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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 05 Dec 2011 12:55:48 -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/2011/Dec/05/t1323107807r29vksw49w3h01n.htm/, Retrieved Fri, 03 May 2024 13:27:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151121, Retrieved Fri, 03 May 2024 13:27:28 +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] [Aantal niet-werke...] [2011-12-05 17:55:48] [4352eab26b4a512b718de67a19830b91] [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=151121&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=151121&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151121&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	0.169752	1.8595	0.0327
2	0.149108	1.6334	0.052503
3	0.105324	1.1538	0.125443
4	0.112541	1.2328	0.110025
5	0.111375	1.2201	0.112418
6	0.135242	1.4815	0.070547
7	0.060536	0.6631	0.254257
8	0.12724	1.3938	0.08297
9	0.147544	1.6163	0.054331
10	-0.089994	-0.9858	0.163098
11	0.06042	0.6619	0.254662
12	-0.267942	-2.9352	0.001998
13	-0.066658	-0.7302	0.233343
14	0.093537	1.0246	0.153796
15	0.006433	0.0705	0.471969
16	-0.067503	-0.7395	0.230537
17	-0.096193	-1.0537	0.147059
18	-0.070996	-0.7777	0.219133
19	-0.069631	-0.7628	0.223548
20	-0.079873	-0.875	0.191672
21	-0.198469	-2.1741	0.015829

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.169752 & 1.8595 & 0.0327 \tabularnewline
2 & 0.149108 & 1.6334 & 0.052503 \tabularnewline
3 & 0.105324 & 1.1538 & 0.125443 \tabularnewline
4 & 0.112541 & 1.2328 & 0.110025 \tabularnewline
5 & 0.111375 & 1.2201 & 0.112418 \tabularnewline
6 & 0.135242 & 1.4815 & 0.070547 \tabularnewline
7 & 0.060536 & 0.6631 & 0.254257 \tabularnewline
8 & 0.12724 & 1.3938 & 0.08297 \tabularnewline
9 & 0.147544 & 1.6163 & 0.054331 \tabularnewline
10 & -0.089994 & -0.9858 & 0.163098 \tabularnewline
11 & 0.06042 & 0.6619 & 0.254662 \tabularnewline
12 & -0.267942 & -2.9352 & 0.001998 \tabularnewline
13 & -0.066658 & -0.7302 & 0.233343 \tabularnewline
14 & 0.093537 & 1.0246 & 0.153796 \tabularnewline
15 & 0.006433 & 0.0705 & 0.471969 \tabularnewline
16 & -0.067503 & -0.7395 & 0.230537 \tabularnewline
17 & -0.096193 & -1.0537 & 0.147059 \tabularnewline
18 & -0.070996 & -0.7777 & 0.219133 \tabularnewline
19 & -0.069631 & -0.7628 & 0.223548 \tabularnewline
20 & -0.079873 & -0.875 & 0.191672 \tabularnewline
21 & -0.198469 & -2.1741 & 0.015829 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151121&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]0.169752[/C][C]1.8595[/C][C]0.0327[/C][/ROW]
[ROW][C]2[/C][C]0.149108[/C][C]1.6334[/C][C]0.052503[/C][/ROW]
[ROW][C]3[/C][C]0.105324[/C][C]1.1538[/C][C]0.125443[/C][/ROW]
[ROW][C]4[/C][C]0.112541[/C][C]1.2328[/C][C]0.110025[/C][/ROW]
[ROW][C]5[/C][C]0.111375[/C][C]1.2201[/C][C]0.112418[/C][/ROW]
[ROW][C]6[/C][C]0.135242[/C][C]1.4815[/C][C]0.070547[/C][/ROW]
[ROW][C]7[/C][C]0.060536[/C][C]0.6631[/C][C]0.254257[/C][/ROW]
[ROW][C]8[/C][C]0.12724[/C][C]1.3938[/C][C]0.08297[/C][/ROW]
[ROW][C]9[/C][C]0.147544[/C][C]1.6163[/C][C]0.054331[/C][/ROW]
[ROW][C]10[/C][C]-0.089994[/C][C]-0.9858[/C][C]0.163098[/C][/ROW]
[ROW][C]11[/C][C]0.06042[/C][C]0.6619[/C][C]0.254662[/C][/ROW]
[ROW][C]12[/C][C]-0.267942[/C][C]-2.9352[/C][C]0.001998[/C][/ROW]
[ROW][C]13[/C][C]-0.066658[/C][C]-0.7302[/C][C]0.233343[/C][/ROW]
[ROW][C]14[/C][C]0.093537[/C][C]1.0246[/C][C]0.153796[/C][/ROW]
[ROW][C]15[/C][C]0.006433[/C][C]0.0705[/C][C]0.471969[/C][/ROW]
[ROW][C]16[/C][C]-0.067503[/C][C]-0.7395[/C][C]0.230537[/C][/ROW]
[ROW][C]17[/C][C]-0.096193[/C][C]-1.0537[/C][C]0.147059[/C][/ROW]
[ROW][C]18[/C][C]-0.070996[/C][C]-0.7777[/C][C]0.219133[/C][/ROW]
[ROW][C]19[/C][C]-0.069631[/C][C]-0.7628[/C][C]0.223548[/C][/ROW]
[ROW][C]20[/C][C]-0.079873[/C][C]-0.875[/C][C]0.191672[/C][/ROW]
[ROW][C]21[/C][C]-0.198469[/C][C]-2.1741[/C][C]0.015829[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151121&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151121&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	0.169752	1.8595	0.0327
2	0.149108	1.6334	0.052503
3	0.105324	1.1538	0.125443
4	0.112541	1.2328	0.110025
5	0.111375	1.2201	0.112418
6	0.135242	1.4815	0.070547
7	0.060536	0.6631	0.254257
8	0.12724	1.3938	0.08297
9	0.147544	1.6163	0.054331
10	-0.089994	-0.9858	0.163098
11	0.06042	0.6619	0.254662
12	-0.267942	-2.9352	0.001998
13	-0.066658	-0.7302	0.233343
14	0.093537	1.0246	0.153796
15	0.006433	0.0705	0.471969
16	-0.067503	-0.7395	0.230537
17	-0.096193	-1.0537	0.147059
18	-0.070996	-0.7777	0.219133
19	-0.069631	-0.7628	0.223548
20	-0.079873	-0.875	0.191672
21	-0.198469	-2.1741	0.015829

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.169752	1.8595	0.0327
2	0.123862	1.3568	0.08869
3	0.064962	0.7116	0.239039
4	0.073162	0.8015	0.212227
5	0.06795	0.7444	0.229059
6	0.088139	0.9655	0.168113
7	-0.001221	-0.0134	0.494677
8	0.081972	0.898	0.185502
9	0.095483	1.046	0.14884
10	-0.179614	-1.9676	0.025712
11	0.043511	0.4766	0.317245
12	-0.328802	-3.6018	0.00023
13	-0.01743	-0.1909	0.424447
14	0.162044	1.7751	0.039208
15	-0.007697	-0.0843	0.466474
16	-0.030111	-0.3299	0.371044
17	-0.103211	-1.1306	0.130235
18	0.025898	0.2837	0.388565
19	-0.010053	-0.1101	0.456245
20	-0.049446	-0.5417	0.29453
21	-0.06436	-0.705	0.241078

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.169752 & 1.8595 & 0.0327 \tabularnewline
2 & 0.123862 & 1.3568 & 0.08869 \tabularnewline
3 & 0.064962 & 0.7116 & 0.239039 \tabularnewline
4 & 0.073162 & 0.8015 & 0.212227 \tabularnewline
5 & 0.06795 & 0.7444 & 0.229059 \tabularnewline
6 & 0.088139 & 0.9655 & 0.168113 \tabularnewline
7 & -0.001221 & -0.0134 & 0.494677 \tabularnewline
8 & 0.081972 & 0.898 & 0.185502 \tabularnewline
9 & 0.095483 & 1.046 & 0.14884 \tabularnewline
10 & -0.179614 & -1.9676 & 0.025712 \tabularnewline
11 & 0.043511 & 0.4766 & 0.317245 \tabularnewline
12 & -0.328802 & -3.6018 & 0.00023 \tabularnewline
13 & -0.01743 & -0.1909 & 0.424447 \tabularnewline
14 & 0.162044 & 1.7751 & 0.039208 \tabularnewline
15 & -0.007697 & -0.0843 & 0.466474 \tabularnewline
16 & -0.030111 & -0.3299 & 0.371044 \tabularnewline
17 & -0.103211 & -1.1306 & 0.130235 \tabularnewline
18 & 0.025898 & 0.2837 & 0.388565 \tabularnewline
19 & -0.010053 & -0.1101 & 0.456245 \tabularnewline
20 & -0.049446 & -0.5417 & 0.29453 \tabularnewline
21 & -0.06436 & -0.705 & 0.241078 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151121&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]0.169752[/C][C]1.8595[/C][C]0.0327[/C][/ROW]
[ROW][C]2[/C][C]0.123862[/C][C]1.3568[/C][C]0.08869[/C][/ROW]
[ROW][C]3[/C][C]0.064962[/C][C]0.7116[/C][C]0.239039[/C][/ROW]
[ROW][C]4[/C][C]0.073162[/C][C]0.8015[/C][C]0.212227[/C][/ROW]
[ROW][C]5[/C][C]0.06795[/C][C]0.7444[/C][C]0.229059[/C][/ROW]
[ROW][C]6[/C][C]0.088139[/C][C]0.9655[/C][C]0.168113[/C][/ROW]
[ROW][C]7[/C][C]-0.001221[/C][C]-0.0134[/C][C]0.494677[/C][/ROW]
[ROW][C]8[/C][C]0.081972[/C][C]0.898[/C][C]0.185502[/C][/ROW]
[ROW][C]9[/C][C]0.095483[/C][C]1.046[/C][C]0.14884[/C][/ROW]
[ROW][C]10[/C][C]-0.179614[/C][C]-1.9676[/C][C]0.025712[/C][/ROW]
[ROW][C]11[/C][C]0.043511[/C][C]0.4766[/C][C]0.317245[/C][/ROW]
[ROW][C]12[/C][C]-0.328802[/C][C]-3.6018[/C][C]0.00023[/C][/ROW]
[ROW][C]13[/C][C]-0.01743[/C][C]-0.1909[/C][C]0.424447[/C][/ROW]
[ROW][C]14[/C][C]0.162044[/C][C]1.7751[/C][C]0.039208[/C][/ROW]
[ROW][C]15[/C][C]-0.007697[/C][C]-0.0843[/C][C]0.466474[/C][/ROW]
[ROW][C]16[/C][C]-0.030111[/C][C]-0.3299[/C][C]0.371044[/C][/ROW]
[ROW][C]17[/C][C]-0.103211[/C][C]-1.1306[/C][C]0.130235[/C][/ROW]
[ROW][C]18[/C][C]0.025898[/C][C]0.2837[/C][C]0.388565[/C][/ROW]
[ROW][C]19[/C][C]-0.010053[/C][C]-0.1101[/C][C]0.456245[/C][/ROW]
[ROW][C]20[/C][C]-0.049446[/C][C]-0.5417[/C][C]0.29453[/C][/ROW]
[ROW][C]21[/C][C]-0.06436[/C][C]-0.705[/C][C]0.241078[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151121&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151121&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	0.169752	1.8595	0.0327
2	0.123862	1.3568	0.08869
3	0.064962	0.7116	0.239039
4	0.073162	0.8015	0.212227
5	0.06795	0.7444	0.229059
6	0.088139	0.9655	0.168113
7	-0.001221	-0.0134	0.494677
8	0.081972	0.898	0.185502
9	0.095483	1.046	0.14884
10	-0.179614	-1.9676	0.025712
11	0.043511	0.4766	0.317245
12	-0.328802	-3.6018	0.00023
13	-0.01743	-0.1909	0.424447
14	0.162044	1.7751	0.039208
15	-0.007697	-0.0843	0.466474
16	-0.030111	-0.3299	0.371044
17	-0.103211	-1.1306	0.130235
18	0.025898	0.2837	0.388565
19	-0.010053	-0.1101	0.456245
20	-0.049446	-0.5417	0.29453
21	-0.06436	-0.705	0.241078

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 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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