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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 19 Dec 2010 21:28:57 +0000

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/2010/Dec/19/t1292794059cc2371y4oi0ofp3.htm/, Retrieved Sun, 05 May 2024 03:11:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112758, Retrieved Sun, 05 May 2024 03:11:36 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

127

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-    D    [(Partial) Autocorrelation Function] [Workshop 9, Stati...] [2010-12-03 13:18:27] [d946de7cca328fbcf207448a112523ab]
-    D      [(Partial) Autocorrelation Function] [Autocorrelatie Fu...] [2010-12-19 14:18:56] [d946de7cca328fbcf207448a112523ab]
- R PD        [(Partial) Autocorrelation Function] [Paper ACF] [2010-12-19 14:22:07] [3635fb7041b1998c5a1332cf9de22bce]
-   PD            [(Partial) Autocorrelation Function] [Paper ACF D=1 d=1...] [2010-12-19 21:28:57] [23a9b79f355c69a75648521a893cf584] [Current]
-   P               [(Partial) Autocorrelation Function] [ACF d=D=1] [2010-12-22 08:48:35] [8081b8996d5947580de3eb171e82db4f] 
-                     [(Partial) Autocorrelation Function] [ACF d=D=1] [2010-12-22 09:14:48] [8081b8996d5947580de3eb171e82db4f] 
-                     [(Partial) Autocorrelation Function] [ACF d=D=1] [2010-12-22 09:14:48] [8081b8996d5947580de3eb171e82db4f] 
-   P               [(Partial) Autocorrelation Function] [Paper ACF D=1 d=1] [2010-12-22 09:16:52] [d946de7cca328fbcf207448a112523ab] 

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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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112758&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112758&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112758&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.26118	-2.2007	0.015504
2	0.090264	0.7606	0.224715
3	0.030071	0.2534	0.400352
4	0.084561	0.7125	0.239239
5	-0.029633	-0.2497	0.401775
6	-0.056848	-0.479	0.316703
7	0.021674	0.1826	0.427804
8	0.036937	0.3112	0.378268
9	-0.220118	-1.8548	0.033892
10	0.099109	0.8351	0.20323
11	0.117152	0.9871	0.163463
12	-0.397945	-3.3531	0.000642
13	0.218677	1.8426	0.034781
14	-0.14676	-1.2366	0.110152
15	0.04	0.337	0.36854
16	-0.105838	-0.8918	0.187754
17	-0.106186	-0.8947	0.186974
18	0.109108	0.9194	0.180511
19	-0.028402	-0.2393	0.405774

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.26118 & -2.2007 & 0.015504 \tabularnewline
2 & 0.090264 & 0.7606 & 0.224715 \tabularnewline
3 & 0.030071 & 0.2534 & 0.400352 \tabularnewline
4 & 0.084561 & 0.7125 & 0.239239 \tabularnewline
5 & -0.029633 & -0.2497 & 0.401775 \tabularnewline
6 & -0.056848 & -0.479 & 0.316703 \tabularnewline
7 & 0.021674 & 0.1826 & 0.427804 \tabularnewline
8 & 0.036937 & 0.3112 & 0.378268 \tabularnewline
9 & -0.220118 & -1.8548 & 0.033892 \tabularnewline
10 & 0.099109 & 0.8351 & 0.20323 \tabularnewline
11 & 0.117152 & 0.9871 & 0.163463 \tabularnewline
12 & -0.397945 & -3.3531 & 0.000642 \tabularnewline
13 & 0.218677 & 1.8426 & 0.034781 \tabularnewline
14 & -0.14676 & -1.2366 & 0.110152 \tabularnewline
15 & 0.04 & 0.337 & 0.36854 \tabularnewline
16 & -0.105838 & -0.8918 & 0.187754 \tabularnewline
17 & -0.106186 & -0.8947 & 0.186974 \tabularnewline
18 & 0.109108 & 0.9194 & 0.180511 \tabularnewline
19 & -0.028402 & -0.2393 & 0.405774 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112758&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]-0.26118[/C][C]-2.2007[/C][C]0.015504[/C][/ROW]
[ROW][C]2[/C][C]0.090264[/C][C]0.7606[/C][C]0.224715[/C][/ROW]
[ROW][C]3[/C][C]0.030071[/C][C]0.2534[/C][C]0.400352[/C][/ROW]
[ROW][C]4[/C][C]0.084561[/C][C]0.7125[/C][C]0.239239[/C][/ROW]
[ROW][C]5[/C][C]-0.029633[/C][C]-0.2497[/C][C]0.401775[/C][/ROW]
[ROW][C]6[/C][C]-0.056848[/C][C]-0.479[/C][C]0.316703[/C][/ROW]
[ROW][C]7[/C][C]0.021674[/C][C]0.1826[/C][C]0.427804[/C][/ROW]
[ROW][C]8[/C][C]0.036937[/C][C]0.3112[/C][C]0.378268[/C][/ROW]
[ROW][C]9[/C][C]-0.220118[/C][C]-1.8548[/C][C]0.033892[/C][/ROW]
[ROW][C]10[/C][C]0.099109[/C][C]0.8351[/C][C]0.20323[/C][/ROW]
[ROW][C]11[/C][C]0.117152[/C][C]0.9871[/C][C]0.163463[/C][/ROW]
[ROW][C]12[/C][C]-0.397945[/C][C]-3.3531[/C][C]0.000642[/C][/ROW]
[ROW][C]13[/C][C]0.218677[/C][C]1.8426[/C][C]0.034781[/C][/ROW]
[ROW][C]14[/C][C]-0.14676[/C][C]-1.2366[/C][C]0.110152[/C][/ROW]
[ROW][C]15[/C][C]0.04[/C][C]0.337[/C][C]0.36854[/C][/ROW]
[ROW][C]16[/C][C]-0.105838[/C][C]-0.8918[/C][C]0.187754[/C][/ROW]
[ROW][C]17[/C][C]-0.106186[/C][C]-0.8947[/C][C]0.186974[/C][/ROW]
[ROW][C]18[/C][C]0.109108[/C][C]0.9194[/C][C]0.180511[/C][/ROW]
[ROW][C]19[/C][C]-0.028402[/C][C]-0.2393[/C][C]0.405774[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112758&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112758&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	-0.26118	-2.2007	0.015504
2	0.090264	0.7606	0.224715
3	0.030071	0.2534	0.400352
4	0.084561	0.7125	0.239239
5	-0.029633	-0.2497	0.401775
6	-0.056848	-0.479	0.316703
7	0.021674	0.1826	0.427804
8	0.036937	0.3112	0.378268
9	-0.220118	-1.8548	0.033892
10	0.099109	0.8351	0.20323
11	0.117152	0.9871	0.163463
12	-0.397945	-3.3531	0.000642
13	0.218677	1.8426	0.034781
14	-0.14676	-1.2366	0.110152
15	0.04	0.337	0.36854
16	-0.105838	-0.8918	0.187754
17	-0.106186	-0.8947	0.186974
18	0.109108	0.9194	0.180511
19	-0.028402	-0.2393	0.405774

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.26118	-2.2007	0.015504
2	0.023663	0.1994	0.421266
3	0.063643	0.5363	0.296725
4	0.113528	0.9566	0.171008
5	0.014072	0.1186	0.452975
6	-0.084417	-0.7113	0.239611
7	-0.027957	-0.2356	0.407223
8	0.04302	0.3625	0.359031
9	-0.204594	-1.7239	0.044535
10	1.6e-05	1e-04	0.499946
11	0.189576	1.5974	0.05731
12	-0.374053	-3.1518	0.001188
13	0.088128	0.7426	0.230093
14	-0.056169	-0.4733	0.318729
15	-0.083453	-0.7032	0.242119
16	0.002845	0.024	0.490471
17	-0.190403	-1.6044	0.056536
18	-0.007012	-0.0591	0.476525
19	0.109411	0.9219	0.179847

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.26118 & -2.2007 & 0.015504 \tabularnewline
2 & 0.023663 & 0.1994 & 0.421266 \tabularnewline
3 & 0.063643 & 0.5363 & 0.296725 \tabularnewline
4 & 0.113528 & 0.9566 & 0.171008 \tabularnewline
5 & 0.014072 & 0.1186 & 0.452975 \tabularnewline
6 & -0.084417 & -0.7113 & 0.239611 \tabularnewline
7 & -0.027957 & -0.2356 & 0.407223 \tabularnewline
8 & 0.04302 & 0.3625 & 0.359031 \tabularnewline
9 & -0.204594 & -1.7239 & 0.044535 \tabularnewline
10 & 1.6e-05 & 1e-04 & 0.499946 \tabularnewline
11 & 0.189576 & 1.5974 & 0.05731 \tabularnewline
12 & -0.374053 & -3.1518 & 0.001188 \tabularnewline
13 & 0.088128 & 0.7426 & 0.230093 \tabularnewline
14 & -0.056169 & -0.4733 & 0.318729 \tabularnewline
15 & -0.083453 & -0.7032 & 0.242119 \tabularnewline
16 & 0.002845 & 0.024 & 0.490471 \tabularnewline
17 & -0.190403 & -1.6044 & 0.056536 \tabularnewline
18 & -0.007012 & -0.0591 & 0.476525 \tabularnewline
19 & 0.109411 & 0.9219 & 0.179847 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112758&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]-0.26118[/C][C]-2.2007[/C][C]0.015504[/C][/ROW]
[ROW][C]2[/C][C]0.023663[/C][C]0.1994[/C][C]0.421266[/C][/ROW]
[ROW][C]3[/C][C]0.063643[/C][C]0.5363[/C][C]0.296725[/C][/ROW]
[ROW][C]4[/C][C]0.113528[/C][C]0.9566[/C][C]0.171008[/C][/ROW]
[ROW][C]5[/C][C]0.014072[/C][C]0.1186[/C][C]0.452975[/C][/ROW]
[ROW][C]6[/C][C]-0.084417[/C][C]-0.7113[/C][C]0.239611[/C][/ROW]
[ROW][C]7[/C][C]-0.027957[/C][C]-0.2356[/C][C]0.407223[/C][/ROW]
[ROW][C]8[/C][C]0.04302[/C][C]0.3625[/C][C]0.359031[/C][/ROW]
[ROW][C]9[/C][C]-0.204594[/C][C]-1.7239[/C][C]0.044535[/C][/ROW]
[ROW][C]10[/C][C]1.6e-05[/C][C]1e-04[/C][C]0.499946[/C][/ROW]
[ROW][C]11[/C][C]0.189576[/C][C]1.5974[/C][C]0.05731[/C][/ROW]
[ROW][C]12[/C][C]-0.374053[/C][C]-3.1518[/C][C]0.001188[/C][/ROW]
[ROW][C]13[/C][C]0.088128[/C][C]0.7426[/C][C]0.230093[/C][/ROW]
[ROW][C]14[/C][C]-0.056169[/C][C]-0.4733[/C][C]0.318729[/C][/ROW]
[ROW][C]15[/C][C]-0.083453[/C][C]-0.7032[/C][C]0.242119[/C][/ROW]
[ROW][C]16[/C][C]0.002845[/C][C]0.024[/C][C]0.490471[/C][/ROW]
[ROW][C]17[/C][C]-0.190403[/C][C]-1.6044[/C][C]0.056536[/C][/ROW]
[ROW][C]18[/C][C]-0.007012[/C][C]-0.0591[/C][C]0.476525[/C][/ROW]
[ROW][C]19[/C][C]0.109411[/C][C]0.9219[/C][C]0.179847[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112758&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112758&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	-0.26118	-2.2007	0.015504
2	0.023663	0.1994	0.421266
3	0.063643	0.5363	0.296725
4	0.113528	0.9566	0.171008
5	0.014072	0.1186	0.452975
6	-0.084417	-0.7113	0.239611
7	-0.027957	-0.2356	0.407223
8	0.04302	0.3625	0.359031
9	-0.204594	-1.7239	0.044535
10	1.6e-05	1e-04	0.499946
11	0.189576	1.5974	0.05731
12	-0.374053	-3.1518	0.001188
13	0.088128	0.7426	0.230093
14	-0.056169	-0.4733	0.318729
15	-0.083453	-0.7032	0.242119
16	0.002845	0.024	0.490471
17	-0.190403	-1.6044	0.056536
18	-0.007012	-0.0591	0.476525
19	0.109411	0.9219	0.179847

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 = 2 ; par2 = equal ; par3 = 4 ; par4 = no ;

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