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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 24 Nov 2007 18:53:58 -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/t11959551429d6ml09vcw6cqnr.htm/, Retrieved Sat, 04 May 2024 05:40:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6375, Retrieved Sat, 04 May 2024 05:40:21 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

230

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

-     [(Partial) Autocorrelation Function] [WS10Q2FINSIT] [2007-11-24 18:03:18] [6b20c0ed55154a4fb9df5a5e4fa0b426]
-   PD    [(Partial) Autocorrelation Function] [WS10Q2WERKL NA DI...] [2007-11-25 01:53:58] [e0964b90cb3acfe235da067e79729c23] [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	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=6375&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=6375&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6375&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	6.8557	0
1	0.146249	1.0026	0.160585
2	0.121059	0.8299	0.205386
3	-0.16185	-1.1096	0.863589
4	-0.151282	-1.0371	0.847511
5	0.014308	0.0981	0.461138
6	-0.111047	-0.7613	0.77486
7	-0.046177	-0.3166	0.623515
8	0.046975	0.322	0.374423
9	0.215168	1.4751	0.073424
10	-0.112706	-0.7727	0.778208
11	-0.076605	-0.5252	0.699036
12	-0.208146	-1.427	0.919902
13	0.088028	0.6035	0.274541
14	0.306002	2.0978	0.020661
15	0.091203	0.6253	0.267414
16	0.097175	0.6662	0.254271

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 6.8557 & 0 \tabularnewline
1 & 0.146249 & 1.0026 & 0.160585 \tabularnewline
2 & 0.121059 & 0.8299 & 0.205386 \tabularnewline
3 & -0.16185 & -1.1096 & 0.863589 \tabularnewline
4 & -0.151282 & -1.0371 & 0.847511 \tabularnewline
5 & 0.014308 & 0.0981 & 0.461138 \tabularnewline
6 & -0.111047 & -0.7613 & 0.77486 \tabularnewline
7 & -0.046177 & -0.3166 & 0.623515 \tabularnewline
8 & 0.046975 & 0.322 & 0.374423 \tabularnewline
9 & 0.215168 & 1.4751 & 0.073424 \tabularnewline
10 & -0.112706 & -0.7727 & 0.778208 \tabularnewline
11 & -0.076605 & -0.5252 & 0.699036 \tabularnewline
12 & -0.208146 & -1.427 & 0.919902 \tabularnewline
13 & 0.088028 & 0.6035 & 0.274541 \tabularnewline
14 & 0.306002 & 2.0978 & 0.020661 \tabularnewline
15 & 0.091203 & 0.6253 & 0.267414 \tabularnewline
16 & 0.097175 & 0.6662 & 0.254271 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6375&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]6.8557[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.146249[/C][C]1.0026[/C][C]0.160585[/C][/ROW]
[ROW][C]2[/C][C]0.121059[/C][C]0.8299[/C][C]0.205386[/C][/ROW]
[ROW][C]3[/C][C]-0.16185[/C][C]-1.1096[/C][C]0.863589[/C][/ROW]
[ROW][C]4[/C][C]-0.151282[/C][C]-1.0371[/C][C]0.847511[/C][/ROW]
[ROW][C]5[/C][C]0.014308[/C][C]0.0981[/C][C]0.461138[/C][/ROW]
[ROW][C]6[/C][C]-0.111047[/C][C]-0.7613[/C][C]0.77486[/C][/ROW]
[ROW][C]7[/C][C]-0.046177[/C][C]-0.3166[/C][C]0.623515[/C][/ROW]
[ROW][C]8[/C][C]0.046975[/C][C]0.322[/C][C]0.374423[/C][/ROW]
[ROW][C]9[/C][C]0.215168[/C][C]1.4751[/C][C]0.073424[/C][/ROW]
[ROW][C]10[/C][C]-0.112706[/C][C]-0.7727[/C][C]0.778208[/C][/ROW]
[ROW][C]11[/C][C]-0.076605[/C][C]-0.5252[/C][C]0.699036[/C][/ROW]
[ROW][C]12[/C][C]-0.208146[/C][C]-1.427[/C][C]0.919902[/C][/ROW]
[ROW][C]13[/C][C]0.088028[/C][C]0.6035[/C][C]0.274541[/C][/ROW]
[ROW][C]14[/C][C]0.306002[/C][C]2.0978[/C][C]0.020661[/C][/ROW]
[ROW][C]15[/C][C]0.091203[/C][C]0.6253[/C][C]0.267414[/C][/ROW]
[ROW][C]16[/C][C]0.097175[/C][C]0.6662[/C][C]0.254271[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6375&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6375&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	6.8557	0
1	0.146249	1.0026	0.160585
2	0.121059	0.8299	0.205386
3	-0.16185	-1.1096	0.863589
4	-0.151282	-1.0371	0.847511
5	0.014308	0.0981	0.461138
6	-0.111047	-0.7613	0.77486
7	-0.046177	-0.3166	0.623515
8	0.046975	0.322	0.374423
9	0.215168	1.4751	0.073424
10	-0.112706	-0.7727	0.778208
11	-0.076605	-0.5252	0.699036
12	-0.208146	-1.427	0.919902
13	0.088028	0.6035	0.274541
14	0.306002	2.0978	0.020661
15	0.091203	0.6253	0.267414
16	0.097175	0.6662	0.254271

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.146249	1.0026	0.160585
1	0.101848	0.6982	0.244235
2	-0.198921	-1.3637	0.910426
3	-0.121642	-0.8339	0.795732
4	0.105258	0.7216	0.237055
5	-0.131496	-0.9015	0.814038
6	-0.088442	-0.6063	0.726393
7	0.116902	0.8014	0.213456
8	0.216156	1.4819	0.072522
9	-0.308301	-2.1136	0.980057
10	-0.083214	-0.5705	0.714468
11	0.009156	0.0628	0.475108
12	0.155017	1.0627	0.146664
13	0.23914	1.6395	0.053897
14	-0.021582	-0.148	0.558495
15	-0.021904	-0.1502	0.559361
16	-0.133913	-0.9181	0.818363

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.146249 & 1.0026 & 0.160585 \tabularnewline
1 & 0.101848 & 0.6982 & 0.244235 \tabularnewline
2 & -0.198921 & -1.3637 & 0.910426 \tabularnewline
3 & -0.121642 & -0.8339 & 0.795732 \tabularnewline
4 & 0.105258 & 0.7216 & 0.237055 \tabularnewline
5 & -0.131496 & -0.9015 & 0.814038 \tabularnewline
6 & -0.088442 & -0.6063 & 0.726393 \tabularnewline
7 & 0.116902 & 0.8014 & 0.213456 \tabularnewline
8 & 0.216156 & 1.4819 & 0.072522 \tabularnewline
9 & -0.308301 & -2.1136 & 0.980057 \tabularnewline
10 & -0.083214 & -0.5705 & 0.714468 \tabularnewline
11 & 0.009156 & 0.0628 & 0.475108 \tabularnewline
12 & 0.155017 & 1.0627 & 0.146664 \tabularnewline
13 & 0.23914 & 1.6395 & 0.053897 \tabularnewline
14 & -0.021582 & -0.148 & 0.558495 \tabularnewline
15 & -0.021904 & -0.1502 & 0.559361 \tabularnewline
16 & -0.133913 & -0.9181 & 0.818363 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6375&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]0.146249[/C][C]1.0026[/C][C]0.160585[/C][/ROW]
[ROW][C]1[/C][C]0.101848[/C][C]0.6982[/C][C]0.244235[/C][/ROW]
[ROW][C]2[/C][C]-0.198921[/C][C]-1.3637[/C][C]0.910426[/C][/ROW]
[ROW][C]3[/C][C]-0.121642[/C][C]-0.8339[/C][C]0.795732[/C][/ROW]
[ROW][C]4[/C][C]0.105258[/C][C]0.7216[/C][C]0.237055[/C][/ROW]
[ROW][C]5[/C][C]-0.131496[/C][C]-0.9015[/C][C]0.814038[/C][/ROW]
[ROW][C]6[/C][C]-0.088442[/C][C]-0.6063[/C][C]0.726393[/C][/ROW]
[ROW][C]7[/C][C]0.116902[/C][C]0.8014[/C][C]0.213456[/C][/ROW]
[ROW][C]8[/C][C]0.216156[/C][C]1.4819[/C][C]0.072522[/C][/ROW]
[ROW][C]9[/C][C]-0.308301[/C][C]-2.1136[/C][C]0.980057[/C][/ROW]
[ROW][C]10[/C][C]-0.083214[/C][C]-0.5705[/C][C]0.714468[/C][/ROW]
[ROW][C]11[/C][C]0.009156[/C][C]0.0628[/C][C]0.475108[/C][/ROW]
[ROW][C]12[/C][C]0.155017[/C][C]1.0627[/C][C]0.146664[/C][/ROW]
[ROW][C]13[/C][C]0.23914[/C][C]1.6395[/C][C]0.053897[/C][/ROW]
[ROW][C]14[/C][C]-0.021582[/C][C]-0.148[/C][C]0.558495[/C][/ROW]
[ROW][C]15[/C][C]-0.021904[/C][C]-0.1502[/C][C]0.559361[/C][/ROW]
[ROW][C]16[/C][C]-0.133913[/C][C]-0.9181[/C][C]0.818363[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6375&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6375&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	0.146249	1.0026	0.160585
1	0.101848	0.6982	0.244235
2	-0.198921	-1.3637	0.910426
3	-0.121642	-0.8339	0.795732
4	0.105258	0.7216	0.237055
5	-0.131496	-0.9015	0.814038
6	-0.088442	-0.6063	0.726393
7	0.116902	0.8014	0.213456
8	0.216156	1.4819	0.072522
9	-0.308301	-2.1136	0.980057
10	-0.083214	-0.5705	0.714468
11	0.009156	0.0628	0.475108
12	0.155017	1.0627	0.146664
13	0.23914	1.6395	0.053897
14	-0.021582	-0.148	0.558495
15	-0.021904	-0.1502	0.559361
16	-0.133913	-0.9181	0.818363

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 2.0 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 2.0 ; 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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