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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 26 Nov 2007 13:29:42 -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/26/t11961084051bsbmtf1mr3vi7w.htm/, Retrieved Thu, 02 May 2024 19:58:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6685, Retrieved Thu, 02 May 2024 19:58:51 +0000

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Estimated Impact

177

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

-       [(Partial) Autocorrelation Function] [] [2007-11-26 20:29:42] [a5d60d21ad00400c5f1209c78aa5829c] [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	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=6685&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=6685&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6685&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	9.6437	0
1	0.963043	9.2872	0
2	0.924407	8.9147	0
3	0.885914	8.5434	0
4	0.844365	8.1428	0
5	0.808331	7.7953	0
6	0.779522	7.5174	0
7	0.752959	7.2613	0
8	0.721982	6.9625	0
9	0.695656	6.7087	0
10	0.669026	6.4519	0
11	0.636165	6.135	0
12	0.599236	5.7788	0
13	0.564521	5.444	0
14	0.52536	5.0664	1e-06
15	0.480282	4.6317	6e-06
16	0.447472	4.3153	2e-05
17	0.412485	3.9779	6.9e-05
18	0.371809	3.5856	0.000269

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 9.6437 & 0 \tabularnewline
1 & 0.963043 & 9.2872 & 0 \tabularnewline
2 & 0.924407 & 8.9147 & 0 \tabularnewline
3 & 0.885914 & 8.5434 & 0 \tabularnewline
4 & 0.844365 & 8.1428 & 0 \tabularnewline
5 & 0.808331 & 7.7953 & 0 \tabularnewline
6 & 0.779522 & 7.5174 & 0 \tabularnewline
7 & 0.752959 & 7.2613 & 0 \tabularnewline
8 & 0.721982 & 6.9625 & 0 \tabularnewline
9 & 0.695656 & 6.7087 & 0 \tabularnewline
10 & 0.669026 & 6.4519 & 0 \tabularnewline
11 & 0.636165 & 6.135 & 0 \tabularnewline
12 & 0.599236 & 5.7788 & 0 \tabularnewline
13 & 0.564521 & 5.444 & 0 \tabularnewline
14 & 0.52536 & 5.0664 & 1e-06 \tabularnewline
15 & 0.480282 & 4.6317 & 6e-06 \tabularnewline
16 & 0.447472 & 4.3153 & 2e-05 \tabularnewline
17 & 0.412485 & 3.9779 & 6.9e-05 \tabularnewline
18 & 0.371809 & 3.5856 & 0.000269 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6685&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]9.6437[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.963043[/C][C]9.2872[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.924407[/C][C]8.9147[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.885914[/C][C]8.5434[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.844365[/C][C]8.1428[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.808331[/C][C]7.7953[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.779522[/C][C]7.5174[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.752959[/C][C]7.2613[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.721982[/C][C]6.9625[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.695656[/C][C]6.7087[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.669026[/C][C]6.4519[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.636165[/C][C]6.135[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.599236[/C][C]5.7788[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.564521[/C][C]5.444[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.52536[/C][C]5.0664[/C][C]1e-06[/C][/ROW]
[ROW][C]15[/C][C]0.480282[/C][C]4.6317[/C][C]6e-06[/C][/ROW]
[ROW][C]16[/C][C]0.447472[/C][C]4.3153[/C][C]2e-05[/C][/ROW]
[ROW][C]17[/C][C]0.412485[/C][C]3.9779[/C][C]6.9e-05[/C][/ROW]
[ROW][C]18[/C][C]0.371809[/C][C]3.5856[/C][C]0.000269[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6685&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6685&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	9.6437	0
1	0.963043	9.2872	0
2	0.924407	8.9147	0
3	0.885914	8.5434	0
4	0.844365	8.1428	0
5	0.808331	7.7953	0
6	0.779522	7.5174	0
7	0.752959	7.2613	0
8	0.721982	6.9625	0
9	0.695656	6.7087	0
10	0.669026	6.4519	0
11	0.636165	6.135	0
12	0.599236	5.7788	0
13	0.564521	5.444	0
14	0.52536	5.0664	1e-06
15	0.480282	4.6317	6e-06
16	0.447472	4.3153	2e-05
17	0.412485	3.9779	6.9e-05
18	0.371809	3.5856	0.000269

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.963043	9.2872	0
1	-0.041963	-0.4047	0.656678
2	-0.017601	-0.1697	0.567208
3	-0.062722	-0.6049	0.726631
4	0.05575	0.5376	0.296056
5	0.076631	0.739	0.230882
6	0.012588	0.1214	0.451819
7	-0.085185	-0.8215	0.793268
8	0.046495	0.4484	0.327462
9	-0.011148	-0.1075	0.54269
10	-0.085051	-0.8202	0.792901
11	-0.084301	-0.813	0.790845
12	0.010816	0.1043	0.458576
13	-0.070562	-0.6805	0.751052
14	-0.107281	-1.0346	0.848227
15	0.117008	1.1284	0.131031
16	-0.061912	-0.5971	0.724041
17	-0.101592	-0.9797	0.835116
18	-0.027023	-0.2606	0.602513

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.963043 & 9.2872 & 0 \tabularnewline
1 & -0.041963 & -0.4047 & 0.656678 \tabularnewline
2 & -0.017601 & -0.1697 & 0.567208 \tabularnewline
3 & -0.062722 & -0.6049 & 0.726631 \tabularnewline
4 & 0.05575 & 0.5376 & 0.296056 \tabularnewline
5 & 0.076631 & 0.739 & 0.230882 \tabularnewline
6 & 0.012588 & 0.1214 & 0.451819 \tabularnewline
7 & -0.085185 & -0.8215 & 0.793268 \tabularnewline
8 & 0.046495 & 0.4484 & 0.327462 \tabularnewline
9 & -0.011148 & -0.1075 & 0.54269 \tabularnewline
10 & -0.085051 & -0.8202 & 0.792901 \tabularnewline
11 & -0.084301 & -0.813 & 0.790845 \tabularnewline
12 & 0.010816 & 0.1043 & 0.458576 \tabularnewline
13 & -0.070562 & -0.6805 & 0.751052 \tabularnewline
14 & -0.107281 & -1.0346 & 0.848227 \tabularnewline
15 & 0.117008 & 1.1284 & 0.131031 \tabularnewline
16 & -0.061912 & -0.5971 & 0.724041 \tabularnewline
17 & -0.101592 & -0.9797 & 0.835116 \tabularnewline
18 & -0.027023 & -0.2606 & 0.602513 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6685&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]0.963043[/C][C]9.2872[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.041963[/C][C]-0.4047[/C][C]0.656678[/C][/ROW]
[ROW][C]2[/C][C]-0.017601[/C][C]-0.1697[/C][C]0.567208[/C][/ROW]
[ROW][C]3[/C][C]-0.062722[/C][C]-0.6049[/C][C]0.726631[/C][/ROW]
[ROW][C]4[/C][C]0.05575[/C][C]0.5376[/C][C]0.296056[/C][/ROW]
[ROW][C]5[/C][C]0.076631[/C][C]0.739[/C][C]0.230882[/C][/ROW]
[ROW][C]6[/C][C]0.012588[/C][C]0.1214[/C][C]0.451819[/C][/ROW]
[ROW][C]7[/C][C]-0.085185[/C][C]-0.8215[/C][C]0.793268[/C][/ROW]
[ROW][C]8[/C][C]0.046495[/C][C]0.4484[/C][C]0.327462[/C][/ROW]
[ROW][C]9[/C][C]-0.011148[/C][C]-0.1075[/C][C]0.54269[/C][/ROW]
[ROW][C]10[/C][C]-0.085051[/C][C]-0.8202[/C][C]0.792901[/C][/ROW]
[ROW][C]11[/C][C]-0.084301[/C][C]-0.813[/C][C]0.790845[/C][/ROW]
[ROW][C]12[/C][C]0.010816[/C][C]0.1043[/C][C]0.458576[/C][/ROW]
[ROW][C]13[/C][C]-0.070562[/C][C]-0.6805[/C][C]0.751052[/C][/ROW]
[ROW][C]14[/C][C]-0.107281[/C][C]-1.0346[/C][C]0.848227[/C][/ROW]
[ROW][C]15[/C][C]0.117008[/C][C]1.1284[/C][C]0.131031[/C][/ROW]
[ROW][C]16[/C][C]-0.061912[/C][C]-0.5971[/C][C]0.724041[/C][/ROW]
[ROW][C]17[/C][C]-0.101592[/C][C]-0.9797[/C][C]0.835116[/C][/ROW]
[ROW][C]18[/C][C]-0.027023[/C][C]-0.2606[/C][C]0.602513[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6685&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6685&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	0.963043	9.2872	0
1	-0.041963	-0.4047	0.656678
2	-0.017601	-0.1697	0.567208
3	-0.062722	-0.6049	0.726631
4	0.05575	0.5376	0.296056
5	0.076631	0.739	0.230882
6	0.012588	0.1214	0.451819
7	-0.085185	-0.8215	0.793268
8	0.046495	0.4484	0.327462
9	-0.011148	-0.1075	0.54269
10	-0.085051	-0.8202	0.792901
11	-0.084301	-0.813	0.790845
12	0.010816	0.1043	0.458576
13	-0.070562	-0.6805	0.751052
14	-0.107281	-1.0346	0.848227
15	0.117008	1.1284	0.131031
16	-0.061912	-0.5971	0.724041
17	-0.101592	-0.9797	0.835116
18	-0.027023	-0.2606	0.602513

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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