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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 05 Dec 2007 12:12:13 -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/Dec/05/t11968811700jm8eilrl00aasx.htm/, Retrieved Fri, 03 May 2024 03:43:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2503, Retrieved Fri, 03 May 2024 03:43:45 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

252

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

-       [(Partial) Autocorrelation Function] [ACF & PACF inflatie] [2007-12-05 19:12:13] [5a8e7c1f041681f87e3014e302618e0c] [Current]

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1,6
1,6
1,4
1,7
1,8
1,9
2,2
2,1
2,4
2,6
2,8
2,7
2,6
2,9
2,8
2,2
2,2
2,2
2
2
1,7
1,4
1,3
1,4
1,3
1,3
1,4
2
1,7
1,8
1,7
1,6
1,7
1,9
1,8
1,7
1,6
1,8
1,6
1,5
1,5
1,3
1,4
1,4
1,3
1,3
1,2
1,1
1,4
1,2
1,5
1,1
1,3
1,5
1,1
1,4
1,3
1,5
1,6
1,7

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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 & 2 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=2503&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]2 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=2503&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2503&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	2 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	7.6811	0
1	-0.217243	-1.6687	0.94976
2	0.078591	0.6037	0.274189
3	0.146327	1.124	0.132791
4	-0.018478	-0.1419	0.556192
5	0.161561	1.241	0.109763
6	-0.093201	-0.7159	0.761558
7	-0.021973	-0.1688	0.566726
8	-0.059112	-0.454	0.67427
9	-0.179098	-1.3757	0.912939
10	0.162064	1.2448	0.109057
11	-0.1565	-1.2021	0.882936
12	-0.411072	-3.1575	0.998746
13	0.158379	1.2165	0.114314
14	-0.115175	-0.8847	0.810039
15	-0.033155	-0.2547	0.600067
16	0.037946	0.2915	0.385857

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & -0.217243 & -1.6687 & 0.94976 \tabularnewline
2 & 0.078591 & 0.6037 & 0.274189 \tabularnewline
3 & 0.146327 & 1.124 & 0.132791 \tabularnewline
4 & -0.018478 & -0.1419 & 0.556192 \tabularnewline
5 & 0.161561 & 1.241 & 0.109763 \tabularnewline
6 & -0.093201 & -0.7159 & 0.761558 \tabularnewline
7 & -0.021973 & -0.1688 & 0.566726 \tabularnewline
8 & -0.059112 & -0.454 & 0.67427 \tabularnewline
9 & -0.179098 & -1.3757 & 0.912939 \tabularnewline
10 & 0.162064 & 1.2448 & 0.109057 \tabularnewline
11 & -0.1565 & -1.2021 & 0.882936 \tabularnewline
12 & -0.411072 & -3.1575 & 0.998746 \tabularnewline
13 & 0.158379 & 1.2165 & 0.114314 \tabularnewline
14 & -0.115175 & -0.8847 & 0.810039 \tabularnewline
15 & -0.033155 & -0.2547 & 0.600067 \tabularnewline
16 & 0.037946 & 0.2915 & 0.385857 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2503&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]7.6811[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.217243[/C][C]-1.6687[/C][C]0.94976[/C][/ROW]
[ROW][C]2[/C][C]0.078591[/C][C]0.6037[/C][C]0.274189[/C][/ROW]
[ROW][C]3[/C][C]0.146327[/C][C]1.124[/C][C]0.132791[/C][/ROW]
[ROW][C]4[/C][C]-0.018478[/C][C]-0.1419[/C][C]0.556192[/C][/ROW]
[ROW][C]5[/C][C]0.161561[/C][C]1.241[/C][C]0.109763[/C][/ROW]
[ROW][C]6[/C][C]-0.093201[/C][C]-0.7159[/C][C]0.761558[/C][/ROW]
[ROW][C]7[/C][C]-0.021973[/C][C]-0.1688[/C][C]0.566726[/C][/ROW]
[ROW][C]8[/C][C]-0.059112[/C][C]-0.454[/C][C]0.67427[/C][/ROW]
[ROW][C]9[/C][C]-0.179098[/C][C]-1.3757[/C][C]0.912939[/C][/ROW]
[ROW][C]10[/C][C]0.162064[/C][C]1.2448[/C][C]0.109057[/C][/ROW]
[ROW][C]11[/C][C]-0.1565[/C][C]-1.2021[/C][C]0.882936[/C][/ROW]
[ROW][C]12[/C][C]-0.411072[/C][C]-3.1575[/C][C]0.998746[/C][/ROW]
[ROW][C]13[/C][C]0.158379[/C][C]1.2165[/C][C]0.114314[/C][/ROW]
[ROW][C]14[/C][C]-0.115175[/C][C]-0.8847[/C][C]0.810039[/C][/ROW]
[ROW][C]15[/C][C]-0.033155[/C][C]-0.2547[/C][C]0.600067[/C][/ROW]
[ROW][C]16[/C][C]0.037946[/C][C]0.2915[/C][C]0.385857[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2503&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2503&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	7.6811	0
1	-0.217243	-1.6687	0.94976
2	0.078591	0.6037	0.274189
3	0.146327	1.124	0.132791
4	-0.018478	-0.1419	0.556192
5	0.161561	1.241	0.109763
6	-0.093201	-0.7159	0.761558
7	-0.021973	-0.1688	0.566726
8	-0.059112	-0.454	0.67427
9	-0.179098	-1.3757	0.912939
10	0.162064	1.2448	0.109057
11	-0.1565	-1.2021	0.882936
12	-0.411072	-3.1575	0.998746
13	0.158379	1.2165	0.114314
14	-0.115175	-0.8847	0.810039
15	-0.033155	-0.2547	0.600067
16	0.037946	0.2915	0.385857

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.217243	-1.6687	0.94976
1	0.032952	0.2531	0.400533
2	0.178611	1.3719	0.087639
3	0.050344	0.3867	0.350184
4	0.156306	1.2006	0.117351
5	-0.060064	-0.4614	0.676882
6	-0.093154	-0.7155	0.761449
7	-0.140319	-1.0778	0.857248
8	-0.228319	-1.7538	0.957667
9	0.100711	0.7736	0.221136
10	-0.007402	-0.0569	0.522574
11	-0.453997	-3.4872	0.999536
12	-0.04204	-0.3229	0.626049
13	0.054537	0.4189	0.338404
14	0.002077	0.016	0.493662
15	0.117833	0.9051	0.184549
16	0.102163	0.7847	0.217876

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.217243 & -1.6687 & 0.94976 \tabularnewline
1 & 0.032952 & 0.2531 & 0.400533 \tabularnewline
2 & 0.178611 & 1.3719 & 0.087639 \tabularnewline
3 & 0.050344 & 0.3867 & 0.350184 \tabularnewline
4 & 0.156306 & 1.2006 & 0.117351 \tabularnewline
5 & -0.060064 & -0.4614 & 0.676882 \tabularnewline
6 & -0.093154 & -0.7155 & 0.761449 \tabularnewline
7 & -0.140319 & -1.0778 & 0.857248 \tabularnewline
8 & -0.228319 & -1.7538 & 0.957667 \tabularnewline
9 & 0.100711 & 0.7736 & 0.221136 \tabularnewline
10 & -0.007402 & -0.0569 & 0.522574 \tabularnewline
11 & -0.453997 & -3.4872 & 0.999536 \tabularnewline
12 & -0.04204 & -0.3229 & 0.626049 \tabularnewline
13 & 0.054537 & 0.4189 & 0.338404 \tabularnewline
14 & 0.002077 & 0.016 & 0.493662 \tabularnewline
15 & 0.117833 & 0.9051 & 0.184549 \tabularnewline
16 & 0.102163 & 0.7847 & 0.217876 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2503&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]-0.217243[/C][C]-1.6687[/C][C]0.94976[/C][/ROW]
[ROW][C]1[/C][C]0.032952[/C][C]0.2531[/C][C]0.400533[/C][/ROW]
[ROW][C]2[/C][C]0.178611[/C][C]1.3719[/C][C]0.087639[/C][/ROW]
[ROW][C]3[/C][C]0.050344[/C][C]0.3867[/C][C]0.350184[/C][/ROW]
[ROW][C]4[/C][C]0.156306[/C][C]1.2006[/C][C]0.117351[/C][/ROW]
[ROW][C]5[/C][C]-0.060064[/C][C]-0.4614[/C][C]0.676882[/C][/ROW]
[ROW][C]6[/C][C]-0.093154[/C][C]-0.7155[/C][C]0.761449[/C][/ROW]
[ROW][C]7[/C][C]-0.140319[/C][C]-1.0778[/C][C]0.857248[/C][/ROW]
[ROW][C]8[/C][C]-0.228319[/C][C]-1.7538[/C][C]0.957667[/C][/ROW]
[ROW][C]9[/C][C]0.100711[/C][C]0.7736[/C][C]0.221136[/C][/ROW]
[ROW][C]10[/C][C]-0.007402[/C][C]-0.0569[/C][C]0.522574[/C][/ROW]
[ROW][C]11[/C][C]-0.453997[/C][C]-3.4872[/C][C]0.999536[/C][/ROW]
[ROW][C]12[/C][C]-0.04204[/C][C]-0.3229[/C][C]0.626049[/C][/ROW]
[ROW][C]13[/C][C]0.054537[/C][C]0.4189[/C][C]0.338404[/C][/ROW]
[ROW][C]14[/C][C]0.002077[/C][C]0.016[/C][C]0.493662[/C][/ROW]
[ROW][C]15[/C][C]0.117833[/C][C]0.9051[/C][C]0.184549[/C][/ROW]
[ROW][C]16[/C][C]0.102163[/C][C]0.7847[/C][C]0.217876[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2503&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2503&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	-0.217243	-1.6687	0.94976
1	0.032952	0.2531	0.400533
2	0.178611	1.3719	0.087639
3	0.050344	0.3867	0.350184
4	0.156306	1.2006	0.117351
5	-0.060064	-0.4614	0.676882
6	-0.093154	-0.7155	0.761449
7	-0.140319	-1.0778	0.857248
8	-0.228319	-1.7538	0.957667
9	0.100711	0.7736	0.221136
10	-0.007402	-0.0569	0.522574
11	-0.453997	-3.4872	0.999536
12	-0.04204	-0.3229	0.626049
13	0.054537	0.4189	0.338404
14	0.002077	0.016	0.493662
15	0.117833	0.9051	0.184549
16	0.102163	0.7847	0.217876

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 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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