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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 03 Dec 2012 14:59:54 -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/2012/Dec/03/t1354564821p1u8h7678kk26hj.htm/, Retrieved Sun, 05 May 2024 11:23:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=195998, Retrieved Sun, 05 May 2024 11:23:13 +0000

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User-defined keywords

Estimated Impact

108

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

-     [(Partial) Autocorrelation Function] [Workshop 9 - auto...] [2012-12-03 19:55:49] [c85dbc843174c8f40de92b1c92b5205a]
- R P   [(Partial) Autocorrelation Function] [Workshop 9 - auto...] [2012-12-03 19:57:39] [c85dbc843174c8f40de92b1c92b5205a]
-   P       [(Partial) Autocorrelation Function] [Workshop 9 - auto...] [2012-12-03 19:59:54] [729cfeb7382ca95684eaaf6b24800101] [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	'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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195998&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195998&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195998&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.057977	-0.6482	0.25902
2	-0.086913	-0.9717	0.166534
3	4.8e-05	5e-04	0.499788
4	-0.501803	-5.6103	0
5	-0.005554	-0.0621	0.475294
6	0.037979	0.4246	0.335921
7	0.198222	2.2162	0.014244
8	0.08584	0.9597	0.169524
9	-0.065037	-0.7271	0.234252
10	0.041043	0.4589	0.32356
11	-0.094699	-1.0588	0.145873
12	-0.102081	-1.1413	0.127963
13	0.116854	1.3065	0.096897
14	0.0077	0.0861	0.465766
15	-0.041986	-0.4694	0.319795
16	0.063658	0.7117	0.238982
17	-0.086438	-0.9664	0.167855
18	0.00962	0.1076	0.457259
19	0.024433	0.2732	0.392588
20	-0.029737	-0.3325	0.370046
21	0.077107	0.8621	0.195146

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.057977 & -0.6482 & 0.25902 \tabularnewline
2 & -0.086913 & -0.9717 & 0.166534 \tabularnewline
3 & 4.8e-05 & 5e-04 & 0.499788 \tabularnewline
4 & -0.501803 & -5.6103 & 0 \tabularnewline
5 & -0.005554 & -0.0621 & 0.475294 \tabularnewline
6 & 0.037979 & 0.4246 & 0.335921 \tabularnewline
7 & 0.198222 & 2.2162 & 0.014244 \tabularnewline
8 & 0.08584 & 0.9597 & 0.169524 \tabularnewline
9 & -0.065037 & -0.7271 & 0.234252 \tabularnewline
10 & 0.041043 & 0.4589 & 0.32356 \tabularnewline
11 & -0.094699 & -1.0588 & 0.145873 \tabularnewline
12 & -0.102081 & -1.1413 & 0.127963 \tabularnewline
13 & 0.116854 & 1.3065 & 0.096897 \tabularnewline
14 & 0.0077 & 0.0861 & 0.465766 \tabularnewline
15 & -0.041986 & -0.4694 & 0.319795 \tabularnewline
16 & 0.063658 & 0.7117 & 0.238982 \tabularnewline
17 & -0.086438 & -0.9664 & 0.167855 \tabularnewline
18 & 0.00962 & 0.1076 & 0.457259 \tabularnewline
19 & 0.024433 & 0.2732 & 0.392588 \tabularnewline
20 & -0.029737 & -0.3325 & 0.370046 \tabularnewline
21 & 0.077107 & 0.8621 & 0.195146 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195998&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]-0.057977[/C][C]-0.6482[/C][C]0.25902[/C][/ROW]
[ROW][C]2[/C][C]-0.086913[/C][C]-0.9717[/C][C]0.166534[/C][/ROW]
[ROW][C]3[/C][C]4.8e-05[/C][C]5e-04[/C][C]0.499788[/C][/ROW]
[ROW][C]4[/C][C]-0.501803[/C][C]-5.6103[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]-0.005554[/C][C]-0.0621[/C][C]0.475294[/C][/ROW]
[ROW][C]6[/C][C]0.037979[/C][C]0.4246[/C][C]0.335921[/C][/ROW]
[ROW][C]7[/C][C]0.198222[/C][C]2.2162[/C][C]0.014244[/C][/ROW]
[ROW][C]8[/C][C]0.08584[/C][C]0.9597[/C][C]0.169524[/C][/ROW]
[ROW][C]9[/C][C]-0.065037[/C][C]-0.7271[/C][C]0.234252[/C][/ROW]
[ROW][C]10[/C][C]0.041043[/C][C]0.4589[/C][C]0.32356[/C][/ROW]
[ROW][C]11[/C][C]-0.094699[/C][C]-1.0588[/C][C]0.145873[/C][/ROW]
[ROW][C]12[/C][C]-0.102081[/C][C]-1.1413[/C][C]0.127963[/C][/ROW]
[ROW][C]13[/C][C]0.116854[/C][C]1.3065[/C][C]0.096897[/C][/ROW]
[ROW][C]14[/C][C]0.0077[/C][C]0.0861[/C][C]0.465766[/C][/ROW]
[ROW][C]15[/C][C]-0.041986[/C][C]-0.4694[/C][C]0.319795[/C][/ROW]
[ROW][C]16[/C][C]0.063658[/C][C]0.7117[/C][C]0.238982[/C][/ROW]
[ROW][C]17[/C][C]-0.086438[/C][C]-0.9664[/C][C]0.167855[/C][/ROW]
[ROW][C]18[/C][C]0.00962[/C][C]0.1076[/C][C]0.457259[/C][/ROW]
[ROW][C]19[/C][C]0.024433[/C][C]0.2732[/C][C]0.392588[/C][/ROW]
[ROW][C]20[/C][C]-0.029737[/C][C]-0.3325[/C][C]0.370046[/C][/ROW]
[ROW][C]21[/C][C]0.077107[/C][C]0.8621[/C][C]0.195146[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195998&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195998&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	-0.057977	-0.6482	0.25902
2	-0.086913	-0.9717	0.166534
3	4.8e-05	5e-04	0.499788
4	-0.501803	-5.6103	0
5	-0.005554	-0.0621	0.475294
6	0.037979	0.4246	0.335921
7	0.198222	2.2162	0.014244
8	0.08584	0.9597	0.169524
9	-0.065037	-0.7271	0.234252
10	0.041043	0.4589	0.32356
11	-0.094699	-1.0588	0.145873
12	-0.102081	-1.1413	0.127963
13	0.116854	1.3065	0.096897
14	0.0077	0.0861	0.465766
15	-0.041986	-0.4694	0.319795
16	0.063658	0.7117	0.238982
17	-0.086438	-0.9664	0.167855
18	0.00962	0.1076	0.457259
19	0.024433	0.2732	0.392588
20	-0.029737	-0.3325	0.370046
21	0.077107	0.8621	0.195146

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.057977	-0.6482	0.25902
2	-0.090579	-1.0127	0.156579
3	-0.010824	-0.121	0.451936
4	-0.516378	-5.7733	0
5	-0.102556	-1.1466	0.126867
6	-0.119712	-1.3384	0.091595
7	0.215611	2.4106	0.008691
8	-0.215113	-2.405	0.008818
9	-0.080522	-0.9003	0.184854
10	-0.026304	-0.2941	0.38459
11	0.1658	1.8537	0.03307
12	-0.196453	-2.1964	0.014953
13	0.082274	0.9199	0.179711
14	-0.064714	-0.7235	0.235356
15	0.073559	0.8224	0.206204
16	-0.113507	-1.269	0.103392
17	-0.009588	-0.1072	0.457401
18	-0.023532	-0.2631	0.396456
19	0.07244	0.8099	0.209767
20	-0.13088	-1.4633	0.07295
21	0.058109	0.6497	0.258547

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.057977 & -0.6482 & 0.25902 \tabularnewline
2 & -0.090579 & -1.0127 & 0.156579 \tabularnewline
3 & -0.010824 & -0.121 & 0.451936 \tabularnewline
4 & -0.516378 & -5.7733 & 0 \tabularnewline
5 & -0.102556 & -1.1466 & 0.126867 \tabularnewline
6 & -0.119712 & -1.3384 & 0.091595 \tabularnewline
7 & 0.215611 & 2.4106 & 0.008691 \tabularnewline
8 & -0.215113 & -2.405 & 0.008818 \tabularnewline
9 & -0.080522 & -0.9003 & 0.184854 \tabularnewline
10 & -0.026304 & -0.2941 & 0.38459 \tabularnewline
11 & 0.1658 & 1.8537 & 0.03307 \tabularnewline
12 & -0.196453 & -2.1964 & 0.014953 \tabularnewline
13 & 0.082274 & 0.9199 & 0.179711 \tabularnewline
14 & -0.064714 & -0.7235 & 0.235356 \tabularnewline
15 & 0.073559 & 0.8224 & 0.206204 \tabularnewline
16 & -0.113507 & -1.269 & 0.103392 \tabularnewline
17 & -0.009588 & -0.1072 & 0.457401 \tabularnewline
18 & -0.023532 & -0.2631 & 0.396456 \tabularnewline
19 & 0.07244 & 0.8099 & 0.209767 \tabularnewline
20 & -0.13088 & -1.4633 & 0.07295 \tabularnewline
21 & 0.058109 & 0.6497 & 0.258547 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195998&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]-0.057977[/C][C]-0.6482[/C][C]0.25902[/C][/ROW]
[ROW][C]2[/C][C]-0.090579[/C][C]-1.0127[/C][C]0.156579[/C][/ROW]
[ROW][C]3[/C][C]-0.010824[/C][C]-0.121[/C][C]0.451936[/C][/ROW]
[ROW][C]4[/C][C]-0.516378[/C][C]-5.7733[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]-0.102556[/C][C]-1.1466[/C][C]0.126867[/C][/ROW]
[ROW][C]6[/C][C]-0.119712[/C][C]-1.3384[/C][C]0.091595[/C][/ROW]
[ROW][C]7[/C][C]0.215611[/C][C]2.4106[/C][C]0.008691[/C][/ROW]
[ROW][C]8[/C][C]-0.215113[/C][C]-2.405[/C][C]0.008818[/C][/ROW]
[ROW][C]9[/C][C]-0.080522[/C][C]-0.9003[/C][C]0.184854[/C][/ROW]
[ROW][C]10[/C][C]-0.026304[/C][C]-0.2941[/C][C]0.38459[/C][/ROW]
[ROW][C]11[/C][C]0.1658[/C][C]1.8537[/C][C]0.03307[/C][/ROW]
[ROW][C]12[/C][C]-0.196453[/C][C]-2.1964[/C][C]0.014953[/C][/ROW]
[ROW][C]13[/C][C]0.082274[/C][C]0.9199[/C][C]0.179711[/C][/ROW]
[ROW][C]14[/C][C]-0.064714[/C][C]-0.7235[/C][C]0.235356[/C][/ROW]
[ROW][C]15[/C][C]0.073559[/C][C]0.8224[/C][C]0.206204[/C][/ROW]
[ROW][C]16[/C][C]-0.113507[/C][C]-1.269[/C][C]0.103392[/C][/ROW]
[ROW][C]17[/C][C]-0.009588[/C][C]-0.1072[/C][C]0.457401[/C][/ROW]
[ROW][C]18[/C][C]-0.023532[/C][C]-0.2631[/C][C]0.396456[/C][/ROW]
[ROW][C]19[/C][C]0.07244[/C][C]0.8099[/C][C]0.209767[/C][/ROW]
[ROW][C]20[/C][C]-0.13088[/C][C]-1.4633[/C][C]0.07295[/C][/ROW]
[ROW][C]21[/C][C]0.058109[/C][C]0.6497[/C][C]0.258547[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195998&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195998&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	-0.057977	-0.6482	0.25902
2	-0.090579	-1.0127	0.156579
3	-0.010824	-0.121	0.451936
4	-0.516378	-5.7733	0
5	-0.102556	-1.1466	0.126867
6	-0.119712	-1.3384	0.091595
7	0.215611	2.4106	0.008691
8	-0.215113	-2.405	0.008818
9	-0.080522	-0.9003	0.184854
10	-0.026304	-0.2941	0.38459
11	0.1658	1.8537	0.03307
12	-0.196453	-2.1964	0.014953
13	0.082274	0.9199	0.179711
14	-0.064714	-0.7235	0.235356
15	0.073559	0.8224	0.206204
16	-0.113507	-1.269	0.103392
17	-0.009588	-0.1072	0.457401
18	-0.023532	-0.2631	0.396456
19	0.07244	0.8099	0.209767
20	-0.13088	-1.4633	0.07295
21	0.058109	0.6497	0.258547

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 = 1 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; 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