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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Nov 2007 06:21:48 -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/22/t1195737285i8zgfyyunj3ootu.htm/, Retrieved Fri, 03 May 2024 00:00:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5982, Retrieved Fri, 03 May 2024 00:00:27 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

W10Q2G7

Estimated Impact

179

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

-       [(Partial) Autocorrelation Function] [Autocorrelation f...] [2007-11-22 13:21:48] [65108f21b143a71c6470aac06bd65b08] [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=5982&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=5982&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5982&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	8.544	0
1	0.68793	5.8777	0
2	0.416274	3.5566	0.000332
3	0.208888	1.7847	0.039229
4	0.071684	0.6125	0.271065
5	-0.002363	-0.0202	0.508026
6	-0.058187	-0.4972	0.689712
7	-0.085695	-0.7322	0.766799
8	-0.192466	-1.6444	0.947807
9	-0.187696	-1.6037	0.943448
10	-0.273499	-2.3368	0.988901
11	-0.332172	-2.8381	0.997063
12	-0.367874	-3.1431	0.998792
13	-0.34942	-2.9854	0.998074
14	-0.234325	-2.0021	0.975504
15	-0.138213	-1.1809	0.87926
16	-0.048912	-0.4179	0.661378
17	-0.124502	-1.0637	0.854526

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.544 & 0 \tabularnewline
1 & 0.68793 & 5.8777 & 0 \tabularnewline
2 & 0.416274 & 3.5566 & 0.000332 \tabularnewline
3 & 0.208888 & 1.7847 & 0.039229 \tabularnewline
4 & 0.071684 & 0.6125 & 0.271065 \tabularnewline
5 & -0.002363 & -0.0202 & 0.508026 \tabularnewline
6 & -0.058187 & -0.4972 & 0.689712 \tabularnewline
7 & -0.085695 & -0.7322 & 0.766799 \tabularnewline
8 & -0.192466 & -1.6444 & 0.947807 \tabularnewline
9 & -0.187696 & -1.6037 & 0.943448 \tabularnewline
10 & -0.273499 & -2.3368 & 0.988901 \tabularnewline
11 & -0.332172 & -2.8381 & 0.997063 \tabularnewline
12 & -0.367874 & -3.1431 & 0.998792 \tabularnewline
13 & -0.34942 & -2.9854 & 0.998074 \tabularnewline
14 & -0.234325 & -2.0021 & 0.975504 \tabularnewline
15 & -0.138213 & -1.1809 & 0.87926 \tabularnewline
16 & -0.048912 & -0.4179 & 0.661378 \tabularnewline
17 & -0.124502 & -1.0637 & 0.854526 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5982&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]8.544[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.68793[/C][C]5.8777[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.416274[/C][C]3.5566[/C][C]0.000332[/C][/ROW]
[ROW][C]3[/C][C]0.208888[/C][C]1.7847[/C][C]0.039229[/C][/ROW]
[ROW][C]4[/C][C]0.071684[/C][C]0.6125[/C][C]0.271065[/C][/ROW]
[ROW][C]5[/C][C]-0.002363[/C][C]-0.0202[/C][C]0.508026[/C][/ROW]
[ROW][C]6[/C][C]-0.058187[/C][C]-0.4972[/C][C]0.689712[/C][/ROW]
[ROW][C]7[/C][C]-0.085695[/C][C]-0.7322[/C][C]0.766799[/C][/ROW]
[ROW][C]8[/C][C]-0.192466[/C][C]-1.6444[/C][C]0.947807[/C][/ROW]
[ROW][C]9[/C][C]-0.187696[/C][C]-1.6037[/C][C]0.943448[/C][/ROW]
[ROW][C]10[/C][C]-0.273499[/C][C]-2.3368[/C][C]0.988901[/C][/ROW]
[ROW][C]11[/C][C]-0.332172[/C][C]-2.8381[/C][C]0.997063[/C][/ROW]
[ROW][C]12[/C][C]-0.367874[/C][C]-3.1431[/C][C]0.998792[/C][/ROW]
[ROW][C]13[/C][C]-0.34942[/C][C]-2.9854[/C][C]0.998074[/C][/ROW]
[ROW][C]14[/C][C]-0.234325[/C][C]-2.0021[/C][C]0.975504[/C][/ROW]
[ROW][C]15[/C][C]-0.138213[/C][C]-1.1809[/C][C]0.87926[/C][/ROW]
[ROW][C]16[/C][C]-0.048912[/C][C]-0.4179[/C][C]0.661378[/C][/ROW]
[ROW][C]17[/C][C]-0.124502[/C][C]-1.0637[/C][C]0.854526[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5982&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5982&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	8.544	0
1	0.68793	5.8777	0
2	0.416274	3.5566	0.000332
3	0.208888	1.7847	0.039229
4	0.071684	0.6125	0.271065
5	-0.002363	-0.0202	0.508026
6	-0.058187	-0.4972	0.689712
7	-0.085695	-0.7322	0.766799
8	-0.192466	-1.6444	0.947807
9	-0.187696	-1.6037	0.943448
10	-0.273499	-2.3368	0.988901
11	-0.332172	-2.8381	0.997063
12	-0.367874	-3.1431	0.998792
13	-0.34942	-2.9854	0.998074
14	-0.234325	-2.0021	0.975504
15	-0.138213	-1.1809	0.87926
16	-0.048912	-0.4179	0.661378
17	-0.124502	-1.0637	0.854526

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.68793	5.8777	0
1	-0.108161	-0.9241	0.820767
2	-0.065399	-0.5588	0.710985
3	-0.03245	-0.2773	0.608815
4	-0.008559	-0.0731	0.529047
5	-0.051579	-0.4407	0.669629
6	-0.019315	-0.165	0.56531
7	-0.207205	-1.7704	0.959579
8	0.086383	0.7381	0.231423
9	-0.251119	-2.1456	0.982383
10	-0.084918	-0.7255	0.76478
11	-0.130861	-1.1181	0.8664
12	-0.035839	-0.3062	0.619842
13	0.057927	0.4949	0.311069
14	-0.014081	-0.1203	0.547715
15	-0.0476	-0.4067	0.657289
16	-0.244282	-2.0871	0.979817
17	-0.060906	-0.5204	0.697812

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.68793 & 5.8777 & 0 \tabularnewline
1 & -0.108161 & -0.9241 & 0.820767 \tabularnewline
2 & -0.065399 & -0.5588 & 0.710985 \tabularnewline
3 & -0.03245 & -0.2773 & 0.608815 \tabularnewline
4 & -0.008559 & -0.0731 & 0.529047 \tabularnewline
5 & -0.051579 & -0.4407 & 0.669629 \tabularnewline
6 & -0.019315 & -0.165 & 0.56531 \tabularnewline
7 & -0.207205 & -1.7704 & 0.959579 \tabularnewline
8 & 0.086383 & 0.7381 & 0.231423 \tabularnewline
9 & -0.251119 & -2.1456 & 0.982383 \tabularnewline
10 & -0.084918 & -0.7255 & 0.76478 \tabularnewline
11 & -0.130861 & -1.1181 & 0.8664 \tabularnewline
12 & -0.035839 & -0.3062 & 0.619842 \tabularnewline
13 & 0.057927 & 0.4949 & 0.311069 \tabularnewline
14 & -0.014081 & -0.1203 & 0.547715 \tabularnewline
15 & -0.0476 & -0.4067 & 0.657289 \tabularnewline
16 & -0.244282 & -2.0871 & 0.979817 \tabularnewline
17 & -0.060906 & -0.5204 & 0.697812 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5982&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]0.68793[/C][C]5.8777[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.108161[/C][C]-0.9241[/C][C]0.820767[/C][/ROW]
[ROW][C]2[/C][C]-0.065399[/C][C]-0.5588[/C][C]0.710985[/C][/ROW]
[ROW][C]3[/C][C]-0.03245[/C][C]-0.2773[/C][C]0.608815[/C][/ROW]
[ROW][C]4[/C][C]-0.008559[/C][C]-0.0731[/C][C]0.529047[/C][/ROW]
[ROW][C]5[/C][C]-0.051579[/C][C]-0.4407[/C][C]0.669629[/C][/ROW]
[ROW][C]6[/C][C]-0.019315[/C][C]-0.165[/C][C]0.56531[/C][/ROW]
[ROW][C]7[/C][C]-0.207205[/C][C]-1.7704[/C][C]0.959579[/C][/ROW]
[ROW][C]8[/C][C]0.086383[/C][C]0.7381[/C][C]0.231423[/C][/ROW]
[ROW][C]9[/C][C]-0.251119[/C][C]-2.1456[/C][C]0.982383[/C][/ROW]
[ROW][C]10[/C][C]-0.084918[/C][C]-0.7255[/C][C]0.76478[/C][/ROW]
[ROW][C]11[/C][C]-0.130861[/C][C]-1.1181[/C][C]0.8664[/C][/ROW]
[ROW][C]12[/C][C]-0.035839[/C][C]-0.3062[/C][C]0.619842[/C][/ROW]
[ROW][C]13[/C][C]0.057927[/C][C]0.4949[/C][C]0.311069[/C][/ROW]
[ROW][C]14[/C][C]-0.014081[/C][C]-0.1203[/C][C]0.547715[/C][/ROW]
[ROW][C]15[/C][C]-0.0476[/C][C]-0.4067[/C][C]0.657289[/C][/ROW]
[ROW][C]16[/C][C]-0.244282[/C][C]-2.0871[/C][C]0.979817[/C][/ROW]
[ROW][C]17[/C][C]-0.060906[/C][C]-0.5204[/C][C]0.697812[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5982&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5982&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	0.68793	5.8777	0
1	-0.108161	-0.9241	0.820767
2	-0.065399	-0.5588	0.710985
3	-0.03245	-0.2773	0.608815
4	-0.008559	-0.0731	0.529047
5	-0.051579	-0.4407	0.669629
6	-0.019315	-0.165	0.56531
7	-0.207205	-1.7704	0.959579
8	0.086383	0.7381	0.231423
9	-0.251119	-2.1456	0.982383
10	-0.084918	-0.7255	0.76478
11	-0.130861	-1.1181	0.8664
12	-0.035839	-0.3062	0.619842
13	0.057927	0.4949	0.311069
14	-0.014081	-0.1203	0.547715
15	-0.0476	-0.4067	0.657289
16	-0.244282	-2.0871	0.979817
17	-0.060906	-0.5204	0.697812

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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