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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 17 Nov 2011 13:37:42 -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/2011/Nov/17/t1321555079j5xdoel9dt1sihz.htm/, Retrieved Sat, 27 Apr 2024 00:46:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=145205, Retrieved Sat, 27 Apr 2024 00:46:52 +0000

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-     [Linear Regression Graphical Model Validation] [Colombia Coffee -...] [2008-02-26 10:22:06] [74be16979710d4c4e7c6647856088456]
- RMPD    [(Partial) Autocorrelation Function] [] [2011-11-17 18:37:42] [c7041fab4904771a5085f5eb0f28763f] [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=145205&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=145205&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145205&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	0.923505	5.8408	0
2	0.846896	5.3562	2e-06
3	0.770713	4.8744	9e-06
4	0.695261	4.3972	3.9e-05
5	0.620881	3.9268	0.000166
6	0.547406	3.4621	0.000645
7	0.475412	3.0068	0.002274
8	0.40516	2.5625	0.007132
9	0.336762	2.1299	0.019693
10	0.270992	1.7139	0.047144
11	0.207911	1.3149	0.098009
12	0.147305	0.9316	0.178556
13	0.089258	0.5645	0.287776
14	0.033635	0.2127	0.416311
15	-0.019235	-0.1216	0.451893
16	-0.069384	-0.4388	0.331576

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.923505 & 5.8408 & 0 \tabularnewline
2 & 0.846896 & 5.3562 & 2e-06 \tabularnewline
3 & 0.770713 & 4.8744 & 9e-06 \tabularnewline
4 & 0.695261 & 4.3972 & 3.9e-05 \tabularnewline
5 & 0.620881 & 3.9268 & 0.000166 \tabularnewline
6 & 0.547406 & 3.4621 & 0.000645 \tabularnewline
7 & 0.475412 & 3.0068 & 0.002274 \tabularnewline
8 & 0.40516 & 2.5625 & 0.007132 \tabularnewline
9 & 0.336762 & 2.1299 & 0.019693 \tabularnewline
10 & 0.270992 & 1.7139 & 0.047144 \tabularnewline
11 & 0.207911 & 1.3149 & 0.098009 \tabularnewline
12 & 0.147305 & 0.9316 & 0.178556 \tabularnewline
13 & 0.089258 & 0.5645 & 0.287776 \tabularnewline
14 & 0.033635 & 0.2127 & 0.416311 \tabularnewline
15 & -0.019235 & -0.1216 & 0.451893 \tabularnewline
16 & -0.069384 & -0.4388 & 0.331576 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145205&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]0.923505[/C][C]5.8408[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.846896[/C][C]5.3562[/C][C]2e-06[/C][/ROW]
[ROW][C]3[/C][C]0.770713[/C][C]4.8744[/C][C]9e-06[/C][/ROW]
[ROW][C]4[/C][C]0.695261[/C][C]4.3972[/C][C]3.9e-05[/C][/ROW]
[ROW][C]5[/C][C]0.620881[/C][C]3.9268[/C][C]0.000166[/C][/ROW]
[ROW][C]6[/C][C]0.547406[/C][C]3.4621[/C][C]0.000645[/C][/ROW]
[ROW][C]7[/C][C]0.475412[/C][C]3.0068[/C][C]0.002274[/C][/ROW]
[ROW][C]8[/C][C]0.40516[/C][C]2.5625[/C][C]0.007132[/C][/ROW]
[ROW][C]9[/C][C]0.336762[/C][C]2.1299[/C][C]0.019693[/C][/ROW]
[ROW][C]10[/C][C]0.270992[/C][C]1.7139[/C][C]0.047144[/C][/ROW]
[ROW][C]11[/C][C]0.207911[/C][C]1.3149[/C][C]0.098009[/C][/ROW]
[ROW][C]12[/C][C]0.147305[/C][C]0.9316[/C][C]0.178556[/C][/ROW]
[ROW][C]13[/C][C]0.089258[/C][C]0.5645[/C][C]0.287776[/C][/ROW]
[ROW][C]14[/C][C]0.033635[/C][C]0.2127[/C][C]0.416311[/C][/ROW]
[ROW][C]15[/C][C]-0.019235[/C][C]-0.1216[/C][C]0.451893[/C][/ROW]
[ROW][C]16[/C][C]-0.069384[/C][C]-0.4388[/C][C]0.331576[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=145205&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145205&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	0.923505	5.8408	0
2	0.846896	5.3562	2e-06
3	0.770713	4.8744	9e-06
4	0.695261	4.3972	3.9e-05
5	0.620881	3.9268	0.000166
6	0.547406	3.4621	0.000645
7	0.475412	3.0068	0.002274
8	0.40516	2.5625	0.007132
9	0.336762	2.1299	0.019693
10	0.270992	1.7139	0.047144
11	0.207911	1.3149	0.098009
12	0.147305	0.9316	0.178556
13	0.089258	0.5645	0.287776
14	0.033635	0.2127	0.416311
15	-0.019235	-0.1216	0.451893
16	-0.069384	-0.4388	0.331576

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.923505	5.8408	0
2	-0.040548	-0.2564	0.39946
3	-0.038574	-0.244	0.404252
4	-0.038048	-0.2406	0.405533
5	-0.037191	-0.2352	0.407621
6	-0.039701	-0.2511	0.401514
7	-0.037331	-0.2361	0.40728
8	-0.036843	-0.233	0.40847
9	-0.037286	-0.2358	0.40739
10	-0.033156	-0.2097	0.417485
11	-0.033438	-0.2115	0.416794
12	-0.035559	-0.2249	0.411602
13	-0.035781	-0.2263	0.41106
14	-0.037479	-0.237	0.406919
15	-0.036096	-0.2283	0.410292
16	-0.036995	-0.234	0.408099

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.923505 & 5.8408 & 0 \tabularnewline
2 & -0.040548 & -0.2564 & 0.39946 \tabularnewline
3 & -0.038574 & -0.244 & 0.404252 \tabularnewline
4 & -0.038048 & -0.2406 & 0.405533 \tabularnewline
5 & -0.037191 & -0.2352 & 0.407621 \tabularnewline
6 & -0.039701 & -0.2511 & 0.401514 \tabularnewline
7 & -0.037331 & -0.2361 & 0.40728 \tabularnewline
8 & -0.036843 & -0.233 & 0.40847 \tabularnewline
9 & -0.037286 & -0.2358 & 0.40739 \tabularnewline
10 & -0.033156 & -0.2097 & 0.417485 \tabularnewline
11 & -0.033438 & -0.2115 & 0.416794 \tabularnewline
12 & -0.035559 & -0.2249 & 0.411602 \tabularnewline
13 & -0.035781 & -0.2263 & 0.41106 \tabularnewline
14 & -0.037479 & -0.237 & 0.406919 \tabularnewline
15 & -0.036096 & -0.2283 & 0.410292 \tabularnewline
16 & -0.036995 & -0.234 & 0.408099 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145205&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]0.923505[/C][C]5.8408[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.040548[/C][C]-0.2564[/C][C]0.39946[/C][/ROW]
[ROW][C]3[/C][C]-0.038574[/C][C]-0.244[/C][C]0.404252[/C][/ROW]
[ROW][C]4[/C][C]-0.038048[/C][C]-0.2406[/C][C]0.405533[/C][/ROW]
[ROW][C]5[/C][C]-0.037191[/C][C]-0.2352[/C][C]0.407621[/C][/ROW]
[ROW][C]6[/C][C]-0.039701[/C][C]-0.2511[/C][C]0.401514[/C][/ROW]
[ROW][C]7[/C][C]-0.037331[/C][C]-0.2361[/C][C]0.40728[/C][/ROW]
[ROW][C]8[/C][C]-0.036843[/C][C]-0.233[/C][C]0.40847[/C][/ROW]
[ROW][C]9[/C][C]-0.037286[/C][C]-0.2358[/C][C]0.40739[/C][/ROW]
[ROW][C]10[/C][C]-0.033156[/C][C]-0.2097[/C][C]0.417485[/C][/ROW]
[ROW][C]11[/C][C]-0.033438[/C][C]-0.2115[/C][C]0.416794[/C][/ROW]
[ROW][C]12[/C][C]-0.035559[/C][C]-0.2249[/C][C]0.411602[/C][/ROW]
[ROW][C]13[/C][C]-0.035781[/C][C]-0.2263[/C][C]0.41106[/C][/ROW]
[ROW][C]14[/C][C]-0.037479[/C][C]-0.237[/C][C]0.406919[/C][/ROW]
[ROW][C]15[/C][C]-0.036096[/C][C]-0.2283[/C][C]0.410292[/C][/ROW]
[ROW][C]16[/C][C]-0.036995[/C][C]-0.234[/C][C]0.408099[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=145205&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145205&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	0.923505	5.8408	0
2	-0.040548	-0.2564	0.39946
3	-0.038574	-0.244	0.404252
4	-0.038048	-0.2406	0.405533
5	-0.037191	-0.2352	0.407621
6	-0.039701	-0.2511	0.401514
7	-0.037331	-0.2361	0.40728
8	-0.036843	-0.233	0.40847
9	-0.037286	-0.2358	0.40739
10	-0.033156	-0.2097	0.417485
11	-0.033438	-0.2115	0.416794
12	-0.035559	-0.2249	0.411602
13	-0.035781	-0.2263	0.41106
14	-0.037479	-0.237	0.406919
15	-0.036096	-0.2283	0.410292
16	-0.036995	-0.234	0.408099

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