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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

Sun, 13 Dec 2009 02:24:34 -0700

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/2009/Dec/13/t1260696307f9kpk9kv5ytd6rt.htm/, Retrieved Sat, 27 Apr 2024 21:42:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67168, Retrieved Sat, 27 Apr 2024 21:42:46 +0000

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Original text written by user:

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No (this computation is public)

User-defined keywords

Estimated Impact

145

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

-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [(Partial) Autocorrelation Function] [paper link 8] [2009-12-13 09:24:34] [a18540c86166a2b66550d1fef0503cc2] [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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67168&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67168&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67168&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.976907	11.7635	0
2	0.955009	11.4998	0
3	0.93532	11.2627	0
4	0.913864	11.0044	0
5	0.89253	10.7475	0
6	0.872822	10.5102	0
7	0.851637	10.2551	0
8	0.831433	10.0118	0
9	0.812907	9.7887	0
10	0.792711	9.5455	0
11	0.773895	9.3189	0
12	0.756269	9.1067	0
13	0.736808	8.8723	0
14	0.718513	8.652	0
15	0.703319	8.4691	0
16	0.68681	8.2703	0
17	0.668775	8.0531	0
18	0.651366	7.8435	0
19	0.632817	7.6201	0
20	0.614054	7.3942	0
21	0.597301	7.1925	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.976907 & 11.7635 & 0 \tabularnewline
2 & 0.955009 & 11.4998 & 0 \tabularnewline
3 & 0.93532 & 11.2627 & 0 \tabularnewline
4 & 0.913864 & 11.0044 & 0 \tabularnewline
5 & 0.89253 & 10.7475 & 0 \tabularnewline
6 & 0.872822 & 10.5102 & 0 \tabularnewline
7 & 0.851637 & 10.2551 & 0 \tabularnewline
8 & 0.831433 & 10.0118 & 0 \tabularnewline
9 & 0.812907 & 9.7887 & 0 \tabularnewline
10 & 0.792711 & 9.5455 & 0 \tabularnewline
11 & 0.773895 & 9.3189 & 0 \tabularnewline
12 & 0.756269 & 9.1067 & 0 \tabularnewline
13 & 0.736808 & 8.8723 & 0 \tabularnewline
14 & 0.718513 & 8.652 & 0 \tabularnewline
15 & 0.703319 & 8.4691 & 0 \tabularnewline
16 & 0.68681 & 8.2703 & 0 \tabularnewline
17 & 0.668775 & 8.0531 & 0 \tabularnewline
18 & 0.651366 & 7.8435 & 0 \tabularnewline
19 & 0.632817 & 7.6201 & 0 \tabularnewline
20 & 0.614054 & 7.3942 & 0 \tabularnewline
21 & 0.597301 & 7.1925 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67168&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]0.976907[/C][C]11.7635[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.955009[/C][C]11.4998[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.93532[/C][C]11.2627[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.913864[/C][C]11.0044[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.89253[/C][C]10.7475[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.872822[/C][C]10.5102[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.851637[/C][C]10.2551[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.831433[/C][C]10.0118[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.812907[/C][C]9.7887[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.792711[/C][C]9.5455[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.773895[/C][C]9.3189[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.756269[/C][C]9.1067[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.736808[/C][C]8.8723[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.718513[/C][C]8.652[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.703319[/C][C]8.4691[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.68681[/C][C]8.2703[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.668775[/C][C]8.0531[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.651366[/C][C]7.8435[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.632817[/C][C]7.6201[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.614054[/C][C]7.3942[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.597301[/C][C]7.1925[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67168&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67168&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	0.976907	11.7635	0
2	0.955009	11.4998	0
3	0.93532	11.2627	0
4	0.913864	11.0044	0
5	0.89253	10.7475	0
6	0.872822	10.5102	0
7	0.851637	10.2551	0
8	0.831433	10.0118	0
9	0.812907	9.7887	0
10	0.792711	9.5455	0
11	0.773895	9.3189	0
12	0.756269	9.1067	0
13	0.736808	8.8723	0
14	0.718513	8.652	0
15	0.703319	8.4691	0
16	0.68681	8.2703	0
17	0.668775	8.0531	0
18	0.651366	7.8435	0
19	0.632817	7.6201	0
20	0.614054	7.3942	0
21	0.597301	7.1925	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.976907	11.7635	0
2	0.014477	0.1743	0.430928
3	0.037874	0.4561	0.324511
4	-0.046471	-0.5596	0.288312
5	-0.008098	-0.0975	0.461225
6	0.02107	0.2537	0.400038
7	-0.039735	-0.4785	0.316515
8	0.011654	0.1403	0.444295
9	0.02173	0.2617	0.396978
10	-0.041103	-0.4949	0.310693
11	0.020303	0.2445	0.4036
12	0.009643	0.1161	0.453862
13	-0.042193	-0.5081	0.306087
14	0.014081	0.1696	0.432797
15	0.050603	0.6093	0.271625
16	-0.025762	-0.3102	0.378419
17	-0.041071	-0.4946	0.310828
18	-0.008729	-0.1051	0.458214
19	-0.029503	-0.3553	0.361455
20	-0.013591	-0.1637	0.435115
21	0.024166	0.291	0.385734

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.976907 & 11.7635 & 0 \tabularnewline
2 & 0.014477 & 0.1743 & 0.430928 \tabularnewline
3 & 0.037874 & 0.4561 & 0.324511 \tabularnewline
4 & -0.046471 & -0.5596 & 0.288312 \tabularnewline
5 & -0.008098 & -0.0975 & 0.461225 \tabularnewline
6 & 0.02107 & 0.2537 & 0.400038 \tabularnewline
7 & -0.039735 & -0.4785 & 0.316515 \tabularnewline
8 & 0.011654 & 0.1403 & 0.444295 \tabularnewline
9 & 0.02173 & 0.2617 & 0.396978 \tabularnewline
10 & -0.041103 & -0.4949 & 0.310693 \tabularnewline
11 & 0.020303 & 0.2445 & 0.4036 \tabularnewline
12 & 0.009643 & 0.1161 & 0.453862 \tabularnewline
13 & -0.042193 & -0.5081 & 0.306087 \tabularnewline
14 & 0.014081 & 0.1696 & 0.432797 \tabularnewline
15 & 0.050603 & 0.6093 & 0.271625 \tabularnewline
16 & -0.025762 & -0.3102 & 0.378419 \tabularnewline
17 & -0.041071 & -0.4946 & 0.310828 \tabularnewline
18 & -0.008729 & -0.1051 & 0.458214 \tabularnewline
19 & -0.029503 & -0.3553 & 0.361455 \tabularnewline
20 & -0.013591 & -0.1637 & 0.435115 \tabularnewline
21 & 0.024166 & 0.291 & 0.385734 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67168&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]0.976907[/C][C]11.7635[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.014477[/C][C]0.1743[/C][C]0.430928[/C][/ROW]
[ROW][C]3[/C][C]0.037874[/C][C]0.4561[/C][C]0.324511[/C][/ROW]
[ROW][C]4[/C][C]-0.046471[/C][C]-0.5596[/C][C]0.288312[/C][/ROW]
[ROW][C]5[/C][C]-0.008098[/C][C]-0.0975[/C][C]0.461225[/C][/ROW]
[ROW][C]6[/C][C]0.02107[/C][C]0.2537[/C][C]0.400038[/C][/ROW]
[ROW][C]7[/C][C]-0.039735[/C][C]-0.4785[/C][C]0.316515[/C][/ROW]
[ROW][C]8[/C][C]0.011654[/C][C]0.1403[/C][C]0.444295[/C][/ROW]
[ROW][C]9[/C][C]0.02173[/C][C]0.2617[/C][C]0.396978[/C][/ROW]
[ROW][C]10[/C][C]-0.041103[/C][C]-0.4949[/C][C]0.310693[/C][/ROW]
[ROW][C]11[/C][C]0.020303[/C][C]0.2445[/C][C]0.4036[/C][/ROW]
[ROW][C]12[/C][C]0.009643[/C][C]0.1161[/C][C]0.453862[/C][/ROW]
[ROW][C]13[/C][C]-0.042193[/C][C]-0.5081[/C][C]0.306087[/C][/ROW]
[ROW][C]14[/C][C]0.014081[/C][C]0.1696[/C][C]0.432797[/C][/ROW]
[ROW][C]15[/C][C]0.050603[/C][C]0.6093[/C][C]0.271625[/C][/ROW]
[ROW][C]16[/C][C]-0.025762[/C][C]-0.3102[/C][C]0.378419[/C][/ROW]
[ROW][C]17[/C][C]-0.041071[/C][C]-0.4946[/C][C]0.310828[/C][/ROW]
[ROW][C]18[/C][C]-0.008729[/C][C]-0.1051[/C][C]0.458214[/C][/ROW]
[ROW][C]19[/C][C]-0.029503[/C][C]-0.3553[/C][C]0.361455[/C][/ROW]
[ROW][C]20[/C][C]-0.013591[/C][C]-0.1637[/C][C]0.435115[/C][/ROW]
[ROW][C]21[/C][C]0.024166[/C][C]0.291[/C][C]0.385734[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67168&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67168&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	0.976907	11.7635	0
2	0.014477	0.1743	0.430928
3	0.037874	0.4561	0.324511
4	-0.046471	-0.5596	0.288312
5	-0.008098	-0.0975	0.461225
6	0.02107	0.2537	0.400038
7	-0.039735	-0.4785	0.316515
8	0.011654	0.1403	0.444295
9	0.02173	0.2617	0.396978
10	-0.041103	-0.4949	0.310693
11	0.020303	0.2445	0.4036
12	0.009643	0.1161	0.453862
13	-0.042193	-0.5081	0.306087
14	0.014081	0.1696	0.432797
15	0.050603	0.6093	0.271625
16	-0.025762	-0.3102	0.378419
17	-0.041071	-0.4946	0.310828
18	-0.008729	-0.1051	0.458214
19	-0.029503	-0.3553	0.361455
20	-0.013591	-0.1637	0.435115
21	0.024166	0.291	0.385734

Figure 1

PNG link

Postscript link

PDF link

Figure 2

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 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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