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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 21 Nov 2013 13:43:26 -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/2013/Nov/21/t13850594173iypbo8ikrz52r2.htm/, Retrieved Fri, 03 May 2024 08:16:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=227368, Retrieved Fri, 03 May 2024 08:16:16 +0000

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-       [(Partial) Autocorrelation Function] [] [2013-11-21 18:43:26] [5d7546d7dacadccf70943ca90d1ce990] [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=227368&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=227368&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227368&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	-0.012223	-0.1114	0.455801
2	0.02839	0.2586	0.398273
3	-0.02298	-0.2094	0.417341
4	-0.081127	-0.7391	0.230964
5	-0.018118	-0.1651	0.434649
6	-0.058953	-0.5371	0.296322
7	-0.014501	-0.1321	0.447608
8	-0.013242	-0.1206	0.452135
9	0.002248	0.0205	0.491856
10	-0.013462	-0.1226	0.451344
11	0.017583	0.1602	0.436561
12	0.00627	0.0571	0.477292
13	-0.007637	-0.0696	0.472349
14	-0.000391	-0.0036	0.498584
15	-0.071618	-0.6525	0.257951
16	-0.003563	-0.0325	0.487092
17	-0.044419	-0.4047	0.343378
18	-0.001819	-0.0166	0.493407
19	0.01838	0.1674	0.433712

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.012223 & -0.1114 & 0.455801 \tabularnewline
2 & 0.02839 & 0.2586 & 0.398273 \tabularnewline
3 & -0.02298 & -0.2094 & 0.417341 \tabularnewline
4 & -0.081127 & -0.7391 & 0.230964 \tabularnewline
5 & -0.018118 & -0.1651 & 0.434649 \tabularnewline
6 & -0.058953 & -0.5371 & 0.296322 \tabularnewline
7 & -0.014501 & -0.1321 & 0.447608 \tabularnewline
8 & -0.013242 & -0.1206 & 0.452135 \tabularnewline
9 & 0.002248 & 0.0205 & 0.491856 \tabularnewline
10 & -0.013462 & -0.1226 & 0.451344 \tabularnewline
11 & 0.017583 & 0.1602 & 0.436561 \tabularnewline
12 & 0.00627 & 0.0571 & 0.477292 \tabularnewline
13 & -0.007637 & -0.0696 & 0.472349 \tabularnewline
14 & -0.000391 & -0.0036 & 0.498584 \tabularnewline
15 & -0.071618 & -0.6525 & 0.257951 \tabularnewline
16 & -0.003563 & -0.0325 & 0.487092 \tabularnewline
17 & -0.044419 & -0.4047 & 0.343378 \tabularnewline
18 & -0.001819 & -0.0166 & 0.493407 \tabularnewline
19 & 0.01838 & 0.1674 & 0.433712 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=227368&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]-0.012223[/C][C]-0.1114[/C][C]0.455801[/C][/ROW]
[ROW][C]2[/C][C]0.02839[/C][C]0.2586[/C][C]0.398273[/C][/ROW]
[ROW][C]3[/C][C]-0.02298[/C][C]-0.2094[/C][C]0.417341[/C][/ROW]
[ROW][C]4[/C][C]-0.081127[/C][C]-0.7391[/C][C]0.230964[/C][/ROW]
[ROW][C]5[/C][C]-0.018118[/C][C]-0.1651[/C][C]0.434649[/C][/ROW]
[ROW][C]6[/C][C]-0.058953[/C][C]-0.5371[/C][C]0.296322[/C][/ROW]
[ROW][C]7[/C][C]-0.014501[/C][C]-0.1321[/C][C]0.447608[/C][/ROW]
[ROW][C]8[/C][C]-0.013242[/C][C]-0.1206[/C][C]0.452135[/C][/ROW]
[ROW][C]9[/C][C]0.002248[/C][C]0.0205[/C][C]0.491856[/C][/ROW]
[ROW][C]10[/C][C]-0.013462[/C][C]-0.1226[/C][C]0.451344[/C][/ROW]
[ROW][C]11[/C][C]0.017583[/C][C]0.1602[/C][C]0.436561[/C][/ROW]
[ROW][C]12[/C][C]0.00627[/C][C]0.0571[/C][C]0.477292[/C][/ROW]
[ROW][C]13[/C][C]-0.007637[/C][C]-0.0696[/C][C]0.472349[/C][/ROW]
[ROW][C]14[/C][C]-0.000391[/C][C]-0.0036[/C][C]0.498584[/C][/ROW]
[ROW][C]15[/C][C]-0.071618[/C][C]-0.6525[/C][C]0.257951[/C][/ROW]
[ROW][C]16[/C][C]-0.003563[/C][C]-0.0325[/C][C]0.487092[/C][/ROW]
[ROW][C]17[/C][C]-0.044419[/C][C]-0.4047[/C][C]0.343378[/C][/ROW]
[ROW][C]18[/C][C]-0.001819[/C][C]-0.0166[/C][C]0.493407[/C][/ROW]
[ROW][C]19[/C][C]0.01838[/C][C]0.1674[/C][C]0.433712[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=227368&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227368&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	-0.012223	-0.1114	0.455801
2	0.02839	0.2586	0.398273
3	-0.02298	-0.2094	0.417341
4	-0.081127	-0.7391	0.230964
5	-0.018118	-0.1651	0.434649
6	-0.058953	-0.5371	0.296322
7	-0.014501	-0.1321	0.447608
8	-0.013242	-0.1206	0.452135
9	0.002248	0.0205	0.491856
10	-0.013462	-0.1226	0.451344
11	0.017583	0.1602	0.436561
12	0.00627	0.0571	0.477292
13	-0.007637	-0.0696	0.472349
14	-0.000391	-0.0036	0.498584
15	-0.071618	-0.6525	0.257951
16	-0.003563	-0.0325	0.487092
17	-0.044419	-0.4047	0.343378
18	-0.001819	-0.0166	0.493407
19	0.01838	0.1674	0.433712

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.012223	-0.1114	0.455801
2	0.028245	0.2573	0.398782
3	-0.022319	-0.2033	0.419686
4	-0.082572	-0.7523	0.227009
5	-0.01899	-0.173	0.431535
6	-0.055678	-0.5073	0.306662
7	-0.019119	-0.1742	0.431074
8	-0.018413	-0.1677	0.433595
9	-0.003258	-0.0297	0.488195
10	-0.023516	-0.2142	0.415443
11	0.011402	0.1039	0.45876
12	0.001112	0.0101	0.49597
13	-0.011955	-0.1089	0.456766
14	-0.005366	-0.0489	0.480563
15	-0.070892	-0.6459	0.260078
16	-0.007752	-0.0706	0.471933
17	-0.042663	-0.3887	0.349255
18	-0.007537	-0.0687	0.472711
19	0.007444	0.0678	0.473048

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.012223 & -0.1114 & 0.455801 \tabularnewline
2 & 0.028245 & 0.2573 & 0.398782 \tabularnewline
3 & -0.022319 & -0.2033 & 0.419686 \tabularnewline
4 & -0.082572 & -0.7523 & 0.227009 \tabularnewline
5 & -0.01899 & -0.173 & 0.431535 \tabularnewline
6 & -0.055678 & -0.5073 & 0.306662 \tabularnewline
7 & -0.019119 & -0.1742 & 0.431074 \tabularnewline
8 & -0.018413 & -0.1677 & 0.433595 \tabularnewline
9 & -0.003258 & -0.0297 & 0.488195 \tabularnewline
10 & -0.023516 & -0.2142 & 0.415443 \tabularnewline
11 & 0.011402 & 0.1039 & 0.45876 \tabularnewline
12 & 0.001112 & 0.0101 & 0.49597 \tabularnewline
13 & -0.011955 & -0.1089 & 0.456766 \tabularnewline
14 & -0.005366 & -0.0489 & 0.480563 \tabularnewline
15 & -0.070892 & -0.6459 & 0.260078 \tabularnewline
16 & -0.007752 & -0.0706 & 0.471933 \tabularnewline
17 & -0.042663 & -0.3887 & 0.349255 \tabularnewline
18 & -0.007537 & -0.0687 & 0.472711 \tabularnewline
19 & 0.007444 & 0.0678 & 0.473048 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=227368&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]-0.012223[/C][C]-0.1114[/C][C]0.455801[/C][/ROW]
[ROW][C]2[/C][C]0.028245[/C][C]0.2573[/C][C]0.398782[/C][/ROW]
[ROW][C]3[/C][C]-0.022319[/C][C]-0.2033[/C][C]0.419686[/C][/ROW]
[ROW][C]4[/C][C]-0.082572[/C][C]-0.7523[/C][C]0.227009[/C][/ROW]
[ROW][C]5[/C][C]-0.01899[/C][C]-0.173[/C][C]0.431535[/C][/ROW]
[ROW][C]6[/C][C]-0.055678[/C][C]-0.5073[/C][C]0.306662[/C][/ROW]
[ROW][C]7[/C][C]-0.019119[/C][C]-0.1742[/C][C]0.431074[/C][/ROW]
[ROW][C]8[/C][C]-0.018413[/C][C]-0.1677[/C][C]0.433595[/C][/ROW]
[ROW][C]9[/C][C]-0.003258[/C][C]-0.0297[/C][C]0.488195[/C][/ROW]
[ROW][C]10[/C][C]-0.023516[/C][C]-0.2142[/C][C]0.415443[/C][/ROW]
[ROW][C]11[/C][C]0.011402[/C][C]0.1039[/C][C]0.45876[/C][/ROW]
[ROW][C]12[/C][C]0.001112[/C][C]0.0101[/C][C]0.49597[/C][/ROW]
[ROW][C]13[/C][C]-0.011955[/C][C]-0.1089[/C][C]0.456766[/C][/ROW]
[ROW][C]14[/C][C]-0.005366[/C][C]-0.0489[/C][C]0.480563[/C][/ROW]
[ROW][C]15[/C][C]-0.070892[/C][C]-0.6459[/C][C]0.260078[/C][/ROW]
[ROW][C]16[/C][C]-0.007752[/C][C]-0.0706[/C][C]0.471933[/C][/ROW]
[ROW][C]17[/C][C]-0.042663[/C][C]-0.3887[/C][C]0.349255[/C][/ROW]
[ROW][C]18[/C][C]-0.007537[/C][C]-0.0687[/C][C]0.472711[/C][/ROW]
[ROW][C]19[/C][C]0.007444[/C][C]0.0678[/C][C]0.473048[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=227368&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=227368&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	-0.012223	-0.1114	0.455801
2	0.028245	0.2573	0.398782
3	-0.022319	-0.2033	0.419686
4	-0.082572	-0.7523	0.227009
5	-0.01899	-0.173	0.431535
6	-0.055678	-0.5073	0.306662
7	-0.019119	-0.1742	0.431074
8	-0.018413	-0.1677	0.433595
9	-0.003258	-0.0297	0.488195
10	-0.023516	-0.2142	0.415443
11	0.011402	0.1039	0.45876
12	0.001112	0.0101	0.49597
13	-0.011955	-0.1089	0.456766
14	-0.005366	-0.0489	0.480563
15	-0.070892	-0.6459	0.260078
16	-0.007752	-0.0706	0.471933
17	-0.042663	-0.3887	0.349255
18	-0.007537	-0.0687	0.472711
19	0.007444	0.0678	0.473048

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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code