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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

Tue, 20 Nov 2012 12:05:10 -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/Nov/20/t1353431152mkh9md1nuwq9jf5.htm/, Retrieved Mon, 29 Apr 2024 21:18:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=191190, Retrieved Mon, 29 Apr 2024 21:18:33 +0000

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

-       [(Partial) Autocorrelation Function] [WS 9 ACF 3] [2012-11-20 17:05:10] [851af2766980873020febd248b5479af] [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	4 seconds
R Server	'George Udny Yule' @ yule.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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191190&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191190&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191190&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	4 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.15942	1.893	0.030203
2	0.121536	1.4432	0.075596
3	0.118735	1.4099	0.080385
4	0.130774	1.5529	0.061349
5	0.126763	1.5052	0.067252
6	0.13528	1.6064	0.055216
7	0.058839	0.6987	0.242952
8	0.129187	1.534	0.063634
9	0.165157	1.9611	0.025917
10	-0.02464	-0.2926	0.385135
11	-0.03637	-0.4319	0.33325
12	-0.218167	-2.5906	0.005294
13	-0.046611	-0.5535	0.290406
14	0.112332	1.3339	0.092199
15	-0.01566	-0.186	0.426375
16	-0.047443	-0.5634	0.287044
17	-0.093952	-1.1156	0.133242
18	-0.061379	-0.7288	0.233656
19	-0.039377	-0.4676	0.320404
20	-0.098843	-1.1737	0.121248
21	-0.168584	-2.0018	0.023611

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.15942 & 1.893 & 0.030203 \tabularnewline
2 & 0.121536 & 1.4432 & 0.075596 \tabularnewline
3 & 0.118735 & 1.4099 & 0.080385 \tabularnewline
4 & 0.130774 & 1.5529 & 0.061349 \tabularnewline
5 & 0.126763 & 1.5052 & 0.067252 \tabularnewline
6 & 0.13528 & 1.6064 & 0.055216 \tabularnewline
7 & 0.058839 & 0.6987 & 0.242952 \tabularnewline
8 & 0.129187 & 1.534 & 0.063634 \tabularnewline
9 & 0.165157 & 1.9611 & 0.025917 \tabularnewline
10 & -0.02464 & -0.2926 & 0.385135 \tabularnewline
11 & -0.03637 & -0.4319 & 0.33325 \tabularnewline
12 & -0.218167 & -2.5906 & 0.005294 \tabularnewline
13 & -0.046611 & -0.5535 & 0.290406 \tabularnewline
14 & 0.112332 & 1.3339 & 0.092199 \tabularnewline
15 & -0.01566 & -0.186 & 0.426375 \tabularnewline
16 & -0.047443 & -0.5634 & 0.287044 \tabularnewline
17 & -0.093952 & -1.1156 & 0.133242 \tabularnewline
18 & -0.061379 & -0.7288 & 0.233656 \tabularnewline
19 & -0.039377 & -0.4676 & 0.320404 \tabularnewline
20 & -0.098843 & -1.1737 & 0.121248 \tabularnewline
21 & -0.168584 & -2.0018 & 0.023611 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191190&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]0.15942[/C][C]1.893[/C][C]0.030203[/C][/ROW]
[ROW][C]2[/C][C]0.121536[/C][C]1.4432[/C][C]0.075596[/C][/ROW]
[ROW][C]3[/C][C]0.118735[/C][C]1.4099[/C][C]0.080385[/C][/ROW]
[ROW][C]4[/C][C]0.130774[/C][C]1.5529[/C][C]0.061349[/C][/ROW]
[ROW][C]5[/C][C]0.126763[/C][C]1.5052[/C][C]0.067252[/C][/ROW]
[ROW][C]6[/C][C]0.13528[/C][C]1.6064[/C][C]0.055216[/C][/ROW]
[ROW][C]7[/C][C]0.058839[/C][C]0.6987[/C][C]0.242952[/C][/ROW]
[ROW][C]8[/C][C]0.129187[/C][C]1.534[/C][C]0.063634[/C][/ROW]
[ROW][C]9[/C][C]0.165157[/C][C]1.9611[/C][C]0.025917[/C][/ROW]
[ROW][C]10[/C][C]-0.02464[/C][C]-0.2926[/C][C]0.385135[/C][/ROW]
[ROW][C]11[/C][C]-0.03637[/C][C]-0.4319[/C][C]0.33325[/C][/ROW]
[ROW][C]12[/C][C]-0.218167[/C][C]-2.5906[/C][C]0.005294[/C][/ROW]
[ROW][C]13[/C][C]-0.046611[/C][C]-0.5535[/C][C]0.290406[/C][/ROW]
[ROW][C]14[/C][C]0.112332[/C][C]1.3339[/C][C]0.092199[/C][/ROW]
[ROW][C]15[/C][C]-0.01566[/C][C]-0.186[/C][C]0.426375[/C][/ROW]
[ROW][C]16[/C][C]-0.047443[/C][C]-0.5634[/C][C]0.287044[/C][/ROW]
[ROW][C]17[/C][C]-0.093952[/C][C]-1.1156[/C][C]0.133242[/C][/ROW]
[ROW][C]18[/C][C]-0.061379[/C][C]-0.7288[/C][C]0.233656[/C][/ROW]
[ROW][C]19[/C][C]-0.039377[/C][C]-0.4676[/C][C]0.320404[/C][/ROW]
[ROW][C]20[/C][C]-0.098843[/C][C]-1.1737[/C][C]0.121248[/C][/ROW]
[ROW][C]21[/C][C]-0.168584[/C][C]-2.0018[/C][C]0.023611[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191190&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191190&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	0.15942	1.893	0.030203
2	0.121536	1.4432	0.075596
3	0.118735	1.4099	0.080385
4	0.130774	1.5529	0.061349
5	0.126763	1.5052	0.067252
6	0.13528	1.6064	0.055216
7	0.058839	0.6987	0.242952
8	0.129187	1.534	0.063634
9	0.165157	1.9611	0.025917
10	-0.02464	-0.2926	0.385135
11	-0.03637	-0.4319	0.33325
12	-0.218167	-2.5906	0.005294
13	-0.046611	-0.5535	0.290406
14	0.112332	1.3339	0.092199
15	-0.01566	-0.186	0.426375
16	-0.047443	-0.5634	0.287044
17	-0.093952	-1.1156	0.133242
18	-0.061379	-0.7288	0.233656
19	-0.039377	-0.4676	0.320404
20	-0.098843	-1.1737	0.121248
21	-0.168584	-2.0018	0.023611

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.15942	1.893	0.030203
2	0.098628	1.1711	0.121758
3	0.08864	1.0525	0.147174
4	0.094181	1.1183	0.132661
5	0.080846	0.96	0.16935
6	0.084284	1.0008	0.159316
7	-0.00444	-0.0527	0.479013
8	0.082675	0.9817	0.163961
9	0.108257	1.2855	0.100365
10	-0.110474	-1.3118	0.095859
11	-0.086035	-1.0216	0.154357
12	-0.271818	-3.2277	0.000776
13	-0.03375	-0.4008	0.344603
14	0.152879	1.8153	0.035799
15	-0.000277	-0.0033	0.498691
16	-0.000895	-0.0106	0.495769
17	-0.090052	-1.0693	0.14338
18	-0.015117	-0.1795	0.428898
19	0.02834	0.3365	0.368488
20	-0.032921	-0.3909	0.348223
21	-0.0709	-0.8419	0.200637

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.15942 & 1.893 & 0.030203 \tabularnewline
2 & 0.098628 & 1.1711 & 0.121758 \tabularnewline
3 & 0.08864 & 1.0525 & 0.147174 \tabularnewline
4 & 0.094181 & 1.1183 & 0.132661 \tabularnewline
5 & 0.080846 & 0.96 & 0.16935 \tabularnewline
6 & 0.084284 & 1.0008 & 0.159316 \tabularnewline
7 & -0.00444 & -0.0527 & 0.479013 \tabularnewline
8 & 0.082675 & 0.9817 & 0.163961 \tabularnewline
9 & 0.108257 & 1.2855 & 0.100365 \tabularnewline
10 & -0.110474 & -1.3118 & 0.095859 \tabularnewline
11 & -0.086035 & -1.0216 & 0.154357 \tabularnewline
12 & -0.271818 & -3.2277 & 0.000776 \tabularnewline
13 & -0.03375 & -0.4008 & 0.344603 \tabularnewline
14 & 0.152879 & 1.8153 & 0.035799 \tabularnewline
15 & -0.000277 & -0.0033 & 0.498691 \tabularnewline
16 & -0.000895 & -0.0106 & 0.495769 \tabularnewline
17 & -0.090052 & -1.0693 & 0.14338 \tabularnewline
18 & -0.015117 & -0.1795 & 0.428898 \tabularnewline
19 & 0.02834 & 0.3365 & 0.368488 \tabularnewline
20 & -0.032921 & -0.3909 & 0.348223 \tabularnewline
21 & -0.0709 & -0.8419 & 0.200637 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=191190&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]0.15942[/C][C]1.893[/C][C]0.030203[/C][/ROW]
[ROW][C]2[/C][C]0.098628[/C][C]1.1711[/C][C]0.121758[/C][/ROW]
[ROW][C]3[/C][C]0.08864[/C][C]1.0525[/C][C]0.147174[/C][/ROW]
[ROW][C]4[/C][C]0.094181[/C][C]1.1183[/C][C]0.132661[/C][/ROW]
[ROW][C]5[/C][C]0.080846[/C][C]0.96[/C][C]0.16935[/C][/ROW]
[ROW][C]6[/C][C]0.084284[/C][C]1.0008[/C][C]0.159316[/C][/ROW]
[ROW][C]7[/C][C]-0.00444[/C][C]-0.0527[/C][C]0.479013[/C][/ROW]
[ROW][C]8[/C][C]0.082675[/C][C]0.9817[/C][C]0.163961[/C][/ROW]
[ROW][C]9[/C][C]0.108257[/C][C]1.2855[/C][C]0.100365[/C][/ROW]
[ROW][C]10[/C][C]-0.110474[/C][C]-1.3118[/C][C]0.095859[/C][/ROW]
[ROW][C]11[/C][C]-0.086035[/C][C]-1.0216[/C][C]0.154357[/C][/ROW]
[ROW][C]12[/C][C]-0.271818[/C][C]-3.2277[/C][C]0.000776[/C][/ROW]
[ROW][C]13[/C][C]-0.03375[/C][C]-0.4008[/C][C]0.344603[/C][/ROW]
[ROW][C]14[/C][C]0.152879[/C][C]1.8153[/C][C]0.035799[/C][/ROW]
[ROW][C]15[/C][C]-0.000277[/C][C]-0.0033[/C][C]0.498691[/C][/ROW]
[ROW][C]16[/C][C]-0.000895[/C][C]-0.0106[/C][C]0.495769[/C][/ROW]
[ROW][C]17[/C][C]-0.090052[/C][C]-1.0693[/C][C]0.14338[/C][/ROW]
[ROW][C]18[/C][C]-0.015117[/C][C]-0.1795[/C][C]0.428898[/C][/ROW]
[ROW][C]19[/C][C]0.02834[/C][C]0.3365[/C][C]0.368488[/C][/ROW]
[ROW][C]20[/C][C]-0.032921[/C][C]-0.3909[/C][C]0.348223[/C][/ROW]
[ROW][C]21[/C][C]-0.0709[/C][C]-0.8419[/C][C]0.200637[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=191190&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=191190&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	0.15942	1.893	0.030203
2	0.098628	1.1711	0.121758
3	0.08864	1.0525	0.147174
4	0.094181	1.1183	0.132661
5	0.080846	0.96	0.16935
6	0.084284	1.0008	0.159316
7	-0.00444	-0.0527	0.479013
8	0.082675	0.9817	0.163961
9	0.108257	1.2855	0.100365
10	-0.110474	-1.3118	0.095859
11	-0.086035	-1.0216	0.154357
12	-0.271818	-3.2277	0.000776
13	-0.03375	-0.4008	0.344603
14	0.152879	1.8153	0.035799
15	-0.000277	-0.0033	0.498691
16	-0.000895	-0.0106	0.495769
17	-0.090052	-1.0693	0.14338
18	-0.015117	-0.1795	0.428898
19	0.02834	0.3365	0.368488
20	-0.032921	-0.3909	0.348223
21	-0.0709	-0.8419	0.200637

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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