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Author's title

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, 06 Dec 2011 03:17:43 -0500

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/2011/Dec/06/t13231594971h0ov0r2ibx5nt7.htm/, Retrieved Mon, 29 Apr 2024 03:13:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151373, Retrieved Mon, 29 Apr 2024 03:13:00 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

140

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMPD  [(Partial) Autocorrelation Function] [ACF (d=0, D=0)] [2011-12-06 08:00:15] [bcad5ea7a7be31884500e96b7abaff18]
- R P     [(Partial) Autocorrelation Function] [ACF (d=1 en D=0)] [2011-12-06 08:08:10] [bcad5ea7a7be31884500e96b7abaff18]
-   P         [(Partial) Autocorrelation Function] [ACF (d=0, D=1)] [2011-12-06 08:17:43] [d14d64ba86ecc27fb5997ae1bd82937b] [Current]
-   P           [(Partial) Autocorrelation Function] [ACF (d=1, D=1)] [2011-12-06 08:18:59] [bcad5ea7a7be31884500e96b7abaff18] 
- RMP             [Spectral Analysis] [CP (d=0, D=0)] [2011-12-06 08:24:51] [bcad5ea7a7be31884500e96b7abaff18] 
- R P               [Spectral Analysis] [CP (d=1, D=0)] [2011-12-06 08:27:06] [bcad5ea7a7be31884500e96b7abaff18] 
-   P                 [Spectral Analysis] [CP (d=0, D=1)] [2011-12-06 08:28:42] [bcad5ea7a7be31884500e96b7abaff18] 
-   P                   [Spectral Analysis] [CP (d=1, D=1)] [2011-12-06 08:30:04] [bcad5ea7a7be31884500e96b7abaff18] 
- RMP                   [Variance Reduction Matrix] [VRM ] [2011-12-06 08:41:26] [bcad5ea7a7be31884500e96b7abaff18] 

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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	'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151373&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151373&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151373&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.215861	1.9784	0.025581
2	0.08261	0.7571	0.225543
3	0.113173	1.0373	0.151298
4	0.019523	0.1789	0.429211
5	-0.071148	-0.6521	0.258065
6	-0.027015	-0.2476	0.402526
7	0.067269	0.6165	0.269606
8	0.068082	0.624	0.267166
9	-0.035008	-0.3209	0.37456
10	0.03516	0.3222	0.374033
11	-0.002414	-0.0221	0.491199
12	-0.209582	-1.9209	0.029071
13	0.165398	1.5159	0.066649
14	-0.010459	-0.0959	0.461929
15	-0.118559	-1.0866	0.140159
16	-0.100483	-0.9209	0.179859
17	0.003336	0.0306	0.487842
18	0.067957	0.6228	0.26754
19	-0.066554	-0.61	0.271761

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.215861 & 1.9784 & 0.025581 \tabularnewline
2 & 0.08261 & 0.7571 & 0.225543 \tabularnewline
3 & 0.113173 & 1.0373 & 0.151298 \tabularnewline
4 & 0.019523 & 0.1789 & 0.429211 \tabularnewline
5 & -0.071148 & -0.6521 & 0.258065 \tabularnewline
6 & -0.027015 & -0.2476 & 0.402526 \tabularnewline
7 & 0.067269 & 0.6165 & 0.269606 \tabularnewline
8 & 0.068082 & 0.624 & 0.267166 \tabularnewline
9 & -0.035008 & -0.3209 & 0.37456 \tabularnewline
10 & 0.03516 & 0.3222 & 0.374033 \tabularnewline
11 & -0.002414 & -0.0221 & 0.491199 \tabularnewline
12 & -0.209582 & -1.9209 & 0.029071 \tabularnewline
13 & 0.165398 & 1.5159 & 0.066649 \tabularnewline
14 & -0.010459 & -0.0959 & 0.461929 \tabularnewline
15 & -0.118559 & -1.0866 & 0.140159 \tabularnewline
16 & -0.100483 & -0.9209 & 0.179859 \tabularnewline
17 & 0.003336 & 0.0306 & 0.487842 \tabularnewline
18 & 0.067957 & 0.6228 & 0.26754 \tabularnewline
19 & -0.066554 & -0.61 & 0.271761 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151373&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]0.215861[/C][C]1.9784[/C][C]0.025581[/C][/ROW]
[ROW][C]2[/C][C]0.08261[/C][C]0.7571[/C][C]0.225543[/C][/ROW]
[ROW][C]3[/C][C]0.113173[/C][C]1.0373[/C][C]0.151298[/C][/ROW]
[ROW][C]4[/C][C]0.019523[/C][C]0.1789[/C][C]0.429211[/C][/ROW]
[ROW][C]5[/C][C]-0.071148[/C][C]-0.6521[/C][C]0.258065[/C][/ROW]
[ROW][C]6[/C][C]-0.027015[/C][C]-0.2476[/C][C]0.402526[/C][/ROW]
[ROW][C]7[/C][C]0.067269[/C][C]0.6165[/C][C]0.269606[/C][/ROW]
[ROW][C]8[/C][C]0.068082[/C][C]0.624[/C][C]0.267166[/C][/ROW]
[ROW][C]9[/C][C]-0.035008[/C][C]-0.3209[/C][C]0.37456[/C][/ROW]
[ROW][C]10[/C][C]0.03516[/C][C]0.3222[/C][C]0.374033[/C][/ROW]
[ROW][C]11[/C][C]-0.002414[/C][C]-0.0221[/C][C]0.491199[/C][/ROW]
[ROW][C]12[/C][C]-0.209582[/C][C]-1.9209[/C][C]0.029071[/C][/ROW]
[ROW][C]13[/C][C]0.165398[/C][C]1.5159[/C][C]0.066649[/C][/ROW]
[ROW][C]14[/C][C]-0.010459[/C][C]-0.0959[/C][C]0.461929[/C][/ROW]
[ROW][C]15[/C][C]-0.118559[/C][C]-1.0866[/C][C]0.140159[/C][/ROW]
[ROW][C]16[/C][C]-0.100483[/C][C]-0.9209[/C][C]0.179859[/C][/ROW]
[ROW][C]17[/C][C]0.003336[/C][C]0.0306[/C][C]0.487842[/C][/ROW]
[ROW][C]18[/C][C]0.067957[/C][C]0.6228[/C][C]0.26754[/C][/ROW]
[ROW][C]19[/C][C]-0.066554[/C][C]-0.61[/C][C]0.271761[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151373&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151373&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	0.215861	1.9784	0.025581
2	0.08261	0.7571	0.225543
3	0.113173	1.0373	0.151298
4	0.019523	0.1789	0.429211
5	-0.071148	-0.6521	0.258065
6	-0.027015	-0.2476	0.402526
7	0.067269	0.6165	0.269606
8	0.068082	0.624	0.267166
9	-0.035008	-0.3209	0.37456
10	0.03516	0.3222	0.374033
11	-0.002414	-0.0221	0.491199
12	-0.209582	-1.9209	0.029071
13	0.165398	1.5159	0.066649
14	-0.010459	-0.0959	0.461929
15	-0.118559	-1.0866	0.140159
16	-0.100483	-0.9209	0.179859
17	0.003336	0.0306	0.487842
18	0.067957	0.6228	0.26754
19	-0.066554	-0.61	0.271761

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.215861	1.9784	0.025581
2	0.037775	0.3462	0.365025
3	0.092286	0.8458	0.200028
4	-0.026535	-0.2432	0.404223
5	-0.08448	-0.7743	0.220472
6	-0.005615	-0.0515	0.479538
7	0.087428	0.8013	0.212611
8	0.059757	0.5477	0.292681
9	-0.068842	-0.6309	0.264895
10	0.027782	0.2546	0.399816
11	-0.029176	-0.2674	0.394906
12	-0.200175	-1.8346	0.03505
13	0.289956	2.6575	0.004711
14	-0.114185	-1.0465	0.149161
15	-0.103887	-0.9521	0.171879
16	-0.091517	-0.8388	0.201989
17	0.041614	0.3814	0.351934
18	0.139423	1.2778	0.102414
19	-0.0749	-0.6865	0.247153

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.215861 & 1.9784 & 0.025581 \tabularnewline
2 & 0.037775 & 0.3462 & 0.365025 \tabularnewline
3 & 0.092286 & 0.8458 & 0.200028 \tabularnewline
4 & -0.026535 & -0.2432 & 0.404223 \tabularnewline
5 & -0.08448 & -0.7743 & 0.220472 \tabularnewline
6 & -0.005615 & -0.0515 & 0.479538 \tabularnewline
7 & 0.087428 & 0.8013 & 0.212611 \tabularnewline
8 & 0.059757 & 0.5477 & 0.292681 \tabularnewline
9 & -0.068842 & -0.6309 & 0.264895 \tabularnewline
10 & 0.027782 & 0.2546 & 0.399816 \tabularnewline
11 & -0.029176 & -0.2674 & 0.394906 \tabularnewline
12 & -0.200175 & -1.8346 & 0.03505 \tabularnewline
13 & 0.289956 & 2.6575 & 0.004711 \tabularnewline
14 & -0.114185 & -1.0465 & 0.149161 \tabularnewline
15 & -0.103887 & -0.9521 & 0.171879 \tabularnewline
16 & -0.091517 & -0.8388 & 0.201989 \tabularnewline
17 & 0.041614 & 0.3814 & 0.351934 \tabularnewline
18 & 0.139423 & 1.2778 & 0.102414 \tabularnewline
19 & -0.0749 & -0.6865 & 0.247153 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151373&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]0.215861[/C][C]1.9784[/C][C]0.025581[/C][/ROW]
[ROW][C]2[/C][C]0.037775[/C][C]0.3462[/C][C]0.365025[/C][/ROW]
[ROW][C]3[/C][C]0.092286[/C][C]0.8458[/C][C]0.200028[/C][/ROW]
[ROW][C]4[/C][C]-0.026535[/C][C]-0.2432[/C][C]0.404223[/C][/ROW]
[ROW][C]5[/C][C]-0.08448[/C][C]-0.7743[/C][C]0.220472[/C][/ROW]
[ROW][C]6[/C][C]-0.005615[/C][C]-0.0515[/C][C]0.479538[/C][/ROW]
[ROW][C]7[/C][C]0.087428[/C][C]0.8013[/C][C]0.212611[/C][/ROW]
[ROW][C]8[/C][C]0.059757[/C][C]0.5477[/C][C]0.292681[/C][/ROW]
[ROW][C]9[/C][C]-0.068842[/C][C]-0.6309[/C][C]0.264895[/C][/ROW]
[ROW][C]10[/C][C]0.027782[/C][C]0.2546[/C][C]0.399816[/C][/ROW]
[ROW][C]11[/C][C]-0.029176[/C][C]-0.2674[/C][C]0.394906[/C][/ROW]
[ROW][C]12[/C][C]-0.200175[/C][C]-1.8346[/C][C]0.03505[/C][/ROW]
[ROW][C]13[/C][C]0.289956[/C][C]2.6575[/C][C]0.004711[/C][/ROW]
[ROW][C]14[/C][C]-0.114185[/C][C]-1.0465[/C][C]0.149161[/C][/ROW]
[ROW][C]15[/C][C]-0.103887[/C][C]-0.9521[/C][C]0.171879[/C][/ROW]
[ROW][C]16[/C][C]-0.091517[/C][C]-0.8388[/C][C]0.201989[/C][/ROW]
[ROW][C]17[/C][C]0.041614[/C][C]0.3814[/C][C]0.351934[/C][/ROW]
[ROW][C]18[/C][C]0.139423[/C][C]1.2778[/C][C]0.102414[/C][/ROW]
[ROW][C]19[/C][C]-0.0749[/C][C]-0.6865[/C][C]0.247153[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151373&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151373&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	0.215861	1.9784	0.025581
2	0.037775	0.3462	0.365025
3	0.092286	0.8458	0.200028
4	-0.026535	-0.2432	0.404223
5	-0.08448	-0.7743	0.220472
6	-0.005615	-0.0515	0.479538
7	0.087428	0.8013	0.212611
8	0.059757	0.5477	0.292681
9	-0.068842	-0.6309	0.264895
10	0.027782	0.2546	0.399816
11	-0.029176	-0.2674	0.394906
12	-0.200175	-1.8346	0.03505
13	0.289956	2.6575	0.004711
14	-0.114185	-1.0465	0.149161
15	-0.103887	-0.9521	0.171879
16	-0.091517	-0.8388	0.201989
17	0.041614	0.3814	0.351934
18	0.139423	1.2778	0.102414
19	-0.0749	-0.6865	0.247153

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code