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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 21 Jan 2015 08:18:40 +0000

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/2015/Jan/21/t1421828328nophii8pzsiy3db.htm/, Retrieved Mon, 13 May 2024 22:58:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=275719, Retrieved Mon, 13 May 2024 22:58:01 +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] [] [2015-01-21 08:18:40] [8fb8f54f5311a3bdb9fc3d530bb27adb] [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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=275719&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=275719&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=275719&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.257177	-3.1707	0.00092
2	-0.134405	-1.6571	0.049786
3	0.049128	0.6057	0.272813
4	-0.003429	-0.0423	0.483169
5	-0.01464	-0.1805	0.428502
6	-0.07483	-0.9226	0.178848
7	0.093451	1.1521	0.125535
8	-0.086072	-1.0612	0.14515
9	0.040127	0.4947	0.310757
10	-0.001415	-0.0174	0.493053
11	0.058978	0.7271	0.234132
12	-0.100314	-1.2368	0.109042
13	0.010433	0.1286	0.448914
14	-0.058201	-0.7176	0.237068
15	-0.088675	-1.0933	0.138004
16	0.118348	1.4591	0.073301
17	-0.133828	-1.6499	0.05051
18	0.039708	0.4896	0.312576
19	0.078811	0.9717	0.166384
20	-0.07705	-0.9499	0.171827
21	0.038312	0.4723	0.318679

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.257177 & -3.1707 & 0.00092 \tabularnewline
2 & -0.134405 & -1.6571 & 0.049786 \tabularnewline
3 & 0.049128 & 0.6057 & 0.272813 \tabularnewline
4 & -0.003429 & -0.0423 & 0.483169 \tabularnewline
5 & -0.01464 & -0.1805 & 0.428502 \tabularnewline
6 & -0.07483 & -0.9226 & 0.178848 \tabularnewline
7 & 0.093451 & 1.1521 & 0.125535 \tabularnewline
8 & -0.086072 & -1.0612 & 0.14515 \tabularnewline
9 & 0.040127 & 0.4947 & 0.310757 \tabularnewline
10 & -0.001415 & -0.0174 & 0.493053 \tabularnewline
11 & 0.058978 & 0.7271 & 0.234132 \tabularnewline
12 & -0.100314 & -1.2368 & 0.109042 \tabularnewline
13 & 0.010433 & 0.1286 & 0.448914 \tabularnewline
14 & -0.058201 & -0.7176 & 0.237068 \tabularnewline
15 & -0.088675 & -1.0933 & 0.138004 \tabularnewline
16 & 0.118348 & 1.4591 & 0.073301 \tabularnewline
17 & -0.133828 & -1.6499 & 0.05051 \tabularnewline
18 & 0.039708 & 0.4896 & 0.312576 \tabularnewline
19 & 0.078811 & 0.9717 & 0.166384 \tabularnewline
20 & -0.07705 & -0.9499 & 0.171827 \tabularnewline
21 & 0.038312 & 0.4723 & 0.318679 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=275719&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]-0.257177[/C][C]-3.1707[/C][C]0.00092[/C][/ROW]
[ROW][C]2[/C][C]-0.134405[/C][C]-1.6571[/C][C]0.049786[/C][/ROW]
[ROW][C]3[/C][C]0.049128[/C][C]0.6057[/C][C]0.272813[/C][/ROW]
[ROW][C]4[/C][C]-0.003429[/C][C]-0.0423[/C][C]0.483169[/C][/ROW]
[ROW][C]5[/C][C]-0.01464[/C][C]-0.1805[/C][C]0.428502[/C][/ROW]
[ROW][C]6[/C][C]-0.07483[/C][C]-0.9226[/C][C]0.178848[/C][/ROW]
[ROW][C]7[/C][C]0.093451[/C][C]1.1521[/C][C]0.125535[/C][/ROW]
[ROW][C]8[/C][C]-0.086072[/C][C]-1.0612[/C][C]0.14515[/C][/ROW]
[ROW][C]9[/C][C]0.040127[/C][C]0.4947[/C][C]0.310757[/C][/ROW]
[ROW][C]10[/C][C]-0.001415[/C][C]-0.0174[/C][C]0.493053[/C][/ROW]
[ROW][C]11[/C][C]0.058978[/C][C]0.7271[/C][C]0.234132[/C][/ROW]
[ROW][C]12[/C][C]-0.100314[/C][C]-1.2368[/C][C]0.109042[/C][/ROW]
[ROW][C]13[/C][C]0.010433[/C][C]0.1286[/C][C]0.448914[/C][/ROW]
[ROW][C]14[/C][C]-0.058201[/C][C]-0.7176[/C][C]0.237068[/C][/ROW]
[ROW][C]15[/C][C]-0.088675[/C][C]-1.0933[/C][C]0.138004[/C][/ROW]
[ROW][C]16[/C][C]0.118348[/C][C]1.4591[/C][C]0.073301[/C][/ROW]
[ROW][C]17[/C][C]-0.133828[/C][C]-1.6499[/C][C]0.05051[/C][/ROW]
[ROW][C]18[/C][C]0.039708[/C][C]0.4896[/C][C]0.312576[/C][/ROW]
[ROW][C]19[/C][C]0.078811[/C][C]0.9717[/C][C]0.166384[/C][/ROW]
[ROW][C]20[/C][C]-0.07705[/C][C]-0.9499[/C][C]0.171827[/C][/ROW]
[ROW][C]21[/C][C]0.038312[/C][C]0.4723[/C][C]0.318679[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=275719&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=275719&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	-0.257177	-3.1707	0.00092
2	-0.134405	-1.6571	0.049786
3	0.049128	0.6057	0.272813
4	-0.003429	-0.0423	0.483169
5	-0.01464	-0.1805	0.428502
6	-0.07483	-0.9226	0.178848
7	0.093451	1.1521	0.125535
8	-0.086072	-1.0612	0.14515
9	0.040127	0.4947	0.310757
10	-0.001415	-0.0174	0.493053
11	0.058978	0.7271	0.234132
12	-0.100314	-1.2368	0.109042
13	0.010433	0.1286	0.448914
14	-0.058201	-0.7176	0.237068
15	-0.088675	-1.0933	0.138004
16	0.118348	1.4591	0.073301
17	-0.133828	-1.6499	0.05051
18	0.039708	0.4896	0.312576
19	0.078811	0.9717	0.166384
20	-0.07705	-0.9499	0.171827
21	0.038312	0.4723	0.318679

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.257177	-3.1707	0.00092
2	-0.214748	-2.6476	0.004481
3	-0.053985	-0.6656	0.253347
4	-0.036619	-0.4515	0.326146
5	-0.025062	-0.309	0.378876
6	-0.100828	-1.2431	0.107873
7	0.039425	0.4861	0.31381
8	-0.085099	-1.0492	0.147882
9	0.015715	0.1938	0.423314
10	-0.019296	-0.2379	0.406143
11	0.073159	0.902	0.18425
12	-0.081863	-1.0093	0.157222
13	-0.011769	-0.1451	0.442412
14	-0.126192	-1.5558	0.060918
15	-0.14556	-1.7946	0.037354
16	0.002038	0.0251	0.489992
17	-0.149963	-1.8489	0.03321
18	-0.057896	-0.7138	0.238226
19	0.037116	0.4576	0.323949
20	-0.091814	-1.132	0.129717
21	0.008644	0.1066	0.457638

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.257177 & -3.1707 & 0.00092 \tabularnewline
2 & -0.214748 & -2.6476 & 0.004481 \tabularnewline
3 & -0.053985 & -0.6656 & 0.253347 \tabularnewline
4 & -0.036619 & -0.4515 & 0.326146 \tabularnewline
5 & -0.025062 & -0.309 & 0.378876 \tabularnewline
6 & -0.100828 & -1.2431 & 0.107873 \tabularnewline
7 & 0.039425 & 0.4861 & 0.31381 \tabularnewline
8 & -0.085099 & -1.0492 & 0.147882 \tabularnewline
9 & 0.015715 & 0.1938 & 0.423314 \tabularnewline
10 & -0.019296 & -0.2379 & 0.406143 \tabularnewline
11 & 0.073159 & 0.902 & 0.18425 \tabularnewline
12 & -0.081863 & -1.0093 & 0.157222 \tabularnewline
13 & -0.011769 & -0.1451 & 0.442412 \tabularnewline
14 & -0.126192 & -1.5558 & 0.060918 \tabularnewline
15 & -0.14556 & -1.7946 & 0.037354 \tabularnewline
16 & 0.002038 & 0.0251 & 0.489992 \tabularnewline
17 & -0.149963 & -1.8489 & 0.03321 \tabularnewline
18 & -0.057896 & -0.7138 & 0.238226 \tabularnewline
19 & 0.037116 & 0.4576 & 0.323949 \tabularnewline
20 & -0.091814 & -1.132 & 0.129717 \tabularnewline
21 & 0.008644 & 0.1066 & 0.457638 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=275719&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]-0.257177[/C][C]-3.1707[/C][C]0.00092[/C][/ROW]
[ROW][C]2[/C][C]-0.214748[/C][C]-2.6476[/C][C]0.004481[/C][/ROW]
[ROW][C]3[/C][C]-0.053985[/C][C]-0.6656[/C][C]0.253347[/C][/ROW]
[ROW][C]4[/C][C]-0.036619[/C][C]-0.4515[/C][C]0.326146[/C][/ROW]
[ROW][C]5[/C][C]-0.025062[/C][C]-0.309[/C][C]0.378876[/C][/ROW]
[ROW][C]6[/C][C]-0.100828[/C][C]-1.2431[/C][C]0.107873[/C][/ROW]
[ROW][C]7[/C][C]0.039425[/C][C]0.4861[/C][C]0.31381[/C][/ROW]
[ROW][C]8[/C][C]-0.085099[/C][C]-1.0492[/C][C]0.147882[/C][/ROW]
[ROW][C]9[/C][C]0.015715[/C][C]0.1938[/C][C]0.423314[/C][/ROW]
[ROW][C]10[/C][C]-0.019296[/C][C]-0.2379[/C][C]0.406143[/C][/ROW]
[ROW][C]11[/C][C]0.073159[/C][C]0.902[/C][C]0.18425[/C][/ROW]
[ROW][C]12[/C][C]-0.081863[/C][C]-1.0093[/C][C]0.157222[/C][/ROW]
[ROW][C]13[/C][C]-0.011769[/C][C]-0.1451[/C][C]0.442412[/C][/ROW]
[ROW][C]14[/C][C]-0.126192[/C][C]-1.5558[/C][C]0.060918[/C][/ROW]
[ROW][C]15[/C][C]-0.14556[/C][C]-1.7946[/C][C]0.037354[/C][/ROW]
[ROW][C]16[/C][C]0.002038[/C][C]0.0251[/C][C]0.489992[/C][/ROW]
[ROW][C]17[/C][C]-0.149963[/C][C]-1.8489[/C][C]0.03321[/C][/ROW]
[ROW][C]18[/C][C]-0.057896[/C][C]-0.7138[/C][C]0.238226[/C][/ROW]
[ROW][C]19[/C][C]0.037116[/C][C]0.4576[/C][C]0.323949[/C][/ROW]
[ROW][C]20[/C][C]-0.091814[/C][C]-1.132[/C][C]0.129717[/C][/ROW]
[ROW][C]21[/C][C]0.008644[/C][C]0.1066[/C][C]0.457638[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=275719&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=275719&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	-0.257177	-3.1707	0.00092
2	-0.214748	-2.6476	0.004481
3	-0.053985	-0.6656	0.253347
4	-0.036619	-0.4515	0.326146
5	-0.025062	-0.309	0.378876
6	-0.100828	-1.2431	0.107873
7	0.039425	0.4861	0.31381
8	-0.085099	-1.0492	0.147882
9	0.015715	0.1938	0.423314
10	-0.019296	-0.2379	0.406143
11	0.073159	0.902	0.18425
12	-0.081863	-1.0093	0.157222
13	-0.011769	-0.1451	0.442412
14	-0.126192	-1.5558	0.060918
15	-0.14556	-1.7946	0.037354
16	0.002038	0.0251	0.489992
17	-0.149963	-1.8489	0.03321
18	-0.057896	-0.7138	0.238226
19	0.037116	0.4576	0.323949
20	-0.091814	-1.132	0.129717
21	0.008644	0.1066	0.457638

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '1'
par3 <- '1'
par2 <- '1'
par1 <- 'Default'
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