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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Nov 2007 09:45:33 -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/23/t1195835846awxcivti1ppqzqm.htm/, Retrieved Mon, 29 Apr 2024 06:44:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6228, Retrieved Mon, 29 Apr 2024 06:44:54 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

168

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

-       [(Partial) Autocorrelation Function] [autocorrelatie we...] [2007-11-23 16:45:33] [bd02e85be52eb1cb060a2c60779eb820] [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=6228&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=6228&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6228&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	0.929125	7.8839	0
2	0.822312	6.9776	0
3	0.722814	6.1333	0
4	0.658488	5.5875	0
5	0.631027	5.3544	0
6	0.600277	5.0935	1e-06
7	0.57611	4.8885	3e-06
8	0.555175	4.7108	6e-06
9	0.564638	4.7911	4e-06
10	0.594892	5.0478	2e-06
11	0.62206	5.2784	1e-06
12	0.619898	5.26	1e-06
13	0.532418	4.5177	1.2e-05
14	0.424475	3.6018	0.000289
15	0.327217	2.7765	0.003499
16	0.258487	2.1933	0.015757
17	0.217457	1.8452	0.034561

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.929125 & 7.8839 & 0 \tabularnewline
2 & 0.822312 & 6.9776 & 0 \tabularnewline
3 & 0.722814 & 6.1333 & 0 \tabularnewline
4 & 0.658488 & 5.5875 & 0 \tabularnewline
5 & 0.631027 & 5.3544 & 0 \tabularnewline
6 & 0.600277 & 5.0935 & 1e-06 \tabularnewline
7 & 0.57611 & 4.8885 & 3e-06 \tabularnewline
8 & 0.555175 & 4.7108 & 6e-06 \tabularnewline
9 & 0.564638 & 4.7911 & 4e-06 \tabularnewline
10 & 0.594892 & 5.0478 & 2e-06 \tabularnewline
11 & 0.62206 & 5.2784 & 1e-06 \tabularnewline
12 & 0.619898 & 5.26 & 1e-06 \tabularnewline
13 & 0.532418 & 4.5177 & 1.2e-05 \tabularnewline
14 & 0.424475 & 3.6018 & 0.000289 \tabularnewline
15 & 0.327217 & 2.7765 & 0.003499 \tabularnewline
16 & 0.258487 & 2.1933 & 0.015757 \tabularnewline
17 & 0.217457 & 1.8452 & 0.034561 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6228&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]0.929125[/C][C]7.8839[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.822312[/C][C]6.9776[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.722814[/C][C]6.1333[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.658488[/C][C]5.5875[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.631027[/C][C]5.3544[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.600277[/C][C]5.0935[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.57611[/C][C]4.8885[/C][C]3e-06[/C][/ROW]
[ROW][C]8[/C][C]0.555175[/C][C]4.7108[/C][C]6e-06[/C][/ROW]
[ROW][C]9[/C][C]0.564638[/C][C]4.7911[/C][C]4e-06[/C][/ROW]
[ROW][C]10[/C][C]0.594892[/C][C]5.0478[/C][C]2e-06[/C][/ROW]
[ROW][C]11[/C][C]0.62206[/C][C]5.2784[/C][C]1e-06[/C][/ROW]
[ROW][C]12[/C][C]0.619898[/C][C]5.26[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.532418[/C][C]4.5177[/C][C]1.2e-05[/C][/ROW]
[ROW][C]14[/C][C]0.424475[/C][C]3.6018[/C][C]0.000289[/C][/ROW]
[ROW][C]15[/C][C]0.327217[/C][C]2.7765[/C][C]0.003499[/C][/ROW]
[ROW][C]16[/C][C]0.258487[/C][C]2.1933[/C][C]0.015757[/C][/ROW]
[ROW][C]17[/C][C]0.217457[/C][C]1.8452[/C][C]0.034561[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6228&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6228&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	0.929125	7.8839	0
2	0.822312	6.9776	0
3	0.722814	6.1333	0
4	0.658488	5.5875	0
5	0.631027	5.3544	0
6	0.600277	5.0935	1e-06
7	0.57611	4.8885	3e-06
8	0.555175	4.7108	6e-06
9	0.564638	4.7911	4e-06
10	0.594892	5.0478	2e-06
11	0.62206	5.2784	1e-06
12	0.619898	5.26	1e-06
13	0.532418	4.5177	1.2e-05
14	0.424475	3.6018	0.000289
15	0.327217	2.7765	0.003499
16	0.258487	2.1933	0.015757
17	0.217457	1.8452	0.034561

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.929125	7.8839	0
1	-0.299591	-2.5421	0.993415
2	0.066234	0.562	0.287926
3	0.17709	1.5027	0.06865
4	0.133853	1.1358	0.129907
5	-0.141375	-1.1996	0.882887
6	0.144333	1.2247	0.112339
7	0.047532	0.4033	0.343953
8	0.249087	2.1136	0.019009
9	0.060025	0.5093	0.306041
10	0.037596	0.319	0.375322
11	-0.126236	-1.0711	0.85616
12	-0.515954	-4.378	0.99998
13	0.058024	0.4924	0.311984
14	-0.042816	-0.3633	0.641278
15	-0.093334	-0.792	0.784509
16	-0.059197	-0.5023	0.691507
17	0.02322	0.197	0.422181

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.929125 & 7.8839 & 0 \tabularnewline
1 & -0.299591 & -2.5421 & 0.993415 \tabularnewline
2 & 0.066234 & 0.562 & 0.287926 \tabularnewline
3 & 0.17709 & 1.5027 & 0.06865 \tabularnewline
4 & 0.133853 & 1.1358 & 0.129907 \tabularnewline
5 & -0.141375 & -1.1996 & 0.882887 \tabularnewline
6 & 0.144333 & 1.2247 & 0.112339 \tabularnewline
7 & 0.047532 & 0.4033 & 0.343953 \tabularnewline
8 & 0.249087 & 2.1136 & 0.019009 \tabularnewline
9 & 0.060025 & 0.5093 & 0.306041 \tabularnewline
10 & 0.037596 & 0.319 & 0.375322 \tabularnewline
11 & -0.126236 & -1.0711 & 0.85616 \tabularnewline
12 & -0.515954 & -4.378 & 0.99998 \tabularnewline
13 & 0.058024 & 0.4924 & 0.311984 \tabularnewline
14 & -0.042816 & -0.3633 & 0.641278 \tabularnewline
15 & -0.093334 & -0.792 & 0.784509 \tabularnewline
16 & -0.059197 & -0.5023 & 0.691507 \tabularnewline
17 & 0.02322 & 0.197 & 0.422181 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6228&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]0.929125[/C][C]7.8839[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.299591[/C][C]-2.5421[/C][C]0.993415[/C][/ROW]
[ROW][C]2[/C][C]0.066234[/C][C]0.562[/C][C]0.287926[/C][/ROW]
[ROW][C]3[/C][C]0.17709[/C][C]1.5027[/C][C]0.06865[/C][/ROW]
[ROW][C]4[/C][C]0.133853[/C][C]1.1358[/C][C]0.129907[/C][/ROW]
[ROW][C]5[/C][C]-0.141375[/C][C]-1.1996[/C][C]0.882887[/C][/ROW]
[ROW][C]6[/C][C]0.144333[/C][C]1.2247[/C][C]0.112339[/C][/ROW]
[ROW][C]7[/C][C]0.047532[/C][C]0.4033[/C][C]0.343953[/C][/ROW]
[ROW][C]8[/C][C]0.249087[/C][C]2.1136[/C][C]0.019009[/C][/ROW]
[ROW][C]9[/C][C]0.060025[/C][C]0.5093[/C][C]0.306041[/C][/ROW]
[ROW][C]10[/C][C]0.037596[/C][C]0.319[/C][C]0.375322[/C][/ROW]
[ROW][C]11[/C][C]-0.126236[/C][C]-1.0711[/C][C]0.85616[/C][/ROW]
[ROW][C]12[/C][C]-0.515954[/C][C]-4.378[/C][C]0.99998[/C][/ROW]
[ROW][C]13[/C][C]0.058024[/C][C]0.4924[/C][C]0.311984[/C][/ROW]
[ROW][C]14[/C][C]-0.042816[/C][C]-0.3633[/C][C]0.641278[/C][/ROW]
[ROW][C]15[/C][C]-0.093334[/C][C]-0.792[/C][C]0.784509[/C][/ROW]
[ROW][C]16[/C][C]-0.059197[/C][C]-0.5023[/C][C]0.691507[/C][/ROW]
[ROW][C]17[/C][C]0.02322[/C][C]0.197[/C][C]0.422181[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6228&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6228&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	0.929125	7.8839	0
1	-0.299591	-2.5421	0.993415
2	0.066234	0.562	0.287926
3	0.17709	1.5027	0.06865
4	0.133853	1.1358	0.129907
5	-0.141375	-1.1996	0.882887
6	0.144333	1.2247	0.112339
7	0.047532	0.4033	0.343953
8	0.249087	2.1136	0.019009
9	0.060025	0.5093	0.306041
10	0.037596	0.319	0.375322
11	-0.126236	-1.0711	0.85616
12	-0.515954	-4.378	0.99998
13	0.058024	0.4924	0.311984
14	-0.042816	-0.3633	0.641278
15	-0.093334	-0.792	0.784509
16	-0.059197	-0.5023	0.691507
17	0.02322	0.197	0.422181

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 ;

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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Input Parameters & R Code