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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 15 Jan 2008 13:43:34 -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/2008/Jan/15/t12004295947hikfn8a10mkzso.htm/, Retrieved Wed, 15 May 2024 07:35:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7968, Retrieved Wed, 15 May 2024 07:35:22 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

300

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

-     [Variance Reduction Matrix] [Inducing Stationa...] [2007-11-24 13:54:20] [b9964c45117f7aac638ab9056d451faa]
- RMPD    [(Partial) Autocorrelation Function] [] [2008-01-15 20:43:34] [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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7968&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7968&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7968&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.6811	0
1	-0.132463	-1.0175	0.843457
2	-0.248335	-1.9075	0.969336
3	0.26629	2.0454	0.022641
4	0.190956	1.4668	0.073876
5	-0.357493	-2.746	0.996007
6	-0.031056	-0.2385	0.593856
7	0.12303	0.945	0.174254
8	-0.071844	-0.5518	0.708431
9	-0.140842	-1.0818	0.858134
10	0.008233	0.0632	0.474895
11	0.081567	0.6265	0.266693
12	-0.113584	-0.8725	0.806751
13	0.036345	0.2792	0.390546
14	0.096068	0.7379	0.231747
15	-0.054282	-0.4169	0.660886
16	-0.087926	-0.6754	0.748961

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & -0.132463 & -1.0175 & 0.843457 \tabularnewline
2 & -0.248335 & -1.9075 & 0.969336 \tabularnewline
3 & 0.26629 & 2.0454 & 0.022641 \tabularnewline
4 & 0.190956 & 1.4668 & 0.073876 \tabularnewline
5 & -0.357493 & -2.746 & 0.996007 \tabularnewline
6 & -0.031056 & -0.2385 & 0.593856 \tabularnewline
7 & 0.12303 & 0.945 & 0.174254 \tabularnewline
8 & -0.071844 & -0.5518 & 0.708431 \tabularnewline
9 & -0.140842 & -1.0818 & 0.858134 \tabularnewline
10 & 0.008233 & 0.0632 & 0.474895 \tabularnewline
11 & 0.081567 & 0.6265 & 0.266693 \tabularnewline
12 & -0.113584 & -0.8725 & 0.806751 \tabularnewline
13 & 0.036345 & 0.2792 & 0.390546 \tabularnewline
14 & 0.096068 & 0.7379 & 0.231747 \tabularnewline
15 & -0.054282 & -0.4169 & 0.660886 \tabularnewline
16 & -0.087926 & -0.6754 & 0.748961 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7968&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]7.6811[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.132463[/C][C]-1.0175[/C][C]0.843457[/C][/ROW]
[ROW][C]2[/C][C]-0.248335[/C][C]-1.9075[/C][C]0.969336[/C][/ROW]
[ROW][C]3[/C][C]0.26629[/C][C]2.0454[/C][C]0.022641[/C][/ROW]
[ROW][C]4[/C][C]0.190956[/C][C]1.4668[/C][C]0.073876[/C][/ROW]
[ROW][C]5[/C][C]-0.357493[/C][C]-2.746[/C][C]0.996007[/C][/ROW]
[ROW][C]6[/C][C]-0.031056[/C][C]-0.2385[/C][C]0.593856[/C][/ROW]
[ROW][C]7[/C][C]0.12303[/C][C]0.945[/C][C]0.174254[/C][/ROW]
[ROW][C]8[/C][C]-0.071844[/C][C]-0.5518[/C][C]0.708431[/C][/ROW]
[ROW][C]9[/C][C]-0.140842[/C][C]-1.0818[/C][C]0.858134[/C][/ROW]
[ROW][C]10[/C][C]0.008233[/C][C]0.0632[/C][C]0.474895[/C][/ROW]
[ROW][C]11[/C][C]0.081567[/C][C]0.6265[/C][C]0.266693[/C][/ROW]
[ROW][C]12[/C][C]-0.113584[/C][C]-0.8725[/C][C]0.806751[/C][/ROW]
[ROW][C]13[/C][C]0.036345[/C][C]0.2792[/C][C]0.390546[/C][/ROW]
[ROW][C]14[/C][C]0.096068[/C][C]0.7379[/C][C]0.231747[/C][/ROW]
[ROW][C]15[/C][C]-0.054282[/C][C]-0.4169[/C][C]0.660886[/C][/ROW]
[ROW][C]16[/C][C]-0.087926[/C][C]-0.6754[/C][C]0.748961[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7968&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7968&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	7.6811	0
1	-0.132463	-1.0175	0.843457
2	-0.248335	-1.9075	0.969336
3	0.26629	2.0454	0.022641
4	0.190956	1.4668	0.073876
5	-0.357493	-2.746	0.996007
6	-0.031056	-0.2385	0.593856
7	0.12303	0.945	0.174254
8	-0.071844	-0.5518	0.708431
9	-0.140842	-1.0818	0.858134
10	0.008233	0.0632	0.474895
11	0.081567	0.6265	0.266693
12	-0.113584	-0.8725	0.806751
13	0.036345	0.2792	0.390546
14	0.096068	0.7379	0.231747
15	-0.054282	-0.4169	0.660886
16	-0.087926	-0.6754	0.748961

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.132463	-1.0175	0.843457
1	-0.27063	-2.0787	0.979001
2	0.207188	1.5914	0.058428
3	0.217741	1.6725	0.049861
4	-0.231263	-1.7764	0.959586
5	-0.102124	-0.7844	0.782037
6	-0.102073	-0.784	0.781922
7	0.014367	0.1104	0.456251
8	-0.005305	-0.0407	0.516182
9	-0.10929	-0.8395	0.797704
10	0.015315	0.1176	0.453379
11	-0.09588	-0.7365	0.767818
12	0.088469	0.6795	0.249725
13	0.05247	0.403	0.344193
14	-0.067164	-0.5159	0.696073
15	-0.084866	-0.6519	0.741491
16	-0.048574	-0.3731	0.644795

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.132463 & -1.0175 & 0.843457 \tabularnewline
1 & -0.27063 & -2.0787 & 0.979001 \tabularnewline
2 & 0.207188 & 1.5914 & 0.058428 \tabularnewline
3 & 0.217741 & 1.6725 & 0.049861 \tabularnewline
4 & -0.231263 & -1.7764 & 0.959586 \tabularnewline
5 & -0.102124 & -0.7844 & 0.782037 \tabularnewline
6 & -0.102073 & -0.784 & 0.781922 \tabularnewline
7 & 0.014367 & 0.1104 & 0.456251 \tabularnewline
8 & -0.005305 & -0.0407 & 0.516182 \tabularnewline
9 & -0.10929 & -0.8395 & 0.797704 \tabularnewline
10 & 0.015315 & 0.1176 & 0.453379 \tabularnewline
11 & -0.09588 & -0.7365 & 0.767818 \tabularnewline
12 & 0.088469 & 0.6795 & 0.249725 \tabularnewline
13 & 0.05247 & 0.403 & 0.344193 \tabularnewline
14 & -0.067164 & -0.5159 & 0.696073 \tabularnewline
15 & -0.084866 & -0.6519 & 0.741491 \tabularnewline
16 & -0.048574 & -0.3731 & 0.644795 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7968&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]-0.132463[/C][C]-1.0175[/C][C]0.843457[/C][/ROW]
[ROW][C]1[/C][C]-0.27063[/C][C]-2.0787[/C][C]0.979001[/C][/ROW]
[ROW][C]2[/C][C]0.207188[/C][C]1.5914[/C][C]0.058428[/C][/ROW]
[ROW][C]3[/C][C]0.217741[/C][C]1.6725[/C][C]0.049861[/C][/ROW]
[ROW][C]4[/C][C]-0.231263[/C][C]-1.7764[/C][C]0.959586[/C][/ROW]
[ROW][C]5[/C][C]-0.102124[/C][C]-0.7844[/C][C]0.782037[/C][/ROW]
[ROW][C]6[/C][C]-0.102073[/C][C]-0.784[/C][C]0.781922[/C][/ROW]
[ROW][C]7[/C][C]0.014367[/C][C]0.1104[/C][C]0.456251[/C][/ROW]
[ROW][C]8[/C][C]-0.005305[/C][C]-0.0407[/C][C]0.516182[/C][/ROW]
[ROW][C]9[/C][C]-0.10929[/C][C]-0.8395[/C][C]0.797704[/C][/ROW]
[ROW][C]10[/C][C]0.015315[/C][C]0.1176[/C][C]0.453379[/C][/ROW]
[ROW][C]11[/C][C]-0.09588[/C][C]-0.7365[/C][C]0.767818[/C][/ROW]
[ROW][C]12[/C][C]0.088469[/C][C]0.6795[/C][C]0.249725[/C][/ROW]
[ROW][C]13[/C][C]0.05247[/C][C]0.403[/C][C]0.344193[/C][/ROW]
[ROW][C]14[/C][C]-0.067164[/C][C]-0.5159[/C][C]0.696073[/C][/ROW]
[ROW][C]15[/C][C]-0.084866[/C][C]-0.6519[/C][C]0.741491[/C][/ROW]
[ROW][C]16[/C][C]-0.048574[/C][C]-0.3731[/C][C]0.644795[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7968&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7968&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	-0.132463	-1.0175	0.843457
1	-0.27063	-2.0787	0.979001
2	0.207188	1.5914	0.058428
3	0.217741	1.6725	0.049861
4	-0.231263	-1.7764	0.959586
5	-0.102124	-0.7844	0.782037
6	-0.102073	-0.784	0.781922
7	0.014367	0.1104	0.456251
8	-0.005305	-0.0407	0.516182
9	-0.10929	-0.8395	0.797704
10	0.015315	0.1176	0.453379
11	-0.09588	-0.7365	0.767818
12	0.088469	0.6795	0.249725
13	0.05247	0.403	0.344193
14	-0.067164	-0.5159	0.696073
15	-0.084866	-0.6519	0.741491
16	-0.048574	-0.3731	0.644795

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 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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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