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Author's title

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

Mon, 27 Dec 2010 18:39:20 +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/27/t1293475634kpzlvib6hbxno3g.htm/, Retrieved Mon, 06 May 2024 21:54:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116083, Retrieved Mon, 06 May 2024 21:54:09 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

103

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

-     [Classical Decomposition] [] [2010-12-20 14:39:41] [1c63f3c303537b65dfa698074d619a3e]
- RMPD    [(Partial) Autocorrelation Function] [] [2010-12-27 18:39:20] [6d519594e32ce09ffe6000a98c6f6a83] [Current]

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Dataseries X:

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Histogram

Boxplots

9.4
9.4
9.5
9.5
9.4
9.4
9.3
9.4
9.4
9.2
9.1
9.1
9.1
9.0
9.0
8.9
8.8
8.7
8.5
8.3
8.1
7.9
7.8
7.6
7.4
7.2
7.0
7.0
6.8
6.8
6.7
6.8
6.7
6.7
6.7
6.5
6.3
6.3
6.3
6.5
6.6
6.5
6.3
6.3
6.5
7.0
7.1
7.3
7.3
7.4
7.4
7.3
7.4
7.5
7.7
7.7
7.7
7.7
7.7
7.8
8.0
8.1
8.1
8.2
8.2
8.2
8.1
8.1
8.2
8.3
8.3
8.4
8.5
8.5
8.4
8.0
7.9
8.1
8.5
8.8
8.8
8.6
8.3
8.3
8.3
8.4
8.4
8.5
8.6
8.6
8.6
8.6
8.6
8.5
8.4
8.4
8.4
8.5
8.5
8.6
8.6
8.4
8.2
8.0
8.0
8.0
8.0
7.9
7.9
7.8
7.8
8.0
7.8
7.4
7.2
7.0
7.0
7.2
7.2
7.2
7.0
6.9
6.8
6.8
6.8
6.9
7.2
7.2
7.2
7.1
7.2
7.3
7.5
7.6
7.7
7.7
7.7
7.8
8.0
8.1
8.1
8.0
8.1
8.2
8.3
8.4
8.4
8.4
8.5
8.5
8.6
8.6
8.5
8.5

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=116083&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=116083&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116083&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	0.972804	12.0722	0
2	0.931613	11.561	0
3	0.884161	10.9721	0
4	0.840664	10.4324	0
5	0.801704	9.9489	0
6	0.758686	9.4151	0
7	0.709455	8.8041	0
8	0.649487	8.0599	0
9	0.58242	7.2276	0
10	0.513283	6.3697	0
11	0.443307	5.5013	0
12	0.371289	4.6076	4e-06
13	0.29804	3.6986	0.000151
14	0.225399	2.7971	0.002907
15	0.151339	1.8781	0.031131
16	0.077859	0.9662	0.167728
17	0.006164	0.0765	0.469565
18	-0.063024	-0.7821	0.217676
19	-0.129805	-1.6108	0.054631
20	-0.194485	-2.4135	0.008487
21	-0.256873	-3.1877	0.000869

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.972804 & 12.0722 & 0 \tabularnewline
2 & 0.931613 & 11.561 & 0 \tabularnewline
3 & 0.884161 & 10.9721 & 0 \tabularnewline
4 & 0.840664 & 10.4324 & 0 \tabularnewline
5 & 0.801704 & 9.9489 & 0 \tabularnewline
6 & 0.758686 & 9.4151 & 0 \tabularnewline
7 & 0.709455 & 8.8041 & 0 \tabularnewline
8 & 0.649487 & 8.0599 & 0 \tabularnewline
9 & 0.58242 & 7.2276 & 0 \tabularnewline
10 & 0.513283 & 6.3697 & 0 \tabularnewline
11 & 0.443307 & 5.5013 & 0 \tabularnewline
12 & 0.371289 & 4.6076 & 4e-06 \tabularnewline
13 & 0.29804 & 3.6986 & 0.000151 \tabularnewline
14 & 0.225399 & 2.7971 & 0.002907 \tabularnewline
15 & 0.151339 & 1.8781 & 0.031131 \tabularnewline
16 & 0.077859 & 0.9662 & 0.167728 \tabularnewline
17 & 0.006164 & 0.0765 & 0.469565 \tabularnewline
18 & -0.063024 & -0.7821 & 0.217676 \tabularnewline
19 & -0.129805 & -1.6108 & 0.054631 \tabularnewline
20 & -0.194485 & -2.4135 & 0.008487 \tabularnewline
21 & -0.256873 & -3.1877 & 0.000869 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116083&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]0.972804[/C][C]12.0722[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.931613[/C][C]11.561[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.884161[/C][C]10.9721[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.840664[/C][C]10.4324[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.801704[/C][C]9.9489[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.758686[/C][C]9.4151[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.709455[/C][C]8.8041[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.649487[/C][C]8.0599[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.58242[/C][C]7.2276[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.513283[/C][C]6.3697[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.443307[/C][C]5.5013[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.371289[/C][C]4.6076[/C][C]4e-06[/C][/ROW]
[ROW][C]13[/C][C]0.29804[/C][C]3.6986[/C][C]0.000151[/C][/ROW]
[ROW][C]14[/C][C]0.225399[/C][C]2.7971[/C][C]0.002907[/C][/ROW]
[ROW][C]15[/C][C]0.151339[/C][C]1.8781[/C][C]0.031131[/C][/ROW]
[ROW][C]16[/C][C]0.077859[/C][C]0.9662[/C][C]0.167728[/C][/ROW]
[ROW][C]17[/C][C]0.006164[/C][C]0.0765[/C][C]0.469565[/C][/ROW]
[ROW][C]18[/C][C]-0.063024[/C][C]-0.7821[/C][C]0.217676[/C][/ROW]
[ROW][C]19[/C][C]-0.129805[/C][C]-1.6108[/C][C]0.054631[/C][/ROW]
[ROW][C]20[/C][C]-0.194485[/C][C]-2.4135[/C][C]0.008487[/C][/ROW]
[ROW][C]21[/C][C]-0.256873[/C][C]-3.1877[/C][C]0.000869[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116083&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116083&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	0.972804	12.0722	0
2	0.931613	11.561	0
3	0.884161	10.9721	0
4	0.840664	10.4324	0
5	0.801704	9.9489	0
6	0.758686	9.4151	0
7	0.709455	8.8041	0
8	0.649487	8.0599	0
9	0.58242	7.2276	0
10	0.513283	6.3697	0
11	0.443307	5.5013	0
12	0.371289	4.6076	4e-06
13	0.29804	3.6986	0.000151
14	0.225399	2.7971	0.002907
15	0.151339	1.8781	0.031131
16	0.077859	0.9662	0.167728
17	0.006164	0.0765	0.469565
18	-0.063024	-0.7821	0.217676
19	-0.129805	-1.6108	0.054631
20	-0.194485	-2.4135	0.008487
21	-0.256873	-3.1877	0.000869

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.972804	12.0722	0
2	-0.274646	-3.4083	0.000417
3	-0.077498	-0.9617	0.168847
4	0.098779	1.2258	0.11107
5	0.026246	0.3257	0.372547
6	-0.160779	-1.9952	0.023892
7	-0.106236	-1.3183	0.094672
8	-0.163366	-2.0273	0.022177
9	-0.098726	-1.2252	0.111193
10	-0.044936	-0.5576	0.288951
11	-0.08194	-1.0169	0.155409
12	-0.12304	-1.5269	0.06442
13	-0.04853	-0.6022	0.273951
14	-0.004767	-0.0592	0.476452
15	-0.088719	-1.101	0.136313
16	-0.040444	-0.5019	0.308226
17	-0.014085	-0.1748	0.430737
18	-0.027438	-0.3405	0.366973
19	-0.038749	-0.4809	0.315648
20	-0.033838	-0.4199	0.337564
21	-0.046834	-0.5812	0.280978

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.972804 & 12.0722 & 0 \tabularnewline
2 & -0.274646 & -3.4083 & 0.000417 \tabularnewline
3 & -0.077498 & -0.9617 & 0.168847 \tabularnewline
4 & 0.098779 & 1.2258 & 0.11107 \tabularnewline
5 & 0.026246 & 0.3257 & 0.372547 \tabularnewline
6 & -0.160779 & -1.9952 & 0.023892 \tabularnewline
7 & -0.106236 & -1.3183 & 0.094672 \tabularnewline
8 & -0.163366 & -2.0273 & 0.022177 \tabularnewline
9 & -0.098726 & -1.2252 & 0.111193 \tabularnewline
10 & -0.044936 & -0.5576 & 0.288951 \tabularnewline
11 & -0.08194 & -1.0169 & 0.155409 \tabularnewline
12 & -0.12304 & -1.5269 & 0.06442 \tabularnewline
13 & -0.04853 & -0.6022 & 0.273951 \tabularnewline
14 & -0.004767 & -0.0592 & 0.476452 \tabularnewline
15 & -0.088719 & -1.101 & 0.136313 \tabularnewline
16 & -0.040444 & -0.5019 & 0.308226 \tabularnewline
17 & -0.014085 & -0.1748 & 0.430737 \tabularnewline
18 & -0.027438 & -0.3405 & 0.366973 \tabularnewline
19 & -0.038749 & -0.4809 & 0.315648 \tabularnewline
20 & -0.033838 & -0.4199 & 0.337564 \tabularnewline
21 & -0.046834 & -0.5812 & 0.280978 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116083&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]0.972804[/C][C]12.0722[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.274646[/C][C]-3.4083[/C][C]0.000417[/C][/ROW]
[ROW][C]3[/C][C]-0.077498[/C][C]-0.9617[/C][C]0.168847[/C][/ROW]
[ROW][C]4[/C][C]0.098779[/C][C]1.2258[/C][C]0.11107[/C][/ROW]
[ROW][C]5[/C][C]0.026246[/C][C]0.3257[/C][C]0.372547[/C][/ROW]
[ROW][C]6[/C][C]-0.160779[/C][C]-1.9952[/C][C]0.023892[/C][/ROW]
[ROW][C]7[/C][C]-0.106236[/C][C]-1.3183[/C][C]0.094672[/C][/ROW]
[ROW][C]8[/C][C]-0.163366[/C][C]-2.0273[/C][C]0.022177[/C][/ROW]
[ROW][C]9[/C][C]-0.098726[/C][C]-1.2252[/C][C]0.111193[/C][/ROW]
[ROW][C]10[/C][C]-0.044936[/C][C]-0.5576[/C][C]0.288951[/C][/ROW]
[ROW][C]11[/C][C]-0.08194[/C][C]-1.0169[/C][C]0.155409[/C][/ROW]
[ROW][C]12[/C][C]-0.12304[/C][C]-1.5269[/C][C]0.06442[/C][/ROW]
[ROW][C]13[/C][C]-0.04853[/C][C]-0.6022[/C][C]0.273951[/C][/ROW]
[ROW][C]14[/C][C]-0.004767[/C][C]-0.0592[/C][C]0.476452[/C][/ROW]
[ROW][C]15[/C][C]-0.088719[/C][C]-1.101[/C][C]0.136313[/C][/ROW]
[ROW][C]16[/C][C]-0.040444[/C][C]-0.5019[/C][C]0.308226[/C][/ROW]
[ROW][C]17[/C][C]-0.014085[/C][C]-0.1748[/C][C]0.430737[/C][/ROW]
[ROW][C]18[/C][C]-0.027438[/C][C]-0.3405[/C][C]0.366973[/C][/ROW]
[ROW][C]19[/C][C]-0.038749[/C][C]-0.4809[/C][C]0.315648[/C][/ROW]
[ROW][C]20[/C][C]-0.033838[/C][C]-0.4199[/C][C]0.337564[/C][/ROW]
[ROW][C]21[/C][C]-0.046834[/C][C]-0.5812[/C][C]0.280978[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116083&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116083&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	0.972804	12.0722	0
2	-0.274646	-3.4083	0.000417
3	-0.077498	-0.9617	0.168847
4	0.098779	1.2258	0.11107
5	0.026246	0.3257	0.372547
6	-0.160779	-1.9952	0.023892
7	-0.106236	-1.3183	0.094672
8	-0.163366	-2.0273	0.022177
9	-0.098726	-1.2252	0.111193
10	-0.044936	-0.5576	0.288951
11	-0.08194	-1.0169	0.155409
12	-0.12304	-1.5269	0.06442
13	-0.04853	-0.6022	0.273951
14	-0.004767	-0.0592	0.476452
15	-0.088719	-1.101	0.136313
16	-0.040444	-0.5019	0.308226
17	-0.014085	-0.1748	0.430737
18	-0.027438	-0.3405	0.366973
19	-0.038749	-0.4809	0.315648
20	-0.033838	-0.4199	0.337564
21	-0.046834	-0.5812	0.280978

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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code