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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 22 May 2015 17:27:29 +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/May/22/t1432312621xvygu2mzgypjxwq.htm/, Retrieved Fri, 03 May 2024 06:53:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279239, Retrieved Fri, 03 May 2024 06:53:33 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

118

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

-       [(Partial) Autocorrelation Function] [] [2015-05-22 16:27:29] [70e23d918d09c907c02097a361cd6415] [Current]

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Dataseries X:

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Histogram

Boxplots

3.5
4.8
6
5.9
3.6
6.8
8.7
8.4
8.1
8.9
8.7
7.8
6.3
7.5
6.8
7
8.8
8.4
7.6
7.9
7.4
8.7
8.7
8
9.4
8.5
5.8
2.8
3.3
4.8
1.8
4.8
-0.9
-6
-9
-21.1
-20.9
-23.5
-20.8
-17.3
-16.1
-13.9
-14.6
-9.2
-9.7
-7.2
-5
-8.1
-6.2
-4.8
-3.1
-1.4
0.6
-0.8
-2
0.2
-0.1
0.3
0.2
2.6
2.5
1.5
5.7
4.3
2.7
1.7
-2.2
-3.2
-0.5
-3.1
-4.8
-1.3
-1.8
-1.7
-2.8
-3.4
-4.9
-4.8
-5.4
-4.7
-6.6
-7.6
-6.8
-5.6
-5.6
-3.7
-5.1
-5.6
-4.1
-3.8
-3.1
-1.4
-2.4
-0.3
-0.3
0.1

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	'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279239&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279239&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279239&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.072566	0.7073	0.240561
2	0.204864	1.9968	0.024356
3	0.21852	2.1299	0.017883
4	-0.166769	-1.6255	0.053689
5	0.073433	0.7157	0.237954
6	-0.095079	-0.9267	0.178212
7	0.075886	0.7396	0.23067
8	-0.098796	-0.9629	0.169011
9	0.042682	0.416	0.339171
10	-0.000654	-0.0064	0.497463
11	-0.151124	-1.473	0.072032
12	0.108467	1.0572	0.146549
13	-0.163733	-1.5959	0.05692
14	-0.032558	-0.3173	0.375844
15	-0.093278	-0.9092	0.182784
16	-0.094515	-0.9212	0.179635
17	-0.064632	-0.63	0.265117
18	-0.11912	-1.161	0.124268
19	-0.016391	-0.1598	0.436707

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.072566 & 0.7073 & 0.240561 \tabularnewline
2 & 0.204864 & 1.9968 & 0.024356 \tabularnewline
3 & 0.21852 & 2.1299 & 0.017883 \tabularnewline
4 & -0.166769 & -1.6255 & 0.053689 \tabularnewline
5 & 0.073433 & 0.7157 & 0.237954 \tabularnewline
6 & -0.095079 & -0.9267 & 0.178212 \tabularnewline
7 & 0.075886 & 0.7396 & 0.23067 \tabularnewline
8 & -0.098796 & -0.9629 & 0.169011 \tabularnewline
9 & 0.042682 & 0.416 & 0.339171 \tabularnewline
10 & -0.000654 & -0.0064 & 0.497463 \tabularnewline
11 & -0.151124 & -1.473 & 0.072032 \tabularnewline
12 & 0.108467 & 1.0572 & 0.146549 \tabularnewline
13 & -0.163733 & -1.5959 & 0.05692 \tabularnewline
14 & -0.032558 & -0.3173 & 0.375844 \tabularnewline
15 & -0.093278 & -0.9092 & 0.182784 \tabularnewline
16 & -0.094515 & -0.9212 & 0.179635 \tabularnewline
17 & -0.064632 & -0.63 & 0.265117 \tabularnewline
18 & -0.11912 & -1.161 & 0.124268 \tabularnewline
19 & -0.016391 & -0.1598 & 0.436707 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279239&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]0.072566[/C][C]0.7073[/C][C]0.240561[/C][/ROW]
[ROW][C]2[/C][C]0.204864[/C][C]1.9968[/C][C]0.024356[/C][/ROW]
[ROW][C]3[/C][C]0.21852[/C][C]2.1299[/C][C]0.017883[/C][/ROW]
[ROW][C]4[/C][C]-0.166769[/C][C]-1.6255[/C][C]0.053689[/C][/ROW]
[ROW][C]5[/C][C]0.073433[/C][C]0.7157[/C][C]0.237954[/C][/ROW]
[ROW][C]6[/C][C]-0.095079[/C][C]-0.9267[/C][C]0.178212[/C][/ROW]
[ROW][C]7[/C][C]0.075886[/C][C]0.7396[/C][C]0.23067[/C][/ROW]
[ROW][C]8[/C][C]-0.098796[/C][C]-0.9629[/C][C]0.169011[/C][/ROW]
[ROW][C]9[/C][C]0.042682[/C][C]0.416[/C][C]0.339171[/C][/ROW]
[ROW][C]10[/C][C]-0.000654[/C][C]-0.0064[/C][C]0.497463[/C][/ROW]
[ROW][C]11[/C][C]-0.151124[/C][C]-1.473[/C][C]0.072032[/C][/ROW]
[ROW][C]12[/C][C]0.108467[/C][C]1.0572[/C][C]0.146549[/C][/ROW]
[ROW][C]13[/C][C]-0.163733[/C][C]-1.5959[/C][C]0.05692[/C][/ROW]
[ROW][C]14[/C][C]-0.032558[/C][C]-0.3173[/C][C]0.375844[/C][/ROW]
[ROW][C]15[/C][C]-0.093278[/C][C]-0.9092[/C][C]0.182784[/C][/ROW]
[ROW][C]16[/C][C]-0.094515[/C][C]-0.9212[/C][C]0.179635[/C][/ROW]
[ROW][C]17[/C][C]-0.064632[/C][C]-0.63[/C][C]0.265117[/C][/ROW]
[ROW][C]18[/C][C]-0.11912[/C][C]-1.161[/C][C]0.124268[/C][/ROW]
[ROW][C]19[/C][C]-0.016391[/C][C]-0.1598[/C][C]0.436707[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279239&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279239&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	0.072566	0.7073	0.240561
2	0.204864	1.9968	0.024356
3	0.21852	2.1299	0.017883
4	-0.166769	-1.6255	0.053689
5	0.073433	0.7157	0.237954
6	-0.095079	-0.9267	0.178212
7	0.075886	0.7396	0.23067
8	-0.098796	-0.9629	0.169011
9	0.042682	0.416	0.339171
10	-0.000654	-0.0064	0.497463
11	-0.151124	-1.473	0.072032
12	0.108467	1.0572	0.146549
13	-0.163733	-1.5959	0.05692
14	-0.032558	-0.3173	0.375844
15	-0.093278	-0.9092	0.182784
16	-0.094515	-0.9212	0.179635
17	-0.064632	-0.63	0.265117
18	-0.11912	-1.161	0.124268
19	-0.016391	-0.1598	0.436707

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.072566	0.7073	0.240561
2	0.200655	1.9557	0.026717
3	0.201193	1.961	0.026404
4	-0.244464	-2.3827	0.009588
5	0.010244	0.0998	0.460337
6	-0.065258	-0.6361	0.263134
7	0.180326	1.7576	0.041019
8	-0.168989	-1.6471	0.051421
9	0.087468	0.8525	0.19803
10	-0.074792	-0.729	0.233903
11	-0.052539	-0.5121	0.304888
12	0.03914	0.3815	0.351848
13	-0.075243	-0.7334	0.232566
14	-0.044243	-0.4312	0.333641
15	-0.114068	-1.1118	0.134516
16	0.020132	0.1962	0.422426
17	-0.086894	-0.8469	0.199579
18	-0.015301	-0.1491	0.440882
19	-0.08209	-0.8001	0.212821

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.072566 & 0.7073 & 0.240561 \tabularnewline
2 & 0.200655 & 1.9557 & 0.026717 \tabularnewline
3 & 0.201193 & 1.961 & 0.026404 \tabularnewline
4 & -0.244464 & -2.3827 & 0.009588 \tabularnewline
5 & 0.010244 & 0.0998 & 0.460337 \tabularnewline
6 & -0.065258 & -0.6361 & 0.263134 \tabularnewline
7 & 0.180326 & 1.7576 & 0.041019 \tabularnewline
8 & -0.168989 & -1.6471 & 0.051421 \tabularnewline
9 & 0.087468 & 0.8525 & 0.19803 \tabularnewline
10 & -0.074792 & -0.729 & 0.233903 \tabularnewline
11 & -0.052539 & -0.5121 & 0.304888 \tabularnewline
12 & 0.03914 & 0.3815 & 0.351848 \tabularnewline
13 & -0.075243 & -0.7334 & 0.232566 \tabularnewline
14 & -0.044243 & -0.4312 & 0.333641 \tabularnewline
15 & -0.114068 & -1.1118 & 0.134516 \tabularnewline
16 & 0.020132 & 0.1962 & 0.422426 \tabularnewline
17 & -0.086894 & -0.8469 & 0.199579 \tabularnewline
18 & -0.015301 & -0.1491 & 0.440882 \tabularnewline
19 & -0.08209 & -0.8001 & 0.212821 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279239&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]0.072566[/C][C]0.7073[/C][C]0.240561[/C][/ROW]
[ROW][C]2[/C][C]0.200655[/C][C]1.9557[/C][C]0.026717[/C][/ROW]
[ROW][C]3[/C][C]0.201193[/C][C]1.961[/C][C]0.026404[/C][/ROW]
[ROW][C]4[/C][C]-0.244464[/C][C]-2.3827[/C][C]0.009588[/C][/ROW]
[ROW][C]5[/C][C]0.010244[/C][C]0.0998[/C][C]0.460337[/C][/ROW]
[ROW][C]6[/C][C]-0.065258[/C][C]-0.6361[/C][C]0.263134[/C][/ROW]
[ROW][C]7[/C][C]0.180326[/C][C]1.7576[/C][C]0.041019[/C][/ROW]
[ROW][C]8[/C][C]-0.168989[/C][C]-1.6471[/C][C]0.051421[/C][/ROW]
[ROW][C]9[/C][C]0.087468[/C][C]0.8525[/C][C]0.19803[/C][/ROW]
[ROW][C]10[/C][C]-0.074792[/C][C]-0.729[/C][C]0.233903[/C][/ROW]
[ROW][C]11[/C][C]-0.052539[/C][C]-0.5121[/C][C]0.304888[/C][/ROW]
[ROW][C]12[/C][C]0.03914[/C][C]0.3815[/C][C]0.351848[/C][/ROW]
[ROW][C]13[/C][C]-0.075243[/C][C]-0.7334[/C][C]0.232566[/C][/ROW]
[ROW][C]14[/C][C]-0.044243[/C][C]-0.4312[/C][C]0.333641[/C][/ROW]
[ROW][C]15[/C][C]-0.114068[/C][C]-1.1118[/C][C]0.134516[/C][/ROW]
[ROW][C]16[/C][C]0.020132[/C][C]0.1962[/C][C]0.422426[/C][/ROW]
[ROW][C]17[/C][C]-0.086894[/C][C]-0.8469[/C][C]0.199579[/C][/ROW]
[ROW][C]18[/C][C]-0.015301[/C][C]-0.1491[/C][C]0.440882[/C][/ROW]
[ROW][C]19[/C][C]-0.08209[/C][C]-0.8001[/C][C]0.212821[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279239&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279239&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	0.072566	0.7073	0.240561
2	0.200655	1.9557	0.026717
3	0.201193	1.961	0.026404
4	-0.244464	-2.3827	0.009588
5	0.010244	0.0998	0.460337
6	-0.065258	-0.6361	0.263134
7	0.180326	1.7576	0.041019
8	-0.168989	-1.6471	0.051421
9	0.087468	0.8525	0.19803
10	-0.074792	-0.729	0.233903
11	-0.052539	-0.5121	0.304888
12	0.03914	0.3815	0.351848
13	-0.075243	-0.7334	0.232566
14	-0.044243	-0.4312	0.333641
15	-0.114068	-1.1118	0.134516
16	0.020132	0.1962	0.422426
17	-0.086894	-0.8469	0.199579
18	-0.015301	-0.1491	0.440882
19	-0.08209	-0.8001	0.212821

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 = 0.01 ; par2 = 0.09 ; par3 = 0.01 ;

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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code