.058209[/C][C]0.6296[/C][C]0.265083[/C][/ROW]
[ROW][C]14[/C][C]0.083416[/C][C]0.9023[/C][C]0.184381[/C][/ROW]
[ROW][C]15[/C][C]-0.001447[/C][C]-0.0157[/C][C]0.49377[/C][/ROW]
[ROW][C]16[/C][C]-0.130377[/C][C]-1.4102[/C][C]0.080561[/C][/ROW]
[ROW][C]17[/C][C]-0.011346[/C][C]-0.1227[/C][C]0.451268[/C][/ROW]
[ROW][C]18[/C][C]-0.094448[/C][C]-1.0216[/C][C]0.154536[/C][/ROW]
[ROW][C]19[/C][C]0.02399[/C][C]0.2595[/C][C]0.397856[/C][/ROW]
[ROW][C]20[/C][C]0.050554[/C][C]0.5468[/C][C]0.29277[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203697&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203697&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.259253	-2.8043	0.002953
2	-0.219036	-2.3692	0.009731
3	0.062415	0.6751	0.250466
4	-0.228782	-2.4747	0.007385
5	0.026104	0.2824	0.389083
6	-0.124928	-1.3513	0.089602
7	-0.235349	-2.5457	0.006103
8	-0.042119	-0.4556	0.324765
9	-0.131315	-1.4204	0.079077
10	-0.329843	-3.5678	0.000261
11	-0.253441	-2.7414	0.00354
12	0.097533	1.055	0.146804
13	0.058209	0.6296	0.265083
14	0.083416	0.9023	0.184381
15	-0.001447	-0.0157	0.49377
16	-0.130377	-1.4102	0.080561
17	-0.011346	-0.1227	0.451268
18	-0.094448	-1.0216	0.154536
19	0.02399	0.2595	0.397856
20	0.050554	0.5468	0.29277

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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('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('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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code