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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 02 Dec 2008 07:50:00 -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/Dec/02/t1228229553h1r02hqxcmxacn8.htm/, Retrieved Sun, 19 May 2024 08:45:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27889, Retrieved Sun, 19 May 2024 08:45:51 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

194

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

F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD  [Cross Correlation Function] [Q7] [2008-12-02 13:17:13] [5387335d8669ad018e3e2def51162329]
- RMPD      [(Partial) Autocorrelation Function] [autocorrelation] [2008-12-02 14:50:00] [c4248bbb85fa4e400deddbf50234dcae] [Current]

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Summary of computational 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 computational 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=27889&T=0

[TABLE]
[ROW][C]Summary of computational 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=27889&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27889&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 computational 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
1	-0.406869	-2.7894	0.003802
2	-0.000705	-0.0048	0.498082
3	0.183735	1.2596	0.107013
4	-0.096934	-0.6645	0.254795
5	0.009353	0.0641	0.474572
6	0.115239	0.79	0.216737
7	-0.059566	-0.4084	0.34243
8	0.081044	0.5556	0.290556
9	0.068321	0.4684	0.320837
10	-0.158616	-1.0874	0.1412
11	0.185879	1.2743	0.104407
12	-0.209824	-1.4385	0.078462
13	0.039386	0.27	0.394164
14	0.089193	0.6115	0.271915
15	-0.021746	-0.1491	0.441063
16	-0.177258	-1.2152	0.115176
17	0.091409	0.6267	0.266954

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.406869 & -2.7894 & 0.003802 \tabularnewline
2 & -0.000705 & -0.0048 & 0.498082 \tabularnewline
3 & 0.183735 & 1.2596 & 0.107013 \tabularnewline
4 & -0.096934 & -0.6645 & 0.254795 \tabularnewline
5 & 0.009353 & 0.0641 & 0.474572 \tabularnewline
6 & 0.115239 & 0.79 & 0.216737 \tabularnewline
7 & -0.059566 & -0.4084 & 0.34243 \tabularnewline
8 & 0.081044 & 0.5556 & 0.290556 \tabularnewline
9 & 0.068321 & 0.4684 & 0.320837 \tabularnewline
10 & -0.158616 & -1.0874 & 0.1412 \tabularnewline
11 & 0.185879 & 1.2743 & 0.104407 \tabularnewline
12 & -0.209824 & -1.4385 & 0.078462 \tabularnewline
13 & 0.039386 & 0.27 & 0.394164 \tabularnewline
14 & 0.089193 & 0.6115 & 0.271915 \tabularnewline
15 & -0.021746 & -0.1491 & 0.441063 \tabularnewline
16 & -0.177258 & -1.2152 & 0.115176 \tabularnewline
17 & 0.091409 & 0.6267 & 0.266954 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27889&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]1[/C][C]-0.406869[/C][C]-2.7894[/C][C]0.003802[/C][/ROW]
[ROW][C]2[/C][C]-0.000705[/C][C]-0.0048[/C][C]0.498082[/C][/ROW]
[ROW][C]3[/C][C]0.183735[/C][C]1.2596[/C][C]0.107013[/C][/ROW]
[ROW][C]4[/C][C]-0.096934[/C][C]-0.6645[/C][C]0.254795[/C][/ROW]
[ROW][C]5[/C][C]0.009353[/C][C]0.0641[/C][C]0.474572[/C][/ROW]
[ROW][C]6[/C][C]0.115239[/C][C]0.79[/C][C]0.216737[/C][/ROW]
[ROW][C]7[/C][C]-0.059566[/C][C]-0.4084[/C][C]0.34243[/C][/ROW]
[ROW][C]8[/C][C]0.081044[/C][C]0.5556[/C][C]0.290556[/C][/ROW]
[ROW][C]9[/C][C]0.068321[/C][C]0.4684[/C][C]0.320837[/C][/ROW]
[ROW][C]10[/C][C]-0.158616[/C][C]-1.0874[/C][C]0.1412[/C][/ROW]
[ROW][C]11[/C][C]0.185879[/C][C]1.2743[/C][C]0.104407[/C][/ROW]
[ROW][C]12[/C][C]-0.209824[/C][C]-1.4385[/C][C]0.078462[/C][/ROW]
[ROW][C]13[/C][C]0.039386[/C][C]0.27[/C][C]0.394164[/C][/ROW]
[ROW][C]14[/C][C]0.089193[/C][C]0.6115[/C][C]0.271915[/C][/ROW]
[ROW][C]15[/C][C]-0.021746[/C][C]-0.1491[/C][C]0.441063[/C][/ROW]
[ROW][C]16[/C][C]-0.177258[/C][C]-1.2152[/C][C]0.115176[/C][/ROW]
[ROW][C]17[/C][C]0.091409[/C][C]0.6267[/C][C]0.266954[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27889&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27889&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
1	-0.406869	-2.7894	0.003802
2	-0.000705	-0.0048	0.498082
3	0.183735	1.2596	0.107013
4	-0.096934	-0.6645	0.254795
5	0.009353	0.0641	0.474572
6	0.115239	0.79	0.216737
7	-0.059566	-0.4084	0.34243
8	0.081044	0.5556	0.290556
9	0.068321	0.4684	0.320837
10	-0.158616	-1.0874	0.1412
11	0.185879	1.2743	0.104407
12	-0.209824	-1.4385	0.078462
13	0.039386	0.27	0.394164
14	0.089193	0.6115	0.271915
15	-0.021746	-0.1491	0.441063
16	-0.177258	-1.2152	0.115176
17	0.091409	0.6267	0.266954

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.406869	-2.7894	0.003802
2	-0.199228	-1.3658	0.089245
3	0.1277	0.8755	0.192885
4	0.05062	0.347	0.365058
5	0.010787	0.074	0.47068
6	0.105931	0.7262	0.235651
7	0.050846	0.3486	0.364479
8	0.105891	0.726	0.235733
9	0.136803	0.9379	0.176552
10	-0.086642	-0.594	0.277685
11	0.074226	0.5089	0.306613
12	-0.196656	-1.3482	0.092027
13	-0.108596	-0.7445	0.230141
14	-0.013239	-0.0908	0.464034
15	0.080491	0.5518	0.291843
16	-0.184763	-1.2667	0.105757
17	-0.140875	-0.9658	0.169546

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.406869 & -2.7894 & 0.003802 \tabularnewline
2 & -0.199228 & -1.3658 & 0.089245 \tabularnewline
3 & 0.1277 & 0.8755 & 0.192885 \tabularnewline
4 & 0.05062 & 0.347 & 0.365058 \tabularnewline
5 & 0.010787 & 0.074 & 0.47068 \tabularnewline
6 & 0.105931 & 0.7262 & 0.235651 \tabularnewline
7 & 0.050846 & 0.3486 & 0.364479 \tabularnewline
8 & 0.105891 & 0.726 & 0.235733 \tabularnewline
9 & 0.136803 & 0.9379 & 0.176552 \tabularnewline
10 & -0.086642 & -0.594 & 0.277685 \tabularnewline
11 & 0.074226 & 0.5089 & 0.306613 \tabularnewline
12 & -0.196656 & -1.3482 & 0.092027 \tabularnewline
13 & -0.108596 & -0.7445 & 0.230141 \tabularnewline
14 & -0.013239 & -0.0908 & 0.464034 \tabularnewline
15 & 0.080491 & 0.5518 & 0.291843 \tabularnewline
16 & -0.184763 & -1.2667 & 0.105757 \tabularnewline
17 & -0.140875 & -0.9658 & 0.169546 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27889&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]1[/C][C]-0.406869[/C][C]-2.7894[/C][C]0.003802[/C][/ROW]
[ROW][C]2[/C][C]-0.199228[/C][C]-1.3658[/C][C]0.089245[/C][/ROW]
[ROW][C]3[/C][C]0.1277[/C][C]0.8755[/C][C]0.192885[/C][/ROW]
[ROW][C]4[/C][C]0.05062[/C][C]0.347[/C][C]0.365058[/C][/ROW]
[ROW][C]5[/C][C]0.010787[/C][C]0.074[/C][C]0.47068[/C][/ROW]
[ROW][C]6[/C][C]0.105931[/C][C]0.7262[/C][C]0.235651[/C][/ROW]
[ROW][C]7[/C][C]0.050846[/C][C]0.3486[/C][C]0.364479[/C][/ROW]
[ROW][C]8[/C][C]0.105891[/C][C]0.726[/C][C]0.235733[/C][/ROW]
[ROW][C]9[/C][C]0.136803[/C][C]0.9379[/C][C]0.176552[/C][/ROW]
[ROW][C]10[/C][C]-0.086642[/C][C]-0.594[/C][C]0.277685[/C][/ROW]
[ROW][C]11[/C][C]0.074226[/C][C]0.5089[/C][C]0.306613[/C][/ROW]
[ROW][C]12[/C][C]-0.196656[/C][C]-1.3482[/C][C]0.092027[/C][/ROW]
[ROW][C]13[/C][C]-0.108596[/C][C]-0.7445[/C][C]0.230141[/C][/ROW]
[ROW][C]14[/C][C]-0.013239[/C][C]-0.0908[/C][C]0.464034[/C][/ROW]
[ROW][C]15[/C][C]0.080491[/C][C]0.5518[/C][C]0.291843[/C][/ROW]
[ROW][C]16[/C][C]-0.184763[/C][C]-1.2667[/C][C]0.105757[/C][/ROW]
[ROW][C]17[/C][C]-0.140875[/C][C]-0.9658[/C][C]0.169546[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27889&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27889&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
1	-0.406869	-2.7894	0.003802
2	-0.199228	-1.3658	0.089245
3	0.1277	0.8755	0.192885
4	0.05062	0.347	0.365058
5	0.010787	0.074	0.47068
6	0.105931	0.7262	0.235651
7	0.050846	0.3486	0.364479
8	0.105891	0.726	0.235733
9	0.136803	0.9379	0.176552
10	-0.086642	-0.594	0.277685
11	0.074226	0.5089	0.306613
12	-0.196656	-1.3482	0.092027
13	-0.108596	-0.7445	0.230141
14	-0.013239	-0.0908	0.464034
15	0.080491	0.5518	0.291843
16	-0.184763	-1.2667	0.105757
17	-0.140875	-0.9658	0.169546

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 1 ; par4 = 12 ; par5 = 1 ; par6 = 0 ; par7 = 1 ;

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 2:(par1+1)) {
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(abs(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,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(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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Dataset

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Figures (Output of Computation)

Input Parameters & R Code