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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 16 Dec 2010 20:02:21 +0000

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/2010/Dec/16/t1292529620i0eqs9niotroqhl.htm/, Retrieved Fri, 03 May 2024 04:10:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111248, Retrieved Fri, 03 May 2024 04:10:14 +0000

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176

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-       [(Partial) Autocorrelation Function] [] [2010-12-16 20:02:21] [e7b77eb06cdf8868fc9cf2043e42b3da] [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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111248&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111248&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111248&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.604353	6.2806	0
2	0.599153	6.2266	0
3	0.682312	7.0908	0
4	0.554848	5.7661	0
5	0.560453	5.8244	0
6	0.554155	5.7589	0
7	0.532278	5.5316	0
8	0.494208	5.136	1e-06
9	0.565184	5.8736	0
10	0.499059	5.1864	1e-06
11	0.478643	4.9742	1e-06
12	0.568137	5.9042	0
13	0.406634	4.2259	2.5e-05
14	0.427841	4.4463	1.1e-05
15	0.425308	4.4199	1.2e-05
16	0.322919	3.3559	0.000546
17	0.342198	3.5562	0.00028
18	0.334626	3.4775	0.000365
19	0.253072	2.63	0.004893
20	0.237941	2.4728	0.007484

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.604353 & 6.2806 & 0 \tabularnewline
2 & 0.599153 & 6.2266 & 0 \tabularnewline
3 & 0.682312 & 7.0908 & 0 \tabularnewline
4 & 0.554848 & 5.7661 & 0 \tabularnewline
5 & 0.560453 & 5.8244 & 0 \tabularnewline
6 & 0.554155 & 5.7589 & 0 \tabularnewline
7 & 0.532278 & 5.5316 & 0 \tabularnewline
8 & 0.494208 & 5.136 & 1e-06 \tabularnewline
9 & 0.565184 & 5.8736 & 0 \tabularnewline
10 & 0.499059 & 5.1864 & 1e-06 \tabularnewline
11 & 0.478643 & 4.9742 & 1e-06 \tabularnewline
12 & 0.568137 & 5.9042 & 0 \tabularnewline
13 & 0.406634 & 4.2259 & 2.5e-05 \tabularnewline
14 & 0.427841 & 4.4463 & 1.1e-05 \tabularnewline
15 & 0.425308 & 4.4199 & 1.2e-05 \tabularnewline
16 & 0.322919 & 3.3559 & 0.000546 \tabularnewline
17 & 0.342198 & 3.5562 & 0.00028 \tabularnewline
18 & 0.334626 & 3.4775 & 0.000365 \tabularnewline
19 & 0.253072 & 2.63 & 0.004893 \tabularnewline
20 & 0.237941 & 2.4728 & 0.007484 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111248&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]0.604353[/C][C]6.2806[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.599153[/C][C]6.2266[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.682312[/C][C]7.0908[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.554848[/C][C]5.7661[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.560453[/C][C]5.8244[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.554155[/C][C]5.7589[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.532278[/C][C]5.5316[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.494208[/C][C]5.136[/C][C]1e-06[/C][/ROW]
[ROW][C]9[/C][C]0.565184[/C][C]5.8736[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.499059[/C][C]5.1864[/C][C]1e-06[/C][/ROW]
[ROW][C]11[/C][C]0.478643[/C][C]4.9742[/C][C]1e-06[/C][/ROW]
[ROW][C]12[/C][C]0.568137[/C][C]5.9042[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.406634[/C][C]4.2259[/C][C]2.5e-05[/C][/ROW]
[ROW][C]14[/C][C]0.427841[/C][C]4.4463[/C][C]1.1e-05[/C][/ROW]
[ROW][C]15[/C][C]0.425308[/C][C]4.4199[/C][C]1.2e-05[/C][/ROW]
[ROW][C]16[/C][C]0.322919[/C][C]3.3559[/C][C]0.000546[/C][/ROW]
[ROW][C]17[/C][C]0.342198[/C][C]3.5562[/C][C]0.00028[/C][/ROW]
[ROW][C]18[/C][C]0.334626[/C][C]3.4775[/C][C]0.000365[/C][/ROW]
[ROW][C]19[/C][C]0.253072[/C][C]2.63[/C][C]0.004893[/C][/ROW]
[ROW][C]20[/C][C]0.237941[/C][C]2.4728[/C][C]0.007484[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111248&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111248&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	0.604353	6.2806	0
2	0.599153	6.2266	0
3	0.682312	7.0908	0
4	0.554848	5.7661	0
5	0.560453	5.8244	0
6	0.554155	5.7589	0
7	0.532278	5.5316	0
8	0.494208	5.136	1e-06
9	0.565184	5.8736	0
10	0.499059	5.1864	1e-06
11	0.478643	4.9742	1e-06
12	0.568137	5.9042	0
13	0.406634	4.2259	2.5e-05
14	0.427841	4.4463	1.1e-05
15	0.425308	4.4199	1.2e-05
16	0.322919	3.3559	0.000546
17	0.342198	3.5562	0.00028
18	0.334626	3.4775	0.000365
19	0.253072	2.63	0.004893
20	0.237941	2.4728	0.007484

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.604353	6.2806	0
2	0.368504	3.8296	0.000108
3	0.420994	4.3751	1.4e-05
4	0.047294	0.4915	0.312037
5	0.080649	0.8381	0.201904
6	0.028751	0.2988	0.382838
7	0.08253	0.8577	0.196484
8	-0.017984	-0.1869	0.426046
9	0.19204	1.9957	0.02424
10	-0.00875	-0.0909	0.463858
11	0.017671	0.1836	0.427318
12	0.138018	1.4343	0.077184
13	-0.180731	-1.8782	0.031525
14	-0.04817	-0.5006	0.308835
15	-0.092231	-0.9585	0.169978
16	-0.114155	-1.1863	0.119047
17	-0.033707	-0.3503	0.3634
18	-0.001927	-0.02	0.492029
19	-0.117019	-1.2161	0.113299
20	-0.067522	-0.7017	0.242186

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.604353 & 6.2806 & 0 \tabularnewline
2 & 0.368504 & 3.8296 & 0.000108 \tabularnewline
3 & 0.420994 & 4.3751 & 1.4e-05 \tabularnewline
4 & 0.047294 & 0.4915 & 0.312037 \tabularnewline
5 & 0.080649 & 0.8381 & 0.201904 \tabularnewline
6 & 0.028751 & 0.2988 & 0.382838 \tabularnewline
7 & 0.08253 & 0.8577 & 0.196484 \tabularnewline
8 & -0.017984 & -0.1869 & 0.426046 \tabularnewline
9 & 0.19204 & 1.9957 & 0.02424 \tabularnewline
10 & -0.00875 & -0.0909 & 0.463858 \tabularnewline
11 & 0.017671 & 0.1836 & 0.427318 \tabularnewline
12 & 0.138018 & 1.4343 & 0.077184 \tabularnewline
13 & -0.180731 & -1.8782 & 0.031525 \tabularnewline
14 & -0.04817 & -0.5006 & 0.308835 \tabularnewline
15 & -0.092231 & -0.9585 & 0.169978 \tabularnewline
16 & -0.114155 & -1.1863 & 0.119047 \tabularnewline
17 & -0.033707 & -0.3503 & 0.3634 \tabularnewline
18 & -0.001927 & -0.02 & 0.492029 \tabularnewline
19 & -0.117019 & -1.2161 & 0.113299 \tabularnewline
20 & -0.067522 & -0.7017 & 0.242186 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111248&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]0.604353[/C][C]6.2806[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.368504[/C][C]3.8296[/C][C]0.000108[/C][/ROW]
[ROW][C]3[/C][C]0.420994[/C][C]4.3751[/C][C]1.4e-05[/C][/ROW]
[ROW][C]4[/C][C]0.047294[/C][C]0.4915[/C][C]0.312037[/C][/ROW]
[ROW][C]5[/C][C]0.080649[/C][C]0.8381[/C][C]0.201904[/C][/ROW]
[ROW][C]6[/C][C]0.028751[/C][C]0.2988[/C][C]0.382838[/C][/ROW]
[ROW][C]7[/C][C]0.08253[/C][C]0.8577[/C][C]0.196484[/C][/ROW]
[ROW][C]8[/C][C]-0.017984[/C][C]-0.1869[/C][C]0.426046[/C][/ROW]
[ROW][C]9[/C][C]0.19204[/C][C]1.9957[/C][C]0.02424[/C][/ROW]
[ROW][C]10[/C][C]-0.00875[/C][C]-0.0909[/C][C]0.463858[/C][/ROW]
[ROW][C]11[/C][C]0.017671[/C][C]0.1836[/C][C]0.427318[/C][/ROW]
[ROW][C]12[/C][C]0.138018[/C][C]1.4343[/C][C]0.077184[/C][/ROW]
[ROW][C]13[/C][C]-0.180731[/C][C]-1.8782[/C][C]0.031525[/C][/ROW]
[ROW][C]14[/C][C]-0.04817[/C][C]-0.5006[/C][C]0.308835[/C][/ROW]
[ROW][C]15[/C][C]-0.092231[/C][C]-0.9585[/C][C]0.169978[/C][/ROW]
[ROW][C]16[/C][C]-0.114155[/C][C]-1.1863[/C][C]0.119047[/C][/ROW]
[ROW][C]17[/C][C]-0.033707[/C][C]-0.3503[/C][C]0.3634[/C][/ROW]
[ROW][C]18[/C][C]-0.001927[/C][C]-0.02[/C][C]0.492029[/C][/ROW]
[ROW][C]19[/C][C]-0.117019[/C][C]-1.2161[/C][C]0.113299[/C][/ROW]
[ROW][C]20[/C][C]-0.067522[/C][C]-0.7017[/C][C]0.242186[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111248&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111248&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	0.604353	6.2806	0
2	0.368504	3.8296	0.000108
3	0.420994	4.3751	1.4e-05
4	0.047294	0.4915	0.312037
5	0.080649	0.8381	0.201904
6	0.028751	0.2988	0.382838
7	0.08253	0.8577	0.196484
8	-0.017984	-0.1869	0.426046
9	0.19204	1.9957	0.02424
10	-0.00875	-0.0909	0.463858
11	0.017671	0.1836	0.427318
12	0.138018	1.4343	0.077184
13	-0.180731	-1.8782	0.031525
14	-0.04817	-0.5006	0.308835
15	-0.092231	-0.9585	0.169978
16	-0.114155	-1.1863	0.119047
17	-0.033707	-0.3503	0.3634
18	-0.001927	-0.02	0.492029
19	-0.117019	-1.2161	0.113299
20	-0.067522	-0.7017	0.242186

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code