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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 07 Dec 2011 15:41:55 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/07/t13232908896bgekqmm8hcw9j2.htm/, Retrieved Thu, 02 May 2024 20:16:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=152715, Retrieved Thu, 02 May 2024 20:16:06 +0000

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-       [(Partial) Autocorrelation Function] [ACF] [2011-12-07 20:41:55] [614dd89c388120cee0dd25886939832b] [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	2 seconds
R Server	'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152715&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152715&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152715&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	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.198028	1.9403	0.027641
2	0.238041	2.3323	0.010887
3	0.198919	1.949	0.027107
4	0.130082	1.2745	0.102774
5	0.089849	0.8803	0.190438
6	0.168486	1.6508	0.051022
7	0.07409	0.7259	0.234824
8	0.153816	1.5071	0.067537
9	0.082824	0.8115	0.209542
10	-0.068232	-0.6685	0.252698
11	0.086589	0.8484	0.199164
12	-0.222056	-2.1757	0.016016
13	-0.110446	-1.0821	0.14095
14	0.040804	0.3998	0.345097
15	-0.006678	-0.0654	0.473984
16	-0.101716	-0.9966	0.160731
17	-0.044954	-0.4405	0.3303
18	-0.109918	-1.077	0.142096
19	-0.059462	-0.5826	0.280761
20	-0.084831	-0.8312	0.203969

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.198028 & 1.9403 & 0.027641 \tabularnewline
2 & 0.238041 & 2.3323 & 0.010887 \tabularnewline
3 & 0.198919 & 1.949 & 0.027107 \tabularnewline
4 & 0.130082 & 1.2745 & 0.102774 \tabularnewline
5 & 0.089849 & 0.8803 & 0.190438 \tabularnewline
6 & 0.168486 & 1.6508 & 0.051022 \tabularnewline
7 & 0.07409 & 0.7259 & 0.234824 \tabularnewline
8 & 0.153816 & 1.5071 & 0.067537 \tabularnewline
9 & 0.082824 & 0.8115 & 0.209542 \tabularnewline
10 & -0.068232 & -0.6685 & 0.252698 \tabularnewline
11 & 0.086589 & 0.8484 & 0.199164 \tabularnewline
12 & -0.222056 & -2.1757 & 0.016016 \tabularnewline
13 & -0.110446 & -1.0821 & 0.14095 \tabularnewline
14 & 0.040804 & 0.3998 & 0.345097 \tabularnewline
15 & -0.006678 & -0.0654 & 0.473984 \tabularnewline
16 & -0.101716 & -0.9966 & 0.160731 \tabularnewline
17 & -0.044954 & -0.4405 & 0.3303 \tabularnewline
18 & -0.109918 & -1.077 & 0.142096 \tabularnewline
19 & -0.059462 & -0.5826 & 0.280761 \tabularnewline
20 & -0.084831 & -0.8312 & 0.203969 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152715&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]0.198028[/C][C]1.9403[/C][C]0.027641[/C][/ROW]
[ROW][C]2[/C][C]0.238041[/C][C]2.3323[/C][C]0.010887[/C][/ROW]
[ROW][C]3[/C][C]0.198919[/C][C]1.949[/C][C]0.027107[/C][/ROW]
[ROW][C]4[/C][C]0.130082[/C][C]1.2745[/C][C]0.102774[/C][/ROW]
[ROW][C]5[/C][C]0.089849[/C][C]0.8803[/C][C]0.190438[/C][/ROW]
[ROW][C]6[/C][C]0.168486[/C][C]1.6508[/C][C]0.051022[/C][/ROW]
[ROW][C]7[/C][C]0.07409[/C][C]0.7259[/C][C]0.234824[/C][/ROW]
[ROW][C]8[/C][C]0.153816[/C][C]1.5071[/C][C]0.067537[/C][/ROW]
[ROW][C]9[/C][C]0.082824[/C][C]0.8115[/C][C]0.209542[/C][/ROW]
[ROW][C]10[/C][C]-0.068232[/C][C]-0.6685[/C][C]0.252698[/C][/ROW]
[ROW][C]11[/C][C]0.086589[/C][C]0.8484[/C][C]0.199164[/C][/ROW]
[ROW][C]12[/C][C]-0.222056[/C][C]-2.1757[/C][C]0.016016[/C][/ROW]
[ROW][C]13[/C][C]-0.110446[/C][C]-1.0821[/C][C]0.14095[/C][/ROW]
[ROW][C]14[/C][C]0.040804[/C][C]0.3998[/C][C]0.345097[/C][/ROW]
[ROW][C]15[/C][C]-0.006678[/C][C]-0.0654[/C][C]0.473984[/C][/ROW]
[ROW][C]16[/C][C]-0.101716[/C][C]-0.9966[/C][C]0.160731[/C][/ROW]
[ROW][C]17[/C][C]-0.044954[/C][C]-0.4405[/C][C]0.3303[/C][/ROW]
[ROW][C]18[/C][C]-0.109918[/C][C]-1.077[/C][C]0.142096[/C][/ROW]
[ROW][C]19[/C][C]-0.059462[/C][C]-0.5826[/C][C]0.280761[/C][/ROW]
[ROW][C]20[/C][C]-0.084831[/C][C]-0.8312[/C][C]0.203969[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152715&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152715&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	0.198028	1.9403	0.027641
2	0.238041	2.3323	0.010887
3	0.198919	1.949	0.027107
4	0.130082	1.2745	0.102774
5	0.089849	0.8803	0.190438
6	0.168486	1.6508	0.051022
7	0.07409	0.7259	0.234824
8	0.153816	1.5071	0.067537
9	0.082824	0.8115	0.209542
10	-0.068232	-0.6685	0.252698
11	0.086589	0.8484	0.199164
12	-0.222056	-2.1757	0.016016
13	-0.110446	-1.0821	0.14095
14	0.040804	0.3998	0.345097
15	-0.006678	-0.0654	0.473984
16	-0.101716	-0.9966	0.160731
17	-0.044954	-0.4405	0.3303
18	-0.109918	-1.077	0.142096
19	-0.059462	-0.5826	0.280761
20	-0.084831	-0.8312	0.203969

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.198028	1.9403	0.027641
2	0.206941	2.0276	0.022686
3	0.131089	1.2844	0.101045
4	0.037529	0.3677	0.356952
5	0.000482	0.0047	0.498122
6	0.110606	1.0837	0.140602
7	0.000534	0.0052	0.497919
8	0.088547	0.8676	0.193895
9	-6.8e-05	-7e-04	0.499733
10	-0.163188	-1.5989	0.056564
11	0.069652	0.6824	0.2483
12	-0.278055	-2.7244	0.003828
13	-0.063626	-0.6234	0.267249
14	0.139858	1.3703	0.086891
15	0.050014	0.49	0.312615
16	-0.081082	-0.7944	0.21445
17	-0.068845	-0.6745	0.250794
18	-0.000575	-0.0056	0.49776
19	0.021074	0.2065	0.418425
20	-0.012603	-0.1235	0.450992

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.198028 & 1.9403 & 0.027641 \tabularnewline
2 & 0.206941 & 2.0276 & 0.022686 \tabularnewline
3 & 0.131089 & 1.2844 & 0.101045 \tabularnewline
4 & 0.037529 & 0.3677 & 0.356952 \tabularnewline
5 & 0.000482 & 0.0047 & 0.498122 \tabularnewline
6 & 0.110606 & 1.0837 & 0.140602 \tabularnewline
7 & 0.000534 & 0.0052 & 0.497919 \tabularnewline
8 & 0.088547 & 0.8676 & 0.193895 \tabularnewline
9 & -6.8e-05 & -7e-04 & 0.499733 \tabularnewline
10 & -0.163188 & -1.5989 & 0.056564 \tabularnewline
11 & 0.069652 & 0.6824 & 0.2483 \tabularnewline
12 & -0.278055 & -2.7244 & 0.003828 \tabularnewline
13 & -0.063626 & -0.6234 & 0.267249 \tabularnewline
14 & 0.139858 & 1.3703 & 0.086891 \tabularnewline
15 & 0.050014 & 0.49 & 0.312615 \tabularnewline
16 & -0.081082 & -0.7944 & 0.21445 \tabularnewline
17 & -0.068845 & -0.6745 & 0.250794 \tabularnewline
18 & -0.000575 & -0.0056 & 0.49776 \tabularnewline
19 & 0.021074 & 0.2065 & 0.418425 \tabularnewline
20 & -0.012603 & -0.1235 & 0.450992 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152715&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]0.198028[/C][C]1.9403[/C][C]0.027641[/C][/ROW]
[ROW][C]2[/C][C]0.206941[/C][C]2.0276[/C][C]0.022686[/C][/ROW]
[ROW][C]3[/C][C]0.131089[/C][C]1.2844[/C][C]0.101045[/C][/ROW]
[ROW][C]4[/C][C]0.037529[/C][C]0.3677[/C][C]0.356952[/C][/ROW]
[ROW][C]5[/C][C]0.000482[/C][C]0.0047[/C][C]0.498122[/C][/ROW]
[ROW][C]6[/C][C]0.110606[/C][C]1.0837[/C][C]0.140602[/C][/ROW]
[ROW][C]7[/C][C]0.000534[/C][C]0.0052[/C][C]0.497919[/C][/ROW]
[ROW][C]8[/C][C]0.088547[/C][C]0.8676[/C][C]0.193895[/C][/ROW]
[ROW][C]9[/C][C]-6.8e-05[/C][C]-7e-04[/C][C]0.499733[/C][/ROW]
[ROW][C]10[/C][C]-0.163188[/C][C]-1.5989[/C][C]0.056564[/C][/ROW]
[ROW][C]11[/C][C]0.069652[/C][C]0.6824[/C][C]0.2483[/C][/ROW]
[ROW][C]12[/C][C]-0.278055[/C][C]-2.7244[/C][C]0.003828[/C][/ROW]
[ROW][C]13[/C][C]-0.063626[/C][C]-0.6234[/C][C]0.267249[/C][/ROW]
[ROW][C]14[/C][C]0.139858[/C][C]1.3703[/C][C]0.086891[/C][/ROW]
[ROW][C]15[/C][C]0.050014[/C][C]0.49[/C][C]0.312615[/C][/ROW]
[ROW][C]16[/C][C]-0.081082[/C][C]-0.7944[/C][C]0.21445[/C][/ROW]
[ROW][C]17[/C][C]-0.068845[/C][C]-0.6745[/C][C]0.250794[/C][/ROW]
[ROW][C]18[/C][C]-0.000575[/C][C]-0.0056[/C][C]0.49776[/C][/ROW]
[ROW][C]19[/C][C]0.021074[/C][C]0.2065[/C][C]0.418425[/C][/ROW]
[ROW][C]20[/C][C]-0.012603[/C][C]-0.1235[/C][C]0.450992[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152715&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152715&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	0.198028	1.9403	0.027641
2	0.206941	2.0276	0.022686
3	0.131089	1.2844	0.101045
4	0.037529	0.3677	0.356952
5	0.000482	0.0047	0.498122
6	0.110606	1.0837	0.140602
7	0.000534	0.0052	0.497919
8	0.088547	0.8676	0.193895
9	-6.8e-05	-7e-04	0.499733
10	-0.163188	-1.5989	0.056564
11	0.069652	0.6824	0.2483
12	-0.278055	-2.7244	0.003828
13	-0.063626	-0.6234	0.267249
14	0.139858	1.3703	0.086891
15	0.050014	0.49	0.312615
16	-0.081082	-0.7944	0.21445
17	-0.068845	-0.6745	0.250794
18	-0.000575	-0.0056	0.49776
19	0.021074	0.2065	0.418425
20	-0.012603	-0.1235	0.450992

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 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code