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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Oct 2015 22:10:29 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/23/t1445634677pd2z22mh3vw1iow.htm/, Retrieved Tue, 14 May 2024 11:33:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282995, Retrieved Tue, 14 May 2024 11:33:02 +0000

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-       [(Partial) Autocorrelation Function] [] [2015-10-23 21:10:29] [c7db9dbe56b0646da05788291b2eebd0] [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	'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282995&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282995&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282995&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.959739	7.4341	0
2	0.912499	7.0682	0
3	0.858765	6.652	0
4	0.801372	6.2074	0
5	0.744593	5.7676	0
6	0.691834	5.3589	1e-06
7	0.646984	5.0115	3e-06
8	0.600177	4.649	9e-06
9	0.55199	4.2757	3.5e-05
10	0.502748	3.8943	0.000125
11	0.453817	3.5152	0.000421
12	0.403424	3.1249	0.00137
13	0.354706	2.7475	0.003959
14	0.310445	2.4047	0.009644
15	0.26269	2.0348	0.023149
16	0.220305	1.7065	0.046545
17	0.178246	1.3807	0.086248

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.959739 & 7.4341 & 0 \tabularnewline
2 & 0.912499 & 7.0682 & 0 \tabularnewline
3 & 0.858765 & 6.652 & 0 \tabularnewline
4 & 0.801372 & 6.2074 & 0 \tabularnewline
5 & 0.744593 & 5.7676 & 0 \tabularnewline
6 & 0.691834 & 5.3589 & 1e-06 \tabularnewline
7 & 0.646984 & 5.0115 & 3e-06 \tabularnewline
8 & 0.600177 & 4.649 & 9e-06 \tabularnewline
9 & 0.55199 & 4.2757 & 3.5e-05 \tabularnewline
10 & 0.502748 & 3.8943 & 0.000125 \tabularnewline
11 & 0.453817 & 3.5152 & 0.000421 \tabularnewline
12 & 0.403424 & 3.1249 & 0.00137 \tabularnewline
13 & 0.354706 & 2.7475 & 0.003959 \tabularnewline
14 & 0.310445 & 2.4047 & 0.009644 \tabularnewline
15 & 0.26269 & 2.0348 & 0.023149 \tabularnewline
16 & 0.220305 & 1.7065 & 0.046545 \tabularnewline
17 & 0.178246 & 1.3807 & 0.086248 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282995&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]0.959739[/C][C]7.4341[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.912499[/C][C]7.0682[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.858765[/C][C]6.652[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.801372[/C][C]6.2074[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.744593[/C][C]5.7676[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.691834[/C][C]5.3589[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.646984[/C][C]5.0115[/C][C]3e-06[/C][/ROW]
[ROW][C]8[/C][C]0.600177[/C][C]4.649[/C][C]9e-06[/C][/ROW]
[ROW][C]9[/C][C]0.55199[/C][C]4.2757[/C][C]3.5e-05[/C][/ROW]
[ROW][C]10[/C][C]0.502748[/C][C]3.8943[/C][C]0.000125[/C][/ROW]
[ROW][C]11[/C][C]0.453817[/C][C]3.5152[/C][C]0.000421[/C][/ROW]
[ROW][C]12[/C][C]0.403424[/C][C]3.1249[/C][C]0.00137[/C][/ROW]
[ROW][C]13[/C][C]0.354706[/C][C]2.7475[/C][C]0.003959[/C][/ROW]
[ROW][C]14[/C][C]0.310445[/C][C]2.4047[/C][C]0.009644[/C][/ROW]
[ROW][C]15[/C][C]0.26269[/C][C]2.0348[/C][C]0.023149[/C][/ROW]
[ROW][C]16[/C][C]0.220305[/C][C]1.7065[/C][C]0.046545[/C][/ROW]
[ROW][C]17[/C][C]0.178246[/C][C]1.3807[/C][C]0.086248[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282995&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282995&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	0.959739	7.4341	0
2	0.912499	7.0682	0
3	0.858765	6.652	0
4	0.801372	6.2074	0
5	0.744593	5.7676	0
6	0.691834	5.3589	1e-06
7	0.646984	5.0115	3e-06
8	0.600177	4.649	9e-06
9	0.55199	4.2757	3.5e-05
10	0.502748	3.8943	0.000125
11	0.453817	3.5152	0.000421
12	0.403424	3.1249	0.00137
13	0.354706	2.7475	0.003959
14	0.310445	2.4047	0.009644
15	0.26269	2.0348	0.023149
16	0.220305	1.7065	0.046545
17	0.178246	1.3807	0.086248

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.959739	7.4341	0
2	-0.109002	-0.8443	0.20092
3	-0.100576	-0.7791	0.219504
4	-0.063915	-0.4951	0.311175
5	-0.01232	-0.0954	0.462145
6	0.023493	0.182	0.428107
7	0.063639	0.4929	0.311925
8	-0.075881	-0.5878	0.279446
9	-0.061539	-0.4767	0.317661
10	-0.044208	-0.3424	0.366611
11	-0.015894	-0.1231	0.451215
12	-0.040686	-0.3152	0.37687
13	-0.006221	-0.0482	0.480864
14	0.010921	0.0846	0.466434
15	-0.095266	-0.7379	0.231718
16	0.030044	0.2327	0.408386
17	-0.035532	-0.2752	0.392042

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.959739 & 7.4341 & 0 \tabularnewline
2 & -0.109002 & -0.8443 & 0.20092 \tabularnewline
3 & -0.100576 & -0.7791 & 0.219504 \tabularnewline
4 & -0.063915 & -0.4951 & 0.311175 \tabularnewline
5 & -0.01232 & -0.0954 & 0.462145 \tabularnewline
6 & 0.023493 & 0.182 & 0.428107 \tabularnewline
7 & 0.063639 & 0.4929 & 0.311925 \tabularnewline
8 & -0.075881 & -0.5878 & 0.279446 \tabularnewline
9 & -0.061539 & -0.4767 & 0.317661 \tabularnewline
10 & -0.044208 & -0.3424 & 0.366611 \tabularnewline
11 & -0.015894 & -0.1231 & 0.451215 \tabularnewline
12 & -0.040686 & -0.3152 & 0.37687 \tabularnewline
13 & -0.006221 & -0.0482 & 0.480864 \tabularnewline
14 & 0.010921 & 0.0846 & 0.466434 \tabularnewline
15 & -0.095266 & -0.7379 & 0.231718 \tabularnewline
16 & 0.030044 & 0.2327 & 0.408386 \tabularnewline
17 & -0.035532 & -0.2752 & 0.392042 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282995&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]0.959739[/C][C]7.4341[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.109002[/C][C]-0.8443[/C][C]0.20092[/C][/ROW]
[ROW][C]3[/C][C]-0.100576[/C][C]-0.7791[/C][C]0.219504[/C][/ROW]
[ROW][C]4[/C][C]-0.063915[/C][C]-0.4951[/C][C]0.311175[/C][/ROW]
[ROW][C]5[/C][C]-0.01232[/C][C]-0.0954[/C][C]0.462145[/C][/ROW]
[ROW][C]6[/C][C]0.023493[/C][C]0.182[/C][C]0.428107[/C][/ROW]
[ROW][C]7[/C][C]0.063639[/C][C]0.4929[/C][C]0.311925[/C][/ROW]
[ROW][C]8[/C][C]-0.075881[/C][C]-0.5878[/C][C]0.279446[/C][/ROW]
[ROW][C]9[/C][C]-0.061539[/C][C]-0.4767[/C][C]0.317661[/C][/ROW]
[ROW][C]10[/C][C]-0.044208[/C][C]-0.3424[/C][C]0.366611[/C][/ROW]
[ROW][C]11[/C][C]-0.015894[/C][C]-0.1231[/C][C]0.451215[/C][/ROW]
[ROW][C]12[/C][C]-0.040686[/C][C]-0.3152[/C][C]0.37687[/C][/ROW]
[ROW][C]13[/C][C]-0.006221[/C][C]-0.0482[/C][C]0.480864[/C][/ROW]
[ROW][C]14[/C][C]0.010921[/C][C]0.0846[/C][C]0.466434[/C][/ROW]
[ROW][C]15[/C][C]-0.095266[/C][C]-0.7379[/C][C]0.231718[/C][/ROW]
[ROW][C]16[/C][C]0.030044[/C][C]0.2327[/C][C]0.408386[/C][/ROW]
[ROW][C]17[/C][C]-0.035532[/C][C]-0.2752[/C][C]0.392042[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282995&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282995&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	0.959739	7.4341	0
2	-0.109002	-0.8443	0.20092
3	-0.100576	-0.7791	0.219504
4	-0.063915	-0.4951	0.311175
5	-0.01232	-0.0954	0.462145
6	0.023493	0.182	0.428107
7	0.063639	0.4929	0.311925
8	-0.075881	-0.5878	0.279446
9	-0.061539	-0.4767	0.317661
10	-0.044208	-0.3424	0.366611
11	-0.015894	-0.1231	0.451215
12	-0.040686	-0.3152	0.37687
13	-0.006221	-0.0482	0.480864
14	0.010921	0.0846	0.466434
15	-0.095266	-0.7379	0.231718
16	0.030044	0.2327	0.408386
17	-0.035532	-0.2752	0.392042

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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