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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 21 Oct 2015 15:27:02 +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/2015/Oct/21/t1445437640e40m5pg8ghkqr7i.htm/, Retrieved Wed, 15 May 2024 02:04:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282725, Retrieved Wed, 15 May 2024 02:04:23 +0000

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Estimated Impact

103

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [] [2015-10-21 14:27:02] [1faf68c5110a4cb4d7d9116a9189ca68] [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	'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282725&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282725&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282725&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	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.052538	0.4427	0.329665
2	-0.048864	-0.4117	0.340888
3	-0.001839	-0.0155	0.493841
4	-0.392755	-3.3094	0.000735
5	-0.170121	-1.4335	0.078057
6	0.017072	0.1439	0.443013
7	-0.042355	-0.3569	0.361117
8	-0.098917	-0.8335	0.203683
9	0.161378	1.3598	0.089098
10	0.017172	0.1447	0.442682
11	-0.025013	-0.2108	0.416838
12	0.238059	2.0059	0.024338
13	-0.16434	-1.3848	0.085232
14	0.032057	0.2701	0.393926
15	0.04473	0.3769	0.353685
16	-0.18445	-1.5542	0.062291
17	-0.031453	-0.265	0.395878
18	-0.034227	-0.2884	0.386939

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.052538 & 0.4427 & 0.329665 \tabularnewline
2 & -0.048864 & -0.4117 & 0.340888 \tabularnewline
3 & -0.001839 & -0.0155 & 0.493841 \tabularnewline
4 & -0.392755 & -3.3094 & 0.000735 \tabularnewline
5 & -0.170121 & -1.4335 & 0.078057 \tabularnewline
6 & 0.017072 & 0.1439 & 0.443013 \tabularnewline
7 & -0.042355 & -0.3569 & 0.361117 \tabularnewline
8 & -0.098917 & -0.8335 & 0.203683 \tabularnewline
9 & 0.161378 & 1.3598 & 0.089098 \tabularnewline
10 & 0.017172 & 0.1447 & 0.442682 \tabularnewline
11 & -0.025013 & -0.2108 & 0.416838 \tabularnewline
12 & 0.238059 & 2.0059 & 0.024338 \tabularnewline
13 & -0.16434 & -1.3848 & 0.085232 \tabularnewline
14 & 0.032057 & 0.2701 & 0.393926 \tabularnewline
15 & 0.04473 & 0.3769 & 0.353685 \tabularnewline
16 & -0.18445 & -1.5542 & 0.062291 \tabularnewline
17 & -0.031453 & -0.265 & 0.395878 \tabularnewline
18 & -0.034227 & -0.2884 & 0.386939 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282725&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]0.052538[/C][C]0.4427[/C][C]0.329665[/C][/ROW]
[ROW][C]2[/C][C]-0.048864[/C][C]-0.4117[/C][C]0.340888[/C][/ROW]
[ROW][C]3[/C][C]-0.001839[/C][C]-0.0155[/C][C]0.493841[/C][/ROW]
[ROW][C]4[/C][C]-0.392755[/C][C]-3.3094[/C][C]0.000735[/C][/ROW]
[ROW][C]5[/C][C]-0.170121[/C][C]-1.4335[/C][C]0.078057[/C][/ROW]
[ROW][C]6[/C][C]0.017072[/C][C]0.1439[/C][C]0.443013[/C][/ROW]
[ROW][C]7[/C][C]-0.042355[/C][C]-0.3569[/C][C]0.361117[/C][/ROW]
[ROW][C]8[/C][C]-0.098917[/C][C]-0.8335[/C][C]0.203683[/C][/ROW]
[ROW][C]9[/C][C]0.161378[/C][C]1.3598[/C][C]0.089098[/C][/ROW]
[ROW][C]10[/C][C]0.017172[/C][C]0.1447[/C][C]0.442682[/C][/ROW]
[ROW][C]11[/C][C]-0.025013[/C][C]-0.2108[/C][C]0.416838[/C][/ROW]
[ROW][C]12[/C][C]0.238059[/C][C]2.0059[/C][C]0.024338[/C][/ROW]
[ROW][C]13[/C][C]-0.16434[/C][C]-1.3848[/C][C]0.085232[/C][/ROW]
[ROW][C]14[/C][C]0.032057[/C][C]0.2701[/C][C]0.393926[/C][/ROW]
[ROW][C]15[/C][C]0.04473[/C][C]0.3769[/C][C]0.353685[/C][/ROW]
[ROW][C]16[/C][C]-0.18445[/C][C]-1.5542[/C][C]0.062291[/C][/ROW]
[ROW][C]17[/C][C]-0.031453[/C][C]-0.265[/C][C]0.395878[/C][/ROW]
[ROW][C]18[/C][C]-0.034227[/C][C]-0.2884[/C][C]0.386939[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282725&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282725&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	0.052538	0.4427	0.329665
2	-0.048864	-0.4117	0.340888
3	-0.001839	-0.0155	0.493841
4	-0.392755	-3.3094	0.000735
5	-0.170121	-1.4335	0.078057
6	0.017072	0.1439	0.443013
7	-0.042355	-0.3569	0.361117
8	-0.098917	-0.8335	0.203683
9	0.161378	1.3598	0.089098
10	0.017172	0.1447	0.442682
11	-0.025013	-0.2108	0.416838
12	0.238059	2.0059	0.024338
13	-0.16434	-1.3848	0.085232
14	0.032057	0.2701	0.393926
15	0.04473	0.3769	0.353685
16	-0.18445	-1.5542	0.062291
17	-0.031453	-0.265	0.395878
18	-0.034227	-0.2884	0.386939

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.052538	0.4427	0.329665
2	-0.051767	-0.4362	0.332009
3	0.003601	0.0303	0.487941
4	-0.397546	-3.3498	0.000649
5	-0.150205	-1.2656	0.104889
6	-0.026282	-0.2215	0.412687
7	-0.068981	-0.5812	0.28146
8	-0.308126	-2.5963	0.005722
9	0.025201	0.2123	0.416222
10	-0.06072	-0.5116	0.305247
11	-0.095804	-0.8073	0.211107
12	0.074234	0.6255	0.266821
13	-0.203723	-1.7166	0.045206
14	0.088813	0.7484	0.22836
15	-0.050133	-0.4224	0.336995
16	-0.116613	-0.9826	0.164571
17	-0.113437	-0.9558	0.171199
18	-0.094448	-0.7958	0.214392

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.052538 & 0.4427 & 0.329665 \tabularnewline
2 & -0.051767 & -0.4362 & 0.332009 \tabularnewline
3 & 0.003601 & 0.0303 & 0.487941 \tabularnewline
4 & -0.397546 & -3.3498 & 0.000649 \tabularnewline
5 & -0.150205 & -1.2656 & 0.104889 \tabularnewline
6 & -0.026282 & -0.2215 & 0.412687 \tabularnewline
7 & -0.068981 & -0.5812 & 0.28146 \tabularnewline
8 & -0.308126 & -2.5963 & 0.005722 \tabularnewline
9 & 0.025201 & 0.2123 & 0.416222 \tabularnewline
10 & -0.06072 & -0.5116 & 0.305247 \tabularnewline
11 & -0.095804 & -0.8073 & 0.211107 \tabularnewline
12 & 0.074234 & 0.6255 & 0.266821 \tabularnewline
13 & -0.203723 & -1.7166 & 0.045206 \tabularnewline
14 & 0.088813 & 0.7484 & 0.22836 \tabularnewline
15 & -0.050133 & -0.4224 & 0.336995 \tabularnewline
16 & -0.116613 & -0.9826 & 0.164571 \tabularnewline
17 & -0.113437 & -0.9558 & 0.171199 \tabularnewline
18 & -0.094448 & -0.7958 & 0.214392 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282725&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]0.052538[/C][C]0.4427[/C][C]0.329665[/C][/ROW]
[ROW][C]2[/C][C]-0.051767[/C][C]-0.4362[/C][C]0.332009[/C][/ROW]
[ROW][C]3[/C][C]0.003601[/C][C]0.0303[/C][C]0.487941[/C][/ROW]
[ROW][C]4[/C][C]-0.397546[/C][C]-3.3498[/C][C]0.000649[/C][/ROW]
[ROW][C]5[/C][C]-0.150205[/C][C]-1.2656[/C][C]0.104889[/C][/ROW]
[ROW][C]6[/C][C]-0.026282[/C][C]-0.2215[/C][C]0.412687[/C][/ROW]
[ROW][C]7[/C][C]-0.068981[/C][C]-0.5812[/C][C]0.28146[/C][/ROW]
[ROW][C]8[/C][C]-0.308126[/C][C]-2.5963[/C][C]0.005722[/C][/ROW]
[ROW][C]9[/C][C]0.025201[/C][C]0.2123[/C][C]0.416222[/C][/ROW]
[ROW][C]10[/C][C]-0.06072[/C][C]-0.5116[/C][C]0.305247[/C][/ROW]
[ROW][C]11[/C][C]-0.095804[/C][C]-0.8073[/C][C]0.211107[/C][/ROW]
[ROW][C]12[/C][C]0.074234[/C][C]0.6255[/C][C]0.266821[/C][/ROW]
[ROW][C]13[/C][C]-0.203723[/C][C]-1.7166[/C][C]0.045206[/C][/ROW]
[ROW][C]14[/C][C]0.088813[/C][C]0.7484[/C][C]0.22836[/C][/ROW]
[ROW][C]15[/C][C]-0.050133[/C][C]-0.4224[/C][C]0.336995[/C][/ROW]
[ROW][C]16[/C][C]-0.116613[/C][C]-0.9826[/C][C]0.164571[/C][/ROW]
[ROW][C]17[/C][C]-0.113437[/C][C]-0.9558[/C][C]0.171199[/C][/ROW]
[ROW][C]18[/C][C]-0.094448[/C][C]-0.7958[/C][C]0.214392[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282725&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282725&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	0.052538	0.4427	0.329665
2	-0.051767	-0.4362	0.332009
3	0.003601	0.0303	0.487941
4	-0.397546	-3.3498	0.000649
5	-0.150205	-1.2656	0.104889
6	-0.026282	-0.2215	0.412687
7	-0.068981	-0.5812	0.28146
8	-0.308126	-2.5963	0.005722
9	0.025201	0.2123	0.416222
10	-0.06072	-0.5116	0.305247
11	-0.095804	-0.8073	0.211107
12	0.074234	0.6255	0.266821
13	-0.203723	-1.7166	0.045206
14	0.088813	0.7484	0.22836
15	-0.050133	-0.4224	0.336995
16	-0.116613	-0.9826	0.164571
17	-0.113437	-0.9558	0.171199
18	-0.094448	-0.7958	0.214392

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