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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 28 May 2016 18:39:01 +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/2016/May/28/t1464457193js01et4kdlpuz2r.htm/, Retrieved Fri, 03 May 2024 05:45:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295645, Retrieved Fri, 03 May 2024 05:45:01 +0000

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Estimated Impact

111

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

-     [(Partial) Autocorrelation Function] [Opgave 7 eigen reeks] [2016-03-15 22:15:59] [29ab9c45344d5c037bf74b62f65f8e78]
- R PD    [(Partial) Autocorrelation Function] [Opgave 7 eigen re...] [2016-05-28 17:39:01] [0996086de175370e0a22efa864593ca4] [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=295645&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=295645&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295645&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	0.055623	0.4272	0.335378
2	-0.233141	-1.7908	0.039229
3	-0.389091	-2.9887	0.00204
4	-0.031455	-0.2416	0.404959
5	0.236926	1.8199	0.036927
6	0.08494	0.6524	0.258327
7	0.122479	0.9408	0.175326
8	-0.094384	-0.725	0.235666
9	-0.299401	-2.2997	0.012509
10	-0.223797	-1.719	0.045427
11	0.093728	0.7199	0.237203
12	0.271876	2.0883	0.020547
13	0.124848	0.959	0.170743
14	-0.180068	-1.3831	0.085919
15	-0.163927	-1.2591	0.106468
16	-0.105147	-0.8076	0.211269
17	0.079313	0.6092	0.27236

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.055623 & 0.4272 & 0.335378 \tabularnewline
2 & -0.233141 & -1.7908 & 0.039229 \tabularnewline
3 & -0.389091 & -2.9887 & 0.00204 \tabularnewline
4 & -0.031455 & -0.2416 & 0.404959 \tabularnewline
5 & 0.236926 & 1.8199 & 0.036927 \tabularnewline
6 & 0.08494 & 0.6524 & 0.258327 \tabularnewline
7 & 0.122479 & 0.9408 & 0.175326 \tabularnewline
8 & -0.094384 & -0.725 & 0.235666 \tabularnewline
9 & -0.299401 & -2.2997 & 0.012509 \tabularnewline
10 & -0.223797 & -1.719 & 0.045427 \tabularnewline
11 & 0.093728 & 0.7199 & 0.237203 \tabularnewline
12 & 0.271876 & 2.0883 & 0.020547 \tabularnewline
13 & 0.124848 & 0.959 & 0.170743 \tabularnewline
14 & -0.180068 & -1.3831 & 0.085919 \tabularnewline
15 & -0.163927 & -1.2591 & 0.106468 \tabularnewline
16 & -0.105147 & -0.8076 & 0.211269 \tabularnewline
17 & 0.079313 & 0.6092 & 0.27236 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295645&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]0.055623[/C][C]0.4272[/C][C]0.335378[/C][/ROW]
[ROW][C]2[/C][C]-0.233141[/C][C]-1.7908[/C][C]0.039229[/C][/ROW]
[ROW][C]3[/C][C]-0.389091[/C][C]-2.9887[/C][C]0.00204[/C][/ROW]
[ROW][C]4[/C][C]-0.031455[/C][C]-0.2416[/C][C]0.404959[/C][/ROW]
[ROW][C]5[/C][C]0.236926[/C][C]1.8199[/C][C]0.036927[/C][/ROW]
[ROW][C]6[/C][C]0.08494[/C][C]0.6524[/C][C]0.258327[/C][/ROW]
[ROW][C]7[/C][C]0.122479[/C][C]0.9408[/C][C]0.175326[/C][/ROW]
[ROW][C]8[/C][C]-0.094384[/C][C]-0.725[/C][C]0.235666[/C][/ROW]
[ROW][C]9[/C][C]-0.299401[/C][C]-2.2997[/C][C]0.012509[/C][/ROW]
[ROW][C]10[/C][C]-0.223797[/C][C]-1.719[/C][C]0.045427[/C][/ROW]
[ROW][C]11[/C][C]0.093728[/C][C]0.7199[/C][C]0.237203[/C][/ROW]
[ROW][C]12[/C][C]0.271876[/C][C]2.0883[/C][C]0.020547[/C][/ROW]
[ROW][C]13[/C][C]0.124848[/C][C]0.959[/C][C]0.170743[/C][/ROW]
[ROW][C]14[/C][C]-0.180068[/C][C]-1.3831[/C][C]0.085919[/C][/ROW]
[ROW][C]15[/C][C]-0.163927[/C][C]-1.2591[/C][C]0.106468[/C][/ROW]
[ROW][C]16[/C][C]-0.105147[/C][C]-0.8076[/C][C]0.211269[/C][/ROW]
[ROW][C]17[/C][C]0.079313[/C][C]0.6092[/C][C]0.27236[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295645&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295645&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	0.055623	0.4272	0.335378
2	-0.233141	-1.7908	0.039229
3	-0.389091	-2.9887	0.00204
4	-0.031455	-0.2416	0.404959
5	0.236926	1.8199	0.036927
6	0.08494	0.6524	0.258327
7	0.122479	0.9408	0.175326
8	-0.094384	-0.725	0.235666
9	-0.299401	-2.2997	0.012509
10	-0.223797	-1.719	0.045427
11	0.093728	0.7199	0.237203
12	0.271876	2.0883	0.020547
13	0.124848	0.959	0.170743
14	-0.180068	-1.3831	0.085919
15	-0.163927	-1.2591	0.106468
16	-0.105147	-0.8076	0.211269
17	0.079313	0.6092	0.27236

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.055623	0.4272	0.335378
2	-0.236968	-1.8202	0.036902
3	-0.382463	-2.9378	0.002355
4	-0.084386	-0.6482	0.25969
5	0.077035	0.5917	0.27815
6	-0.095488	-0.7335	0.233092
7	0.185583	1.4255	0.079642
8	0.038718	0.2974	0.383603
9	-0.294176	-2.2596	0.013776
10	-0.228976	-1.7588	0.041899
11	-0.045846	-0.3521	0.362991
12	-0.081575	-0.6266	0.266673
13	-0.007932	-0.0609	0.47581
14	-0.051289	-0.394	0.347517
15	-0.025721	-0.1976	0.422033
16	-0.126108	-0.9687	0.168336
17	-0.081526	-0.6262	0.266794

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.055623 & 0.4272 & 0.335378 \tabularnewline
2 & -0.236968 & -1.8202 & 0.036902 \tabularnewline
3 & -0.382463 & -2.9378 & 0.002355 \tabularnewline
4 & -0.084386 & -0.6482 & 0.25969 \tabularnewline
5 & 0.077035 & 0.5917 & 0.27815 \tabularnewline
6 & -0.095488 & -0.7335 & 0.233092 \tabularnewline
7 & 0.185583 & 1.4255 & 0.079642 \tabularnewline
8 & 0.038718 & 0.2974 & 0.383603 \tabularnewline
9 & -0.294176 & -2.2596 & 0.013776 \tabularnewline
10 & -0.228976 & -1.7588 & 0.041899 \tabularnewline
11 & -0.045846 & -0.3521 & 0.362991 \tabularnewline
12 & -0.081575 & -0.6266 & 0.266673 \tabularnewline
13 & -0.007932 & -0.0609 & 0.47581 \tabularnewline
14 & -0.051289 & -0.394 & 0.347517 \tabularnewline
15 & -0.025721 & -0.1976 & 0.422033 \tabularnewline
16 & -0.126108 & -0.9687 & 0.168336 \tabularnewline
17 & -0.081526 & -0.6262 & 0.266794 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295645&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]0.055623[/C][C]0.4272[/C][C]0.335378[/C][/ROW]
[ROW][C]2[/C][C]-0.236968[/C][C]-1.8202[/C][C]0.036902[/C][/ROW]
[ROW][C]3[/C][C]-0.382463[/C][C]-2.9378[/C][C]0.002355[/C][/ROW]
[ROW][C]4[/C][C]-0.084386[/C][C]-0.6482[/C][C]0.25969[/C][/ROW]
[ROW][C]5[/C][C]0.077035[/C][C]0.5917[/C][C]0.27815[/C][/ROW]
[ROW][C]6[/C][C]-0.095488[/C][C]-0.7335[/C][C]0.233092[/C][/ROW]
[ROW][C]7[/C][C]0.185583[/C][C]1.4255[/C][C]0.079642[/C][/ROW]
[ROW][C]8[/C][C]0.038718[/C][C]0.2974[/C][C]0.383603[/C][/ROW]
[ROW][C]9[/C][C]-0.294176[/C][C]-2.2596[/C][C]0.013776[/C][/ROW]
[ROW][C]10[/C][C]-0.228976[/C][C]-1.7588[/C][C]0.041899[/C][/ROW]
[ROW][C]11[/C][C]-0.045846[/C][C]-0.3521[/C][C]0.362991[/C][/ROW]
[ROW][C]12[/C][C]-0.081575[/C][C]-0.6266[/C][C]0.266673[/C][/ROW]
[ROW][C]13[/C][C]-0.007932[/C][C]-0.0609[/C][C]0.47581[/C][/ROW]
[ROW][C]14[/C][C]-0.051289[/C][C]-0.394[/C][C]0.347517[/C][/ROW]
[ROW][C]15[/C][C]-0.025721[/C][C]-0.1976[/C][C]0.422033[/C][/ROW]
[ROW][C]16[/C][C]-0.126108[/C][C]-0.9687[/C][C]0.168336[/C][/ROW]
[ROW][C]17[/C][C]-0.081526[/C][C]-0.6262[/C][C]0.266794[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295645&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295645&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	0.055623	0.4272	0.335378
2	-0.236968	-1.8202	0.036902
3	-0.382463	-2.9378	0.002355
4	-0.084386	-0.6482	0.25969
5	0.077035	0.5917	0.27815
6	-0.095488	-0.7335	0.233092
7	0.185583	1.4255	0.079642
8	0.038718	0.2974	0.383603
9	-0.294176	-2.2596	0.013776
10	-0.228976	-1.7588	0.041899
11	-0.045846	-0.3521	0.362991
12	-0.081575	-0.6266	0.266673
13	-0.007932	-0.0609	0.47581
14	-0.051289	-0.394	0.347517
15	-0.025721	-0.1976	0.422033
16	-0.126108	-0.9687	0.168336
17	-0.081526	-0.6262	0.266794

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)
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')

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Input Parameters & R Code