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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 29 Nov 2007 05:15:01 -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/29/t1196337869qqp5haop7hksre9.htm/, Retrieved Fri, 03 May 2024 06:33:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7449, Retrieved Fri, 03 May 2024 06:33:26 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

162

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

-       [(Partial) Autocorrelation Function] [tot industri�le p...] [2007-11-29 12:15:01] [dd38921fafddee0dfc20da83e9650a2a] [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	3 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 & 3 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=7449&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]3 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=7449&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7449&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	3 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	6.9282	0
1	0.093015	0.6444	0.261183
2	0.130192	0.902	0.185782
3	0.419675	2.9076	0.00275
4	0.142888	0.99	0.16358
5	0.047107	0.3264	0.372784
6	0.16581	1.1488	0.128173
7	-0.088048	-0.61	0.727635
8	-0.009373	-0.0649	0.525753
9	0.067922	0.4706	0.320038
10	-0.251437	-1.742	0.956044
11	-0.175376	-1.215	0.884854
12	-0.240532	-1.6665	0.948932
13	-0.18496	-1.2814	0.896903
14	-0.055476	-0.3843	0.648791
15	-0.226843	-1.5716	0.938695
16	-0.225468	-1.5621	0.937582

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 6.9282 & 0 \tabularnewline
1 & 0.093015 & 0.6444 & 0.261183 \tabularnewline
2 & 0.130192 & 0.902 & 0.185782 \tabularnewline
3 & 0.419675 & 2.9076 & 0.00275 \tabularnewline
4 & 0.142888 & 0.99 & 0.16358 \tabularnewline
5 & 0.047107 & 0.3264 & 0.372784 \tabularnewline
6 & 0.16581 & 1.1488 & 0.128173 \tabularnewline
7 & -0.088048 & -0.61 & 0.727635 \tabularnewline
8 & -0.009373 & -0.0649 & 0.525753 \tabularnewline
9 & 0.067922 & 0.4706 & 0.320038 \tabularnewline
10 & -0.251437 & -1.742 & 0.956044 \tabularnewline
11 & -0.175376 & -1.215 & 0.884854 \tabularnewline
12 & -0.240532 & -1.6665 & 0.948932 \tabularnewline
13 & -0.18496 & -1.2814 & 0.896903 \tabularnewline
14 & -0.055476 & -0.3843 & 0.648791 \tabularnewline
15 & -0.226843 & -1.5716 & 0.938695 \tabularnewline
16 & -0.225468 & -1.5621 & 0.937582 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7449&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]6.9282[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.093015[/C][C]0.6444[/C][C]0.261183[/C][/ROW]
[ROW][C]2[/C][C]0.130192[/C][C]0.902[/C][C]0.185782[/C][/ROW]
[ROW][C]3[/C][C]0.419675[/C][C]2.9076[/C][C]0.00275[/C][/ROW]
[ROW][C]4[/C][C]0.142888[/C][C]0.99[/C][C]0.16358[/C][/ROW]
[ROW][C]5[/C][C]0.047107[/C][C]0.3264[/C][C]0.372784[/C][/ROW]
[ROW][C]6[/C][C]0.16581[/C][C]1.1488[/C][C]0.128173[/C][/ROW]
[ROW][C]7[/C][C]-0.088048[/C][C]-0.61[/C][C]0.727635[/C][/ROW]
[ROW][C]8[/C][C]-0.009373[/C][C]-0.0649[/C][C]0.525753[/C][/ROW]
[ROW][C]9[/C][C]0.067922[/C][C]0.4706[/C][C]0.320038[/C][/ROW]
[ROW][C]10[/C][C]-0.251437[/C][C]-1.742[/C][C]0.956044[/C][/ROW]
[ROW][C]11[/C][C]-0.175376[/C][C]-1.215[/C][C]0.884854[/C][/ROW]
[ROW][C]12[/C][C]-0.240532[/C][C]-1.6665[/C][C]0.948932[/C][/ROW]
[ROW][C]13[/C][C]-0.18496[/C][C]-1.2814[/C][C]0.896903[/C][/ROW]
[ROW][C]14[/C][C]-0.055476[/C][C]-0.3843[/C][C]0.648791[/C][/ROW]
[ROW][C]15[/C][C]-0.226843[/C][C]-1.5716[/C][C]0.938695[/C][/ROW]
[ROW][C]16[/C][C]-0.225468[/C][C]-1.5621[/C][C]0.937582[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7449&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7449&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	6.9282	0
1	0.093015	0.6444	0.261183
2	0.130192	0.902	0.185782
3	0.419675	2.9076	0.00275
4	0.142888	0.99	0.16358
5	0.047107	0.3264	0.372784
6	0.16581	1.1488	0.128173
7	-0.088048	-0.61	0.727635
8	-0.009373	-0.0649	0.525753
9	0.067922	0.4706	0.320038
10	-0.251437	-1.742	0.956044
11	-0.175376	-1.215	0.884854
12	-0.240532	-1.6665	0.948932
13	-0.18496	-1.2814	0.896903
14	-0.055476	-0.3843	0.648791
15	-0.226843	-1.5716	0.938695
16	-0.225468	-1.5621	0.937582

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.093015	0.6444	0.261183
1	0.122601	0.8494	0.199937
2	0.407238	2.8214	0.003467
3	0.098313	0.6811	0.249531
4	-0.058608	-0.406	0.656743
5	-0.034624	-0.2399	0.594278
6	-0.229792	-1.592	0.941031
7	-0.046321	-0.3209	0.62517
8	0.054901	0.3804	0.352676
9	-0.179252	-1.2419	0.889845
10	-0.156386	-1.0835	0.857994
11	-0.328505	-2.276	0.986325
12	-0.007696	-0.0533	0.52115
13	0.253833	1.7586	0.042509
14	0.089	0.6166	0.270204
15	-0.081355	-0.5636	0.71219
16	0.09288	0.6435	0.261485

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.093015 & 0.6444 & 0.261183 \tabularnewline
1 & 0.122601 & 0.8494 & 0.199937 \tabularnewline
2 & 0.407238 & 2.8214 & 0.003467 \tabularnewline
3 & 0.098313 & 0.6811 & 0.249531 \tabularnewline
4 & -0.058608 & -0.406 & 0.656743 \tabularnewline
5 & -0.034624 & -0.2399 & 0.594278 \tabularnewline
6 & -0.229792 & -1.592 & 0.941031 \tabularnewline
7 & -0.046321 & -0.3209 & 0.62517 \tabularnewline
8 & 0.054901 & 0.3804 & 0.352676 \tabularnewline
9 & -0.179252 & -1.2419 & 0.889845 \tabularnewline
10 & -0.156386 & -1.0835 & 0.857994 \tabularnewline
11 & -0.328505 & -2.276 & 0.986325 \tabularnewline
12 & -0.007696 & -0.0533 & 0.52115 \tabularnewline
13 & 0.253833 & 1.7586 & 0.042509 \tabularnewline
14 & 0.089 & 0.6166 & 0.270204 \tabularnewline
15 & -0.081355 & -0.5636 & 0.71219 \tabularnewline
16 & 0.09288 & 0.6435 & 0.261485 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7449&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]0.093015[/C][C]0.6444[/C][C]0.261183[/C][/ROW]
[ROW][C]1[/C][C]0.122601[/C][C]0.8494[/C][C]0.199937[/C][/ROW]
[ROW][C]2[/C][C]0.407238[/C][C]2.8214[/C][C]0.003467[/C][/ROW]
[ROW][C]3[/C][C]0.098313[/C][C]0.6811[/C][C]0.249531[/C][/ROW]
[ROW][C]4[/C][C]-0.058608[/C][C]-0.406[/C][C]0.656743[/C][/ROW]
[ROW][C]5[/C][C]-0.034624[/C][C]-0.2399[/C][C]0.594278[/C][/ROW]
[ROW][C]6[/C][C]-0.229792[/C][C]-1.592[/C][C]0.941031[/C][/ROW]
[ROW][C]7[/C][C]-0.046321[/C][C]-0.3209[/C][C]0.62517[/C][/ROW]
[ROW][C]8[/C][C]0.054901[/C][C]0.3804[/C][C]0.352676[/C][/ROW]
[ROW][C]9[/C][C]-0.179252[/C][C]-1.2419[/C][C]0.889845[/C][/ROW]
[ROW][C]10[/C][C]-0.156386[/C][C]-1.0835[/C][C]0.857994[/C][/ROW]
[ROW][C]11[/C][C]-0.328505[/C][C]-2.276[/C][C]0.986325[/C][/ROW]
[ROW][C]12[/C][C]-0.007696[/C][C]-0.0533[/C][C]0.52115[/C][/ROW]
[ROW][C]13[/C][C]0.253833[/C][C]1.7586[/C][C]0.042509[/C][/ROW]
[ROW][C]14[/C][C]0.089[/C][C]0.6166[/C][C]0.270204[/C][/ROW]
[ROW][C]15[/C][C]-0.081355[/C][C]-0.5636[/C][C]0.71219[/C][/ROW]
[ROW][C]16[/C][C]0.09288[/C][C]0.6435[/C][C]0.261485[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7449&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7449&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	0.093015	0.6444	0.261183
1	0.122601	0.8494	0.199937
2	0.407238	2.8214	0.003467
3	0.098313	0.6811	0.249531
4	-0.058608	-0.406	0.656743
5	-0.034624	-0.2399	0.594278
6	-0.229792	-1.592	0.941031
7	-0.046321	-0.3209	0.62517
8	0.054901	0.3804	0.352676
9	-0.179252	-1.2419	0.889845
10	-0.156386	-1.0835	0.857994
11	-0.328505	-2.276	0.986325
12	-0.007696	-0.0533	0.52115
13	0.253833	1.7586	0.042509
14	0.089	0.6166	0.270204
15	-0.081355	-0.5636	0.71219
16	0.09288	0.6435	0.261485

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 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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 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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Dataset

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Figures (Output of Computation)

Input Parameters & R Code