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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 10 Jan 2014 21:59:44 -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/2014/Jan/10/t1389409215bggmkl5y6wjd08t.htm/, Retrieved Sun, 19 May 2024 12:17:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232885, Retrieved Sun, 19 May 2024 12:17:27 +0000

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Estimated Impact

156

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

-       [(Partial) Autocorrelation Function] [] [2014-01-11 02:59:44] [c13b0833c91505664fff70cc44050808] [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	3 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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232885&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]3 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=232885&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232885&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	3 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.112165	1.0219	0.154905
2	-0.205472	-1.8719	0.032368
3	-0.291303	-2.6539	0.004767
4	-0.217858	-1.9848	0.025236
5	0.067602	0.6159	0.269828
6	0.343503	3.1295	0.001208
7	0.21656	1.973	0.025914
8	-0.067149	-0.6118	0.271185
9	-0.314507	-2.8653	0.002638
10	-0.069729	-0.6353	0.263504
11	0.162875	1.4839	0.070817
12	0.307269	2.7993	0.003183
13	0.110597	1.0076	0.158291
14	-0.235743	-2.1477	0.017326
15	-0.238809	-2.1756	0.016213
16	-0.173177	-1.5777	0.059217
17	0.123602	1.1261	0.131691
18	0.346628	3.1579	0.001108
19	0.14717	1.3408	0.091824

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.112165 & 1.0219 & 0.154905 \tabularnewline
2 & -0.205472 & -1.8719 & 0.032368 \tabularnewline
3 & -0.291303 & -2.6539 & 0.004767 \tabularnewline
4 & -0.217858 & -1.9848 & 0.025236 \tabularnewline
5 & 0.067602 & 0.6159 & 0.269828 \tabularnewline
6 & 0.343503 & 3.1295 & 0.001208 \tabularnewline
7 & 0.21656 & 1.973 & 0.025914 \tabularnewline
8 & -0.067149 & -0.6118 & 0.271185 \tabularnewline
9 & -0.314507 & -2.8653 & 0.002638 \tabularnewline
10 & -0.069729 & -0.6353 & 0.263504 \tabularnewline
11 & 0.162875 & 1.4839 & 0.070817 \tabularnewline
12 & 0.307269 & 2.7993 & 0.003183 \tabularnewline
13 & 0.110597 & 1.0076 & 0.158291 \tabularnewline
14 & -0.235743 & -2.1477 & 0.017326 \tabularnewline
15 & -0.238809 & -2.1756 & 0.016213 \tabularnewline
16 & -0.173177 & -1.5777 & 0.059217 \tabularnewline
17 & 0.123602 & 1.1261 & 0.131691 \tabularnewline
18 & 0.346628 & 3.1579 & 0.001108 \tabularnewline
19 & 0.14717 & 1.3408 & 0.091824 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232885&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]0.112165[/C][C]1.0219[/C][C]0.154905[/C][/ROW]
[ROW][C]2[/C][C]-0.205472[/C][C]-1.8719[/C][C]0.032368[/C][/ROW]
[ROW][C]3[/C][C]-0.291303[/C][C]-2.6539[/C][C]0.004767[/C][/ROW]
[ROW][C]4[/C][C]-0.217858[/C][C]-1.9848[/C][C]0.025236[/C][/ROW]
[ROW][C]5[/C][C]0.067602[/C][C]0.6159[/C][C]0.269828[/C][/ROW]
[ROW][C]6[/C][C]0.343503[/C][C]3.1295[/C][C]0.001208[/C][/ROW]
[ROW][C]7[/C][C]0.21656[/C][C]1.973[/C][C]0.025914[/C][/ROW]
[ROW][C]8[/C][C]-0.067149[/C][C]-0.6118[/C][C]0.271185[/C][/ROW]
[ROW][C]9[/C][C]-0.314507[/C][C]-2.8653[/C][C]0.002638[/C][/ROW]
[ROW][C]10[/C][C]-0.069729[/C][C]-0.6353[/C][C]0.263504[/C][/ROW]
[ROW][C]11[/C][C]0.162875[/C][C]1.4839[/C][C]0.070817[/C][/ROW]
[ROW][C]12[/C][C]0.307269[/C][C]2.7993[/C][C]0.003183[/C][/ROW]
[ROW][C]13[/C][C]0.110597[/C][C]1.0076[/C][C]0.158291[/C][/ROW]
[ROW][C]14[/C][C]-0.235743[/C][C]-2.1477[/C][C]0.017326[/C][/ROW]
[ROW][C]15[/C][C]-0.238809[/C][C]-2.1756[/C][C]0.016213[/C][/ROW]
[ROW][C]16[/C][C]-0.173177[/C][C]-1.5777[/C][C]0.059217[/C][/ROW]
[ROW][C]17[/C][C]0.123602[/C][C]1.1261[/C][C]0.131691[/C][/ROW]
[ROW][C]18[/C][C]0.346628[/C][C]3.1579[/C][C]0.001108[/C][/ROW]
[ROW][C]19[/C][C]0.14717[/C][C]1.3408[/C][C]0.091824[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232885&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232885&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	0.112165	1.0219	0.154905
2	-0.205472	-1.8719	0.032368
3	-0.291303	-2.6539	0.004767
4	-0.217858	-1.9848	0.025236
5	0.067602	0.6159	0.269828
6	0.343503	3.1295	0.001208
7	0.21656	1.973	0.025914
8	-0.067149	-0.6118	0.271185
9	-0.314507	-2.8653	0.002638
10	-0.069729	-0.6353	0.263504
11	0.162875	1.4839	0.070817
12	0.307269	2.7993	0.003183
13	0.110597	1.0076	0.158291
14	-0.235743	-2.1477	0.017326
15	-0.238809	-2.1756	0.016213
16	-0.173177	-1.5777	0.059217
17	0.123602	1.1261	0.131691
18	0.346628	3.1579	0.001108
19	0.14717	1.3408	0.091824

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.112165	1.0219	0.154905
2	-0.220832	-2.0119	0.023739
3	-0.253813	-2.3123	0.011618
4	-0.232214	-2.1156	0.018689
5	-0.020032	-0.1825	0.427817
6	0.211997	1.9314	0.028424
7	0.12449	1.1342	0.129996
8	0.00243	0.0221	0.491196
9	-0.155144	-1.4134	0.080635
10	0.116257	1.0591	0.146302
11	0.160892	1.4658	0.073242
12	0.201692	1.8375	0.034857
13	0.009573	0.0872	0.465356
14	-0.180082	-1.6406	0.05233
15	-0.009486	-0.0864	0.465671
16	-0.110344	-1.0053	0.158841
17	-0.017802	-0.1622	0.435778
18	0.045983	0.4189	0.338177
19	0.002892	0.0263	0.489522

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.112165 & 1.0219 & 0.154905 \tabularnewline
2 & -0.220832 & -2.0119 & 0.023739 \tabularnewline
3 & -0.253813 & -2.3123 & 0.011618 \tabularnewline
4 & -0.232214 & -2.1156 & 0.018689 \tabularnewline
5 & -0.020032 & -0.1825 & 0.427817 \tabularnewline
6 & 0.211997 & 1.9314 & 0.028424 \tabularnewline
7 & 0.12449 & 1.1342 & 0.129996 \tabularnewline
8 & 0.00243 & 0.0221 & 0.491196 \tabularnewline
9 & -0.155144 & -1.4134 & 0.080635 \tabularnewline
10 & 0.116257 & 1.0591 & 0.146302 \tabularnewline
11 & 0.160892 & 1.4658 & 0.073242 \tabularnewline
12 & 0.201692 & 1.8375 & 0.034857 \tabularnewline
13 & 0.009573 & 0.0872 & 0.465356 \tabularnewline
14 & -0.180082 & -1.6406 & 0.05233 \tabularnewline
15 & -0.009486 & -0.0864 & 0.465671 \tabularnewline
16 & -0.110344 & -1.0053 & 0.158841 \tabularnewline
17 & -0.017802 & -0.1622 & 0.435778 \tabularnewline
18 & 0.045983 & 0.4189 & 0.338177 \tabularnewline
19 & 0.002892 & 0.0263 & 0.489522 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232885&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]0.112165[/C][C]1.0219[/C][C]0.154905[/C][/ROW]
[ROW][C]2[/C][C]-0.220832[/C][C]-2.0119[/C][C]0.023739[/C][/ROW]
[ROW][C]3[/C][C]-0.253813[/C][C]-2.3123[/C][C]0.011618[/C][/ROW]
[ROW][C]4[/C][C]-0.232214[/C][C]-2.1156[/C][C]0.018689[/C][/ROW]
[ROW][C]5[/C][C]-0.020032[/C][C]-0.1825[/C][C]0.427817[/C][/ROW]
[ROW][C]6[/C][C]0.211997[/C][C]1.9314[/C][C]0.028424[/C][/ROW]
[ROW][C]7[/C][C]0.12449[/C][C]1.1342[/C][C]0.129996[/C][/ROW]
[ROW][C]8[/C][C]0.00243[/C][C]0.0221[/C][C]0.491196[/C][/ROW]
[ROW][C]9[/C][C]-0.155144[/C][C]-1.4134[/C][C]0.080635[/C][/ROW]
[ROW][C]10[/C][C]0.116257[/C][C]1.0591[/C][C]0.146302[/C][/ROW]
[ROW][C]11[/C][C]0.160892[/C][C]1.4658[/C][C]0.073242[/C][/ROW]
[ROW][C]12[/C][C]0.201692[/C][C]1.8375[/C][C]0.034857[/C][/ROW]
[ROW][C]13[/C][C]0.009573[/C][C]0.0872[/C][C]0.465356[/C][/ROW]
[ROW][C]14[/C][C]-0.180082[/C][C]-1.6406[/C][C]0.05233[/C][/ROW]
[ROW][C]15[/C][C]-0.009486[/C][C]-0.0864[/C][C]0.465671[/C][/ROW]
[ROW][C]16[/C][C]-0.110344[/C][C]-1.0053[/C][C]0.158841[/C][/ROW]
[ROW][C]17[/C][C]-0.017802[/C][C]-0.1622[/C][C]0.435778[/C][/ROW]
[ROW][C]18[/C][C]0.045983[/C][C]0.4189[/C][C]0.338177[/C][/ROW]
[ROW][C]19[/C][C]0.002892[/C][C]0.0263[/C][C]0.489522[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232885&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232885&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	0.112165	1.0219	0.154905
2	-0.220832	-2.0119	0.023739
3	-0.253813	-2.3123	0.011618
4	-0.232214	-2.1156	0.018689
5	-0.020032	-0.1825	0.427817
6	0.211997	1.9314	0.028424
7	0.12449	1.1342	0.129996
8	0.00243	0.0221	0.491196
9	-0.155144	-1.4134	0.080635
10	0.116257	1.0591	0.146302
11	0.160892	1.4658	0.073242
12	0.201692	1.8375	0.034857
13	0.009573	0.0872	0.465356
14	-0.180082	-1.6406	0.05233
15	-0.009486	-0.0864	0.465671
16	-0.110344	-1.0053	0.158841
17	-0.017802	-0.1622	0.435778
18	0.045983	0.4189	0.338177
19	0.002892	0.0263	0.489522

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '1'
par2 <- '1'
par1 <- 'Default'
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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code