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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 18 Nov 2012 11:44:24 -0500

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/2012/Nov/18/t13532570929c6bu9bu4dqp2j2.htm/, Retrieved Mon, 29 Apr 2024 18:01:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=190255, Retrieved Mon, 29 Apr 2024 18:01:25 +0000

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Estimated Impact

107

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-       [(Partial) Autocorrelation Function] [autocorrelatie va...] [2012-11-18 16:44:24] [5f6947d5d5479fbcf21e52ac422c0dd8] [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	'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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=190255&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=190255&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=190255&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.871901	7.3983	0
2	0.746276	6.3324	0
3	0.622281	5.2802	1e-06
4	0.570957	4.8447	4e-06
5	0.521064	4.4214	1.7e-05
6	0.47227	4.0073	7.4e-05
7	0.42889	3.6393	0.000256
8	0.391035	3.318	0.000712
9	0.359225	3.0481	0.00161
10	0.322152	2.7336	0.00394
11	0.289951	2.4603	0.008141
12	0.258483	2.1933	0.015758
13	0.236114	2.0035	0.024444
14	0.212494	1.8031	0.03778
15	0.190046	1.6126	0.055604
16	0.161866	1.3735	0.086933
17	0.140339	1.1908	0.118819
18	0.116931	0.9922	0.162214

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.871901 & 7.3983 & 0 \tabularnewline
2 & 0.746276 & 6.3324 & 0 \tabularnewline
3 & 0.622281 & 5.2802 & 1e-06 \tabularnewline
4 & 0.570957 & 4.8447 & 4e-06 \tabularnewline
5 & 0.521064 & 4.4214 & 1.7e-05 \tabularnewline
6 & 0.47227 & 4.0073 & 7.4e-05 \tabularnewline
7 & 0.42889 & 3.6393 & 0.000256 \tabularnewline
8 & 0.391035 & 3.318 & 0.000712 \tabularnewline
9 & 0.359225 & 3.0481 & 0.00161 \tabularnewline
10 & 0.322152 & 2.7336 & 0.00394 \tabularnewline
11 & 0.289951 & 2.4603 & 0.008141 \tabularnewline
12 & 0.258483 & 2.1933 & 0.015758 \tabularnewline
13 & 0.236114 & 2.0035 & 0.024444 \tabularnewline
14 & 0.212494 & 1.8031 & 0.03778 \tabularnewline
15 & 0.190046 & 1.6126 & 0.055604 \tabularnewline
16 & 0.161866 & 1.3735 & 0.086933 \tabularnewline
17 & 0.140339 & 1.1908 & 0.118819 \tabularnewline
18 & 0.116931 & 0.9922 & 0.162214 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=190255&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]0.871901[/C][C]7.3983[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.746276[/C][C]6.3324[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.622281[/C][C]5.2802[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]0.570957[/C][C]4.8447[/C][C]4e-06[/C][/ROW]
[ROW][C]5[/C][C]0.521064[/C][C]4.4214[/C][C]1.7e-05[/C][/ROW]
[ROW][C]6[/C][C]0.47227[/C][C]4.0073[/C][C]7.4e-05[/C][/ROW]
[ROW][C]7[/C][C]0.42889[/C][C]3.6393[/C][C]0.000256[/C][/ROW]
[ROW][C]8[/C][C]0.391035[/C][C]3.318[/C][C]0.000712[/C][/ROW]
[ROW][C]9[/C][C]0.359225[/C][C]3.0481[/C][C]0.00161[/C][/ROW]
[ROW][C]10[/C][C]0.322152[/C][C]2.7336[/C][C]0.00394[/C][/ROW]
[ROW][C]11[/C][C]0.289951[/C][C]2.4603[/C][C]0.008141[/C][/ROW]
[ROW][C]12[/C][C]0.258483[/C][C]2.1933[/C][C]0.015758[/C][/ROW]
[ROW][C]13[/C][C]0.236114[/C][C]2.0035[/C][C]0.024444[/C][/ROW]
[ROW][C]14[/C][C]0.212494[/C][C]1.8031[/C][C]0.03778[/C][/ROW]
[ROW][C]15[/C][C]0.190046[/C][C]1.6126[/C][C]0.055604[/C][/ROW]
[ROW][C]16[/C][C]0.161866[/C][C]1.3735[/C][C]0.086933[/C][/ROW]
[ROW][C]17[/C][C]0.140339[/C][C]1.1908[/C][C]0.118819[/C][/ROW]
[ROW][C]18[/C][C]0.116931[/C][C]0.9922[/C][C]0.162214[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=190255&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=190255&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	0.871901	7.3983	0
2	0.746276	6.3324	0
3	0.622281	5.2802	1e-06
4	0.570957	4.8447	4e-06
5	0.521064	4.4214	1.7e-05
6	0.47227	4.0073	7.4e-05
7	0.42889	3.6393	0.000256
8	0.391035	3.318	0.000712
9	0.359225	3.0481	0.00161
10	0.322152	2.7336	0.00394
11	0.289951	2.4603	0.008141
12	0.258483	2.1933	0.015758
13	0.236114	2.0035	0.024444
14	0.212494	1.8031	0.03778
15	0.190046	1.6126	0.055604
16	0.161866	1.3735	0.086933
17	0.140339	1.1908	0.118819
18	0.116931	0.9922	0.162214

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.871901	7.3983	0
2	-0.058112	-0.4931	0.311723
3	-0.065034	-0.5518	0.291387
4	0.229051	1.9436	0.027929
5	-0.031299	-0.2656	0.39566
6	-0.035235	-0.299	0.382909
7	0.069553	0.5902	0.278459
8	-0.005676	-0.0482	0.480861
9	-0.003176	-0.027	0.489286
10	-0.014224	-0.1207	0.452134
11	0.005957	0.0505	0.479914
12	-0.008659	-0.0735	0.470818
13	0.012533	0.1063	0.457802
14	-0.010481	-0.0889	0.464692
15	-0.0092	-0.0781	0.468997
16	-0.026727	-0.2268	0.410617
17	0.009609	0.0815	0.467622
18	-0.023779	-0.2018	0.420333

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.871901 & 7.3983 & 0 \tabularnewline
2 & -0.058112 & -0.4931 & 0.311723 \tabularnewline
3 & -0.065034 & -0.5518 & 0.291387 \tabularnewline
4 & 0.229051 & 1.9436 & 0.027929 \tabularnewline
5 & -0.031299 & -0.2656 & 0.39566 \tabularnewline
6 & -0.035235 & -0.299 & 0.382909 \tabularnewline
7 & 0.069553 & 0.5902 & 0.278459 \tabularnewline
8 & -0.005676 & -0.0482 & 0.480861 \tabularnewline
9 & -0.003176 & -0.027 & 0.489286 \tabularnewline
10 & -0.014224 & -0.1207 & 0.452134 \tabularnewline
11 & 0.005957 & 0.0505 & 0.479914 \tabularnewline
12 & -0.008659 & -0.0735 & 0.470818 \tabularnewline
13 & 0.012533 & 0.1063 & 0.457802 \tabularnewline
14 & -0.010481 & -0.0889 & 0.464692 \tabularnewline
15 & -0.0092 & -0.0781 & 0.468997 \tabularnewline
16 & -0.026727 & -0.2268 & 0.410617 \tabularnewline
17 & 0.009609 & 0.0815 & 0.467622 \tabularnewline
18 & -0.023779 & -0.2018 & 0.420333 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=190255&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]0.871901[/C][C]7.3983[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.058112[/C][C]-0.4931[/C][C]0.311723[/C][/ROW]
[ROW][C]3[/C][C]-0.065034[/C][C]-0.5518[/C][C]0.291387[/C][/ROW]
[ROW][C]4[/C][C]0.229051[/C][C]1.9436[/C][C]0.027929[/C][/ROW]
[ROW][C]5[/C][C]-0.031299[/C][C]-0.2656[/C][C]0.39566[/C][/ROW]
[ROW][C]6[/C][C]-0.035235[/C][C]-0.299[/C][C]0.382909[/C][/ROW]
[ROW][C]7[/C][C]0.069553[/C][C]0.5902[/C][C]0.278459[/C][/ROW]
[ROW][C]8[/C][C]-0.005676[/C][C]-0.0482[/C][C]0.480861[/C][/ROW]
[ROW][C]9[/C][C]-0.003176[/C][C]-0.027[/C][C]0.489286[/C][/ROW]
[ROW][C]10[/C][C]-0.014224[/C][C]-0.1207[/C][C]0.452134[/C][/ROW]
[ROW][C]11[/C][C]0.005957[/C][C]0.0505[/C][C]0.479914[/C][/ROW]
[ROW][C]12[/C][C]-0.008659[/C][C]-0.0735[/C][C]0.470818[/C][/ROW]
[ROW][C]13[/C][C]0.012533[/C][C]0.1063[/C][C]0.457802[/C][/ROW]
[ROW][C]14[/C][C]-0.010481[/C][C]-0.0889[/C][C]0.464692[/C][/ROW]
[ROW][C]15[/C][C]-0.0092[/C][C]-0.0781[/C][C]0.468997[/C][/ROW]
[ROW][C]16[/C][C]-0.026727[/C][C]-0.2268[/C][C]0.410617[/C][/ROW]
[ROW][C]17[/C][C]0.009609[/C][C]0.0815[/C][C]0.467622[/C][/ROW]
[ROW][C]18[/C][C]-0.023779[/C][C]-0.2018[/C][C]0.420333[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=190255&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=190255&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	0.871901	7.3983	0
2	-0.058112	-0.4931	0.311723
3	-0.065034	-0.5518	0.291387
4	0.229051	1.9436	0.027929
5	-0.031299	-0.2656	0.39566
6	-0.035235	-0.299	0.382909
7	0.069553	0.5902	0.278459
8	-0.005676	-0.0482	0.480861
9	-0.003176	-0.027	0.489286
10	-0.014224	-0.1207	0.452134
11	0.005957	0.0505	0.479914
12	-0.008659	-0.0735	0.470818
13	0.012533	0.1063	0.457802
14	-0.010481	-0.0889	0.464692
15	-0.0092	-0.0781	0.468997
16	-0.026727	-0.2268	0.410617
17	0.009609	0.0815	0.467622
18	-0.023779	-0.2018	0.420333

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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Input Parameters & R Code