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Author's title

Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 24 Dec 2010 16:50:22 +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/24/t12932094198pgon9m776k1gti.htm/, Retrieved Tue, 30 Apr 2024 07:00:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115195, Retrieved Tue, 30 Apr 2024 07:00:46 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

120

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
- R PD    [(Partial) Autocorrelation Function] [ACF van de goudpr...] [2010-12-24 16:13:00] [96348ef82925ade81ab3c243141d80f1]
-    D        [(Partial) Autocorrelation Function] [autocorrelatiefun...] [2010-12-24 16:50:22] [03bcd8c83ef1a42b4029a16ba47a4880] [Current]
-    D          [(Partial) Autocorrelation Function] [autocorrelatiefun...] [2010-12-24 16:55:11] [96348ef82925ade81ab3c243141d80f1] 
-   PD            [(Partial) Autocorrelation Function] [ACF goudprijzen m...] [2010-12-28 18:54:34] [30b3e197115d238a51c18bcedc33a6a5] 
-   P           [(Partial) Autocorrelation Function] [ACF inflatie] [2010-12-28 18:50:30] [30b3e197115d238a51c18bcedc33a6a5] 

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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	1 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 & 1 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115195&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]1 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=115195&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115195&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	1 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.951333	8.7191	0
2	0.902993	8.2761	0
3	0.865296	7.9306	0
4	0.827667	7.5857	0
5	0.790475	7.2448	0
6	0.757679	6.9442	0
7	0.72648	6.6583	0
8	0.693882	6.3595	0
9	0.66428	6.0882	0
10	0.623745	5.7167	0
11	0.577846	5.296	0
12	0.544729	4.9925	2e-06
13	0.51573	4.7267	5e-06
14	0.483793	4.434	1.4e-05
15	0.450468	4.1286	4.3e-05
16	0.423741	3.8837	0.000102
17	0.398915	3.6561	0.000223
18	0.367305	3.3664	0.000575
19	0.341322	3.1283	0.001209

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.951333 & 8.7191 & 0 \tabularnewline
2 & 0.902993 & 8.2761 & 0 \tabularnewline
3 & 0.865296 & 7.9306 & 0 \tabularnewline
4 & 0.827667 & 7.5857 & 0 \tabularnewline
5 & 0.790475 & 7.2448 & 0 \tabularnewline
6 & 0.757679 & 6.9442 & 0 \tabularnewline
7 & 0.72648 & 6.6583 & 0 \tabularnewline
8 & 0.693882 & 6.3595 & 0 \tabularnewline
9 & 0.66428 & 6.0882 & 0 \tabularnewline
10 & 0.623745 & 5.7167 & 0 \tabularnewline
11 & 0.577846 & 5.296 & 0 \tabularnewline
12 & 0.544729 & 4.9925 & 2e-06 \tabularnewline
13 & 0.51573 & 4.7267 & 5e-06 \tabularnewline
14 & 0.483793 & 4.434 & 1.4e-05 \tabularnewline
15 & 0.450468 & 4.1286 & 4.3e-05 \tabularnewline
16 & 0.423741 & 3.8837 & 0.000102 \tabularnewline
17 & 0.398915 & 3.6561 & 0.000223 \tabularnewline
18 & 0.367305 & 3.3664 & 0.000575 \tabularnewline
19 & 0.341322 & 3.1283 & 0.001209 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115195&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]0.951333[/C][C]8.7191[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.902993[/C][C]8.2761[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.865296[/C][C]7.9306[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.827667[/C][C]7.5857[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.790475[/C][C]7.2448[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.757679[/C][C]6.9442[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.72648[/C][C]6.6583[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.693882[/C][C]6.3595[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.66428[/C][C]6.0882[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.623745[/C][C]5.7167[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.577846[/C][C]5.296[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.544729[/C][C]4.9925[/C][C]2e-06[/C][/ROW]
[ROW][C]13[/C][C]0.51573[/C][C]4.7267[/C][C]5e-06[/C][/ROW]
[ROW][C]14[/C][C]0.483793[/C][C]4.434[/C][C]1.4e-05[/C][/ROW]
[ROW][C]15[/C][C]0.450468[/C][C]4.1286[/C][C]4.3e-05[/C][/ROW]
[ROW][C]16[/C][C]0.423741[/C][C]3.8837[/C][C]0.000102[/C][/ROW]
[ROW][C]17[/C][C]0.398915[/C][C]3.6561[/C][C]0.000223[/C][/ROW]
[ROW][C]18[/C][C]0.367305[/C][C]3.3664[/C][C]0.000575[/C][/ROW]
[ROW][C]19[/C][C]0.341322[/C][C]3.1283[/C][C]0.001209[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115195&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115195&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	0.951333	8.7191	0
2	0.902993	8.2761	0
3	0.865296	7.9306	0
4	0.827667	7.5857	0
5	0.790475	7.2448	0
6	0.757679	6.9442	0
7	0.72648	6.6583	0
8	0.693882	6.3595	0
9	0.66428	6.0882	0
10	0.623745	5.7167	0
11	0.577846	5.296	0
12	0.544729	4.9925	2e-06
13	0.51573	4.7267	5e-06
14	0.483793	4.434	1.4e-05
15	0.450468	4.1286	4.3e-05
16	0.423741	3.8837	0.000102
17	0.398915	3.6561	0.000223
18	0.367305	3.3664	0.000575
19	0.341322	3.1283	0.001209

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.951333	8.7191	0
2	-0.021503	-0.1971	0.42212
3	0.086731	0.7949	0.214454
4	-0.019288	-0.1768	0.430055
5	-0.004201	-0.0385	0.48469
6	0.026095	0.2392	0.405779
7	3e-04	0.0027	0.498907
8	-0.023292	-0.2135	0.415738
9	0.016661	0.1527	0.439501
10	-0.135412	-1.2411	0.109017
11	-0.072635	-0.6657	0.253709
12	0.086768	0.7952	0.214357
13	0.010687	0.0979	0.461104
14	-0.026756	-0.2452	0.40344
15	-0.037688	-0.3454	0.365324
16	0.037542	0.3441	0.365823
17	0.011466	0.1051	0.458279
18	-0.078645	-0.7208	0.236519
19	0.049752	0.456	0.32479

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.951333 & 8.7191 & 0 \tabularnewline
2 & -0.021503 & -0.1971 & 0.42212 \tabularnewline
3 & 0.086731 & 0.7949 & 0.214454 \tabularnewline
4 & -0.019288 & -0.1768 & 0.430055 \tabularnewline
5 & -0.004201 & -0.0385 & 0.48469 \tabularnewline
6 & 0.026095 & 0.2392 & 0.405779 \tabularnewline
7 & 3e-04 & 0.0027 & 0.498907 \tabularnewline
8 & -0.023292 & -0.2135 & 0.415738 \tabularnewline
9 & 0.016661 & 0.1527 & 0.439501 \tabularnewline
10 & -0.135412 & -1.2411 & 0.109017 \tabularnewline
11 & -0.072635 & -0.6657 & 0.253709 \tabularnewline
12 & 0.086768 & 0.7952 & 0.214357 \tabularnewline
13 & 0.010687 & 0.0979 & 0.461104 \tabularnewline
14 & -0.026756 & -0.2452 & 0.40344 \tabularnewline
15 & -0.037688 & -0.3454 & 0.365324 \tabularnewline
16 & 0.037542 & 0.3441 & 0.365823 \tabularnewline
17 & 0.011466 & 0.1051 & 0.458279 \tabularnewline
18 & -0.078645 & -0.7208 & 0.236519 \tabularnewline
19 & 0.049752 & 0.456 & 0.32479 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115195&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]0.951333[/C][C]8.7191[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.021503[/C][C]-0.1971[/C][C]0.42212[/C][/ROW]
[ROW][C]3[/C][C]0.086731[/C][C]0.7949[/C][C]0.214454[/C][/ROW]
[ROW][C]4[/C][C]-0.019288[/C][C]-0.1768[/C][C]0.430055[/C][/ROW]
[ROW][C]5[/C][C]-0.004201[/C][C]-0.0385[/C][C]0.48469[/C][/ROW]
[ROW][C]6[/C][C]0.026095[/C][C]0.2392[/C][C]0.405779[/C][/ROW]
[ROW][C]7[/C][C]3e-04[/C][C]0.0027[/C][C]0.498907[/C][/ROW]
[ROW][C]8[/C][C]-0.023292[/C][C]-0.2135[/C][C]0.415738[/C][/ROW]
[ROW][C]9[/C][C]0.016661[/C][C]0.1527[/C][C]0.439501[/C][/ROW]
[ROW][C]10[/C][C]-0.135412[/C][C]-1.2411[/C][C]0.109017[/C][/ROW]
[ROW][C]11[/C][C]-0.072635[/C][C]-0.6657[/C][C]0.253709[/C][/ROW]
[ROW][C]12[/C][C]0.086768[/C][C]0.7952[/C][C]0.214357[/C][/ROW]
[ROW][C]13[/C][C]0.010687[/C][C]0.0979[/C][C]0.461104[/C][/ROW]
[ROW][C]14[/C][C]-0.026756[/C][C]-0.2452[/C][C]0.40344[/C][/ROW]
[ROW][C]15[/C][C]-0.037688[/C][C]-0.3454[/C][C]0.365324[/C][/ROW]
[ROW][C]16[/C][C]0.037542[/C][C]0.3441[/C][C]0.365823[/C][/ROW]
[ROW][C]17[/C][C]0.011466[/C][C]0.1051[/C][C]0.458279[/C][/ROW]
[ROW][C]18[/C][C]-0.078645[/C][C]-0.7208[/C][C]0.236519[/C][/ROW]
[ROW][C]19[/C][C]0.049752[/C][C]0.456[/C][C]0.32479[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115195&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115195&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	0.951333	8.7191	0
2	-0.021503	-0.1971	0.42212
3	0.086731	0.7949	0.214454
4	-0.019288	-0.1768	0.430055
5	-0.004201	-0.0385	0.48469
6	0.026095	0.2392	0.405779
7	3e-04	0.0027	0.498907
8	-0.023292	-0.2135	0.415738
9	0.016661	0.1527	0.439501
10	-0.135412	-1.2411	0.109017
11	-0.072635	-0.6657	0.253709
12	0.086768	0.7952	0.214357
13	0.010687	0.0979	0.461104
14	-0.026756	-0.2452	0.40344
15	-0.037688	-0.3454	0.365324
16	0.037542	0.3441	0.365823
17	0.011466	0.1051	0.458279
18	-0.078645	-0.7208	0.236519
19	0.049752	0.456	0.32479

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 = 12 ;

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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code