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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 06:41:40 -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/t1195824781ansuo0aomrn3m8g.htm/, Retrieved Sun, 28 Apr 2024 23:21:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6169, Retrieved Sun, 28 Apr 2024 23:21:49 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

208

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

-     [(Partial) Autocorrelation Function] [Partiel Autocorre...] [2007-11-22 13:00:02] [ced1562ed3c62c3bc1f3b66b8f83b537]
-    D    [(Partial) Autocorrelation Function] [WS 9] [2007-11-23 13:41:40] [d41d8cd98f00b204e9800998ecf8427e] [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=6169&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=6169&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6169&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	7.746	0
1	0.122236	0.9468	0.17376
2	0.048074	0.3724	0.35546
3	0.04318	0.3345	0.369595
4	0.026007	0.2014	0.420514
5	0.115683	0.8961	0.186897
6	0.043789	0.3392	0.367825
7	0.052178	0.4042	0.343762
8	0.100579	0.7791	0.219497
9	0.112402	0.8707	0.193704
10	-0.146299	-1.1332	0.869187
11	-0.031061	-0.2406	0.594657
12	-0.189782	-1.47	0.926613
13	0.020383	0.1579	0.437539
14	0.184477	1.429	0.079102
15	0.097615	0.7561	0.226266
16	0.112678	0.8728	0.193125
17	-0.104877	-0.8124	0.790106

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.122236 & 0.9468 & 0.17376 \tabularnewline
2 & 0.048074 & 0.3724 & 0.35546 \tabularnewline
3 & 0.04318 & 0.3345 & 0.369595 \tabularnewline
4 & 0.026007 & 0.2014 & 0.420514 \tabularnewline
5 & 0.115683 & 0.8961 & 0.186897 \tabularnewline
6 & 0.043789 & 0.3392 & 0.367825 \tabularnewline
7 & 0.052178 & 0.4042 & 0.343762 \tabularnewline
8 & 0.100579 & 0.7791 & 0.219497 \tabularnewline
9 & 0.112402 & 0.8707 & 0.193704 \tabularnewline
10 & -0.146299 & -1.1332 & 0.869187 \tabularnewline
11 & -0.031061 & -0.2406 & 0.594657 \tabularnewline
12 & -0.189782 & -1.47 & 0.926613 \tabularnewline
13 & 0.020383 & 0.1579 & 0.437539 \tabularnewline
14 & 0.184477 & 1.429 & 0.079102 \tabularnewline
15 & 0.097615 & 0.7561 & 0.226266 \tabularnewline
16 & 0.112678 & 0.8728 & 0.193125 \tabularnewline
17 & -0.104877 & -0.8124 & 0.790106 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6169&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.122236[/C][C]0.9468[/C][C]0.17376[/C][/ROW]
[ROW][C]2[/C][C]0.048074[/C][C]0.3724[/C][C]0.35546[/C][/ROW]
[ROW][C]3[/C][C]0.04318[/C][C]0.3345[/C][C]0.369595[/C][/ROW]
[ROW][C]4[/C][C]0.026007[/C][C]0.2014[/C][C]0.420514[/C][/ROW]
[ROW][C]5[/C][C]0.115683[/C][C]0.8961[/C][C]0.186897[/C][/ROW]
[ROW][C]6[/C][C]0.043789[/C][C]0.3392[/C][C]0.367825[/C][/ROW]
[ROW][C]7[/C][C]0.052178[/C][C]0.4042[/C][C]0.343762[/C][/ROW]
[ROW][C]8[/C][C]0.100579[/C][C]0.7791[/C][C]0.219497[/C][/ROW]
[ROW][C]9[/C][C]0.112402[/C][C]0.8707[/C][C]0.193704[/C][/ROW]
[ROW][C]10[/C][C]-0.146299[/C][C]-1.1332[/C][C]0.869187[/C][/ROW]
[ROW][C]11[/C][C]-0.031061[/C][C]-0.2406[/C][C]0.594657[/C][/ROW]
[ROW][C]12[/C][C]-0.189782[/C][C]-1.47[/C][C]0.926613[/C][/ROW]
[ROW][C]13[/C][C]0.020383[/C][C]0.1579[/C][C]0.437539[/C][/ROW]
[ROW][C]14[/C][C]0.184477[/C][C]1.429[/C][C]0.079102[/C][/ROW]
[ROW][C]15[/C][C]0.097615[/C][C]0.7561[/C][C]0.226266[/C][/ROW]
[ROW][C]16[/C][C]0.112678[/C][C]0.8728[/C][C]0.193125[/C][/ROW]
[ROW][C]17[/C][C]-0.104877[/C][C]-0.8124[/C][C]0.790106[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6169&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6169&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	7.746	0
1	0.122236	0.9468	0.17376
2	0.048074	0.3724	0.35546
3	0.04318	0.3345	0.369595
4	0.026007	0.2014	0.420514
5	0.115683	0.8961	0.186897
6	0.043789	0.3392	0.367825
7	0.052178	0.4042	0.343762
8	0.100579	0.7791	0.219497
9	0.112402	0.8707	0.193704
10	-0.146299	-1.1332	0.869187
11	-0.031061	-0.2406	0.594657
12	-0.189782	-1.47	0.926613
13	0.020383	0.1579	0.437539
14	0.184477	1.429	0.079102
15	0.097615	0.7561	0.226266
16	0.112678	0.8728	0.193125
17	-0.104877	-0.8124	0.790106

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.122236	0.9468	0.17376
1	0.033635	0.2605	0.39767
2	0.033935	0.2629	0.39678
3	0.015652	0.1212	0.451952
4	0.109853	0.8509	0.199099
5	0.01549	0.12	0.452447
6	0.037438	0.29	0.386411
7	0.08328	0.6451	0.260667
8	0.087976	0.6815	0.249101
9	-0.196815	-1.5245	0.933684
10	-0.011743	-0.091	0.536088
11	-0.206516	-1.5997	0.942537
12	0.059815	0.4633	0.322404
13	0.178593	1.3834	0.085837
14	0.117156	0.9075	0.18389
15	0.097327	0.7539	0.226931
16	-0.126752	-0.9818	0.834934
17	0.186852	1.4473	0.076502

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.122236 & 0.9468 & 0.17376 \tabularnewline
1 & 0.033635 & 0.2605 & 0.39767 \tabularnewline
2 & 0.033935 & 0.2629 & 0.39678 \tabularnewline
3 & 0.015652 & 0.1212 & 0.451952 \tabularnewline
4 & 0.109853 & 0.8509 & 0.199099 \tabularnewline
5 & 0.01549 & 0.12 & 0.452447 \tabularnewline
6 & 0.037438 & 0.29 & 0.386411 \tabularnewline
7 & 0.08328 & 0.6451 & 0.260667 \tabularnewline
8 & 0.087976 & 0.6815 & 0.249101 \tabularnewline
9 & -0.196815 & -1.5245 & 0.933684 \tabularnewline
10 & -0.011743 & -0.091 & 0.536088 \tabularnewline
11 & -0.206516 & -1.5997 & 0.942537 \tabularnewline
12 & 0.059815 & 0.4633 & 0.322404 \tabularnewline
13 & 0.178593 & 1.3834 & 0.085837 \tabularnewline
14 & 0.117156 & 0.9075 & 0.18389 \tabularnewline
15 & 0.097327 & 0.7539 & 0.226931 \tabularnewline
16 & -0.126752 & -0.9818 & 0.834934 \tabularnewline
17 & 0.186852 & 1.4473 & 0.076502 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6169&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]0.122236[/C][C]0.9468[/C][C]0.17376[/C][/ROW]
[ROW][C]1[/C][C]0.033635[/C][C]0.2605[/C][C]0.39767[/C][/ROW]
[ROW][C]2[/C][C]0.033935[/C][C]0.2629[/C][C]0.39678[/C][/ROW]
[ROW][C]3[/C][C]0.015652[/C][C]0.1212[/C][C]0.451952[/C][/ROW]
[ROW][C]4[/C][C]0.109853[/C][C]0.8509[/C][C]0.199099[/C][/ROW]
[ROW][C]5[/C][C]0.01549[/C][C]0.12[/C][C]0.452447[/C][/ROW]
[ROW][C]6[/C][C]0.037438[/C][C]0.29[/C][C]0.386411[/C][/ROW]
[ROW][C]7[/C][C]0.08328[/C][C]0.6451[/C][C]0.260667[/C][/ROW]
[ROW][C]8[/C][C]0.087976[/C][C]0.6815[/C][C]0.249101[/C][/ROW]
[ROW][C]9[/C][C]-0.196815[/C][C]-1.5245[/C][C]0.933684[/C][/ROW]
[ROW][C]10[/C][C]-0.011743[/C][C]-0.091[/C][C]0.536088[/C][/ROW]
[ROW][C]11[/C][C]-0.206516[/C][C]-1.5997[/C][C]0.942537[/C][/ROW]
[ROW][C]12[/C][C]0.059815[/C][C]0.4633[/C][C]0.322404[/C][/ROW]
[ROW][C]13[/C][C]0.178593[/C][C]1.3834[/C][C]0.085837[/C][/ROW]
[ROW][C]14[/C][C]0.117156[/C][C]0.9075[/C][C]0.18389[/C][/ROW]
[ROW][C]15[/C][C]0.097327[/C][C]0.7539[/C][C]0.226931[/C][/ROW]
[ROW][C]16[/C][C]-0.126752[/C][C]-0.9818[/C][C]0.834934[/C][/ROW]
[ROW][C]17[/C][C]0.186852[/C][C]1.4473[/C][C]0.076502[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6169&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6169&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	0.122236	0.9468	0.17376
1	0.033635	0.2605	0.39767
2	0.033935	0.2629	0.39678
3	0.015652	0.1212	0.451952
4	0.109853	0.8509	0.199099
5	0.01549	0.12	0.452447
6	0.037438	0.29	0.386411
7	0.08328	0.6451	0.260667
8	0.087976	0.6815	0.249101
9	-0.196815	-1.5245	0.933684
10	-0.011743	-0.091	0.536088
11	-0.206516	-1.5997	0.942537
12	0.059815	0.4633	0.322404
13	0.178593	1.3834	0.085837
14	0.117156	0.9075	0.18389
15	0.097327	0.7539	0.226931
16	-0.126752	-0.9818	0.834934
17	0.186852	1.4473	0.076502

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 = 1 ; par4 = 1 ; 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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