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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 05 Mar 2015 13:40:35 +0000

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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/Mar/05/t1425562863e910p1ksdwqex7a.htm/, Retrieved Fri, 17 May 2024 19:16:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=277948, Retrieved Fri, 17 May 2024 19:16:09 +0000

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Estimated Impact

102

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-       [(Partial) Autocorrelation Function] [] [2015-03-05 13:40:35] [d95fe07e11cd60b998b93c9c7758de3b] [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	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277948&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277948&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277948&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.031093	0.262	0.397042
2	-0.429689	-3.6206	0.000274
3	-0.166368	-1.4018	0.08266
4	0.287671	2.424	0.008951
5	-0.029165	-0.2457	0.403294
6	-0.24699	-2.0812	0.020513
7	-0.031666	-0.2668	0.395188
8	0.255267	2.1509	0.017444
9	-0.173023	-1.4579	0.074637
10	-0.385705	-3.25	0.000883
11	0.039875	0.336	0.368933
12	0.786294	6.6254	0
13	0.045782	0.3858	0.350412
14	-0.396559	-3.3415	0.000666
15	-0.140839	-1.1867	0.119645
16	0.233695	1.9692	0.02642
17	-0.023372	-0.1969	0.42222
18	-0.19592	-1.6508	0.051593

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.031093 & 0.262 & 0.397042 \tabularnewline
2 & -0.429689 & -3.6206 & 0.000274 \tabularnewline
3 & -0.166368 & -1.4018 & 0.08266 \tabularnewline
4 & 0.287671 & 2.424 & 0.008951 \tabularnewline
5 & -0.029165 & -0.2457 & 0.403294 \tabularnewline
6 & -0.24699 & -2.0812 & 0.020513 \tabularnewline
7 & -0.031666 & -0.2668 & 0.395188 \tabularnewline
8 & 0.255267 & 2.1509 & 0.017444 \tabularnewline
9 & -0.173023 & -1.4579 & 0.074637 \tabularnewline
10 & -0.385705 & -3.25 & 0.000883 \tabularnewline
11 & 0.039875 & 0.336 & 0.368933 \tabularnewline
12 & 0.786294 & 6.6254 & 0 \tabularnewline
13 & 0.045782 & 0.3858 & 0.350412 \tabularnewline
14 & -0.396559 & -3.3415 & 0.000666 \tabularnewline
15 & -0.140839 & -1.1867 & 0.119645 \tabularnewline
16 & 0.233695 & 1.9692 & 0.02642 \tabularnewline
17 & -0.023372 & -0.1969 & 0.42222 \tabularnewline
18 & -0.19592 & -1.6508 & 0.051593 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277948&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]0.031093[/C][C]0.262[/C][C]0.397042[/C][/ROW]
[ROW][C]2[/C][C]-0.429689[/C][C]-3.6206[/C][C]0.000274[/C][/ROW]
[ROW][C]3[/C][C]-0.166368[/C][C]-1.4018[/C][C]0.08266[/C][/ROW]
[ROW][C]4[/C][C]0.287671[/C][C]2.424[/C][C]0.008951[/C][/ROW]
[ROW][C]5[/C][C]-0.029165[/C][C]-0.2457[/C][C]0.403294[/C][/ROW]
[ROW][C]6[/C][C]-0.24699[/C][C]-2.0812[/C][C]0.020513[/C][/ROW]
[ROW][C]7[/C][C]-0.031666[/C][C]-0.2668[/C][C]0.395188[/C][/ROW]
[ROW][C]8[/C][C]0.255267[/C][C]2.1509[/C][C]0.017444[/C][/ROW]
[ROW][C]9[/C][C]-0.173023[/C][C]-1.4579[/C][C]0.074637[/C][/ROW]
[ROW][C]10[/C][C]-0.385705[/C][C]-3.25[/C][C]0.000883[/C][/ROW]
[ROW][C]11[/C][C]0.039875[/C][C]0.336[/C][C]0.368933[/C][/ROW]
[ROW][C]12[/C][C]0.786294[/C][C]6.6254[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.045782[/C][C]0.3858[/C][C]0.350412[/C][/ROW]
[ROW][C]14[/C][C]-0.396559[/C][C]-3.3415[/C][C]0.000666[/C][/ROW]
[ROW][C]15[/C][C]-0.140839[/C][C]-1.1867[/C][C]0.119645[/C][/ROW]
[ROW][C]16[/C][C]0.233695[/C][C]1.9692[/C][C]0.02642[/C][/ROW]
[ROW][C]17[/C][C]-0.023372[/C][C]-0.1969[/C][C]0.42222[/C][/ROW]
[ROW][C]18[/C][C]-0.19592[/C][C]-1.6508[/C][C]0.051593[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277948&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277948&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	0.031093	0.262	0.397042
2	-0.429689	-3.6206	0.000274
3	-0.166368	-1.4018	0.08266
4	0.287671	2.424	0.008951
5	-0.029165	-0.2457	0.403294
6	-0.24699	-2.0812	0.020513
7	-0.031666	-0.2668	0.395188
8	0.255267	2.1509	0.017444
9	-0.173023	-1.4579	0.074637
10	-0.385705	-3.25	0.000883
11	0.039875	0.336	0.368933
12	0.786294	6.6254	0
13	0.045782	0.3858	0.350412
14	-0.396559	-3.3415	0.000666
15	-0.140839	-1.1867	0.119645
16	0.233695	1.9692	0.02642
17	-0.023372	-0.1969	0.42222
18	-0.19592	-1.6508	0.051593

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.031093	0.262	0.397042
2	-0.431072	-3.6323	0.000264
3	-0.164552	-1.3865	0.08496
4	0.134336	1.1319	0.130735
5	-0.208862	-1.7599	0.041366
6	-0.14371	-1.2109	0.11497
7	-0.051315	-0.4324	0.333384
8	0.047801	0.4028	0.344161
9	-0.313684	-2.6431	0.00505
10	-0.367739	-3.0986	0.001393
11	-0.19718	-1.6615	0.050515
12	0.61277	5.1633	1e-06
13	0.036722	0.3094	0.378952
14	0.061383	0.5172	0.303305
15	0.015818	0.1333	0.447172
16	-0.183152	-1.5433	0.063606
17	-0.06066	-0.5111	0.305424
18	0.021278	0.1793	0.42911

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.031093 & 0.262 & 0.397042 \tabularnewline
2 & -0.431072 & -3.6323 & 0.000264 \tabularnewline
3 & -0.164552 & -1.3865 & 0.08496 \tabularnewline
4 & 0.134336 & 1.1319 & 0.130735 \tabularnewline
5 & -0.208862 & -1.7599 & 0.041366 \tabularnewline
6 & -0.14371 & -1.2109 & 0.11497 \tabularnewline
7 & -0.051315 & -0.4324 & 0.333384 \tabularnewline
8 & 0.047801 & 0.4028 & 0.344161 \tabularnewline
9 & -0.313684 & -2.6431 & 0.00505 \tabularnewline
10 & -0.367739 & -3.0986 & 0.001393 \tabularnewline
11 & -0.19718 & -1.6615 & 0.050515 \tabularnewline
12 & 0.61277 & 5.1633 & 1e-06 \tabularnewline
13 & 0.036722 & 0.3094 & 0.378952 \tabularnewline
14 & 0.061383 & 0.5172 & 0.303305 \tabularnewline
15 & 0.015818 & 0.1333 & 0.447172 \tabularnewline
16 & -0.183152 & -1.5433 & 0.063606 \tabularnewline
17 & -0.06066 & -0.5111 & 0.305424 \tabularnewline
18 & 0.021278 & 0.1793 & 0.42911 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277948&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]0.031093[/C][C]0.262[/C][C]0.397042[/C][/ROW]
[ROW][C]2[/C][C]-0.431072[/C][C]-3.6323[/C][C]0.000264[/C][/ROW]
[ROW][C]3[/C][C]-0.164552[/C][C]-1.3865[/C][C]0.08496[/C][/ROW]
[ROW][C]4[/C][C]0.134336[/C][C]1.1319[/C][C]0.130735[/C][/ROW]
[ROW][C]5[/C][C]-0.208862[/C][C]-1.7599[/C][C]0.041366[/C][/ROW]
[ROW][C]6[/C][C]-0.14371[/C][C]-1.2109[/C][C]0.11497[/C][/ROW]
[ROW][C]7[/C][C]-0.051315[/C][C]-0.4324[/C][C]0.333384[/C][/ROW]
[ROW][C]8[/C][C]0.047801[/C][C]0.4028[/C][C]0.344161[/C][/ROW]
[ROW][C]9[/C][C]-0.313684[/C][C]-2.6431[/C][C]0.00505[/C][/ROW]
[ROW][C]10[/C][C]-0.367739[/C][C]-3.0986[/C][C]0.001393[/C][/ROW]
[ROW][C]11[/C][C]-0.19718[/C][C]-1.6615[/C][C]0.050515[/C][/ROW]
[ROW][C]12[/C][C]0.61277[/C][C]5.1633[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.036722[/C][C]0.3094[/C][C]0.378952[/C][/ROW]
[ROW][C]14[/C][C]0.061383[/C][C]0.5172[/C][C]0.303305[/C][/ROW]
[ROW][C]15[/C][C]0.015818[/C][C]0.1333[/C][C]0.447172[/C][/ROW]
[ROW][C]16[/C][C]-0.183152[/C][C]-1.5433[/C][C]0.063606[/C][/ROW]
[ROW][C]17[/C][C]-0.06066[/C][C]-0.5111[/C][C]0.305424[/C][/ROW]
[ROW][C]18[/C][C]0.021278[/C][C]0.1793[/C][C]0.42911[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277948&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277948&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	0.031093	0.262	0.397042
2	-0.431072	-3.6323	0.000264
3	-0.164552	-1.3865	0.08496
4	0.134336	1.1319	0.130735
5	-0.208862	-1.7599	0.041366
6	-0.14371	-1.2109	0.11497
7	-0.051315	-0.4324	0.333384
8	0.047801	0.4028	0.344161
9	-0.313684	-2.6431	0.00505
10	-0.367739	-3.0986	0.001393
11	-0.19718	-1.6615	0.050515
12	0.61277	5.1633	1e-06
13	0.036722	0.3094	0.378952
14	0.061383	0.5172	0.303305
15	0.015818	0.1333	0.447172
16	-0.183152	-1.5433	0.063606
17	-0.06066	-0.5111	0.305424
18	0.021278	0.1793	0.42911

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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Input Parameters & R Code