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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 14 Dec 2014 09:59:55 +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/2014/Dec/14/t1418551212d2xar4jgd2zij6u.htm/, Retrieved Thu, 16 May 2024 12:26:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267379, Retrieved Thu, 16 May 2024 12:26:47 +0000

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-       [(Partial) Autocorrelation Function] [] [2014-12-14 09:59:55] [c7f962214140f976f2c4b1bb2571d9df] [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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267379&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267379&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267379&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.252186	-2.125	0.018536
2	-0.097372	-0.8205	0.207348
3	-0.09068	-0.7641	0.223674
4	0.036786	0.31	0.378747
5	-0.180954	-1.5247	0.065882
6	-0.014823	-0.1249	0.450478
7	0.17137	1.444	0.07657
8	-0.096079	-0.8096	0.210446
9	0.178287	1.5023	0.06873
10	0.041413	0.349	0.364078
11	-0.096357	-0.8119	0.209777
12	-0.399224	-3.3639	0.000621
13	0.094901	0.7997	0.21329
14	0.182473	1.5375	0.064303
15	-0.025038	-0.211	0.416755
16	0.089308	0.7525	0.227113
17	0.114852	0.9678	0.168225
18	-0.028097	-0.2367	0.406767
19	-0.104934	-0.8842	0.189788

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.252186 & -2.125 & 0.018536 \tabularnewline
2 & -0.097372 & -0.8205 & 0.207348 \tabularnewline
3 & -0.09068 & -0.7641 & 0.223674 \tabularnewline
4 & 0.036786 & 0.31 & 0.378747 \tabularnewline
5 & -0.180954 & -1.5247 & 0.065882 \tabularnewline
6 & -0.014823 & -0.1249 & 0.450478 \tabularnewline
7 & 0.17137 & 1.444 & 0.07657 \tabularnewline
8 & -0.096079 & -0.8096 & 0.210446 \tabularnewline
9 & 0.178287 & 1.5023 & 0.06873 \tabularnewline
10 & 0.041413 & 0.349 & 0.364078 \tabularnewline
11 & -0.096357 & -0.8119 & 0.209777 \tabularnewline
12 & -0.399224 & -3.3639 & 0.000621 \tabularnewline
13 & 0.094901 & 0.7997 & 0.21329 \tabularnewline
14 & 0.182473 & 1.5375 & 0.064303 \tabularnewline
15 & -0.025038 & -0.211 & 0.416755 \tabularnewline
16 & 0.089308 & 0.7525 & 0.227113 \tabularnewline
17 & 0.114852 & 0.9678 & 0.168225 \tabularnewline
18 & -0.028097 & -0.2367 & 0.406767 \tabularnewline
19 & -0.104934 & -0.8842 & 0.189788 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267379&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]-0.252186[/C][C]-2.125[/C][C]0.018536[/C][/ROW]
[ROW][C]2[/C][C]-0.097372[/C][C]-0.8205[/C][C]0.207348[/C][/ROW]
[ROW][C]3[/C][C]-0.09068[/C][C]-0.7641[/C][C]0.223674[/C][/ROW]
[ROW][C]4[/C][C]0.036786[/C][C]0.31[/C][C]0.378747[/C][/ROW]
[ROW][C]5[/C][C]-0.180954[/C][C]-1.5247[/C][C]0.065882[/C][/ROW]
[ROW][C]6[/C][C]-0.014823[/C][C]-0.1249[/C][C]0.450478[/C][/ROW]
[ROW][C]7[/C][C]0.17137[/C][C]1.444[/C][C]0.07657[/C][/ROW]
[ROW][C]8[/C][C]-0.096079[/C][C]-0.8096[/C][C]0.210446[/C][/ROW]
[ROW][C]9[/C][C]0.178287[/C][C]1.5023[/C][C]0.06873[/C][/ROW]
[ROW][C]10[/C][C]0.041413[/C][C]0.349[/C][C]0.364078[/C][/ROW]
[ROW][C]11[/C][C]-0.096357[/C][C]-0.8119[/C][C]0.209777[/C][/ROW]
[ROW][C]12[/C][C]-0.399224[/C][C]-3.3639[/C][C]0.000621[/C][/ROW]
[ROW][C]13[/C][C]0.094901[/C][C]0.7997[/C][C]0.21329[/C][/ROW]
[ROW][C]14[/C][C]0.182473[/C][C]1.5375[/C][C]0.064303[/C][/ROW]
[ROW][C]15[/C][C]-0.025038[/C][C]-0.211[/C][C]0.416755[/C][/ROW]
[ROW][C]16[/C][C]0.089308[/C][C]0.7525[/C][C]0.227113[/C][/ROW]
[ROW][C]17[/C][C]0.114852[/C][C]0.9678[/C][C]0.168225[/C][/ROW]
[ROW][C]18[/C][C]-0.028097[/C][C]-0.2367[/C][C]0.406767[/C][/ROW]
[ROW][C]19[/C][C]-0.104934[/C][C]-0.8842[/C][C]0.189788[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267379&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267379&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	-0.252186	-2.125	0.018536
2	-0.097372	-0.8205	0.207348
3	-0.09068	-0.7641	0.223674
4	0.036786	0.31	0.378747
5	-0.180954	-1.5247	0.065882
6	-0.014823	-0.1249	0.450478
7	0.17137	1.444	0.07657
8	-0.096079	-0.8096	0.210446
9	0.178287	1.5023	0.06873
10	0.041413	0.349	0.364078
11	-0.096357	-0.8119	0.209777
12	-0.399224	-3.3639	0.000621
13	0.094901	0.7997	0.21329
14	0.182473	1.5375	0.064303
15	-0.025038	-0.211	0.416755
16	0.089308	0.7525	0.227113
17	0.114852	0.9678	0.168225
18	-0.028097	-0.2367	0.406767
19	-0.104934	-0.8842	0.189788

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.252186	-2.125	0.018536
2	-0.171902	-1.4485	0.075944
3	-0.17916	-1.5096	0.067788
4	-0.068081	-0.5737	0.284005
5	-0.259349	-2.1853	0.016084
6	-0.211869	-1.7852	0.039247
7	0.015849	0.1335	0.447069
8	-0.16185	-1.3638	0.088474
9	0.124703	1.0508	0.148465
10	0.1285	1.0828	0.141289
11	-0.026265	-0.2213	0.412743
12	-0.41014	-3.4559	0.000465
13	-0.297358	-2.5056	0.00726
14	-0.027904	-0.2351	0.407393
15	-0.049707	-0.4188	0.338298
16	0.010366	0.0873	0.465322
17	0.055774	0.47	0.319911
18	-0.010841	-0.0913	0.463738
19	0.023837	0.2009	0.420693

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.252186 & -2.125 & 0.018536 \tabularnewline
2 & -0.171902 & -1.4485 & 0.075944 \tabularnewline
3 & -0.17916 & -1.5096 & 0.067788 \tabularnewline
4 & -0.068081 & -0.5737 & 0.284005 \tabularnewline
5 & -0.259349 & -2.1853 & 0.016084 \tabularnewline
6 & -0.211869 & -1.7852 & 0.039247 \tabularnewline
7 & 0.015849 & 0.1335 & 0.447069 \tabularnewline
8 & -0.16185 & -1.3638 & 0.088474 \tabularnewline
9 & 0.124703 & 1.0508 & 0.148465 \tabularnewline
10 & 0.1285 & 1.0828 & 0.141289 \tabularnewline
11 & -0.026265 & -0.2213 & 0.412743 \tabularnewline
12 & -0.41014 & -3.4559 & 0.000465 \tabularnewline
13 & -0.297358 & -2.5056 & 0.00726 \tabularnewline
14 & -0.027904 & -0.2351 & 0.407393 \tabularnewline
15 & -0.049707 & -0.4188 & 0.338298 \tabularnewline
16 & 0.010366 & 0.0873 & 0.465322 \tabularnewline
17 & 0.055774 & 0.47 & 0.319911 \tabularnewline
18 & -0.010841 & -0.0913 & 0.463738 \tabularnewline
19 & 0.023837 & 0.2009 & 0.420693 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267379&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]-0.252186[/C][C]-2.125[/C][C]0.018536[/C][/ROW]
[ROW][C]2[/C][C]-0.171902[/C][C]-1.4485[/C][C]0.075944[/C][/ROW]
[ROW][C]3[/C][C]-0.17916[/C][C]-1.5096[/C][C]0.067788[/C][/ROW]
[ROW][C]4[/C][C]-0.068081[/C][C]-0.5737[/C][C]0.284005[/C][/ROW]
[ROW][C]5[/C][C]-0.259349[/C][C]-2.1853[/C][C]0.016084[/C][/ROW]
[ROW][C]6[/C][C]-0.211869[/C][C]-1.7852[/C][C]0.039247[/C][/ROW]
[ROW][C]7[/C][C]0.015849[/C][C]0.1335[/C][C]0.447069[/C][/ROW]
[ROW][C]8[/C][C]-0.16185[/C][C]-1.3638[/C][C]0.088474[/C][/ROW]
[ROW][C]9[/C][C]0.124703[/C][C]1.0508[/C][C]0.148465[/C][/ROW]
[ROW][C]10[/C][C]0.1285[/C][C]1.0828[/C][C]0.141289[/C][/ROW]
[ROW][C]11[/C][C]-0.026265[/C][C]-0.2213[/C][C]0.412743[/C][/ROW]
[ROW][C]12[/C][C]-0.41014[/C][C]-3.4559[/C][C]0.000465[/C][/ROW]
[ROW][C]13[/C][C]-0.297358[/C][C]-2.5056[/C][C]0.00726[/C][/ROW]
[ROW][C]14[/C][C]-0.027904[/C][C]-0.2351[/C][C]0.407393[/C][/ROW]
[ROW][C]15[/C][C]-0.049707[/C][C]-0.4188[/C][C]0.338298[/C][/ROW]
[ROW][C]16[/C][C]0.010366[/C][C]0.0873[/C][C]0.465322[/C][/ROW]
[ROW][C]17[/C][C]0.055774[/C][C]0.47[/C][C]0.319911[/C][/ROW]
[ROW][C]18[/C][C]-0.010841[/C][C]-0.0913[/C][C]0.463738[/C][/ROW]
[ROW][C]19[/C][C]0.023837[/C][C]0.2009[/C][C]0.420693[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267379&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267379&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	-0.252186	-2.125	0.018536
2	-0.171902	-1.4485	0.075944
3	-0.17916	-1.5096	0.067788
4	-0.068081	-0.5737	0.284005
5	-0.259349	-2.1853	0.016084
6	-0.211869	-1.7852	0.039247
7	0.015849	0.1335	0.447069
8	-0.16185	-1.3638	0.088474
9	0.124703	1.0508	0.148465
10	0.1285	1.0828	0.141289
11	-0.026265	-0.2213	0.412743
12	-0.41014	-3.4559	0.000465
13	-0.297358	-2.5056	0.00726
14	-0.027904	-0.2351	0.407393
15	-0.049707	-0.4188	0.338298
16	0.010366	0.0873	0.465322
17	0.055774	0.47	0.319911
18	-0.010841	-0.0913	0.463738
19	0.023837	0.2009	0.420693

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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