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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 29 Dec 2010 16:02:38 +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/2010/Dec/29/t12936384414yduhytekx1tjvw.htm/, Retrieved Fri, 03 May 2024 12:29:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116933, Retrieved Fri, 03 May 2024 12:29:13 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

100

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

-       [(Partial) Autocorrelation Function] [paper PAC notes] [2010-12-29 16:02:38] [be9f1751361e0e66b042227828c71db5] [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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116933&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116933&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116933&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.974474	14.2886	0
2	0.964252	14.1387	0
3	0.954852	14.0009	0
4	0.9465	13.8784	0
5	0.931397	13.657	0
6	0.925493	13.5704	0
7	0.910604	13.3521	0
8	0.902891	13.239	0
9	0.889728	13.046	0
10	0.877685	12.8694	0
11	0.866352	12.7032	0
12	0.870216	12.7599	0
13	0.844545	12.3835	0
14	0.832844	12.2119	0
15	0.82176	12.0494	0
16	0.811924	11.9051	0
17	0.795362	11.6623	0
18	0.787378	11.5452	0
19	0.770863	11.3031	0
20	0.761538	11.1663	0
21	0.747128	10.955	0
22	0.733397	10.7537	0
23	0.72033	10.5621	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.974474 & 14.2886 & 0 \tabularnewline
2 & 0.964252 & 14.1387 & 0 \tabularnewline
3 & 0.954852 & 14.0009 & 0 \tabularnewline
4 & 0.9465 & 13.8784 & 0 \tabularnewline
5 & 0.931397 & 13.657 & 0 \tabularnewline
6 & 0.925493 & 13.5704 & 0 \tabularnewline
7 & 0.910604 & 13.3521 & 0 \tabularnewline
8 & 0.902891 & 13.239 & 0 \tabularnewline
9 & 0.889728 & 13.046 & 0 \tabularnewline
10 & 0.877685 & 12.8694 & 0 \tabularnewline
11 & 0.866352 & 12.7032 & 0 \tabularnewline
12 & 0.870216 & 12.7599 & 0 \tabularnewline
13 & 0.844545 & 12.3835 & 0 \tabularnewline
14 & 0.832844 & 12.2119 & 0 \tabularnewline
15 & 0.82176 & 12.0494 & 0 \tabularnewline
16 & 0.811924 & 11.9051 & 0 \tabularnewline
17 & 0.795362 & 11.6623 & 0 \tabularnewline
18 & 0.787378 & 11.5452 & 0 \tabularnewline
19 & 0.770863 & 11.3031 & 0 \tabularnewline
20 & 0.761538 & 11.1663 & 0 \tabularnewline
21 & 0.747128 & 10.955 & 0 \tabularnewline
22 & 0.733397 & 10.7537 & 0 \tabularnewline
23 & 0.72033 & 10.5621 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116933&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]0.974474[/C][C]14.2886[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.964252[/C][C]14.1387[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.954852[/C][C]14.0009[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.9465[/C][C]13.8784[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.931397[/C][C]13.657[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.925493[/C][C]13.5704[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.910604[/C][C]13.3521[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.902891[/C][C]13.239[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.889728[/C][C]13.046[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.877685[/C][C]12.8694[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.866352[/C][C]12.7032[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.870216[/C][C]12.7599[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.844545[/C][C]12.3835[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.832844[/C][C]12.2119[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.82176[/C][C]12.0494[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.811924[/C][C]11.9051[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.795362[/C][C]11.6623[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.787378[/C][C]11.5452[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.770863[/C][C]11.3031[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.761538[/C][C]11.1663[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.747128[/C][C]10.955[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.733397[/C][C]10.7537[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.72033[/C][C]10.5621[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116933&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116933&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	0.974474	14.2886	0
2	0.964252	14.1387	0
3	0.954852	14.0009	0
4	0.9465	13.8784	0
5	0.931397	13.657	0
6	0.925493	13.5704	0
7	0.910604	13.3521	0
8	0.902891	13.239	0
9	0.889728	13.046	0
10	0.877685	12.8694	0
11	0.866352	12.7032	0
12	0.870216	12.7599	0
13	0.844545	12.3835	0
14	0.832844	12.2119	0
15	0.82176	12.0494	0
16	0.811924	11.9051	0
17	0.795362	11.6623	0
18	0.787378	11.5452	0
19	0.770863	11.3031	0
20	0.761538	11.1663	0
21	0.747128	10.955	0
22	0.733397	10.7537	0
23	0.72033	10.5621	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.974474	14.2886	0
2	0.290735	4.263	1.5e-05
3	0.110216	1.6161	0.053771
4	0.06254	0.917	0.180082
5	-0.120333	-1.7644	0.03954
6	0.112999	1.6569	0.049501
7	-0.120103	-1.7611	0.039825
8	0.076829	1.1265	0.130597
9	-0.061456	-0.9011	0.184267
10	-0.05063	-0.7424	0.229335
11	0.042344	0.6209	0.267666
12	0.30019	4.4016	8e-06
13	-0.457978	-6.7153	0
14	0.068848	1.0095	0.156934
15	0.030844	0.4523	0.325768
16	0.010471	0.1535	0.43906
17	-0.006787	-0.0995	0.460409
18	-0.024856	-0.3645	0.357935
19	-0.031456	-0.4612	0.322547
20	0.028083	0.4118	0.340457
21	-0.024426	-0.3581	0.360291
22	-0.016437	-0.241	0.404885
23	0.04235	0.621	0.267635

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.974474 & 14.2886 & 0 \tabularnewline
2 & 0.290735 & 4.263 & 1.5e-05 \tabularnewline
3 & 0.110216 & 1.6161 & 0.053771 \tabularnewline
4 & 0.06254 & 0.917 & 0.180082 \tabularnewline
5 & -0.120333 & -1.7644 & 0.03954 \tabularnewline
6 & 0.112999 & 1.6569 & 0.049501 \tabularnewline
7 & -0.120103 & -1.7611 & 0.039825 \tabularnewline
8 & 0.076829 & 1.1265 & 0.130597 \tabularnewline
9 & -0.061456 & -0.9011 & 0.184267 \tabularnewline
10 & -0.05063 & -0.7424 & 0.229335 \tabularnewline
11 & 0.042344 & 0.6209 & 0.267666 \tabularnewline
12 & 0.30019 & 4.4016 & 8e-06 \tabularnewline
13 & -0.457978 & -6.7153 & 0 \tabularnewline
14 & 0.068848 & 1.0095 & 0.156934 \tabularnewline
15 & 0.030844 & 0.4523 & 0.325768 \tabularnewline
16 & 0.010471 & 0.1535 & 0.43906 \tabularnewline
17 & -0.006787 & -0.0995 & 0.460409 \tabularnewline
18 & -0.024856 & -0.3645 & 0.357935 \tabularnewline
19 & -0.031456 & -0.4612 & 0.322547 \tabularnewline
20 & 0.028083 & 0.4118 & 0.340457 \tabularnewline
21 & -0.024426 & -0.3581 & 0.360291 \tabularnewline
22 & -0.016437 & -0.241 & 0.404885 \tabularnewline
23 & 0.04235 & 0.621 & 0.267635 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116933&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]0.974474[/C][C]14.2886[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.290735[/C][C]4.263[/C][C]1.5e-05[/C][/ROW]
[ROW][C]3[/C][C]0.110216[/C][C]1.6161[/C][C]0.053771[/C][/ROW]
[ROW][C]4[/C][C]0.06254[/C][C]0.917[/C][C]0.180082[/C][/ROW]
[ROW][C]5[/C][C]-0.120333[/C][C]-1.7644[/C][C]0.03954[/C][/ROW]
[ROW][C]6[/C][C]0.112999[/C][C]1.6569[/C][C]0.049501[/C][/ROW]
[ROW][C]7[/C][C]-0.120103[/C][C]-1.7611[/C][C]0.039825[/C][/ROW]
[ROW][C]8[/C][C]0.076829[/C][C]1.1265[/C][C]0.130597[/C][/ROW]
[ROW][C]9[/C][C]-0.061456[/C][C]-0.9011[/C][C]0.184267[/C][/ROW]
[ROW][C]10[/C][C]-0.05063[/C][C]-0.7424[/C][C]0.229335[/C][/ROW]
[ROW][C]11[/C][C]0.042344[/C][C]0.6209[/C][C]0.267666[/C][/ROW]
[ROW][C]12[/C][C]0.30019[/C][C]4.4016[/C][C]8e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.457978[/C][C]-6.7153[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.068848[/C][C]1.0095[/C][C]0.156934[/C][/ROW]
[ROW][C]15[/C][C]0.030844[/C][C]0.4523[/C][C]0.325768[/C][/ROW]
[ROW][C]16[/C][C]0.010471[/C][C]0.1535[/C][C]0.43906[/C][/ROW]
[ROW][C]17[/C][C]-0.006787[/C][C]-0.0995[/C][C]0.460409[/C][/ROW]
[ROW][C]18[/C][C]-0.024856[/C][C]-0.3645[/C][C]0.357935[/C][/ROW]
[ROW][C]19[/C][C]-0.031456[/C][C]-0.4612[/C][C]0.322547[/C][/ROW]
[ROW][C]20[/C][C]0.028083[/C][C]0.4118[/C][C]0.340457[/C][/ROW]
[ROW][C]21[/C][C]-0.024426[/C][C]-0.3581[/C][C]0.360291[/C][/ROW]
[ROW][C]22[/C][C]-0.016437[/C][C]-0.241[/C][C]0.404885[/C][/ROW]
[ROW][C]23[/C][C]0.04235[/C][C]0.621[/C][C]0.267635[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116933&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116933&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	0.974474	14.2886	0
2	0.290735	4.263	1.5e-05
3	0.110216	1.6161	0.053771
4	0.06254	0.917	0.180082
5	-0.120333	-1.7644	0.03954
6	0.112999	1.6569	0.049501
7	-0.120103	-1.7611	0.039825
8	0.076829	1.1265	0.130597
9	-0.061456	-0.9011	0.184267
10	-0.05063	-0.7424	0.229335
11	0.042344	0.6209	0.267666
12	0.30019	4.4016	8e-06
13	-0.457978	-6.7153	0
14	0.068848	1.0095	0.156934
15	0.030844	0.4523	0.325768
16	0.010471	0.1535	0.43906
17	-0.006787	-0.0995	0.460409
18	-0.024856	-0.3645	0.357935
19	-0.031456	-0.4612	0.322547
20	0.028083	0.4118	0.340457
21	-0.024426	-0.3581	0.360291
22	-0.016437	-0.241	0.404885
23	0.04235	0.621	0.267635

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 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code