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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 26 Nov 2009 02:23:21 -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/Nov/26/t12592274748ygt1bmbizdgc03.htm/, Retrieved Sun, 28 Apr 2024 19:49:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59725, Retrieved Sun, 28 Apr 2024 19:49:58 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Basisjaar 2000 = 100

Estimated Impact

158

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:16:10] [b98453cac15ba1066b407e146608df68]
-   PD          [(Partial) Autocorrelation Function] [Grondstofprijsind...] [2009-11-26 09:23:21] [d41d8cd98f00b204e9800998ecf8427e] [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=59725&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=59725&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59725&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	-0.177899	-1.0525	0.149899
2	-0.102058	-0.6038	0.274941
3	-0.151003	-0.8933	0.188887
4	0.097933	0.5794	0.283022
5	-0.26176	-1.5486	0.065238
6	-0.014886	-0.0881	0.465163
7	0.237934	1.4076	0.08403
8	-0.029897	-0.1769	0.430314
9	-0.147708	-0.8739	0.194077
10	0.04124	0.244	0.404336
11	0.303304	1.7944	0.040698
12	-0.365431	-2.1619	0.018773
13	-0.027685	-0.1638	0.435421
14	0.018089	0.107	0.457694
15	0.139526	0.8254	0.207354
16	-0.082954	-0.4908	0.313328
17	-0.003952	-0.0234	0.490741

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.177899 & -1.0525 & 0.149899 \tabularnewline
2 & -0.102058 & -0.6038 & 0.274941 \tabularnewline
3 & -0.151003 & -0.8933 & 0.188887 \tabularnewline
4 & 0.097933 & 0.5794 & 0.283022 \tabularnewline
5 & -0.26176 & -1.5486 & 0.065238 \tabularnewline
6 & -0.014886 & -0.0881 & 0.465163 \tabularnewline
7 & 0.237934 & 1.4076 & 0.08403 \tabularnewline
8 & -0.029897 & -0.1769 & 0.430314 \tabularnewline
9 & -0.147708 & -0.8739 & 0.194077 \tabularnewline
10 & 0.04124 & 0.244 & 0.404336 \tabularnewline
11 & 0.303304 & 1.7944 & 0.040698 \tabularnewline
12 & -0.365431 & -2.1619 & 0.018773 \tabularnewline
13 & -0.027685 & -0.1638 & 0.435421 \tabularnewline
14 & 0.018089 & 0.107 & 0.457694 \tabularnewline
15 & 0.139526 & 0.8254 & 0.207354 \tabularnewline
16 & -0.082954 & -0.4908 & 0.313328 \tabularnewline
17 & -0.003952 & -0.0234 & 0.490741 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59725&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]-0.177899[/C][C]-1.0525[/C][C]0.149899[/C][/ROW]
[ROW][C]2[/C][C]-0.102058[/C][C]-0.6038[/C][C]0.274941[/C][/ROW]
[ROW][C]3[/C][C]-0.151003[/C][C]-0.8933[/C][C]0.188887[/C][/ROW]
[ROW][C]4[/C][C]0.097933[/C][C]0.5794[/C][C]0.283022[/C][/ROW]
[ROW][C]5[/C][C]-0.26176[/C][C]-1.5486[/C][C]0.065238[/C][/ROW]
[ROW][C]6[/C][C]-0.014886[/C][C]-0.0881[/C][C]0.465163[/C][/ROW]
[ROW][C]7[/C][C]0.237934[/C][C]1.4076[/C][C]0.08403[/C][/ROW]
[ROW][C]8[/C][C]-0.029897[/C][C]-0.1769[/C][C]0.430314[/C][/ROW]
[ROW][C]9[/C][C]-0.147708[/C][C]-0.8739[/C][C]0.194077[/C][/ROW]
[ROW][C]10[/C][C]0.04124[/C][C]0.244[/C][C]0.404336[/C][/ROW]
[ROW][C]11[/C][C]0.303304[/C][C]1.7944[/C][C]0.040698[/C][/ROW]
[ROW][C]12[/C][C]-0.365431[/C][C]-2.1619[/C][C]0.018773[/C][/ROW]
[ROW][C]13[/C][C]-0.027685[/C][C]-0.1638[/C][C]0.435421[/C][/ROW]
[ROW][C]14[/C][C]0.018089[/C][C]0.107[/C][C]0.457694[/C][/ROW]
[ROW][C]15[/C][C]0.139526[/C][C]0.8254[/C][C]0.207354[/C][/ROW]
[ROW][C]16[/C][C]-0.082954[/C][C]-0.4908[/C][C]0.313328[/C][/ROW]
[ROW][C]17[/C][C]-0.003952[/C][C]-0.0234[/C][C]0.490741[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59725&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59725&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	-0.177899	-1.0525	0.149899
2	-0.102058	-0.6038	0.274941
3	-0.151003	-0.8933	0.188887
4	0.097933	0.5794	0.283022
5	-0.26176	-1.5486	0.065238
6	-0.014886	-0.0881	0.465163
7	0.237934	1.4076	0.08403
8	-0.029897	-0.1769	0.430314
9	-0.147708	-0.8739	0.194077
10	0.04124	0.244	0.404336
11	0.303304	1.7944	0.040698
12	-0.365431	-2.1619	0.018773
13	-0.027685	-0.1638	0.435421
14	0.018089	0.107	0.457694
15	0.139526	0.8254	0.207354
16	-0.082954	-0.4908	0.313328
17	-0.003952	-0.0234	0.490741

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.177899	-1.0525	0.149899
2	-0.138076	-0.8169	0.209765
3	-0.206581	-1.2221	0.114909
4	0.008734	0.0517	0.479541
5	-0.314057	-1.858	0.0358
6	-0.185547	-1.0977	0.139913
7	0.141128	0.8349	0.204712
8	-0.103184	-0.6104	0.272756
9	-0.161457	-0.9552	0.173015
10	-0.034336	-0.2031	0.420104
11	0.253123	1.4975	0.071614
12	-0.278769	-1.6492	0.054026
13	-0.107634	-0.6368	0.264209
14	-0.081811	-0.484	0.3157
15	-0.014751	-0.0873	0.465478
16	0.101596	0.601	0.27584
17	-0.228161	-1.3498	0.09287

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.177899 & -1.0525 & 0.149899 \tabularnewline
2 & -0.138076 & -0.8169 & 0.209765 \tabularnewline
3 & -0.206581 & -1.2221 & 0.114909 \tabularnewline
4 & 0.008734 & 0.0517 & 0.479541 \tabularnewline
5 & -0.314057 & -1.858 & 0.0358 \tabularnewline
6 & -0.185547 & -1.0977 & 0.139913 \tabularnewline
7 & 0.141128 & 0.8349 & 0.204712 \tabularnewline
8 & -0.103184 & -0.6104 & 0.272756 \tabularnewline
9 & -0.161457 & -0.9552 & 0.173015 \tabularnewline
10 & -0.034336 & -0.2031 & 0.420104 \tabularnewline
11 & 0.253123 & 1.4975 & 0.071614 \tabularnewline
12 & -0.278769 & -1.6492 & 0.054026 \tabularnewline
13 & -0.107634 & -0.6368 & 0.264209 \tabularnewline
14 & -0.081811 & -0.484 & 0.3157 \tabularnewline
15 & -0.014751 & -0.0873 & 0.465478 \tabularnewline
16 & 0.101596 & 0.601 & 0.27584 \tabularnewline
17 & -0.228161 & -1.3498 & 0.09287 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59725&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]-0.177899[/C][C]-1.0525[/C][C]0.149899[/C][/ROW]
[ROW][C]2[/C][C]-0.138076[/C][C]-0.8169[/C][C]0.209765[/C][/ROW]
[ROW][C]3[/C][C]-0.206581[/C][C]-1.2221[/C][C]0.114909[/C][/ROW]
[ROW][C]4[/C][C]0.008734[/C][C]0.0517[/C][C]0.479541[/C][/ROW]
[ROW][C]5[/C][C]-0.314057[/C][C]-1.858[/C][C]0.0358[/C][/ROW]
[ROW][C]6[/C][C]-0.185547[/C][C]-1.0977[/C][C]0.139913[/C][/ROW]
[ROW][C]7[/C][C]0.141128[/C][C]0.8349[/C][C]0.204712[/C][/ROW]
[ROW][C]8[/C][C]-0.103184[/C][C]-0.6104[/C][C]0.272756[/C][/ROW]
[ROW][C]9[/C][C]-0.161457[/C][C]-0.9552[/C][C]0.173015[/C][/ROW]
[ROW][C]10[/C][C]-0.034336[/C][C]-0.2031[/C][C]0.420104[/C][/ROW]
[ROW][C]11[/C][C]0.253123[/C][C]1.4975[/C][C]0.071614[/C][/ROW]
[ROW][C]12[/C][C]-0.278769[/C][C]-1.6492[/C][C]0.054026[/C][/ROW]
[ROW][C]13[/C][C]-0.107634[/C][C]-0.6368[/C][C]0.264209[/C][/ROW]
[ROW][C]14[/C][C]-0.081811[/C][C]-0.484[/C][C]0.3157[/C][/ROW]
[ROW][C]15[/C][C]-0.014751[/C][C]-0.0873[/C][C]0.465478[/C][/ROW]
[ROW][C]16[/C][C]0.101596[/C][C]0.601[/C][C]0.27584[/C][/ROW]
[ROW][C]17[/C][C]-0.228161[/C][C]-1.3498[/C][C]0.09287[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59725&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59725&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	-0.177899	-1.0525	0.149899
2	-0.138076	-0.8169	0.209765
3	-0.206581	-1.2221	0.114909
4	0.008734	0.0517	0.479541
5	-0.314057	-1.858	0.0358
6	-0.185547	-1.0977	0.139913
7	0.141128	0.8349	0.204712
8	-0.103184	-0.6104	0.272756
9	-0.161457	-0.9552	0.173015
10	-0.034336	-0.2031	0.420104
11	0.253123	1.4975	0.071614
12	-0.278769	-1.6492	0.054026
13	-0.107634	-0.6368	0.264209
14	-0.081811	-0.484	0.3157
15	-0.014751	-0.0873	0.465478
16	0.101596	0.601	0.27584
17	-0.228161	-1.3498	0.09287

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 2.0 ; par3 = 2 ; par4 = 2 ; par5 = 12 ; par6 = MA ; 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