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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 04 Dec 2009 02:03:45 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/04/t12599174647sbmb852qr49hd7.htm/, Retrieved Sun, 28 Apr 2024 14:03:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63190, Retrieved Sun, 28 Apr 2024 14:03:34 +0000

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No (this computation is public)

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Estimated Impact

153

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

-     [Univariate Data Series] [Werkloosheid bij ...] [2009-11-03 09:24:35] [1ff3eeaee490dfcff07aa4917fec66b8]
- RMPD    [(Partial) Autocorrelation Function] [ACF] [2009-12-04 09:03:45] [cfc54cb9f3f8d85fe8957f0f7c48844d] [Current]

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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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63190&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63190&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63190&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.107038	-0.8222	0.207144
2	-0.058467	-0.4491	0.327505
3	0.044646	0.3429	0.366433
4	0.056096	0.4309	0.334061
5	-0.036369	-0.2794	0.390474
6	0.206088	1.583	0.059385
7	0.054947	0.4221	0.337259
8	-0.033489	-0.2572	0.398945
9	-0.013448	-0.1033	0.45904
10	-0.147564	-1.1335	0.130803
11	0.390714	3.0011	0.001969
12	-0.148845	-1.1433	0.128765
13	-0.104758	-0.8047	0.212123
14	-0.021662	-0.1664	0.434209
15	0.036834	0.2829	0.389112
16	-0.163691	-1.2573	0.106794
17	0.116794	0.8971	0.186653
18	-0.071937	-0.5526	0.291325

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.107038 & -0.8222 & 0.207144 \tabularnewline
2 & -0.058467 & -0.4491 & 0.327505 \tabularnewline
3 & 0.044646 & 0.3429 & 0.366433 \tabularnewline
4 & 0.056096 & 0.4309 & 0.334061 \tabularnewline
5 & -0.036369 & -0.2794 & 0.390474 \tabularnewline
6 & 0.206088 & 1.583 & 0.059385 \tabularnewline
7 & 0.054947 & 0.4221 & 0.337259 \tabularnewline
8 & -0.033489 & -0.2572 & 0.398945 \tabularnewline
9 & -0.013448 & -0.1033 & 0.45904 \tabularnewline
10 & -0.147564 & -1.1335 & 0.130803 \tabularnewline
11 & 0.390714 & 3.0011 & 0.001969 \tabularnewline
12 & -0.148845 & -1.1433 & 0.128765 \tabularnewline
13 & -0.104758 & -0.8047 & 0.212123 \tabularnewline
14 & -0.021662 & -0.1664 & 0.434209 \tabularnewline
15 & 0.036834 & 0.2829 & 0.389112 \tabularnewline
16 & -0.163691 & -1.2573 & 0.106794 \tabularnewline
17 & 0.116794 & 0.8971 & 0.186653 \tabularnewline
18 & -0.071937 & -0.5526 & 0.291325 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63190&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]-0.107038[/C][C]-0.8222[/C][C]0.207144[/C][/ROW]
[ROW][C]2[/C][C]-0.058467[/C][C]-0.4491[/C][C]0.327505[/C][/ROW]
[ROW][C]3[/C][C]0.044646[/C][C]0.3429[/C][C]0.366433[/C][/ROW]
[ROW][C]4[/C][C]0.056096[/C][C]0.4309[/C][C]0.334061[/C][/ROW]
[ROW][C]5[/C][C]-0.036369[/C][C]-0.2794[/C][C]0.390474[/C][/ROW]
[ROW][C]6[/C][C]0.206088[/C][C]1.583[/C][C]0.059385[/C][/ROW]
[ROW][C]7[/C][C]0.054947[/C][C]0.4221[/C][C]0.337259[/C][/ROW]
[ROW][C]8[/C][C]-0.033489[/C][C]-0.2572[/C][C]0.398945[/C][/ROW]
[ROW][C]9[/C][C]-0.013448[/C][C]-0.1033[/C][C]0.45904[/C][/ROW]
[ROW][C]10[/C][C]-0.147564[/C][C]-1.1335[/C][C]0.130803[/C][/ROW]
[ROW][C]11[/C][C]0.390714[/C][C]3.0011[/C][C]0.001969[/C][/ROW]
[ROW][C]12[/C][C]-0.148845[/C][C]-1.1433[/C][C]0.128765[/C][/ROW]
[ROW][C]13[/C][C]-0.104758[/C][C]-0.8047[/C][C]0.212123[/C][/ROW]
[ROW][C]14[/C][C]-0.021662[/C][C]-0.1664[/C][C]0.434209[/C][/ROW]
[ROW][C]15[/C][C]0.036834[/C][C]0.2829[/C][C]0.389112[/C][/ROW]
[ROW][C]16[/C][C]-0.163691[/C][C]-1.2573[/C][C]0.106794[/C][/ROW]
[ROW][C]17[/C][C]0.116794[/C][C]0.8971[/C][C]0.186653[/C][/ROW]
[ROW][C]18[/C][C]-0.071937[/C][C]-0.5526[/C][C]0.291325[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63190&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63190&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	-0.107038	-0.8222	0.207144
2	-0.058467	-0.4491	0.327505
3	0.044646	0.3429	0.366433
4	0.056096	0.4309	0.334061
5	-0.036369	-0.2794	0.390474
6	0.206088	1.583	0.059385
7	0.054947	0.4221	0.337259
8	-0.033489	-0.2572	0.398945
9	-0.013448	-0.1033	0.45904
10	-0.147564	-1.1335	0.130803
11	0.390714	3.0011	0.001969
12	-0.148845	-1.1433	0.128765
13	-0.104758	-0.8047	0.212123
14	-0.021662	-0.1664	0.434209
15	0.036834	0.2829	0.389112
16	-0.163691	-1.2573	0.106794
17	0.116794	0.8971	0.186653
18	-0.071937	-0.5526	0.291325

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.107038	-0.8222	0.207144
2	-0.070735	-0.5433	0.294477
3	0.030881	0.2372	0.406662
4	0.06156	0.4729	0.319032
5	-0.018736	-0.1439	0.44303
6	0.209794	1.6115	0.056208
7	0.099012	0.7605	0.224984
8	0.009718	0.0746	0.470373
9	-0.020721	-0.1592	0.437043
10	-0.200581	-1.5407	0.064369
11	0.383313	2.9443	0.002312
12	-0.181662	-1.3954	0.084067
13	-0.109196	-0.8388	0.202498
14	-0.071284	-0.5475	0.293034
15	-0.023674	-0.1818	0.428164
16	-0.039004	-0.2996	0.382768
17	-0.066462	-0.5105	0.305802
18	-0.093663	-0.7194	0.237354

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.107038 & -0.8222 & 0.207144 \tabularnewline
2 & -0.070735 & -0.5433 & 0.294477 \tabularnewline
3 & 0.030881 & 0.2372 & 0.406662 \tabularnewline
4 & 0.06156 & 0.4729 & 0.319032 \tabularnewline
5 & -0.018736 & -0.1439 & 0.44303 \tabularnewline
6 & 0.209794 & 1.6115 & 0.056208 \tabularnewline
7 & 0.099012 & 0.7605 & 0.224984 \tabularnewline
8 & 0.009718 & 0.0746 & 0.470373 \tabularnewline
9 & -0.020721 & -0.1592 & 0.437043 \tabularnewline
10 & -0.200581 & -1.5407 & 0.064369 \tabularnewline
11 & 0.383313 & 2.9443 & 0.002312 \tabularnewline
12 & -0.181662 & -1.3954 & 0.084067 \tabularnewline
13 & -0.109196 & -0.8388 & 0.202498 \tabularnewline
14 & -0.071284 & -0.5475 & 0.293034 \tabularnewline
15 & -0.023674 & -0.1818 & 0.428164 \tabularnewline
16 & -0.039004 & -0.2996 & 0.382768 \tabularnewline
17 & -0.066462 & -0.5105 & 0.305802 \tabularnewline
18 & -0.093663 & -0.7194 & 0.237354 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63190&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]-0.107038[/C][C]-0.8222[/C][C]0.207144[/C][/ROW]
[ROW][C]2[/C][C]-0.070735[/C][C]-0.5433[/C][C]0.294477[/C][/ROW]
[ROW][C]3[/C][C]0.030881[/C][C]0.2372[/C][C]0.406662[/C][/ROW]
[ROW][C]4[/C][C]0.06156[/C][C]0.4729[/C][C]0.319032[/C][/ROW]
[ROW][C]5[/C][C]-0.018736[/C][C]-0.1439[/C][C]0.44303[/C][/ROW]
[ROW][C]6[/C][C]0.209794[/C][C]1.6115[/C][C]0.056208[/C][/ROW]
[ROW][C]7[/C][C]0.099012[/C][C]0.7605[/C][C]0.224984[/C][/ROW]
[ROW][C]8[/C][C]0.009718[/C][C]0.0746[/C][C]0.470373[/C][/ROW]
[ROW][C]9[/C][C]-0.020721[/C][C]-0.1592[/C][C]0.437043[/C][/ROW]
[ROW][C]10[/C][C]-0.200581[/C][C]-1.5407[/C][C]0.064369[/C][/ROW]
[ROW][C]11[/C][C]0.383313[/C][C]2.9443[/C][C]0.002312[/C][/ROW]
[ROW][C]12[/C][C]-0.181662[/C][C]-1.3954[/C][C]0.084067[/C][/ROW]
[ROW][C]13[/C][C]-0.109196[/C][C]-0.8388[/C][C]0.202498[/C][/ROW]
[ROW][C]14[/C][C]-0.071284[/C][C]-0.5475[/C][C]0.293034[/C][/ROW]
[ROW][C]15[/C][C]-0.023674[/C][C]-0.1818[/C][C]0.428164[/C][/ROW]
[ROW][C]16[/C][C]-0.039004[/C][C]-0.2996[/C][C]0.382768[/C][/ROW]
[ROW][C]17[/C][C]-0.066462[/C][C]-0.5105[/C][C]0.305802[/C][/ROW]
[ROW][C]18[/C][C]-0.093663[/C][C]-0.7194[/C][C]0.237354[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63190&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63190&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	-0.107038	-0.8222	0.207144
2	-0.070735	-0.5433	0.294477
3	0.030881	0.2372	0.406662
4	0.06156	0.4729	0.319032
5	-0.018736	-0.1439	0.44303
6	0.209794	1.6115	0.056208
7	0.099012	0.7605	0.224984
8	0.009718	0.0746	0.470373
9	-0.020721	-0.1592	0.437043
10	-0.200581	-1.5407	0.064369
11	0.383313	2.9443	0.002312
12	-0.181662	-1.3954	0.084067
13	-0.109196	-0.8388	0.202498
14	-0.071284	-0.5475	0.293034
15	-0.023674	-0.1818	0.428164
16	-0.039004	-0.2996	0.382768
17	-0.066462	-0.5105	0.305802
18	-0.093663	-0.7194	0.237354

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = -0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = -0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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 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')

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Tables (Output of Computation)

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Input Parameters & R Code