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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 24 Nov 2007 07:18:16 -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/24/t11959133893zahci2kyv65f9g.htm/, Retrieved Fri, 03 May 2024 14:49:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6310, Retrieved Fri, 03 May 2024 14:49:34 +0000

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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)

-       [(Partial) Autocorrelation Function] [Partial Autocorre...] [2007-11-24 14:18:16] [6b5c00822e2ce0f7cf73539c28d95782] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6310&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]2 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=6310&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6310&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.6811	0
1	-0.065817	-0.5056	0.692472
2	0.209138	1.6064	0.05676
3	-0.173139	-1.3299	0.905666
4	-0.033978	-0.261	0.602494
5	-0.186361	-1.4315	0.921214
6	-0.143773	-1.1043	0.863036
7	-0.189995	-1.4594	0.925117
8	0.072557	0.5573	0.289708
9	-0.048315	-0.3711	0.644059
10	0.151441	1.1632	0.124707
11	-0.017752	-0.1364	0.553999
12	0.295249	2.2679	0.013507
13	-0.029851	-0.2293	0.590282
14	0.017879	0.1373	0.445617
15	-0.179978	-1.3824	0.913976
16	0.009674	0.0743	0.470509

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & -0.065817 & -0.5056 & 0.692472 \tabularnewline
2 & 0.209138 & 1.6064 & 0.05676 \tabularnewline
3 & -0.173139 & -1.3299 & 0.905666 \tabularnewline
4 & -0.033978 & -0.261 & 0.602494 \tabularnewline
5 & -0.186361 & -1.4315 & 0.921214 \tabularnewline
6 & -0.143773 & -1.1043 & 0.863036 \tabularnewline
7 & -0.189995 & -1.4594 & 0.925117 \tabularnewline
8 & 0.072557 & 0.5573 & 0.289708 \tabularnewline
9 & -0.048315 & -0.3711 & 0.644059 \tabularnewline
10 & 0.151441 & 1.1632 & 0.124707 \tabularnewline
11 & -0.017752 & -0.1364 & 0.553999 \tabularnewline
12 & 0.295249 & 2.2679 & 0.013507 \tabularnewline
13 & -0.029851 & -0.2293 & 0.590282 \tabularnewline
14 & 0.017879 & 0.1373 & 0.445617 \tabularnewline
15 & -0.179978 & -1.3824 & 0.913976 \tabularnewline
16 & 0.009674 & 0.0743 & 0.470509 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6310&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]-0.065817[/C][C]-0.5056[/C][C]0.692472[/C][/ROW]
[ROW][C]2[/C][C]0.209138[/C][C]1.6064[/C][C]0.05676[/C][/ROW]
[ROW][C]3[/C][C]-0.173139[/C][C]-1.3299[/C][C]0.905666[/C][/ROW]
[ROW][C]4[/C][C]-0.033978[/C][C]-0.261[/C][C]0.602494[/C][/ROW]
[ROW][C]5[/C][C]-0.186361[/C][C]-1.4315[/C][C]0.921214[/C][/ROW]
[ROW][C]6[/C][C]-0.143773[/C][C]-1.1043[/C][C]0.863036[/C][/ROW]
[ROW][C]7[/C][C]-0.189995[/C][C]-1.4594[/C][C]0.925117[/C][/ROW]
[ROW][C]8[/C][C]0.072557[/C][C]0.5573[/C][C]0.289708[/C][/ROW]
[ROW][C]9[/C][C]-0.048315[/C][C]-0.3711[/C][C]0.644059[/C][/ROW]
[ROW][C]10[/C][C]0.151441[/C][C]1.1632[/C][C]0.124707[/C][/ROW]
[ROW][C]11[/C][C]-0.017752[/C][C]-0.1364[/C][C]0.553999[/C][/ROW]
[ROW][C]12[/C][C]0.295249[/C][C]2.2679[/C][C]0.013507[/C][/ROW]
[ROW][C]13[/C][C]-0.029851[/C][C]-0.2293[/C][C]0.590282[/C][/ROW]
[ROW][C]14[/C][C]0.017879[/C][C]0.1373[/C][C]0.445617[/C][/ROW]
[ROW][C]15[/C][C]-0.179978[/C][C]-1.3824[/C][C]0.913976[/C][/ROW]
[ROW][C]16[/C][C]0.009674[/C][C]0.0743[/C][C]0.470509[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6310&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6310&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	-0.065817	-0.5056	0.692472
2	0.209138	1.6064	0.05676
3	-0.173139	-1.3299	0.905666
4	-0.033978	-0.261	0.602494
5	-0.186361	-1.4315	0.921214
6	-0.143773	-1.1043	0.863036
7	-0.189995	-1.4594	0.925117
8	0.072557	0.5573	0.289708
9	-0.048315	-0.3711	0.644059
10	0.151441	1.1632	0.124707
11	-0.017752	-0.1364	0.553999
12	0.295249	2.2679	0.013507
13	-0.029851	-0.2293	0.590282
14	0.017879	0.1373	0.445617
15	-0.179978	-1.3824	0.913976
16	0.009674	0.0743	0.470509

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.065817	-0.5056	0.692472
1	0.205698	1.58	0.059728
2	-0.15591	-1.1976	0.882063
3	-0.095718	-0.7352	0.767443
4	-0.133827	-1.0279	0.845914
5	-0.172524	-1.3252	0.90489
6	-0.188252	-1.446	0.923264
7	0.057349	0.4405	0.33059
8	-0.053683	-0.4123	0.659211
9	0.023373	0.1795	0.429068
10	-0.046768	-0.3592	0.639647
11	0.207292	1.5922	0.058337
12	-0.006168	-0.0474	0.518814
13	-0.095084	-0.7304	0.765967
14	-0.099134	-0.7615	0.775294
15	0.044335	0.3405	0.36733
16	-0.070474	-0.5413	0.704837

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.065817 & -0.5056 & 0.692472 \tabularnewline
1 & 0.205698 & 1.58 & 0.059728 \tabularnewline
2 & -0.15591 & -1.1976 & 0.882063 \tabularnewline
3 & -0.095718 & -0.7352 & 0.767443 \tabularnewline
4 & -0.133827 & -1.0279 & 0.845914 \tabularnewline
5 & -0.172524 & -1.3252 & 0.90489 \tabularnewline
6 & -0.188252 & -1.446 & 0.923264 \tabularnewline
7 & 0.057349 & 0.4405 & 0.33059 \tabularnewline
8 & -0.053683 & -0.4123 & 0.659211 \tabularnewline
9 & 0.023373 & 0.1795 & 0.429068 \tabularnewline
10 & -0.046768 & -0.3592 & 0.639647 \tabularnewline
11 & 0.207292 & 1.5922 & 0.058337 \tabularnewline
12 & -0.006168 & -0.0474 & 0.518814 \tabularnewline
13 & -0.095084 & -0.7304 & 0.765967 \tabularnewline
14 & -0.099134 & -0.7615 & 0.775294 \tabularnewline
15 & 0.044335 & 0.3405 & 0.36733 \tabularnewline
16 & -0.070474 & -0.5413 & 0.704837 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6310&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]-0.065817[/C][C]-0.5056[/C][C]0.692472[/C][/ROW]
[ROW][C]1[/C][C]0.205698[/C][C]1.58[/C][C]0.059728[/C][/ROW]
[ROW][C]2[/C][C]-0.15591[/C][C]-1.1976[/C][C]0.882063[/C][/ROW]
[ROW][C]3[/C][C]-0.095718[/C][C]-0.7352[/C][C]0.767443[/C][/ROW]
[ROW][C]4[/C][C]-0.133827[/C][C]-1.0279[/C][C]0.845914[/C][/ROW]
[ROW][C]5[/C][C]-0.172524[/C][C]-1.3252[/C][C]0.90489[/C][/ROW]
[ROW][C]6[/C][C]-0.188252[/C][C]-1.446[/C][C]0.923264[/C][/ROW]
[ROW][C]7[/C][C]0.057349[/C][C]0.4405[/C][C]0.33059[/C][/ROW]
[ROW][C]8[/C][C]-0.053683[/C][C]-0.4123[/C][C]0.659211[/C][/ROW]
[ROW][C]9[/C][C]0.023373[/C][C]0.1795[/C][C]0.429068[/C][/ROW]
[ROW][C]10[/C][C]-0.046768[/C][C]-0.3592[/C][C]0.639647[/C][/ROW]
[ROW][C]11[/C][C]0.207292[/C][C]1.5922[/C][C]0.058337[/C][/ROW]
[ROW][C]12[/C][C]-0.006168[/C][C]-0.0474[/C][C]0.518814[/C][/ROW]
[ROW][C]13[/C][C]-0.095084[/C][C]-0.7304[/C][C]0.765967[/C][/ROW]
[ROW][C]14[/C][C]-0.099134[/C][C]-0.7615[/C][C]0.775294[/C][/ROW]
[ROW][C]15[/C][C]0.044335[/C][C]0.3405[/C][C]0.36733[/C][/ROW]
[ROW][C]16[/C][C]-0.070474[/C][C]-0.5413[/C][C]0.704837[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6310&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6310&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	-0.065817	-0.5056	0.692472
1	0.205698	1.58	0.059728
2	-0.15591	-1.1976	0.882063
3	-0.095718	-0.7352	0.767443
4	-0.133827	-1.0279	0.845914
5	-0.172524	-1.3252	0.90489
6	-0.188252	-1.446	0.923264
7	0.057349	0.4405	0.33059
8	-0.053683	-0.4123	0.659211
9	0.023373	0.1795	0.429068
10	-0.046768	-0.3592	0.639647
11	0.207292	1.5922	0.058337
12	-0.006168	-0.0474	0.518814
13	-0.095084	-0.7304	0.765967
14	-0.099134	-0.7615	0.775294
15	0.044335	0.3405	0.36733
16	-0.070474	-0.5413	0.704837

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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Input Parameters & R Code