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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 18 Nov 2013 06:20:58 -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/2013/Nov/18/t1384773683i8u0un3hskfmwzq.htm/, Retrieved Sat, 27 Apr 2024 11:34:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=226017, Retrieved Sat, 27 Apr 2024 11:34:16 +0000

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-       [(Partial) Autocorrelation Function] [] [2013-11-18 11:20:58] [764249a9cc4864d99a8b0ce95556daaa] [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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226017&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226017&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226017&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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.551146	4.6766	7e-06
2	0.076714	0.6509	0.258579
3	-0.19625	-1.6652	0.050106
4	-0.286128	-2.4279	0.008844
5	-0.271716	-2.3056	0.012009
6	-0.421235	-3.5743	0.000316
7	-0.335881	-2.85	0.002849
8	-0.274947	-2.333	0.011223
9	-0.175475	-1.489	0.070433
10	0.140511	1.1923	0.118534
11	0.508286	4.313	2.5e-05
12	0.747062	6.339	0
13	0.439423	3.7286	0.00019
14	0.007787	0.0661	0.47375
15	-0.231218	-1.962	0.026817
16	-0.272038	-2.3083	0.011928
17	-0.249417	-2.1164	0.018885
18	-0.364608	-3.0938	0.001406

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.551146 & 4.6766 & 7e-06 \tabularnewline
2 & 0.076714 & 0.6509 & 0.258579 \tabularnewline
3 & -0.19625 & -1.6652 & 0.050106 \tabularnewline
4 & -0.286128 & -2.4279 & 0.008844 \tabularnewline
5 & -0.271716 & -2.3056 & 0.012009 \tabularnewline
6 & -0.421235 & -3.5743 & 0.000316 \tabularnewline
7 & -0.335881 & -2.85 & 0.002849 \tabularnewline
8 & -0.274947 & -2.333 & 0.011223 \tabularnewline
9 & -0.175475 & -1.489 & 0.070433 \tabularnewline
10 & 0.140511 & 1.1923 & 0.118534 \tabularnewline
11 & 0.508286 & 4.313 & 2.5e-05 \tabularnewline
12 & 0.747062 & 6.339 & 0 \tabularnewline
13 & 0.439423 & 3.7286 & 0.00019 \tabularnewline
14 & 0.007787 & 0.0661 & 0.47375 \tabularnewline
15 & -0.231218 & -1.962 & 0.026817 \tabularnewline
16 & -0.272038 & -2.3083 & 0.011928 \tabularnewline
17 & -0.249417 & -2.1164 & 0.018885 \tabularnewline
18 & -0.364608 & -3.0938 & 0.001406 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226017&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]0.551146[/C][C]4.6766[/C][C]7e-06[/C][/ROW]
[ROW][C]2[/C][C]0.076714[/C][C]0.6509[/C][C]0.258579[/C][/ROW]
[ROW][C]3[/C][C]-0.19625[/C][C]-1.6652[/C][C]0.050106[/C][/ROW]
[ROW][C]4[/C][C]-0.286128[/C][C]-2.4279[/C][C]0.008844[/C][/ROW]
[ROW][C]5[/C][C]-0.271716[/C][C]-2.3056[/C][C]0.012009[/C][/ROW]
[ROW][C]6[/C][C]-0.421235[/C][C]-3.5743[/C][C]0.000316[/C][/ROW]
[ROW][C]7[/C][C]-0.335881[/C][C]-2.85[/C][C]0.002849[/C][/ROW]
[ROW][C]8[/C][C]-0.274947[/C][C]-2.333[/C][C]0.011223[/C][/ROW]
[ROW][C]9[/C][C]-0.175475[/C][C]-1.489[/C][C]0.070433[/C][/ROW]
[ROW][C]10[/C][C]0.140511[/C][C]1.1923[/C][C]0.118534[/C][/ROW]
[ROW][C]11[/C][C]0.508286[/C][C]4.313[/C][C]2.5e-05[/C][/ROW]
[ROW][C]12[/C][C]0.747062[/C][C]6.339[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.439423[/C][C]3.7286[/C][C]0.00019[/C][/ROW]
[ROW][C]14[/C][C]0.007787[/C][C]0.0661[/C][C]0.47375[/C][/ROW]
[ROW][C]15[/C][C]-0.231218[/C][C]-1.962[/C][C]0.026817[/C][/ROW]
[ROW][C]16[/C][C]-0.272038[/C][C]-2.3083[/C][C]0.011928[/C][/ROW]
[ROW][C]17[/C][C]-0.249417[/C][C]-2.1164[/C][C]0.018885[/C][/ROW]
[ROW][C]18[/C][C]-0.364608[/C][C]-3.0938[/C][C]0.001406[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226017&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226017&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	0.551146	4.6766	7e-06
2	0.076714	0.6509	0.258579
3	-0.19625	-1.6652	0.050106
4	-0.286128	-2.4279	0.008844
5	-0.271716	-2.3056	0.012009
6	-0.421235	-3.5743	0.000316
7	-0.335881	-2.85	0.002849
8	-0.274947	-2.333	0.011223
9	-0.175475	-1.489	0.070433
10	0.140511	1.1923	0.118534
11	0.508286	4.313	2.5e-05
12	0.747062	6.339	0
13	0.439423	3.7286	0.00019
14	0.007787	0.0661	0.47375
15	-0.231218	-1.962	0.026817
16	-0.272038	-2.3083	0.011928
17	-0.249417	-2.1164	0.018885
18	-0.364608	-3.0938	0.001406

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.551146	4.6766	7e-06
2	-0.326107	-2.7671	0.003592
3	-0.11666	-0.9899	0.16277
4	-0.109798	-0.9317	0.17731
5	-0.108799	-0.9232	0.179496
6	-0.447984	-3.8013	0.000149
7	0.040369	0.3425	0.36647
8	-0.420784	-3.5705	0.00032
9	-0.222106	-1.8846	0.031758
10	0.105425	0.8946	0.187001
11	0.36888	3.1301	0.001262
12	0.277703	2.3564	0.010589
13	-0.098505	-0.8358	0.203004
14	-0.083343	-0.7072	0.240867
15	-0.154213	-1.3085	0.097426
16	0.016873	0.1432	0.443277
17	-0.024846	-0.2108	0.416808
18	-0.062841	-0.5332	0.29776

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.551146 & 4.6766 & 7e-06 \tabularnewline
2 & -0.326107 & -2.7671 & 0.003592 \tabularnewline
3 & -0.11666 & -0.9899 & 0.16277 \tabularnewline
4 & -0.109798 & -0.9317 & 0.17731 \tabularnewline
5 & -0.108799 & -0.9232 & 0.179496 \tabularnewline
6 & -0.447984 & -3.8013 & 0.000149 \tabularnewline
7 & 0.040369 & 0.3425 & 0.36647 \tabularnewline
8 & -0.420784 & -3.5705 & 0.00032 \tabularnewline
9 & -0.222106 & -1.8846 & 0.031758 \tabularnewline
10 & 0.105425 & 0.8946 & 0.187001 \tabularnewline
11 & 0.36888 & 3.1301 & 0.001262 \tabularnewline
12 & 0.277703 & 2.3564 & 0.010589 \tabularnewline
13 & -0.098505 & -0.8358 & 0.203004 \tabularnewline
14 & -0.083343 & -0.7072 & 0.240867 \tabularnewline
15 & -0.154213 & -1.3085 & 0.097426 \tabularnewline
16 & 0.016873 & 0.1432 & 0.443277 \tabularnewline
17 & -0.024846 & -0.2108 & 0.416808 \tabularnewline
18 & -0.062841 & -0.5332 & 0.29776 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226017&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]0.551146[/C][C]4.6766[/C][C]7e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.326107[/C][C]-2.7671[/C][C]0.003592[/C][/ROW]
[ROW][C]3[/C][C]-0.11666[/C][C]-0.9899[/C][C]0.16277[/C][/ROW]
[ROW][C]4[/C][C]-0.109798[/C][C]-0.9317[/C][C]0.17731[/C][/ROW]
[ROW][C]5[/C][C]-0.108799[/C][C]-0.9232[/C][C]0.179496[/C][/ROW]
[ROW][C]6[/C][C]-0.447984[/C][C]-3.8013[/C][C]0.000149[/C][/ROW]
[ROW][C]7[/C][C]0.040369[/C][C]0.3425[/C][C]0.36647[/C][/ROW]
[ROW][C]8[/C][C]-0.420784[/C][C]-3.5705[/C][C]0.00032[/C][/ROW]
[ROW][C]9[/C][C]-0.222106[/C][C]-1.8846[/C][C]0.031758[/C][/ROW]
[ROW][C]10[/C][C]0.105425[/C][C]0.8946[/C][C]0.187001[/C][/ROW]
[ROW][C]11[/C][C]0.36888[/C][C]3.1301[/C][C]0.001262[/C][/ROW]
[ROW][C]12[/C][C]0.277703[/C][C]2.3564[/C][C]0.010589[/C][/ROW]
[ROW][C]13[/C][C]-0.098505[/C][C]-0.8358[/C][C]0.203004[/C][/ROW]
[ROW][C]14[/C][C]-0.083343[/C][C]-0.7072[/C][C]0.240867[/C][/ROW]
[ROW][C]15[/C][C]-0.154213[/C][C]-1.3085[/C][C]0.097426[/C][/ROW]
[ROW][C]16[/C][C]0.016873[/C][C]0.1432[/C][C]0.443277[/C][/ROW]
[ROW][C]17[/C][C]-0.024846[/C][C]-0.2108[/C][C]0.416808[/C][/ROW]
[ROW][C]18[/C][C]-0.062841[/C][C]-0.5332[/C][C]0.29776[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226017&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226017&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	0.551146	4.6766	7e-06
2	-0.326107	-2.7671	0.003592
3	-0.11666	-0.9899	0.16277
4	-0.109798	-0.9317	0.17731
5	-0.108799	-0.9232	0.179496
6	-0.447984	-3.8013	0.000149
7	0.040369	0.3425	0.36647
8	-0.420784	-3.5705	0.00032
9	-0.222106	-1.8846	0.031758
10	0.105425	0.8946	0.187001
11	0.36888	3.1301	0.001262
12	0.277703	2.3564	0.010589
13	-0.098505	-0.8358	0.203004
14	-0.083343	-0.7072	0.240867
15	-0.154213	-1.3085	0.097426
16	0.016873	0.1432	0.443277
17	-0.024846	-0.2108	0.416808
18	-0.062841	-0.5332	0.29776

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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Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code