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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 20 Nov 2013 19:15:54 -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/2013/Nov/20/t1384993001hhfc2o6257pmc4h.htm/, Retrieved Wed, 01 May 2024 13:19:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=226752, Retrieved Wed, 01 May 2024 13:19:06 +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] [] [2013-11-21 00:15:54] [da6056b86d6cc6ac74ca244744435ec9] [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	'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226752&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226752&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226752&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	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.133994	-1.2207	0.11282
2	-0.445606	-4.0597	5.5e-05
3	0.065327	0.5952	0.27668
4	0.316906	2.8872	0.002477
5	-0.057391	-0.5229	0.301232
6	-0.258014	-2.3506	0.010557
7	-0.056039	-0.5105	0.305514
8	0.273041	2.4875	0.007433
9	0.079734	0.7264	0.234815
10	-0.506342	-4.613	7e-06
11	-0.017627	-0.1606	0.436403
12	0.648086	5.9043	0
13	-0.10806	-0.9845	0.163871
14	-0.303446	-2.7645	0.003511
15	-0.007776	-0.0708	0.471846
16	0.266256	2.4257	0.008723
17	-0.029713	-0.2707	0.393646
18	-0.140698	-1.2818	0.101737
19	-0.110786	-1.0093	0.15788

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.133994 & -1.2207 & 0.11282 \tabularnewline
2 & -0.445606 & -4.0597 & 5.5e-05 \tabularnewline
3 & 0.065327 & 0.5952 & 0.27668 \tabularnewline
4 & 0.316906 & 2.8872 & 0.002477 \tabularnewline
5 & -0.057391 & -0.5229 & 0.301232 \tabularnewline
6 & -0.258014 & -2.3506 & 0.010557 \tabularnewline
7 & -0.056039 & -0.5105 & 0.305514 \tabularnewline
8 & 0.273041 & 2.4875 & 0.007433 \tabularnewline
9 & 0.079734 & 0.7264 & 0.234815 \tabularnewline
10 & -0.506342 & -4.613 & 7e-06 \tabularnewline
11 & -0.017627 & -0.1606 & 0.436403 \tabularnewline
12 & 0.648086 & 5.9043 & 0 \tabularnewline
13 & -0.10806 & -0.9845 & 0.163871 \tabularnewline
14 & -0.303446 & -2.7645 & 0.003511 \tabularnewline
15 & -0.007776 & -0.0708 & 0.471846 \tabularnewline
16 & 0.266256 & 2.4257 & 0.008723 \tabularnewline
17 & -0.029713 & -0.2707 & 0.393646 \tabularnewline
18 & -0.140698 & -1.2818 & 0.101737 \tabularnewline
19 & -0.110786 & -1.0093 & 0.15788 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226752&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]-0.133994[/C][C]-1.2207[/C][C]0.11282[/C][/ROW]
[ROW][C]2[/C][C]-0.445606[/C][C]-4.0597[/C][C]5.5e-05[/C][/ROW]
[ROW][C]3[/C][C]0.065327[/C][C]0.5952[/C][C]0.27668[/C][/ROW]
[ROW][C]4[/C][C]0.316906[/C][C]2.8872[/C][C]0.002477[/C][/ROW]
[ROW][C]5[/C][C]-0.057391[/C][C]-0.5229[/C][C]0.301232[/C][/ROW]
[ROW][C]6[/C][C]-0.258014[/C][C]-2.3506[/C][C]0.010557[/C][/ROW]
[ROW][C]7[/C][C]-0.056039[/C][C]-0.5105[/C][C]0.305514[/C][/ROW]
[ROW][C]8[/C][C]0.273041[/C][C]2.4875[/C][C]0.007433[/C][/ROW]
[ROW][C]9[/C][C]0.079734[/C][C]0.7264[/C][C]0.234815[/C][/ROW]
[ROW][C]10[/C][C]-0.506342[/C][C]-4.613[/C][C]7e-06[/C][/ROW]
[ROW][C]11[/C][C]-0.017627[/C][C]-0.1606[/C][C]0.436403[/C][/ROW]
[ROW][C]12[/C][C]0.648086[/C][C]5.9043[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.10806[/C][C]-0.9845[/C][C]0.163871[/C][/ROW]
[ROW][C]14[/C][C]-0.303446[/C][C]-2.7645[/C][C]0.003511[/C][/ROW]
[ROW][C]15[/C][C]-0.007776[/C][C]-0.0708[/C][C]0.471846[/C][/ROW]
[ROW][C]16[/C][C]0.266256[/C][C]2.4257[/C][C]0.008723[/C][/ROW]
[ROW][C]17[/C][C]-0.029713[/C][C]-0.2707[/C][C]0.393646[/C][/ROW]
[ROW][C]18[/C][C]-0.140698[/C][C]-1.2818[/C][C]0.101737[/C][/ROW]
[ROW][C]19[/C][C]-0.110786[/C][C]-1.0093[/C][C]0.15788[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226752&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226752&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	-0.133994	-1.2207	0.11282
2	-0.445606	-4.0597	5.5e-05
3	0.065327	0.5952	0.27668
4	0.316906	2.8872	0.002477
5	-0.057391	-0.5229	0.301232
6	-0.258014	-2.3506	0.010557
7	-0.056039	-0.5105	0.305514
8	0.273041	2.4875	0.007433
9	0.079734	0.7264	0.234815
10	-0.506342	-4.613	7e-06
11	-0.017627	-0.1606	0.436403
12	0.648086	5.9043	0
13	-0.10806	-0.9845	0.163871
14	-0.303446	-2.7645	0.003511
15	-0.007776	-0.0708	0.471846
16	0.266256	2.4257	0.008723
17	-0.029713	-0.2707	0.393646
18	-0.140698	-1.2818	0.101737
19	-0.110786	-1.0093	0.15788

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.133994	-1.2207	0.11282
2	-0.472035	-4.3004	2.3e-05
3	-0.112438	-1.0244	0.15432
4	0.130004	1.1844	0.119818
5	0.036728	0.3346	0.369382
6	-0.088654	-0.8077	0.210793
7	-0.177826	-1.6201	0.054505
8	0.060854	0.5544	0.290396
9	0.106871	0.9736	0.166532
10	-0.38724	-3.5279	0.000343
11	-0.161933	-1.4753	0.07196
12	0.430748	3.9243	8.9e-05
13	0.036372	0.3314	0.370603
14	0.184982	1.6853	0.047847
15	-0.105551	-0.9616	0.169517
16	-0.068671	-0.6256	0.266638
17	-0.058076	-0.5291	0.299075
18	0.130559	1.1895	0.118827
19	-0.009318	-0.0849	0.466277

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.133994 & -1.2207 & 0.11282 \tabularnewline
2 & -0.472035 & -4.3004 & 2.3e-05 \tabularnewline
3 & -0.112438 & -1.0244 & 0.15432 \tabularnewline
4 & 0.130004 & 1.1844 & 0.119818 \tabularnewline
5 & 0.036728 & 0.3346 & 0.369382 \tabularnewline
6 & -0.088654 & -0.8077 & 0.210793 \tabularnewline
7 & -0.177826 & -1.6201 & 0.054505 \tabularnewline
8 & 0.060854 & 0.5544 & 0.290396 \tabularnewline
9 & 0.106871 & 0.9736 & 0.166532 \tabularnewline
10 & -0.38724 & -3.5279 & 0.000343 \tabularnewline
11 & -0.161933 & -1.4753 & 0.07196 \tabularnewline
12 & 0.430748 & 3.9243 & 8.9e-05 \tabularnewline
13 & 0.036372 & 0.3314 & 0.370603 \tabularnewline
14 & 0.184982 & 1.6853 & 0.047847 \tabularnewline
15 & -0.105551 & -0.9616 & 0.169517 \tabularnewline
16 & -0.068671 & -0.6256 & 0.266638 \tabularnewline
17 & -0.058076 & -0.5291 & 0.299075 \tabularnewline
18 & 0.130559 & 1.1895 & 0.118827 \tabularnewline
19 & -0.009318 & -0.0849 & 0.466277 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226752&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]-0.133994[/C][C]-1.2207[/C][C]0.11282[/C][/ROW]
[ROW][C]2[/C][C]-0.472035[/C][C]-4.3004[/C][C]2.3e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.112438[/C][C]-1.0244[/C][C]0.15432[/C][/ROW]
[ROW][C]4[/C][C]0.130004[/C][C]1.1844[/C][C]0.119818[/C][/ROW]
[ROW][C]5[/C][C]0.036728[/C][C]0.3346[/C][C]0.369382[/C][/ROW]
[ROW][C]6[/C][C]-0.088654[/C][C]-0.8077[/C][C]0.210793[/C][/ROW]
[ROW][C]7[/C][C]-0.177826[/C][C]-1.6201[/C][C]0.054505[/C][/ROW]
[ROW][C]8[/C][C]0.060854[/C][C]0.5544[/C][C]0.290396[/C][/ROW]
[ROW][C]9[/C][C]0.106871[/C][C]0.9736[/C][C]0.166532[/C][/ROW]
[ROW][C]10[/C][C]-0.38724[/C][C]-3.5279[/C][C]0.000343[/C][/ROW]
[ROW][C]11[/C][C]-0.161933[/C][C]-1.4753[/C][C]0.07196[/C][/ROW]
[ROW][C]12[/C][C]0.430748[/C][C]3.9243[/C][C]8.9e-05[/C][/ROW]
[ROW][C]13[/C][C]0.036372[/C][C]0.3314[/C][C]0.370603[/C][/ROW]
[ROW][C]14[/C][C]0.184982[/C][C]1.6853[/C][C]0.047847[/C][/ROW]
[ROW][C]15[/C][C]-0.105551[/C][C]-0.9616[/C][C]0.169517[/C][/ROW]
[ROW][C]16[/C][C]-0.068671[/C][C]-0.6256[/C][C]0.266638[/C][/ROW]
[ROW][C]17[/C][C]-0.058076[/C][C]-0.5291[/C][C]0.299075[/C][/ROW]
[ROW][C]18[/C][C]0.130559[/C][C]1.1895[/C][C]0.118827[/C][/ROW]
[ROW][C]19[/C][C]-0.009318[/C][C]-0.0849[/C][C]0.466277[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226752&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226752&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	-0.133994	-1.2207	0.11282
2	-0.472035	-4.3004	2.3e-05
3	-0.112438	-1.0244	0.15432
4	0.130004	1.1844	0.119818
5	0.036728	0.3346	0.369382
6	-0.088654	-0.8077	0.210793
7	-0.177826	-1.6201	0.054505
8	0.060854	0.5544	0.290396
9	0.106871	0.9736	0.166532
10	-0.38724	-3.5279	0.000343
11	-0.161933	-1.4753	0.07196
12	0.430748	3.9243	8.9e-05
13	0.036372	0.3314	0.370603
14	0.184982	1.6853	0.047847
15	-0.105551	-0.9616	0.169517
16	-0.068671	-0.6256	0.266638
17	-0.058076	-0.5291	0.299075
18	0.130559	1.1895	0.118827
19	-0.009318	-0.0849	0.466277

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)
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