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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 01 Apr 2012 11:05:57 -0400

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/2012/Apr/01/t1333292802arnyipqu11m2ymt.htm/, Retrieved Wed, 01 May 2024 01:40:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=164247, Retrieved Wed, 01 May 2024 01:40:07 +0000

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Estimated Impact

227

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-       [(Partial) Autocorrelation Function] [Kleding en kledin...] [2012-04-01 15:05:57] [675223405f94cd8491f4a89fc80aa26c] [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	'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164247&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164247&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164247&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.531561	4.1175	5.9e-05
2	-0.032213	-0.2495	0.401905
3	-0.358828	-2.7795	0.00363
4	-0.219001	-1.6964	0.047499
5	0.226674	1.7558	0.042112
6	0.430885	3.3376	0.000728
7	0.241878	1.8736	0.032931
8	-0.193945	-1.5023	0.069134
9	-0.377676	-2.9255	0.002425
10	-0.165302	-1.2804	0.102663
11	0.328118	2.5416	0.006818
12	0.600222	4.6493	9e-06
13	0.299718	2.3216	0.011834
14	-0.145597	-1.1278	0.13195
15	-0.436508	-3.3812	0.000637
16	-0.29393	-2.2768	0.01319
17	0.032168	0.2492	0.40204

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.531561 & 4.1175 & 5.9e-05 \tabularnewline
2 & -0.032213 & -0.2495 & 0.401905 \tabularnewline
3 & -0.358828 & -2.7795 & 0.00363 \tabularnewline
4 & -0.219001 & -1.6964 & 0.047499 \tabularnewline
5 & 0.226674 & 1.7558 & 0.042112 \tabularnewline
6 & 0.430885 & 3.3376 & 0.000728 \tabularnewline
7 & 0.241878 & 1.8736 & 0.032931 \tabularnewline
8 & -0.193945 & -1.5023 & 0.069134 \tabularnewline
9 & -0.377676 & -2.9255 & 0.002425 \tabularnewline
10 & -0.165302 & -1.2804 & 0.102663 \tabularnewline
11 & 0.328118 & 2.5416 & 0.006818 \tabularnewline
12 & 0.600222 & 4.6493 & 9e-06 \tabularnewline
13 & 0.299718 & 2.3216 & 0.011834 \tabularnewline
14 & -0.145597 & -1.1278 & 0.13195 \tabularnewline
15 & -0.436508 & -3.3812 & 0.000637 \tabularnewline
16 & -0.29393 & -2.2768 & 0.01319 \tabularnewline
17 & 0.032168 & 0.2492 & 0.40204 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164247&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]0.531561[/C][C]4.1175[/C][C]5.9e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.032213[/C][C]-0.2495[/C][C]0.401905[/C][/ROW]
[ROW][C]3[/C][C]-0.358828[/C][C]-2.7795[/C][C]0.00363[/C][/ROW]
[ROW][C]4[/C][C]-0.219001[/C][C]-1.6964[/C][C]0.047499[/C][/ROW]
[ROW][C]5[/C][C]0.226674[/C][C]1.7558[/C][C]0.042112[/C][/ROW]
[ROW][C]6[/C][C]0.430885[/C][C]3.3376[/C][C]0.000728[/C][/ROW]
[ROW][C]7[/C][C]0.241878[/C][C]1.8736[/C][C]0.032931[/C][/ROW]
[ROW][C]8[/C][C]-0.193945[/C][C]-1.5023[/C][C]0.069134[/C][/ROW]
[ROW][C]9[/C][C]-0.377676[/C][C]-2.9255[/C][C]0.002425[/C][/ROW]
[ROW][C]10[/C][C]-0.165302[/C][C]-1.2804[/C][C]0.102663[/C][/ROW]
[ROW][C]11[/C][C]0.328118[/C][C]2.5416[/C][C]0.006818[/C][/ROW]
[ROW][C]12[/C][C]0.600222[/C][C]4.6493[/C][C]9e-06[/C][/ROW]
[ROW][C]13[/C][C]0.299718[/C][C]2.3216[/C][C]0.011834[/C][/ROW]
[ROW][C]14[/C][C]-0.145597[/C][C]-1.1278[/C][C]0.13195[/C][/ROW]
[ROW][C]15[/C][C]-0.436508[/C][C]-3.3812[/C][C]0.000637[/C][/ROW]
[ROW][C]16[/C][C]-0.29393[/C][C]-2.2768[/C][C]0.01319[/C][/ROW]
[ROW][C]17[/C][C]0.032168[/C][C]0.2492[/C][C]0.40204[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164247&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164247&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	0.531561	4.1175	5.9e-05
2	-0.032213	-0.2495	0.401905
3	-0.358828	-2.7795	0.00363
4	-0.219001	-1.6964	0.047499
5	0.226674	1.7558	0.042112
6	0.430885	3.3376	0.000728
7	0.241878	1.8736	0.032931
8	-0.193945	-1.5023	0.069134
9	-0.377676	-2.9255	0.002425
10	-0.165302	-1.2804	0.102663
11	0.328118	2.5416	0.006818
12	0.600222	4.6493	9e-06
13	0.299718	2.3216	0.011834
14	-0.145597	-1.1278	0.13195
15	-0.436508	-3.3812	0.000637
16	-0.29393	-2.2768	0.01319
17	0.032168	0.2492	0.40204

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.531561	4.1175	5.9e-05
2	-0.438738	-3.3985	0.000605
3	-0.174295	-1.3501	0.09103
4	0.19723	1.5277	0.065916
5	0.337347	2.6131	0.005662
6	-0.023061	-0.1786	0.429416
7	-0.119778	-0.9278	0.178615
8	-0.186853	-1.4474	0.076501
9	0.090433	0.7005	0.243165
10	0.114521	0.8871	0.189291
11	0.314262	2.4343	0.008957
12	0.144836	1.1219	0.133188
13	-0.252233	-1.9538	0.027697
14	-0.006324	-0.049	0.480547
15	-0.058303	-0.4516	0.326588
16	-0.072614	-0.5625	0.287947
17	-0.233103	-1.8056	0.037998

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.531561 & 4.1175 & 5.9e-05 \tabularnewline
2 & -0.438738 & -3.3985 & 0.000605 \tabularnewline
3 & -0.174295 & -1.3501 & 0.09103 \tabularnewline
4 & 0.19723 & 1.5277 & 0.065916 \tabularnewline
5 & 0.337347 & 2.6131 & 0.005662 \tabularnewline
6 & -0.023061 & -0.1786 & 0.429416 \tabularnewline
7 & -0.119778 & -0.9278 & 0.178615 \tabularnewline
8 & -0.186853 & -1.4474 & 0.076501 \tabularnewline
9 & 0.090433 & 0.7005 & 0.243165 \tabularnewline
10 & 0.114521 & 0.8871 & 0.189291 \tabularnewline
11 & 0.314262 & 2.4343 & 0.008957 \tabularnewline
12 & 0.144836 & 1.1219 & 0.133188 \tabularnewline
13 & -0.252233 & -1.9538 & 0.027697 \tabularnewline
14 & -0.006324 & -0.049 & 0.480547 \tabularnewline
15 & -0.058303 & -0.4516 & 0.326588 \tabularnewline
16 & -0.072614 & -0.5625 & 0.287947 \tabularnewline
17 & -0.233103 & -1.8056 & 0.037998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164247&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]0.531561[/C][C]4.1175[/C][C]5.9e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.438738[/C][C]-3.3985[/C][C]0.000605[/C][/ROW]
[ROW][C]3[/C][C]-0.174295[/C][C]-1.3501[/C][C]0.09103[/C][/ROW]
[ROW][C]4[/C][C]0.19723[/C][C]1.5277[/C][C]0.065916[/C][/ROW]
[ROW][C]5[/C][C]0.337347[/C][C]2.6131[/C][C]0.005662[/C][/ROW]
[ROW][C]6[/C][C]-0.023061[/C][C]-0.1786[/C][C]0.429416[/C][/ROW]
[ROW][C]7[/C][C]-0.119778[/C][C]-0.9278[/C][C]0.178615[/C][/ROW]
[ROW][C]8[/C][C]-0.186853[/C][C]-1.4474[/C][C]0.076501[/C][/ROW]
[ROW][C]9[/C][C]0.090433[/C][C]0.7005[/C][C]0.243165[/C][/ROW]
[ROW][C]10[/C][C]0.114521[/C][C]0.8871[/C][C]0.189291[/C][/ROW]
[ROW][C]11[/C][C]0.314262[/C][C]2.4343[/C][C]0.008957[/C][/ROW]
[ROW][C]12[/C][C]0.144836[/C][C]1.1219[/C][C]0.133188[/C][/ROW]
[ROW][C]13[/C][C]-0.252233[/C][C]-1.9538[/C][C]0.027697[/C][/ROW]
[ROW][C]14[/C][C]-0.006324[/C][C]-0.049[/C][C]0.480547[/C][/ROW]
[ROW][C]15[/C][C]-0.058303[/C][C]-0.4516[/C][C]0.326588[/C][/ROW]
[ROW][C]16[/C][C]-0.072614[/C][C]-0.5625[/C][C]0.287947[/C][/ROW]
[ROW][C]17[/C][C]-0.233103[/C][C]-1.8056[/C][C]0.037998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164247&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164247&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	0.531561	4.1175	5.9e-05
2	-0.438738	-3.3985	0.000605
3	-0.174295	-1.3501	0.09103
4	0.19723	1.5277	0.065916
5	0.337347	2.6131	0.005662
6	-0.023061	-0.1786	0.429416
7	-0.119778	-0.9278	0.178615
8	-0.186853	-1.4474	0.076501
9	0.090433	0.7005	0.243165
10	0.114521	0.8871	0.189291
11	0.314262	2.4343	0.008957
12	0.144836	1.1219	0.133188
13	-0.252233	-1.9538	0.027697
14	-0.006324	-0.049	0.480547
15	-0.058303	-0.4516	0.326588
16	-0.072614	-0.5625	0.287947
17	-0.233103	-1.8056	0.037998

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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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