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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 24 Nov 2019 20:53:16 +0100

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/2019/Nov/24/t1574626596tdaomkxsnxinofj.htm/, Retrieved Fri, 17 May 2024 05:20:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=318950, Retrieved Fri, 17 May 2024 05:20:28 +0000

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Estimated Impact

107

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-       [(Partial) Autocorrelation Function] [] [2019-11-24 19:53:16] [d41d8cd98f00b204e9800998ecf8427e] [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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=318950&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=318950&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318950&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.137965	0.9949	0.162202
2	0.111005	0.8005	0.213541
3	0.052245	0.3767	0.353949
4	0.085255	0.6148	0.27069
5	0.038167	0.2752	0.392116
6	0.051568	0.3719	0.355754
7	-0.027147	-0.1958	0.422782
8	-0.00684	-0.0493	0.480424
9	-0.020105	-0.145	0.442643
10	0.02017	0.1455	0.442459
11	0.038863	0.2802	0.390201
12	-0.080385	-0.5797	0.282322
13	0.023056	0.1663	0.4343
14	0.049897	0.3598	0.360223
15	0.130647	0.9421	0.175247
16	-0.083559	-0.6026	0.274713
17	-0.028004	-0.2019	0.420377

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.137965 & 0.9949 & 0.162202 \tabularnewline
2 & 0.111005 & 0.8005 & 0.213541 \tabularnewline
3 & 0.052245 & 0.3767 & 0.353949 \tabularnewline
4 & 0.085255 & 0.6148 & 0.27069 \tabularnewline
5 & 0.038167 & 0.2752 & 0.392116 \tabularnewline
6 & 0.051568 & 0.3719 & 0.355754 \tabularnewline
7 & -0.027147 & -0.1958 & 0.422782 \tabularnewline
8 & -0.00684 & -0.0493 & 0.480424 \tabularnewline
9 & -0.020105 & -0.145 & 0.442643 \tabularnewline
10 & 0.02017 & 0.1455 & 0.442459 \tabularnewline
11 & 0.038863 & 0.2802 & 0.390201 \tabularnewline
12 & -0.080385 & -0.5797 & 0.282322 \tabularnewline
13 & 0.023056 & 0.1663 & 0.4343 \tabularnewline
14 & 0.049897 & 0.3598 & 0.360223 \tabularnewline
15 & 0.130647 & 0.9421 & 0.175247 \tabularnewline
16 & -0.083559 & -0.6026 & 0.274713 \tabularnewline
17 & -0.028004 & -0.2019 & 0.420377 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=318950&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]0.137965[/C][C]0.9949[/C][C]0.162202[/C][/ROW]
[ROW][C]2[/C][C]0.111005[/C][C]0.8005[/C][C]0.213541[/C][/ROW]
[ROW][C]3[/C][C]0.052245[/C][C]0.3767[/C][C]0.353949[/C][/ROW]
[ROW][C]4[/C][C]0.085255[/C][C]0.6148[/C][C]0.27069[/C][/ROW]
[ROW][C]5[/C][C]0.038167[/C][C]0.2752[/C][C]0.392116[/C][/ROW]
[ROW][C]6[/C][C]0.051568[/C][C]0.3719[/C][C]0.355754[/C][/ROW]
[ROW][C]7[/C][C]-0.027147[/C][C]-0.1958[/C][C]0.422782[/C][/ROW]
[ROW][C]8[/C][C]-0.00684[/C][C]-0.0493[/C][C]0.480424[/C][/ROW]
[ROW][C]9[/C][C]-0.020105[/C][C]-0.145[/C][C]0.442643[/C][/ROW]
[ROW][C]10[/C][C]0.02017[/C][C]0.1455[/C][C]0.442459[/C][/ROW]
[ROW][C]11[/C][C]0.038863[/C][C]0.2802[/C][C]0.390201[/C][/ROW]
[ROW][C]12[/C][C]-0.080385[/C][C]-0.5797[/C][C]0.282322[/C][/ROW]
[ROW][C]13[/C][C]0.023056[/C][C]0.1663[/C][C]0.4343[/C][/ROW]
[ROW][C]14[/C][C]0.049897[/C][C]0.3598[/C][C]0.360223[/C][/ROW]
[ROW][C]15[/C][C]0.130647[/C][C]0.9421[/C][C]0.175247[/C][/ROW]
[ROW][C]16[/C][C]-0.083559[/C][C]-0.6026[/C][C]0.274713[/C][/ROW]
[ROW][C]17[/C][C]-0.028004[/C][C]-0.2019[/C][C]0.420377[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=318950&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318950&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	0.137965	0.9949	0.162202
2	0.111005	0.8005	0.213541
3	0.052245	0.3767	0.353949
4	0.085255	0.6148	0.27069
5	0.038167	0.2752	0.392116
6	0.051568	0.3719	0.355754
7	-0.027147	-0.1958	0.422782
8	-0.00684	-0.0493	0.480424
9	-0.020105	-0.145	0.442643
10	0.02017	0.1455	0.442459
11	0.038863	0.2802	0.390201
12	-0.080385	-0.5797	0.282322
13	0.023056	0.1663	0.4343
14	0.049897	0.3598	0.360223
15	0.130647	0.9421	0.175247
16	-0.083559	-0.6026	0.274713
17	-0.028004	-0.2019	0.420377

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.137965	0.9949	0.162202
2	0.093755	0.6761	0.250994
3	0.026154	0.1886	0.425569
4	0.067098	0.4839	0.31526
5	0.012622	0.091	0.463915
6	0.030926	0.223	0.412201
7	-0.04801	-0.3462	0.365293
8	-0.012557	-0.0906	0.464098
9	-0.017317	-0.1249	0.450551
10	0.023327	0.1682	0.433533
11	0.04299	0.31	0.378898
12	-0.09475	-0.6833	0.24874
13	0.044029	0.3175	0.37607
14	0.054957	0.3963	0.346753
15	0.117314	0.846	0.200724
16	-0.125984	-0.9085	0.183907
17	-0.034237	-0.2469	0.402984

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.137965 & 0.9949 & 0.162202 \tabularnewline
2 & 0.093755 & 0.6761 & 0.250994 \tabularnewline
3 & 0.026154 & 0.1886 & 0.425569 \tabularnewline
4 & 0.067098 & 0.4839 & 0.31526 \tabularnewline
5 & 0.012622 & 0.091 & 0.463915 \tabularnewline
6 & 0.030926 & 0.223 & 0.412201 \tabularnewline
7 & -0.04801 & -0.3462 & 0.365293 \tabularnewline
8 & -0.012557 & -0.0906 & 0.464098 \tabularnewline
9 & -0.017317 & -0.1249 & 0.450551 \tabularnewline
10 & 0.023327 & 0.1682 & 0.433533 \tabularnewline
11 & 0.04299 & 0.31 & 0.378898 \tabularnewline
12 & -0.09475 & -0.6833 & 0.24874 \tabularnewline
13 & 0.044029 & 0.3175 & 0.37607 \tabularnewline
14 & 0.054957 & 0.3963 & 0.346753 \tabularnewline
15 & 0.117314 & 0.846 & 0.200724 \tabularnewline
16 & -0.125984 & -0.9085 & 0.183907 \tabularnewline
17 & -0.034237 & -0.2469 & 0.402984 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=318950&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]0.137965[/C][C]0.9949[/C][C]0.162202[/C][/ROW]
[ROW][C]2[/C][C]0.093755[/C][C]0.6761[/C][C]0.250994[/C][/ROW]
[ROW][C]3[/C][C]0.026154[/C][C]0.1886[/C][C]0.425569[/C][/ROW]
[ROW][C]4[/C][C]0.067098[/C][C]0.4839[/C][C]0.31526[/C][/ROW]
[ROW][C]5[/C][C]0.012622[/C][C]0.091[/C][C]0.463915[/C][/ROW]
[ROW][C]6[/C][C]0.030926[/C][C]0.223[/C][C]0.412201[/C][/ROW]
[ROW][C]7[/C][C]-0.04801[/C][C]-0.3462[/C][C]0.365293[/C][/ROW]
[ROW][C]8[/C][C]-0.012557[/C][C]-0.0906[/C][C]0.464098[/C][/ROW]
[ROW][C]9[/C][C]-0.017317[/C][C]-0.1249[/C][C]0.450551[/C][/ROW]
[ROW][C]10[/C][C]0.023327[/C][C]0.1682[/C][C]0.433533[/C][/ROW]
[ROW][C]11[/C][C]0.04299[/C][C]0.31[/C][C]0.378898[/C][/ROW]
[ROW][C]12[/C][C]-0.09475[/C][C]-0.6833[/C][C]0.24874[/C][/ROW]
[ROW][C]13[/C][C]0.044029[/C][C]0.3175[/C][C]0.37607[/C][/ROW]
[ROW][C]14[/C][C]0.054957[/C][C]0.3963[/C][C]0.346753[/C][/ROW]
[ROW][C]15[/C][C]0.117314[/C][C]0.846[/C][C]0.200724[/C][/ROW]
[ROW][C]16[/C][C]-0.125984[/C][C]-0.9085[/C][C]0.183907[/C][/ROW]
[ROW][C]17[/C][C]-0.034237[/C][C]-0.2469[/C][C]0.402984[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=318950&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318950&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	0.137965	0.9949	0.162202
2	0.093755	0.6761	0.250994
3	0.026154	0.1886	0.425569
4	0.067098	0.4839	0.31526
5	0.012622	0.091	0.463915
6	0.030926	0.223	0.412201
7	-0.04801	-0.3462	0.365293
8	-0.012557	-0.0906	0.464098
9	-0.017317	-0.1249	0.450551
10	0.023327	0.1682	0.433533
11	0.04299	0.31	0.378898
12	-0.09475	-0.6833	0.24874
13	0.044029	0.3175	0.37607
14	0.054957	0.3963	0.346753
15	0.117314	0.846	0.200724
16	-0.125984	-0.9085	0.183907
17	-0.034237	-0.2469	0.402984

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)
x <- na.omit(x)
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,'ACF(k)',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,'PACF(k)',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