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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Oct 2015 19:26:56 +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/t1445624863vgzfzwttd7zvr3v.htm/, Retrieved Tue, 14 May 2024 00:06:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282959, Retrieved Tue, 14 May 2024 00:06:43 +0000

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-       [(Partial) Autocorrelation Function] [] [2015-10-23 18:26:56] [baf7db162d56d42e62a4d339fc25c05c] [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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282959&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282959&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282959&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.534655	4.5051	1.3e-05
2	0.270508	2.2793	0.012828
3	0.17867	1.5055	0.068316
4	0.049225	0.4148	0.339777
5	-0.211675	-1.7836	0.03938
6	-0.206504	-1.74	0.043093
7	-0.093787	-0.7903	0.216003
8	-0.13279	-1.1189	0.133476
9	-0.064826	-0.5462	0.293308
10	-0.075207	-0.6337	0.264154
11	-0.060956	-0.5136	0.304553
12	-0.083645	-0.7048	0.241618
13	-0.06034	-0.5084	0.306364
14	-0.119147	-1.0039	0.159406
15	-0.129272	-1.0893	0.139861
16	-0.062301	-0.525	0.300623
17	-0.19253	-1.6223	0.054587
18	-0.112794	-0.9504	0.172563

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.534655 & 4.5051 & 1.3e-05 \tabularnewline
2 & 0.270508 & 2.2793 & 0.012828 \tabularnewline
3 & 0.17867 & 1.5055 & 0.068316 \tabularnewline
4 & 0.049225 & 0.4148 & 0.339777 \tabularnewline
5 & -0.211675 & -1.7836 & 0.03938 \tabularnewline
6 & -0.206504 & -1.74 & 0.043093 \tabularnewline
7 & -0.093787 & -0.7903 & 0.216003 \tabularnewline
8 & -0.13279 & -1.1189 & 0.133476 \tabularnewline
9 & -0.064826 & -0.5462 & 0.293308 \tabularnewline
10 & -0.075207 & -0.6337 & 0.264154 \tabularnewline
11 & -0.060956 & -0.5136 & 0.304553 \tabularnewline
12 & -0.083645 & -0.7048 & 0.241618 \tabularnewline
13 & -0.06034 & -0.5084 & 0.306364 \tabularnewline
14 & -0.119147 & -1.0039 & 0.159406 \tabularnewline
15 & -0.129272 & -1.0893 & 0.139861 \tabularnewline
16 & -0.062301 & -0.525 & 0.300623 \tabularnewline
17 & -0.19253 & -1.6223 & 0.054587 \tabularnewline
18 & -0.112794 & -0.9504 & 0.172563 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282959&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]0.534655[/C][C]4.5051[/C][C]1.3e-05[/C][/ROW]
[ROW][C]2[/C][C]0.270508[/C][C]2.2793[/C][C]0.012828[/C][/ROW]
[ROW][C]3[/C][C]0.17867[/C][C]1.5055[/C][C]0.068316[/C][/ROW]
[ROW][C]4[/C][C]0.049225[/C][C]0.4148[/C][C]0.339777[/C][/ROW]
[ROW][C]5[/C][C]-0.211675[/C][C]-1.7836[/C][C]0.03938[/C][/ROW]
[ROW][C]6[/C][C]-0.206504[/C][C]-1.74[/C][C]0.043093[/C][/ROW]
[ROW][C]7[/C][C]-0.093787[/C][C]-0.7903[/C][C]0.216003[/C][/ROW]
[ROW][C]8[/C][C]-0.13279[/C][C]-1.1189[/C][C]0.133476[/C][/ROW]
[ROW][C]9[/C][C]-0.064826[/C][C]-0.5462[/C][C]0.293308[/C][/ROW]
[ROW][C]10[/C][C]-0.075207[/C][C]-0.6337[/C][C]0.264154[/C][/ROW]
[ROW][C]11[/C][C]-0.060956[/C][C]-0.5136[/C][C]0.304553[/C][/ROW]
[ROW][C]12[/C][C]-0.083645[/C][C]-0.7048[/C][C]0.241618[/C][/ROW]
[ROW][C]13[/C][C]-0.06034[/C][C]-0.5084[/C][C]0.306364[/C][/ROW]
[ROW][C]14[/C][C]-0.119147[/C][C]-1.0039[/C][C]0.159406[/C][/ROW]
[ROW][C]15[/C][C]-0.129272[/C][C]-1.0893[/C][C]0.139861[/C][/ROW]
[ROW][C]16[/C][C]-0.062301[/C][C]-0.525[/C][C]0.300623[/C][/ROW]
[ROW][C]17[/C][C]-0.19253[/C][C]-1.6223[/C][C]0.054587[/C][/ROW]
[ROW][C]18[/C][C]-0.112794[/C][C]-0.9504[/C][C]0.172563[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282959&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282959&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	0.534655	4.5051	1.3e-05
2	0.270508	2.2793	0.012828
3	0.17867	1.5055	0.068316
4	0.049225	0.4148	0.339777
5	-0.211675	-1.7836	0.03938
6	-0.206504	-1.74	0.043093
7	-0.093787	-0.7903	0.216003
8	-0.13279	-1.1189	0.133476
9	-0.064826	-0.5462	0.293308
10	-0.075207	-0.6337	0.264154
11	-0.060956	-0.5136	0.304553
12	-0.083645	-0.7048	0.241618
13	-0.06034	-0.5084	0.306364
14	-0.119147	-1.0039	0.159406
15	-0.129272	-1.0893	0.139861
16	-0.062301	-0.525	0.300623
17	-0.19253	-1.6223	0.054587
18	-0.112794	-0.9504	0.172563

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.534655	4.5051	1.3e-05
2	-0.021492	-0.1811	0.428403
3	0.059433	0.5008	0.309034
4	-0.092458	-0.7791	0.219266
5	-0.295936	-2.4936	0.007489
6	0.044242	0.3728	0.355208
7	0.088143	0.7427	0.230055
8	-0.091654	-0.7723	0.221254
9	0.09606	0.8094	0.21049
10	-0.190345	-1.6039	0.05659
11	-0.016735	-0.141	0.444129
12	-0.011909	-0.1003	0.460175
13	-0.035434	-0.2986	0.383069
14	-0.078537	-0.6618	0.255133
15	-0.05895	-0.4967	0.310459
16	0.00658	0.0554	0.477971
17	-0.250307	-2.1091	0.019231
18	0.130995	1.1038	0.136706

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.534655 & 4.5051 & 1.3e-05 \tabularnewline
2 & -0.021492 & -0.1811 & 0.428403 \tabularnewline
3 & 0.059433 & 0.5008 & 0.309034 \tabularnewline
4 & -0.092458 & -0.7791 & 0.219266 \tabularnewline
5 & -0.295936 & -2.4936 & 0.007489 \tabularnewline
6 & 0.044242 & 0.3728 & 0.355208 \tabularnewline
7 & 0.088143 & 0.7427 & 0.230055 \tabularnewline
8 & -0.091654 & -0.7723 & 0.221254 \tabularnewline
9 & 0.09606 & 0.8094 & 0.21049 \tabularnewline
10 & -0.190345 & -1.6039 & 0.05659 \tabularnewline
11 & -0.016735 & -0.141 & 0.444129 \tabularnewline
12 & -0.011909 & -0.1003 & 0.460175 \tabularnewline
13 & -0.035434 & -0.2986 & 0.383069 \tabularnewline
14 & -0.078537 & -0.6618 & 0.255133 \tabularnewline
15 & -0.05895 & -0.4967 & 0.310459 \tabularnewline
16 & 0.00658 & 0.0554 & 0.477971 \tabularnewline
17 & -0.250307 & -2.1091 & 0.019231 \tabularnewline
18 & 0.130995 & 1.1038 & 0.136706 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282959&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]0.534655[/C][C]4.5051[/C][C]1.3e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.021492[/C][C]-0.1811[/C][C]0.428403[/C][/ROW]
[ROW][C]3[/C][C]0.059433[/C][C]0.5008[/C][C]0.309034[/C][/ROW]
[ROW][C]4[/C][C]-0.092458[/C][C]-0.7791[/C][C]0.219266[/C][/ROW]
[ROW][C]5[/C][C]-0.295936[/C][C]-2.4936[/C][C]0.007489[/C][/ROW]
[ROW][C]6[/C][C]0.044242[/C][C]0.3728[/C][C]0.355208[/C][/ROW]
[ROW][C]7[/C][C]0.088143[/C][C]0.7427[/C][C]0.230055[/C][/ROW]
[ROW][C]8[/C][C]-0.091654[/C][C]-0.7723[/C][C]0.221254[/C][/ROW]
[ROW][C]9[/C][C]0.09606[/C][C]0.8094[/C][C]0.21049[/C][/ROW]
[ROW][C]10[/C][C]-0.190345[/C][C]-1.6039[/C][C]0.05659[/C][/ROW]
[ROW][C]11[/C][C]-0.016735[/C][C]-0.141[/C][C]0.444129[/C][/ROW]
[ROW][C]12[/C][C]-0.011909[/C][C]-0.1003[/C][C]0.460175[/C][/ROW]
[ROW][C]13[/C][C]-0.035434[/C][C]-0.2986[/C][C]0.383069[/C][/ROW]
[ROW][C]14[/C][C]-0.078537[/C][C]-0.6618[/C][C]0.255133[/C][/ROW]
[ROW][C]15[/C][C]-0.05895[/C][C]-0.4967[/C][C]0.310459[/C][/ROW]
[ROW][C]16[/C][C]0.00658[/C][C]0.0554[/C][C]0.477971[/C][/ROW]
[ROW][C]17[/C][C]-0.250307[/C][C]-2.1091[/C][C]0.019231[/C][/ROW]
[ROW][C]18[/C][C]0.130995[/C][C]1.1038[/C][C]0.136706[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282959&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282959&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	0.534655	4.5051	1.3e-05
2	-0.021492	-0.1811	0.428403
3	0.059433	0.5008	0.309034
4	-0.092458	-0.7791	0.219266
5	-0.295936	-2.4936	0.007489
6	0.044242	0.3728	0.355208
7	0.088143	0.7427	0.230055
8	-0.091654	-0.7723	0.221254
9	0.09606	0.8094	0.21049
10	-0.190345	-1.6039	0.05659
11	-0.016735	-0.141	0.444129
12	-0.011909	-0.1003	0.460175
13	-0.035434	-0.2986	0.383069
14	-0.078537	-0.6618	0.255133
15	-0.05895	-0.4967	0.310459
16	0.00658	0.0554	0.477971
17	-0.250307	-2.1091	0.019231
18	0.130995	1.1038	0.136706

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 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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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Dataset

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Figures (Output of Computation)

Input Parameters & R Code