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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 06 Dec 2007 07:53:03 -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/Dec/06/t1196952051u4guo6tjpzf9575.htm/, Retrieved Fri, 03 May 2024 10:56:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2641, Retrieved Fri, 03 May 2024 10:56:20 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

202

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

-       [(Partial) Autocorrelation Function] [WS4: Q2 Uitvoer] [2007-12-06 14:53:03] [9b75aacdafaeee3fe66fbd4de075ccd6] [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=2641&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=2641&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2641&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	6.9282	0
1	-0.065942	-0.4569	0.675083
2	0.058992	0.4087	0.342286
3	0.328405	2.2753	0.013698
4	-0.01706	-0.1182	0.546796
5	-0.020241	-0.1402	0.555468
6	0.073604	0.5099	0.306215
7	-0.281202	-1.9482	0.971376
8	0.017606	0.122	0.451712
9	-0.050208	-0.3478	0.635263
10	-0.162527	-1.126	0.867122
11	-0.090051	-0.6239	0.732174
12	-0.191055	-1.3237	0.904058
13	-0.070301	-0.4871	0.685783
14	0.068802	0.4767	0.31788
15	-0.097321	-0.6743	0.74831
16	-0.161318	-1.1176	0.86536

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 6.9282 & 0 \tabularnewline
1 & -0.065942 & -0.4569 & 0.675083 \tabularnewline
2 & 0.058992 & 0.4087 & 0.342286 \tabularnewline
3 & 0.328405 & 2.2753 & 0.013698 \tabularnewline
4 & -0.01706 & -0.1182 & 0.546796 \tabularnewline
5 & -0.020241 & -0.1402 & 0.555468 \tabularnewline
6 & 0.073604 & 0.5099 & 0.306215 \tabularnewline
7 & -0.281202 & -1.9482 & 0.971376 \tabularnewline
8 & 0.017606 & 0.122 & 0.451712 \tabularnewline
9 & -0.050208 & -0.3478 & 0.635263 \tabularnewline
10 & -0.162527 & -1.126 & 0.867122 \tabularnewline
11 & -0.090051 & -0.6239 & 0.732174 \tabularnewline
12 & -0.191055 & -1.3237 & 0.904058 \tabularnewline
13 & -0.070301 & -0.4871 & 0.685783 \tabularnewline
14 & 0.068802 & 0.4767 & 0.31788 \tabularnewline
15 & -0.097321 & -0.6743 & 0.74831 \tabularnewline
16 & -0.161318 & -1.1176 & 0.86536 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2641&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]-0.065942[/C][C]-0.4569[/C][C]0.675083[/C][/ROW]
[ROW][C]2[/C][C]0.058992[/C][C]0.4087[/C][C]0.342286[/C][/ROW]
[ROW][C]3[/C][C]0.328405[/C][C]2.2753[/C][C]0.013698[/C][/ROW]
[ROW][C]4[/C][C]-0.01706[/C][C]-0.1182[/C][C]0.546796[/C][/ROW]
[ROW][C]5[/C][C]-0.020241[/C][C]-0.1402[/C][C]0.555468[/C][/ROW]
[ROW][C]6[/C][C]0.073604[/C][C]0.5099[/C][C]0.306215[/C][/ROW]
[ROW][C]7[/C][C]-0.281202[/C][C]-1.9482[/C][C]0.971376[/C][/ROW]
[ROW][C]8[/C][C]0.017606[/C][C]0.122[/C][C]0.451712[/C][/ROW]
[ROW][C]9[/C][C]-0.050208[/C][C]-0.3478[/C][C]0.635263[/C][/ROW]
[ROW][C]10[/C][C]-0.162527[/C][C]-1.126[/C][C]0.867122[/C][/ROW]
[ROW][C]11[/C][C]-0.090051[/C][C]-0.6239[/C][C]0.732174[/C][/ROW]
[ROW][C]12[/C][C]-0.191055[/C][C]-1.3237[/C][C]0.904058[/C][/ROW]
[ROW][C]13[/C][C]-0.070301[/C][C]-0.4871[/C][C]0.685783[/C][/ROW]
[ROW][C]14[/C][C]0.068802[/C][C]0.4767[/C][C]0.31788[/C][/ROW]
[ROW][C]15[/C][C]-0.097321[/C][C]-0.6743[/C][C]0.74831[/C][/ROW]
[ROW][C]16[/C][C]-0.161318[/C][C]-1.1176[/C][C]0.86536[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2641&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2641&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	-0.065942	-0.4569	0.675083
2	0.058992	0.4087	0.342286
3	0.328405	2.2753	0.013698
4	-0.01706	-0.1182	0.546796
5	-0.020241	-0.1402	0.555468
6	0.073604	0.5099	0.306215
7	-0.281202	-1.9482	0.971376
8	0.017606	0.122	0.451712
9	-0.050208	-0.3478	0.635263
10	-0.162527	-1.126	0.867122
11	-0.090051	-0.6239	0.732174
12	-0.191055	-1.3237	0.904058
13	-0.070301	-0.4871	0.685783
14	0.068802	0.4767	0.31788
15	-0.097321	-0.6743	0.74831
16	-0.161318	-1.1176	0.86536

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.065942	-0.4569	0.675083
1	0.054882	0.3802	0.352725
2	0.338185	2.343	0.01166
3	0.031079	0.2153	0.415215
4	-0.072891	-0.505	0.692068
5	-0.053132	-0.3681	0.642796
6	-0.315427	-2.1853	0.983112
7	-0.012156	-0.0842	0.533385
8	-0.010051	-0.0696	0.527614
9	0.033481	0.232	0.408776
10	-0.084959	-0.5886	0.720559
11	-0.246939	-1.7108	0.953217
12	-0.061347	-0.425	0.663641
13	0.105275	0.7294	0.234661
14	0.116391	0.8064	0.212001
15	-0.192621	-1.3345	0.905835
16	0.003695	0.0256	0.489842

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.065942 & -0.4569 & 0.675083 \tabularnewline
1 & 0.054882 & 0.3802 & 0.352725 \tabularnewline
2 & 0.338185 & 2.343 & 0.01166 \tabularnewline
3 & 0.031079 & 0.2153 & 0.415215 \tabularnewline
4 & -0.072891 & -0.505 & 0.692068 \tabularnewline
5 & -0.053132 & -0.3681 & 0.642796 \tabularnewline
6 & -0.315427 & -2.1853 & 0.983112 \tabularnewline
7 & -0.012156 & -0.0842 & 0.533385 \tabularnewline
8 & -0.010051 & -0.0696 & 0.527614 \tabularnewline
9 & 0.033481 & 0.232 & 0.408776 \tabularnewline
10 & -0.084959 & -0.5886 & 0.720559 \tabularnewline
11 & -0.246939 & -1.7108 & 0.953217 \tabularnewline
12 & -0.061347 & -0.425 & 0.663641 \tabularnewline
13 & 0.105275 & 0.7294 & 0.234661 \tabularnewline
14 & 0.116391 & 0.8064 & 0.212001 \tabularnewline
15 & -0.192621 & -1.3345 & 0.905835 \tabularnewline
16 & 0.003695 & 0.0256 & 0.489842 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2641&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]-0.065942[/C][C]-0.4569[/C][C]0.675083[/C][/ROW]
[ROW][C]1[/C][C]0.054882[/C][C]0.3802[/C][C]0.352725[/C][/ROW]
[ROW][C]2[/C][C]0.338185[/C][C]2.343[/C][C]0.01166[/C][/ROW]
[ROW][C]3[/C][C]0.031079[/C][C]0.2153[/C][C]0.415215[/C][/ROW]
[ROW][C]4[/C][C]-0.072891[/C][C]-0.505[/C][C]0.692068[/C][/ROW]
[ROW][C]5[/C][C]-0.053132[/C][C]-0.3681[/C][C]0.642796[/C][/ROW]
[ROW][C]6[/C][C]-0.315427[/C][C]-2.1853[/C][C]0.983112[/C][/ROW]
[ROW][C]7[/C][C]-0.012156[/C][C]-0.0842[/C][C]0.533385[/C][/ROW]
[ROW][C]8[/C][C]-0.010051[/C][C]-0.0696[/C][C]0.527614[/C][/ROW]
[ROW][C]9[/C][C]0.033481[/C][C]0.232[/C][C]0.408776[/C][/ROW]
[ROW][C]10[/C][C]-0.084959[/C][C]-0.5886[/C][C]0.720559[/C][/ROW]
[ROW][C]11[/C][C]-0.246939[/C][C]-1.7108[/C][C]0.953217[/C][/ROW]
[ROW][C]12[/C][C]-0.061347[/C][C]-0.425[/C][C]0.663641[/C][/ROW]
[ROW][C]13[/C][C]0.105275[/C][C]0.7294[/C][C]0.234661[/C][/ROW]
[ROW][C]14[/C][C]0.116391[/C][C]0.8064[/C][C]0.212001[/C][/ROW]
[ROW][C]15[/C][C]-0.192621[/C][C]-1.3345[/C][C]0.905835[/C][/ROW]
[ROW][C]16[/C][C]0.003695[/C][C]0.0256[/C][C]0.489842[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2641&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2641&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	-0.065942	-0.4569	0.675083
1	0.054882	0.3802	0.352725
2	0.338185	2.343	0.01166
3	0.031079	0.2153	0.415215
4	-0.072891	-0.505	0.692068
5	-0.053132	-0.3681	0.642796
6	-0.315427	-2.1853	0.983112
7	-0.012156	-0.0842	0.533385
8	-0.010051	-0.0696	0.527614
9	0.033481	0.232	0.408776
10	-0.084959	-0.5886	0.720559
11	-0.246939	-1.7108	0.953217
12	-0.061347	-0.425	0.663641
13	0.105275	0.7294	0.234661
14	0.116391	0.8064	0.212001
15	-0.192621	-1.3345	0.905835
16	0.003695	0.0256	0.489842

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 = 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