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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 25 Nov 2007 04:57:00 -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/2007/Nov/25/t11959912635z7qd45rln09euf.htm/, Retrieved Sat, 04 May 2024 14:14:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6412, Retrieved Sat, 04 May 2024 14:14:18 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

210

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

-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2007-11-25 11:57:00] [9fe578921d87f9af8e79a90d6142ba02] [Current]

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Dataseries X:

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Histogram

Boxplots

8.1
8.2
8
8.1
8.3
8.2
8.1
7.7
7.6
7.7
8.2
8.4
8.4
8.6
8.4
8.5
8.7
8.7
8.6
7.4
7.3
7.4
9
9.2
9.2
8.5
8.3
8.3
8.6
8.6
8.5
8.1
8.1
8
8.6
8.7
8.7
8.6
8.4
8.4
8.7
8.7
8.5
8.3
8.3
8.3
8.1
8.2
8.1
8.1
7.9
7.7
8.1
8
7.7
7.8
7.6
7.4
7.7
7.9
7.6

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6412&T=0

[TABLE]
[ROW][C]Summary of compuational 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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6412&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6412&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.8102	0
1	0.678304	5.2977	1e-06
2	0.289972	2.2648	0.013546
3	-0.026422	-0.2064	0.581403
4	-0.007291	-0.0569	0.522612
5	0.143142	1.118	0.133981
6	0.258359	2.0178	0.024006
7	0.15152	1.1834	0.12062
8	-0.015538	-0.1214	0.548096
9	-0.075674	-0.591	0.72166
10	0.042295	0.3303	0.371139
11	0.222149	1.735	0.043892
12	0.338902	2.6469	0.005161
13	0.167585	1.3089	0.097742
14	-0.073149	-0.5713	0.715055
15	-0.279811	-2.1854	0.983645
16	-0.258985	-2.0227	0.976255

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.8102 & 0 \tabularnewline
1 & 0.678304 & 5.2977 & 1e-06 \tabularnewline
2 & 0.289972 & 2.2648 & 0.013546 \tabularnewline
3 & -0.026422 & -0.2064 & 0.581403 \tabularnewline
4 & -0.007291 & -0.0569 & 0.522612 \tabularnewline
5 & 0.143142 & 1.118 & 0.133981 \tabularnewline
6 & 0.258359 & 2.0178 & 0.024006 \tabularnewline
7 & 0.15152 & 1.1834 & 0.12062 \tabularnewline
8 & -0.015538 & -0.1214 & 0.548096 \tabularnewline
9 & -0.075674 & -0.591 & 0.72166 \tabularnewline
10 & 0.042295 & 0.3303 & 0.371139 \tabularnewline
11 & 0.222149 & 1.735 & 0.043892 \tabularnewline
12 & 0.338902 & 2.6469 & 0.005161 \tabularnewline
13 & 0.167585 & 1.3089 & 0.097742 \tabularnewline
14 & -0.073149 & -0.5713 & 0.715055 \tabularnewline
15 & -0.279811 & -2.1854 & 0.983645 \tabularnewline
16 & -0.258985 & -2.0227 & 0.976255 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6412&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]0[/C][C]1[/C][C]7.8102[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.678304[/C][C]5.2977[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.289972[/C][C]2.2648[/C][C]0.013546[/C][/ROW]
[ROW][C]3[/C][C]-0.026422[/C][C]-0.2064[/C][C]0.581403[/C][/ROW]
[ROW][C]4[/C][C]-0.007291[/C][C]-0.0569[/C][C]0.522612[/C][/ROW]
[ROW][C]5[/C][C]0.143142[/C][C]1.118[/C][C]0.133981[/C][/ROW]
[ROW][C]6[/C][C]0.258359[/C][C]2.0178[/C][C]0.024006[/C][/ROW]
[ROW][C]7[/C][C]0.15152[/C][C]1.1834[/C][C]0.12062[/C][/ROW]
[ROW][C]8[/C][C]-0.015538[/C][C]-0.1214[/C][C]0.548096[/C][/ROW]
[ROW][C]9[/C][C]-0.075674[/C][C]-0.591[/C][C]0.72166[/C][/ROW]
[ROW][C]10[/C][C]0.042295[/C][C]0.3303[/C][C]0.371139[/C][/ROW]
[ROW][C]11[/C][C]0.222149[/C][C]1.735[/C][C]0.043892[/C][/ROW]
[ROW][C]12[/C][C]0.338902[/C][C]2.6469[/C][C]0.005161[/C][/ROW]
[ROW][C]13[/C][C]0.167585[/C][C]1.3089[/C][C]0.097742[/C][/ROW]
[ROW][C]14[/C][C]-0.073149[/C][C]-0.5713[/C][C]0.715055[/C][/ROW]
[ROW][C]15[/C][C]-0.279811[/C][C]-2.1854[/C][C]0.983645[/C][/ROW]
[ROW][C]16[/C][C]-0.258985[/C][C]-2.0227[/C][C]0.976255[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6412&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6412&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
0	1	7.8102	0
1	0.678304	5.2977	1e-06
2	0.289972	2.2648	0.013546
3	-0.026422	-0.2064	0.581403
4	-0.007291	-0.0569	0.522612
5	0.143142	1.118	0.133981
6	0.258359	2.0178	0.024006
7	0.15152	1.1834	0.12062
8	-0.015538	-0.1214	0.548096
9	-0.075674	-0.591	0.72166
10	0.042295	0.3303	0.371139
11	0.222149	1.735	0.043892
12	0.338902	2.6469	0.005161
13	0.167585	1.3089	0.097742
14	-0.073149	-0.5713	0.715055
15	-0.279811	-2.1854	0.983645
16	-0.258985	-2.0227	0.976255

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.678304	5.2977	1e-06
1	-0.315101	-2.461	0.99165
2	-0.146729	-1.146	0.871863
3	0.35307	2.7576	0.003836
4	0.086887	0.6786	0.249975
5	-0.039957	-0.3121	0.621977
6	-0.163947	-1.2805	0.897386
7	0.026184	0.2045	0.419322
8	0.160089	1.2503	0.107977
9	0.089766	0.7011	0.242956
10	0.059179	0.4622	0.322792
11	0.118302	0.924	0.179571
12	-0.287084	-2.2422	0.985703
13	-0.056406	-0.4405	0.669449
14	-0.097201	-0.7592	0.774661
15	-0.038774	-0.3028	0.618478
16	-0.004197	-0.0328	0.513022

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.678304 & 5.2977 & 1e-06 \tabularnewline
1 & -0.315101 & -2.461 & 0.99165 \tabularnewline
2 & -0.146729 & -1.146 & 0.871863 \tabularnewline
3 & 0.35307 & 2.7576 & 0.003836 \tabularnewline
4 & 0.086887 & 0.6786 & 0.249975 \tabularnewline
5 & -0.039957 & -0.3121 & 0.621977 \tabularnewline
6 & -0.163947 & -1.2805 & 0.897386 \tabularnewline
7 & 0.026184 & 0.2045 & 0.419322 \tabularnewline
8 & 0.160089 & 1.2503 & 0.107977 \tabularnewline
9 & 0.089766 & 0.7011 & 0.242956 \tabularnewline
10 & 0.059179 & 0.4622 & 0.322792 \tabularnewline
11 & 0.118302 & 0.924 & 0.179571 \tabularnewline
12 & -0.287084 & -2.2422 & 0.985703 \tabularnewline
13 & -0.056406 & -0.4405 & 0.669449 \tabularnewline
14 & -0.097201 & -0.7592 & 0.774661 \tabularnewline
15 & -0.038774 & -0.3028 & 0.618478 \tabularnewline
16 & -0.004197 & -0.0328 & 0.513022 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6412&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]0[/C][C]0.678304[/C][C]5.2977[/C][C]1e-06[/C][/ROW]
[ROW][C]1[/C][C]-0.315101[/C][C]-2.461[/C][C]0.99165[/C][/ROW]
[ROW][C]2[/C][C]-0.146729[/C][C]-1.146[/C][C]0.871863[/C][/ROW]
[ROW][C]3[/C][C]0.35307[/C][C]2.7576[/C][C]0.003836[/C][/ROW]
[ROW][C]4[/C][C]0.086887[/C][C]0.6786[/C][C]0.249975[/C][/ROW]
[ROW][C]5[/C][C]-0.039957[/C][C]-0.3121[/C][C]0.621977[/C][/ROW]
[ROW][C]6[/C][C]-0.163947[/C][C]-1.2805[/C][C]0.897386[/C][/ROW]
[ROW][C]7[/C][C]0.026184[/C][C]0.2045[/C][C]0.419322[/C][/ROW]
[ROW][C]8[/C][C]0.160089[/C][C]1.2503[/C][C]0.107977[/C][/ROW]
[ROW][C]9[/C][C]0.089766[/C][C]0.7011[/C][C]0.242956[/C][/ROW]
[ROW][C]10[/C][C]0.059179[/C][C]0.4622[/C][C]0.322792[/C][/ROW]
[ROW][C]11[/C][C]0.118302[/C][C]0.924[/C][C]0.179571[/C][/ROW]
[ROW][C]12[/C][C]-0.287084[/C][C]-2.2422[/C][C]0.985703[/C][/ROW]
[ROW][C]13[/C][C]-0.056406[/C][C]-0.4405[/C][C]0.669449[/C][/ROW]
[ROW][C]14[/C][C]-0.097201[/C][C]-0.7592[/C][C]0.774661[/C][/ROW]
[ROW][C]15[/C][C]-0.038774[/C][C]-0.3028[/C][C]0.618478[/C][/ROW]
[ROW][C]16[/C][C]-0.004197[/C][C]-0.0328[/C][C]0.513022[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6412&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6412&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
0	0.678304	5.2977	1e-06
1	-0.315101	-2.461	0.99165
2	-0.146729	-1.146	0.871863
3	0.35307	2.7576	0.003836
4	0.086887	0.6786	0.249975
5	-0.039957	-0.3121	0.621977
6	-0.163947	-1.2805	0.897386
7	0.026184	0.2045	0.419322
8	0.160089	1.2503	0.107977
9	0.089766	0.7011	0.242956
10	0.059179	0.4622	0.322792
11	0.118302	0.924	0.179571
12	-0.287084	-2.2422	0.985703
13	-0.056406	-0.4405	0.669449
14	-0.097201	-0.7592	0.774661
15	-0.038774	-0.3028	0.618478
16	-0.004197	-0.0328	0.513022

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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Dataset

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Input Parameters & R Code