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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 10 Jan 2016 11:21:29 +0000

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/2016/Jan/10/t14524249917j2n43nupg0vzkz.htm/, Retrieved Sun, 05 May 2024 03:26:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287744, Retrieved Sun, 05 May 2024 03:26:19 +0000

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

-       [(Partial) Autocorrelation Function] [differenti�ren re...] [2016-01-10 11:21:29] [442c3b7d1457f8bc4e82a9331e05e70d] [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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287744&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287744&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287744&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.24224	2.5057	0.006863
2	0.196989	2.0377	0.022025
3	0.307407	3.1798	0.000964
4	0.181913	1.8817	0.031295
5	0.021491	0.2223	0.412252
6	-0.051427	-0.532	0.297927
7	0.139124	1.4391	0.076519
8	-0.002846	-0.0294	0.488286
9	-0.002569	-0.0266	0.489425
10	-0.077085	-0.7974	0.213501
11	-0.072705	-0.7521	0.226831
12	0.015837	0.1638	0.435092
13	-0.100501	-1.0396	0.150436
14	-0.134249	-1.3887	0.083906
15	-0.073665	-0.762	0.223868
16	-0.202446	-2.0941	0.019306
17	-0.049927	-0.5164	0.303303
18	-0.210657	-2.179	0.015761
19	-0.145748	-1.5076	0.067298
20	-0.091752	-0.9491	0.172356

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.24224 & 2.5057 & 0.006863 \tabularnewline
2 & 0.196989 & 2.0377 & 0.022025 \tabularnewline
3 & 0.307407 & 3.1798 & 0.000964 \tabularnewline
4 & 0.181913 & 1.8817 & 0.031295 \tabularnewline
5 & 0.021491 & 0.2223 & 0.412252 \tabularnewline
6 & -0.051427 & -0.532 & 0.297927 \tabularnewline
7 & 0.139124 & 1.4391 & 0.076519 \tabularnewline
8 & -0.002846 & -0.0294 & 0.488286 \tabularnewline
9 & -0.002569 & -0.0266 & 0.489425 \tabularnewline
10 & -0.077085 & -0.7974 & 0.213501 \tabularnewline
11 & -0.072705 & -0.7521 & 0.226831 \tabularnewline
12 & 0.015837 & 0.1638 & 0.435092 \tabularnewline
13 & -0.100501 & -1.0396 & 0.150436 \tabularnewline
14 & -0.134249 & -1.3887 & 0.083906 \tabularnewline
15 & -0.073665 & -0.762 & 0.223868 \tabularnewline
16 & -0.202446 & -2.0941 & 0.019306 \tabularnewline
17 & -0.049927 & -0.5164 & 0.303303 \tabularnewline
18 & -0.210657 & -2.179 & 0.015761 \tabularnewline
19 & -0.145748 & -1.5076 & 0.067298 \tabularnewline
20 & -0.091752 & -0.9491 & 0.172356 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287744&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]0.24224[/C][C]2.5057[/C][C]0.006863[/C][/ROW]
[ROW][C]2[/C][C]0.196989[/C][C]2.0377[/C][C]0.022025[/C][/ROW]
[ROW][C]3[/C][C]0.307407[/C][C]3.1798[/C][C]0.000964[/C][/ROW]
[ROW][C]4[/C][C]0.181913[/C][C]1.8817[/C][C]0.031295[/C][/ROW]
[ROW][C]5[/C][C]0.021491[/C][C]0.2223[/C][C]0.412252[/C][/ROW]
[ROW][C]6[/C][C]-0.051427[/C][C]-0.532[/C][C]0.297927[/C][/ROW]
[ROW][C]7[/C][C]0.139124[/C][C]1.4391[/C][C]0.076519[/C][/ROW]
[ROW][C]8[/C][C]-0.002846[/C][C]-0.0294[/C][C]0.488286[/C][/ROW]
[ROW][C]9[/C][C]-0.002569[/C][C]-0.0266[/C][C]0.489425[/C][/ROW]
[ROW][C]10[/C][C]-0.077085[/C][C]-0.7974[/C][C]0.213501[/C][/ROW]
[ROW][C]11[/C][C]-0.072705[/C][C]-0.7521[/C][C]0.226831[/C][/ROW]
[ROW][C]12[/C][C]0.015837[/C][C]0.1638[/C][C]0.435092[/C][/ROW]
[ROW][C]13[/C][C]-0.100501[/C][C]-1.0396[/C][C]0.150436[/C][/ROW]
[ROW][C]14[/C][C]-0.134249[/C][C]-1.3887[/C][C]0.083906[/C][/ROW]
[ROW][C]15[/C][C]-0.073665[/C][C]-0.762[/C][C]0.223868[/C][/ROW]
[ROW][C]16[/C][C]-0.202446[/C][C]-2.0941[/C][C]0.019306[/C][/ROW]
[ROW][C]17[/C][C]-0.049927[/C][C]-0.5164[/C][C]0.303303[/C][/ROW]
[ROW][C]18[/C][C]-0.210657[/C][C]-2.179[/C][C]0.015761[/C][/ROW]
[ROW][C]19[/C][C]-0.145748[/C][C]-1.5076[/C][C]0.067298[/C][/ROW]
[ROW][C]20[/C][C]-0.091752[/C][C]-0.9491[/C][C]0.172356[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287744&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287744&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	0.24224	2.5057	0.006863
2	0.196989	2.0377	0.022025
3	0.307407	3.1798	0.000964
4	0.181913	1.8817	0.031295
5	0.021491	0.2223	0.412252
6	-0.051427	-0.532	0.297927
7	0.139124	1.4391	0.076519
8	-0.002846	-0.0294	0.488286
9	-0.002569	-0.0266	0.489425
10	-0.077085	-0.7974	0.213501
11	-0.072705	-0.7521	0.226831
12	0.015837	0.1638	0.435092
13	-0.100501	-1.0396	0.150436
14	-0.134249	-1.3887	0.083906
15	-0.073665	-0.762	0.223868
16	-0.202446	-2.0941	0.019306
17	-0.049927	-0.5164	0.303303
18	-0.210657	-2.179	0.015761
19	-0.145748	-1.5076	0.067298
20	-0.091752	-0.9491	0.172356

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.24224	2.5057	0.006863
2	0.14693	1.5199	0.065748
3	0.250931	2.5956	0.005383
4	0.058178	0.6018	0.274291
5	-0.111434	-1.1527	0.125804
6	-0.166139	-1.7186	0.044294
7	0.143134	1.4806	0.070828
8	-0.000836	-0.0086	0.496558
9	0.048865	0.5055	0.307138
10	-0.156986	-1.6239	0.053672
11	-0.098287	-1.0167	0.155798
12	0.078042	0.8073	0.210651
13	0.00487	0.0504	0.47996
14	-0.098852	-1.0225	0.154417
15	-0.052723	-0.5454	0.293318
16	-0.22743	-2.3526	0.010237
17	0.161335	1.6689	0.049035
18	-0.118716	-1.228	0.111069
19	-0.027449	-0.2839	0.388504
20	-0.062887	-0.6505	0.258378

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.24224 & 2.5057 & 0.006863 \tabularnewline
2 & 0.14693 & 1.5199 & 0.065748 \tabularnewline
3 & 0.250931 & 2.5956 & 0.005383 \tabularnewline
4 & 0.058178 & 0.6018 & 0.274291 \tabularnewline
5 & -0.111434 & -1.1527 & 0.125804 \tabularnewline
6 & -0.166139 & -1.7186 & 0.044294 \tabularnewline
7 & 0.143134 & 1.4806 & 0.070828 \tabularnewline
8 & -0.000836 & -0.0086 & 0.496558 \tabularnewline
9 & 0.048865 & 0.5055 & 0.307138 \tabularnewline
10 & -0.156986 & -1.6239 & 0.053672 \tabularnewline
11 & -0.098287 & -1.0167 & 0.155798 \tabularnewline
12 & 0.078042 & 0.8073 & 0.210651 \tabularnewline
13 & 0.00487 & 0.0504 & 0.47996 \tabularnewline
14 & -0.098852 & -1.0225 & 0.154417 \tabularnewline
15 & -0.052723 & -0.5454 & 0.293318 \tabularnewline
16 & -0.22743 & -2.3526 & 0.010237 \tabularnewline
17 & 0.161335 & 1.6689 & 0.049035 \tabularnewline
18 & -0.118716 & -1.228 & 0.111069 \tabularnewline
19 & -0.027449 & -0.2839 & 0.388504 \tabularnewline
20 & -0.062887 & -0.6505 & 0.258378 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287744&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]0.24224[/C][C]2.5057[/C][C]0.006863[/C][/ROW]
[ROW][C]2[/C][C]0.14693[/C][C]1.5199[/C][C]0.065748[/C][/ROW]
[ROW][C]3[/C][C]0.250931[/C][C]2.5956[/C][C]0.005383[/C][/ROW]
[ROW][C]4[/C][C]0.058178[/C][C]0.6018[/C][C]0.274291[/C][/ROW]
[ROW][C]5[/C][C]-0.111434[/C][C]-1.1527[/C][C]0.125804[/C][/ROW]
[ROW][C]6[/C][C]-0.166139[/C][C]-1.7186[/C][C]0.044294[/C][/ROW]
[ROW][C]7[/C][C]0.143134[/C][C]1.4806[/C][C]0.070828[/C][/ROW]
[ROW][C]8[/C][C]-0.000836[/C][C]-0.0086[/C][C]0.496558[/C][/ROW]
[ROW][C]9[/C][C]0.048865[/C][C]0.5055[/C][C]0.307138[/C][/ROW]
[ROW][C]10[/C][C]-0.156986[/C][C]-1.6239[/C][C]0.053672[/C][/ROW]
[ROW][C]11[/C][C]-0.098287[/C][C]-1.0167[/C][C]0.155798[/C][/ROW]
[ROW][C]12[/C][C]0.078042[/C][C]0.8073[/C][C]0.210651[/C][/ROW]
[ROW][C]13[/C][C]0.00487[/C][C]0.0504[/C][C]0.47996[/C][/ROW]
[ROW][C]14[/C][C]-0.098852[/C][C]-1.0225[/C][C]0.154417[/C][/ROW]
[ROW][C]15[/C][C]-0.052723[/C][C]-0.5454[/C][C]0.293318[/C][/ROW]
[ROW][C]16[/C][C]-0.22743[/C][C]-2.3526[/C][C]0.010237[/C][/ROW]
[ROW][C]17[/C][C]0.161335[/C][C]1.6689[/C][C]0.049035[/C][/ROW]
[ROW][C]18[/C][C]-0.118716[/C][C]-1.228[/C][C]0.111069[/C][/ROW]
[ROW][C]19[/C][C]-0.027449[/C][C]-0.2839[/C][C]0.388504[/C][/ROW]
[ROW][C]20[/C][C]-0.062887[/C][C]-0.6505[/C][C]0.258378[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287744&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287744&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	0.24224	2.5057	0.006863
2	0.14693	1.5199	0.065748
3	0.250931	2.5956	0.005383
4	0.058178	0.6018	0.274291
5	-0.111434	-1.1527	0.125804
6	-0.166139	-1.7186	0.044294
7	0.143134	1.4806	0.070828
8	-0.000836	-0.0086	0.496558
9	0.048865	0.5055	0.307138
10	-0.156986	-1.6239	0.053672
11	-0.098287	-1.0167	0.155798
12	0.078042	0.8073	0.210651
13	0.00487	0.0504	0.47996
14	-0.098852	-1.0225	0.154417
15	-0.052723	-0.5454	0.293318
16	-0.22743	-2.3526	0.010237
17	0.161335	1.6689	0.049035
18	-0.118716	-1.228	0.111069
19	-0.027449	-0.2839	0.388504
20	-0.062887	-0.6505	0.258378

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 = grey ; par2 = no ;

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)
x <- na.omit(x)
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