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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

Wed, 28 Mar 2012 07:09:00 -0400

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/Mar/28/t13329329939hm3zu3f4cbj4wg.htm/, Retrieved Sun, 05 May 2024 11:20:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=164166, Retrieved Sun, 05 May 2024 11:20:31 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W12

Estimated Impact

186

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

-       [(Partial) Autocorrelation Function] [IKO opgave 6 bis ...] [2012-03-28 11:09:00] [93d78dde8d64c5a73537ad1fcc88d508] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164166&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164166&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164166&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.129065	1.1758	0.12151
2	0.042123	0.3838	0.35107
3	0.010137	0.0924	0.463321
4	-0.10393	-0.9469	0.173232
5	-0.11769	-1.0722	0.143368
6	-0.027111	-0.247	0.402761
7	-0.100704	-0.9175	0.180781
8	0.051025	0.4649	0.321624
9	-0.05229	-0.4764	0.317526
10	-0.135718	-1.2365	0.109889
11	0.140751	1.2823	0.101653
12	0.158535	1.4443	0.076206
13	0.247809	2.2576	0.013297
14	0.168274	1.5331	0.064533
15	-0.130069	-1.185	0.119702
16	-0.119132	-1.0853	0.140456
17	-0.013725	-0.125	0.450395
18	-0.144909	-1.3202	0.095202
19	-0.148065	-1.3489	0.090514

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.129065 & 1.1758 & 0.12151 \tabularnewline
2 & 0.042123 & 0.3838 & 0.35107 \tabularnewline
3 & 0.010137 & 0.0924 & 0.463321 \tabularnewline
4 & -0.10393 & -0.9469 & 0.173232 \tabularnewline
5 & -0.11769 & -1.0722 & 0.143368 \tabularnewline
6 & -0.027111 & -0.247 & 0.402761 \tabularnewline
7 & -0.100704 & -0.9175 & 0.180781 \tabularnewline
8 & 0.051025 & 0.4649 & 0.321624 \tabularnewline
9 & -0.05229 & -0.4764 & 0.317526 \tabularnewline
10 & -0.135718 & -1.2365 & 0.109889 \tabularnewline
11 & 0.140751 & 1.2823 & 0.101653 \tabularnewline
12 & 0.158535 & 1.4443 & 0.076206 \tabularnewline
13 & 0.247809 & 2.2576 & 0.013297 \tabularnewline
14 & 0.168274 & 1.5331 & 0.064533 \tabularnewline
15 & -0.130069 & -1.185 & 0.119702 \tabularnewline
16 & -0.119132 & -1.0853 & 0.140456 \tabularnewline
17 & -0.013725 & -0.125 & 0.450395 \tabularnewline
18 & -0.144909 & -1.3202 & 0.095202 \tabularnewline
19 & -0.148065 & -1.3489 & 0.090514 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164166&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]0.129065[/C][C]1.1758[/C][C]0.12151[/C][/ROW]
[ROW][C]2[/C][C]0.042123[/C][C]0.3838[/C][C]0.35107[/C][/ROW]
[ROW][C]3[/C][C]0.010137[/C][C]0.0924[/C][C]0.463321[/C][/ROW]
[ROW][C]4[/C][C]-0.10393[/C][C]-0.9469[/C][C]0.173232[/C][/ROW]
[ROW][C]5[/C][C]-0.11769[/C][C]-1.0722[/C][C]0.143368[/C][/ROW]
[ROW][C]6[/C][C]-0.027111[/C][C]-0.247[/C][C]0.402761[/C][/ROW]
[ROW][C]7[/C][C]-0.100704[/C][C]-0.9175[/C][C]0.180781[/C][/ROW]
[ROW][C]8[/C][C]0.051025[/C][C]0.4649[/C][C]0.321624[/C][/ROW]
[ROW][C]9[/C][C]-0.05229[/C][C]-0.4764[/C][C]0.317526[/C][/ROW]
[ROW][C]10[/C][C]-0.135718[/C][C]-1.2365[/C][C]0.109889[/C][/ROW]
[ROW][C]11[/C][C]0.140751[/C][C]1.2823[/C][C]0.101653[/C][/ROW]
[ROW][C]12[/C][C]0.158535[/C][C]1.4443[/C][C]0.076206[/C][/ROW]
[ROW][C]13[/C][C]0.247809[/C][C]2.2576[/C][C]0.013297[/C][/ROW]
[ROW][C]14[/C][C]0.168274[/C][C]1.5331[/C][C]0.064533[/C][/ROW]
[ROW][C]15[/C][C]-0.130069[/C][C]-1.185[/C][C]0.119702[/C][/ROW]
[ROW][C]16[/C][C]-0.119132[/C][C]-1.0853[/C][C]0.140456[/C][/ROW]
[ROW][C]17[/C][C]-0.013725[/C][C]-0.125[/C][C]0.450395[/C][/ROW]
[ROW][C]18[/C][C]-0.144909[/C][C]-1.3202[/C][C]0.095202[/C][/ROW]
[ROW][C]19[/C][C]-0.148065[/C][C]-1.3489[/C][C]0.090514[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164166&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164166&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	0.129065	1.1758	0.12151
2	0.042123	0.3838	0.35107
3	0.010137	0.0924	0.463321
4	-0.10393	-0.9469	0.173232
5	-0.11769	-1.0722	0.143368
6	-0.027111	-0.247	0.402761
7	-0.100704	-0.9175	0.180781
8	0.051025	0.4649	0.321624
9	-0.05229	-0.4764	0.317526
10	-0.135718	-1.2365	0.109889
11	0.140751	1.2823	0.101653
12	0.158535	1.4443	0.076206
13	0.247809	2.2576	0.013297
14	0.168274	1.5331	0.064533
15	-0.130069	-1.185	0.119702
16	-0.119132	-1.0853	0.140456
17	-0.013725	-0.125	0.450395
18	-0.144909	-1.3202	0.095202
19	-0.148065	-1.3489	0.090514

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.129065	1.1758	0.12151
2	0.025896	0.2359	0.407035
3	0.001525	0.0139	0.494474
4	-0.108361	-0.9872	0.163204
5	-0.094272	-0.8589	0.196446
6	0.005879	0.0536	0.478709
7	-0.09133	-0.8321	0.203883
8	0.069743	0.6354	0.263461
9	-0.085373	-0.7778	0.219454
10	-0.140017	-1.2756	0.102825
11	0.168363	1.5339	0.064434
12	0.134402	1.2245	0.112121
13	0.230674	2.1015	0.019313
14	0.069046	0.629	0.265527
15	-0.201052	-1.8317	0.035294
16	-0.088245	-0.804	0.21186
17	0.078221	0.7126	0.239037
18	-0.010117	-0.0922	0.463391
19	-0.170289	-1.5514	0.062304

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.129065 & 1.1758 & 0.12151 \tabularnewline
2 & 0.025896 & 0.2359 & 0.407035 \tabularnewline
3 & 0.001525 & 0.0139 & 0.494474 \tabularnewline
4 & -0.108361 & -0.9872 & 0.163204 \tabularnewline
5 & -0.094272 & -0.8589 & 0.196446 \tabularnewline
6 & 0.005879 & 0.0536 & 0.478709 \tabularnewline
7 & -0.09133 & -0.8321 & 0.203883 \tabularnewline
8 & 0.069743 & 0.6354 & 0.263461 \tabularnewline
9 & -0.085373 & -0.7778 & 0.219454 \tabularnewline
10 & -0.140017 & -1.2756 & 0.102825 \tabularnewline
11 & 0.168363 & 1.5339 & 0.064434 \tabularnewline
12 & 0.134402 & 1.2245 & 0.112121 \tabularnewline
13 & 0.230674 & 2.1015 & 0.019313 \tabularnewline
14 & 0.069046 & 0.629 & 0.265527 \tabularnewline
15 & -0.201052 & -1.8317 & 0.035294 \tabularnewline
16 & -0.088245 & -0.804 & 0.21186 \tabularnewline
17 & 0.078221 & 0.7126 & 0.239037 \tabularnewline
18 & -0.010117 & -0.0922 & 0.463391 \tabularnewline
19 & -0.170289 & -1.5514 & 0.062304 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164166&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]0.129065[/C][C]1.1758[/C][C]0.12151[/C][/ROW]
[ROW][C]2[/C][C]0.025896[/C][C]0.2359[/C][C]0.407035[/C][/ROW]
[ROW][C]3[/C][C]0.001525[/C][C]0.0139[/C][C]0.494474[/C][/ROW]
[ROW][C]4[/C][C]-0.108361[/C][C]-0.9872[/C][C]0.163204[/C][/ROW]
[ROW][C]5[/C][C]-0.094272[/C][C]-0.8589[/C][C]0.196446[/C][/ROW]
[ROW][C]6[/C][C]0.005879[/C][C]0.0536[/C][C]0.478709[/C][/ROW]
[ROW][C]7[/C][C]-0.09133[/C][C]-0.8321[/C][C]0.203883[/C][/ROW]
[ROW][C]8[/C][C]0.069743[/C][C]0.6354[/C][C]0.263461[/C][/ROW]
[ROW][C]9[/C][C]-0.085373[/C][C]-0.7778[/C][C]0.219454[/C][/ROW]
[ROW][C]10[/C][C]-0.140017[/C][C]-1.2756[/C][C]0.102825[/C][/ROW]
[ROW][C]11[/C][C]0.168363[/C][C]1.5339[/C][C]0.064434[/C][/ROW]
[ROW][C]12[/C][C]0.134402[/C][C]1.2245[/C][C]0.112121[/C][/ROW]
[ROW][C]13[/C][C]0.230674[/C][C]2.1015[/C][C]0.019313[/C][/ROW]
[ROW][C]14[/C][C]0.069046[/C][C]0.629[/C][C]0.265527[/C][/ROW]
[ROW][C]15[/C][C]-0.201052[/C][C]-1.8317[/C][C]0.035294[/C][/ROW]
[ROW][C]16[/C][C]-0.088245[/C][C]-0.804[/C][C]0.21186[/C][/ROW]
[ROW][C]17[/C][C]0.078221[/C][C]0.7126[/C][C]0.239037[/C][/ROW]
[ROW][C]18[/C][C]-0.010117[/C][C]-0.0922[/C][C]0.463391[/C][/ROW]
[ROW][C]19[/C][C]-0.170289[/C][C]-1.5514[/C][C]0.062304[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164166&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164166&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	0.129065	1.1758	0.12151
2	0.025896	0.2359	0.407035
3	0.001525	0.0139	0.494474
4	-0.108361	-0.9872	0.163204
5	-0.094272	-0.8589	0.196446
6	0.005879	0.0536	0.478709
7	-0.09133	-0.8321	0.203883
8	0.069743	0.6354	0.263461
9	-0.085373	-0.7778	0.219454
10	-0.140017	-1.2756	0.102825
11	0.168363	1.5339	0.064434
12	0.134402	1.2245	0.112121
13	0.230674	2.1015	0.019313
14	0.069046	0.629	0.265527
15	-0.201052	-1.8317	0.035294
16	-0.088245	-0.804	0.21186
17	0.078221	0.7126	0.239037
18	-0.010117	-0.0922	0.463391
19	-0.170289	-1.5514	0.062304

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