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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 06 Dec 2007 07:04:23 -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/t11969492855u2iqjn06l24prf.htm/, Retrieved Fri, 03 May 2024 14:53:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2613, Retrieved Fri, 03 May 2024 14:53:51 +0000

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No (this computation is public)

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Estimated Impact

165

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

-       [(Partial) Autocorrelation Function] [WS4:Q2: werkloosheid] [2007-12-06 14:04:23] [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	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=2613&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=2613&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2613&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	6.8557	0
1	-0.005329	-0.0365	0.514493
2	-0.125598	-0.8611	0.80321
3	-0.016515	-0.1132	0.54483
4	-0.048499	-0.3325	0.629503
5	-0.025881	-0.1774	0.570034
6	0.017802	0.122	0.451691
7	0.080812	0.554	0.291097
8	0.04535	0.3109	0.378624
9	0.114134	0.7825	0.218934
10	-0.125142	-0.8579	0.802358
11	0.019482	0.1336	0.447159
12	-0.107984	-0.7403	0.768601
13	-0.060875	-0.4173	0.660835
14	0.179364	1.2297	0.112473
15	0.040439	0.2772	0.391407
16	-0.018832	-0.1291	0.551087

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 6.8557 & 0 \tabularnewline
1 & -0.005329 & -0.0365 & 0.514493 \tabularnewline
2 & -0.125598 & -0.8611 & 0.80321 \tabularnewline
3 & -0.016515 & -0.1132 & 0.54483 \tabularnewline
4 & -0.048499 & -0.3325 & 0.629503 \tabularnewline
5 & -0.025881 & -0.1774 & 0.570034 \tabularnewline
6 & 0.017802 & 0.122 & 0.451691 \tabularnewline
7 & 0.080812 & 0.554 & 0.291097 \tabularnewline
8 & 0.04535 & 0.3109 & 0.378624 \tabularnewline
9 & 0.114134 & 0.7825 & 0.218934 \tabularnewline
10 & -0.125142 & -0.8579 & 0.802358 \tabularnewline
11 & 0.019482 & 0.1336 & 0.447159 \tabularnewline
12 & -0.107984 & -0.7403 & 0.768601 \tabularnewline
13 & -0.060875 & -0.4173 & 0.660835 \tabularnewline
14 & 0.179364 & 1.2297 & 0.112473 \tabularnewline
15 & 0.040439 & 0.2772 & 0.391407 \tabularnewline
16 & -0.018832 & -0.1291 & 0.551087 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2613&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]6.8557[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.005329[/C][C]-0.0365[/C][C]0.514493[/C][/ROW]
[ROW][C]2[/C][C]-0.125598[/C][C]-0.8611[/C][C]0.80321[/C][/ROW]
[ROW][C]3[/C][C]-0.016515[/C][C]-0.1132[/C][C]0.54483[/C][/ROW]
[ROW][C]4[/C][C]-0.048499[/C][C]-0.3325[/C][C]0.629503[/C][/ROW]
[ROW][C]5[/C][C]-0.025881[/C][C]-0.1774[/C][C]0.570034[/C][/ROW]
[ROW][C]6[/C][C]0.017802[/C][C]0.122[/C][C]0.451691[/C][/ROW]
[ROW][C]7[/C][C]0.080812[/C][C]0.554[/C][C]0.291097[/C][/ROW]
[ROW][C]8[/C][C]0.04535[/C][C]0.3109[/C][C]0.378624[/C][/ROW]
[ROW][C]9[/C][C]0.114134[/C][C]0.7825[/C][C]0.218934[/C][/ROW]
[ROW][C]10[/C][C]-0.125142[/C][C]-0.8579[/C][C]0.802358[/C][/ROW]
[ROW][C]11[/C][C]0.019482[/C][C]0.1336[/C][C]0.447159[/C][/ROW]
[ROW][C]12[/C][C]-0.107984[/C][C]-0.7403[/C][C]0.768601[/C][/ROW]
[ROW][C]13[/C][C]-0.060875[/C][C]-0.4173[/C][C]0.660835[/C][/ROW]
[ROW][C]14[/C][C]0.179364[/C][C]1.2297[/C][C]0.112473[/C][/ROW]
[ROW][C]15[/C][C]0.040439[/C][C]0.2772[/C][C]0.391407[/C][/ROW]
[ROW][C]16[/C][C]-0.018832[/C][C]-0.1291[/C][C]0.551087[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2613&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2613&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	6.8557	0
1	-0.005329	-0.0365	0.514493
2	-0.125598	-0.8611	0.80321
3	-0.016515	-0.1132	0.54483
4	-0.048499	-0.3325	0.629503
5	-0.025881	-0.1774	0.570034
6	0.017802	0.122	0.451691
7	0.080812	0.554	0.291097
8	0.04535	0.3109	0.378624
9	0.114134	0.7825	0.218934
10	-0.125142	-0.8579	0.802358
11	0.019482	0.1336	0.447159
12	-0.107984	-0.7403	0.768601
13	-0.060875	-0.4173	0.660835
14	0.179364	1.2297	0.112473
15	0.040439	0.2772	0.391407
16	-0.018832	-0.1291	0.551087

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.005329	-0.0365	0.514493
1	-0.12563	-0.8613	0.80327
2	-0.018226	-0.1249	0.549451
3	-0.065584	-0.4496	0.672476
4	-0.03191	-0.2188	0.58611
5	0.002197	0.0151	0.494025
6	0.072904	0.4998	0.309773
7	0.04672	0.3203	0.375082
8	0.136755	0.9375	0.176636
9	-0.110291	-0.7561	0.773324
10	0.06462	0.443	0.329894
11	-0.136688	-0.9371	0.823248
12	-0.041595	-0.2852	0.611613
13	0.140111	0.9606	0.170847
14	0.013657	0.0936	0.462901
15	-0.003709	-0.0254	0.51009
16	-0.166333	-1.1403	0.870035

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.005329 & -0.0365 & 0.514493 \tabularnewline
1 & -0.12563 & -0.8613 & 0.80327 \tabularnewline
2 & -0.018226 & -0.1249 & 0.549451 \tabularnewline
3 & -0.065584 & -0.4496 & 0.672476 \tabularnewline
4 & -0.03191 & -0.2188 & 0.58611 \tabularnewline
5 & 0.002197 & 0.0151 & 0.494025 \tabularnewline
6 & 0.072904 & 0.4998 & 0.309773 \tabularnewline
7 & 0.04672 & 0.3203 & 0.375082 \tabularnewline
8 & 0.136755 & 0.9375 & 0.176636 \tabularnewline
9 & -0.110291 & -0.7561 & 0.773324 \tabularnewline
10 & 0.06462 & 0.443 & 0.329894 \tabularnewline
11 & -0.136688 & -0.9371 & 0.823248 \tabularnewline
12 & -0.041595 & -0.2852 & 0.611613 \tabularnewline
13 & 0.140111 & 0.9606 & 0.170847 \tabularnewline
14 & 0.013657 & 0.0936 & 0.462901 \tabularnewline
15 & -0.003709 & -0.0254 & 0.51009 \tabularnewline
16 & -0.166333 & -1.1403 & 0.870035 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2613&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]-0.005329[/C][C]-0.0365[/C][C]0.514493[/C][/ROW]
[ROW][C]1[/C][C]-0.12563[/C][C]-0.8613[/C][C]0.80327[/C][/ROW]
[ROW][C]2[/C][C]-0.018226[/C][C]-0.1249[/C][C]0.549451[/C][/ROW]
[ROW][C]3[/C][C]-0.065584[/C][C]-0.4496[/C][C]0.672476[/C][/ROW]
[ROW][C]4[/C][C]-0.03191[/C][C]-0.2188[/C][C]0.58611[/C][/ROW]
[ROW][C]5[/C][C]0.002197[/C][C]0.0151[/C][C]0.494025[/C][/ROW]
[ROW][C]6[/C][C]0.072904[/C][C]0.4998[/C][C]0.309773[/C][/ROW]
[ROW][C]7[/C][C]0.04672[/C][C]0.3203[/C][C]0.375082[/C][/ROW]
[ROW][C]8[/C][C]0.136755[/C][C]0.9375[/C][C]0.176636[/C][/ROW]
[ROW][C]9[/C][C]-0.110291[/C][C]-0.7561[/C][C]0.773324[/C][/ROW]
[ROW][C]10[/C][C]0.06462[/C][C]0.443[/C][C]0.329894[/C][/ROW]
[ROW][C]11[/C][C]-0.136688[/C][C]-0.9371[/C][C]0.823248[/C][/ROW]
[ROW][C]12[/C][C]-0.041595[/C][C]-0.2852[/C][C]0.611613[/C][/ROW]
[ROW][C]13[/C][C]0.140111[/C][C]0.9606[/C][C]0.170847[/C][/ROW]
[ROW][C]14[/C][C]0.013657[/C][C]0.0936[/C][C]0.462901[/C][/ROW]
[ROW][C]15[/C][C]-0.003709[/C][C]-0.0254[/C][C]0.51009[/C][/ROW]
[ROW][C]16[/C][C]-0.166333[/C][C]-1.1403[/C][C]0.870035[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2613&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2613&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	-0.005329	-0.0365	0.514493
1	-0.12563	-0.8613	0.80327
2	-0.018226	-0.1249	0.549451
3	-0.065584	-0.4496	0.672476
4	-0.03191	-0.2188	0.58611
5	0.002197	0.0151	0.494025
6	0.072904	0.4998	0.309773
7	0.04672	0.3203	0.375082
8	0.136755	0.9375	0.176636
9	-0.110291	-0.7561	0.773324
10	0.06462	0.443	0.329894
11	-0.136688	-0.9371	0.823248
12	-0.041595	-0.2852	0.611613
13	0.140111	0.9606	0.170847
14	0.013657	0.0936	0.462901
15	-0.003709	-0.0254	0.51009
16	-0.166333	-1.1403	0.870035

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 = 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 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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