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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 12 Dec 2007 08:47:01 -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/12/t11974735237en5nkatgwyjjbw.htm/, Retrieved Thu, 02 May 2024 20:46:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3221, Retrieved Thu, 02 May 2024 20:46:25 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

265

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

-       [(Partial) Autocorrelation Function] [Inducing stationa...] [2007-12-12 15:47:01] [578856645eee7b4b8f74dcf589866e9b] [Current]

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Summary of compuational 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 compuational 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=3221&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]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=3221&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3221&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.4853	0
1	0.967291	8.2077	0
2	0.92664	7.8628	0
3	0.888463	7.5389	0
4	0.849934	7.2119	0
5	0.805638	6.8361	0
6	0.758645	6.4373	0
7	0.715394	6.0703	0
8	0.67478	5.7257	0
9	0.63681	5.4035	0
10	0.596268	5.0595	2e-06
11	0.550458	4.6708	7e-06
12	0.500742	4.2489	3.2e-05
13	0.452309	3.838	0.000132
14	0.403623	3.4249	0.00051
15	0.354331	3.0066	0.001818
16	0.306184	2.5981	0.005681
17	0.264145	2.2413	0.014043

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.967291 & 8.2077 & 0 \tabularnewline
2 & 0.92664 & 7.8628 & 0 \tabularnewline
3 & 0.888463 & 7.5389 & 0 \tabularnewline
4 & 0.849934 & 7.2119 & 0 \tabularnewline
5 & 0.805638 & 6.8361 & 0 \tabularnewline
6 & 0.758645 & 6.4373 & 0 \tabularnewline
7 & 0.715394 & 6.0703 & 0 \tabularnewline
8 & 0.67478 & 5.7257 & 0 \tabularnewline
9 & 0.63681 & 5.4035 & 0 \tabularnewline
10 & 0.596268 & 5.0595 & 2e-06 \tabularnewline
11 & 0.550458 & 4.6708 & 7e-06 \tabularnewline
12 & 0.500742 & 4.2489 & 3.2e-05 \tabularnewline
13 & 0.452309 & 3.838 & 0.000132 \tabularnewline
14 & 0.403623 & 3.4249 & 0.00051 \tabularnewline
15 & 0.354331 & 3.0066 & 0.001818 \tabularnewline
16 & 0.306184 & 2.5981 & 0.005681 \tabularnewline
17 & 0.264145 & 2.2413 & 0.014043 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3221&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]8.4853[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.967291[/C][C]8.2077[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.92664[/C][C]7.8628[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.888463[/C][C]7.5389[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.849934[/C][C]7.2119[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.805638[/C][C]6.8361[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.758645[/C][C]6.4373[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.715394[/C][C]6.0703[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.67478[/C][C]5.7257[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.63681[/C][C]5.4035[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.596268[/C][C]5.0595[/C][C]2e-06[/C][/ROW]
[ROW][C]11[/C][C]0.550458[/C][C]4.6708[/C][C]7e-06[/C][/ROW]
[ROW][C]12[/C][C]0.500742[/C][C]4.2489[/C][C]3.2e-05[/C][/ROW]
[ROW][C]13[/C][C]0.452309[/C][C]3.838[/C][C]0.000132[/C][/ROW]
[ROW][C]14[/C][C]0.403623[/C][C]3.4249[/C][C]0.00051[/C][/ROW]
[ROW][C]15[/C][C]0.354331[/C][C]3.0066[/C][C]0.001818[/C][/ROW]
[ROW][C]16[/C][C]0.306184[/C][C]2.5981[/C][C]0.005681[/C][/ROW]
[ROW][C]17[/C][C]0.264145[/C][C]2.2413[/C][C]0.014043[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3221&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3221&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	8.4853	0
1	0.967291	8.2077	0
2	0.92664	7.8628	0
3	0.888463	7.5389	0
4	0.849934	7.2119	0
5	0.805638	6.8361	0
6	0.758645	6.4373	0
7	0.715394	6.0703	0
8	0.67478	5.7257	0
9	0.63681	5.4035	0
10	0.596268	5.0595	2e-06
11	0.550458	4.6708	7e-06
12	0.500742	4.2489	3.2e-05
13	0.452309	3.838	0.000132
14	0.403623	3.4249	0.00051
15	0.354331	3.0066	0.001818
16	0.306184	2.5981	0.005681
17	0.264145	2.2413	0.014043

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.967291	8.2077	0
1	-0.140048	-1.1883	0.880699
2	0.032814	0.2784	0.390738
3	-0.037201	-0.3157	0.623414
4	-0.107579	-0.9128	0.817814
5	-0.04678	-0.3969	0.653708
6	0.033132	0.2811	0.389705
7	0.000457	0.0039	0.498459
8	0.022785	0.1933	0.423621
9	-0.067316	-0.5712	0.715178
10	-0.105825	-0.898	0.813898
11	-0.087472	-0.7422	0.769816
12	-0.011616	-0.0986	0.53912
13	-0.03955	-0.3356	0.630922
14	-0.018377	-0.1559	0.561738
15	-0.005107	-0.0433	0.517223
16	0.049107	0.4167	0.339073
17	-0.008932	-0.0758	0.530102

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.967291 & 8.2077 & 0 \tabularnewline
1 & -0.140048 & -1.1883 & 0.880699 \tabularnewline
2 & 0.032814 & 0.2784 & 0.390738 \tabularnewline
3 & -0.037201 & -0.3157 & 0.623414 \tabularnewline
4 & -0.107579 & -0.9128 & 0.817814 \tabularnewline
5 & -0.04678 & -0.3969 & 0.653708 \tabularnewline
6 & 0.033132 & 0.2811 & 0.389705 \tabularnewline
7 & 0.000457 & 0.0039 & 0.498459 \tabularnewline
8 & 0.022785 & 0.1933 & 0.423621 \tabularnewline
9 & -0.067316 & -0.5712 & 0.715178 \tabularnewline
10 & -0.105825 & -0.898 & 0.813898 \tabularnewline
11 & -0.087472 & -0.7422 & 0.769816 \tabularnewline
12 & -0.011616 & -0.0986 & 0.53912 \tabularnewline
13 & -0.03955 & -0.3356 & 0.630922 \tabularnewline
14 & -0.018377 & -0.1559 & 0.561738 \tabularnewline
15 & -0.005107 & -0.0433 & 0.517223 \tabularnewline
16 & 0.049107 & 0.4167 & 0.339073 \tabularnewline
17 & -0.008932 & -0.0758 & 0.530102 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3221&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]0.967291[/C][C]8.2077[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.140048[/C][C]-1.1883[/C][C]0.880699[/C][/ROW]
[ROW][C]2[/C][C]0.032814[/C][C]0.2784[/C][C]0.390738[/C][/ROW]
[ROW][C]3[/C][C]-0.037201[/C][C]-0.3157[/C][C]0.623414[/C][/ROW]
[ROW][C]4[/C][C]-0.107579[/C][C]-0.9128[/C][C]0.817814[/C][/ROW]
[ROW][C]5[/C][C]-0.04678[/C][C]-0.3969[/C][C]0.653708[/C][/ROW]
[ROW][C]6[/C][C]0.033132[/C][C]0.2811[/C][C]0.389705[/C][/ROW]
[ROW][C]7[/C][C]0.000457[/C][C]0.0039[/C][C]0.498459[/C][/ROW]
[ROW][C]8[/C][C]0.022785[/C][C]0.1933[/C][C]0.423621[/C][/ROW]
[ROW][C]9[/C][C]-0.067316[/C][C]-0.5712[/C][C]0.715178[/C][/ROW]
[ROW][C]10[/C][C]-0.105825[/C][C]-0.898[/C][C]0.813898[/C][/ROW]
[ROW][C]11[/C][C]-0.087472[/C][C]-0.7422[/C][C]0.769816[/C][/ROW]
[ROW][C]12[/C][C]-0.011616[/C][C]-0.0986[/C][C]0.53912[/C][/ROW]
[ROW][C]13[/C][C]-0.03955[/C][C]-0.3356[/C][C]0.630922[/C][/ROW]
[ROW][C]14[/C][C]-0.018377[/C][C]-0.1559[/C][C]0.561738[/C][/ROW]
[ROW][C]15[/C][C]-0.005107[/C][C]-0.0433[/C][C]0.517223[/C][/ROW]
[ROW][C]16[/C][C]0.049107[/C][C]0.4167[/C][C]0.339073[/C][/ROW]
[ROW][C]17[/C][C]-0.008932[/C][C]-0.0758[/C][C]0.530102[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3221&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3221&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	0.967291	8.2077	0
1	-0.140048	-1.1883	0.880699
2	0.032814	0.2784	0.390738
3	-0.037201	-0.3157	0.623414
4	-0.107579	-0.9128	0.817814
5	-0.04678	-0.3969	0.653708
6	0.033132	0.2811	0.389705
7	0.000457	0.0039	0.498459
8	0.022785	0.1933	0.423621
9	-0.067316	-0.5712	0.715178
10	-0.105825	-0.898	0.813898
11	-0.087472	-0.7422	0.769816
12	-0.011616	-0.0986	0.53912
13	-0.03955	-0.3356	0.630922
14	-0.018377	-0.1559	0.561738
15	-0.005107	-0.0433	0.517223
16	0.049107	0.4167	0.339073
17	-0.008932	-0.0758	0.530102

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.2 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.2 ; 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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Input Parameters & R Code