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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

Wed, 19 Dec 2012 11:14:25 -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/19/t13559337098t8kdoast0z6f9l.htm/, Retrieved Fri, 01 Nov 2024 00:02:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=202142, Retrieved Fri, 01 Nov 2024 00:02:57 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

125

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

-     [(Partial) Autocorrelation Function] [] [2011-12-18 15:29:31] [97a82ed57455ec27012f2e899dc4f1a4]
- R     [(Partial) Autocorrelation Function] [Paper - Deel 2 - ACF] [2011-12-20 13:06:33] [95a4a8598e82ac3272c4dca488d0ba38]
- R P     [(Partial) Autocorrelation Function] [Paper 4.6.1 ACT mean] [2012-12-19 16:00:10] [527264e3173c1bca10b2a11a99a7175d]
- R P         [(Partial) Autocorrelation Function] [Paper 4.6.1 ACT m...] [2012-12-19 16:14:25] [371a6a7ed53d940ea5eaabc67060a582] [Current]
-   P           [(Partial) Autocorrelation Function] [Paper 4.6.1 ACT m...] [2012-12-19 16:26:53] [527264e3173c1bca10b2a11a99a7175d] 
- RMP           [Spectral Analysis] [Paper 4.6.1 SA be...] [2012-12-19 16:50:19] [527264e3173c1bca10b2a11a99a7175d] 
- RMP           [Spectral Analysis] [Paper 4.6.1 SA be...] [2012-12-19 16:53:13] [527264e3173c1bca10b2a11a99a7175d] 
- RMP           [Spectral Analysis] [Paper 4.6.1 SA be...] [2012-12-19 16:55:15] [527264e3173c1bca10b2a11a99a7175d] 
- RMP           [Spectral Analysis] [Paper 4.6.1 SA be...] [2012-12-19 16:55:55] [527264e3173c1bca10b2a11a99a7175d] 
- RMP           [Spectral Analysis] [Paper 4.6.1 SA be...] [2012-12-19 16:56:33] [527264e3173c1bca10b2a11a99a7175d] 
- RMP           [Variance Reduction Matrix] [Paper 4.6.1 VRM b...] [2012-12-19 17:18:33] [527264e3173c1bca10b2a11a99a7175d] 
- RMP           [Standard Deviation-Mean Plot] [Paper 4.6.2 heter...] [2012-12-19 18:20:59] [527264e3173c1bca10b2a11a99a7175d] 

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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=202142&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=202142&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202142&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	-0.439783	-3.4629	0.000487
2	-0.025308	-0.1993	0.42135
3	-0.006337	-0.0499	0.480181
4	-0.131059	-1.032	0.15305
5	0.216609	1.7056	0.046546
6	-0.001855	-0.0146	0.494196
7	-0.125075	-0.9848	0.164265
8	-0.089179	-0.7022	0.242593
9	0.29259	2.3039	0.012298
10	-0.175512	-1.382	0.085968
11	0.038871	0.3061	0.380287
12	-0.064769	-0.51	0.305933
13	-0.159611	-1.2568	0.106775
14	0.392086	3.0873	0.00151
15	-0.229945	-1.8106	0.037525
16	-0.024	-0.189	0.425365
17	0.029401	0.2315	0.408842
18	0.072629	0.5719	0.284736

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.439783 & -3.4629 & 0.000487 \tabularnewline
2 & -0.025308 & -0.1993 & 0.42135 \tabularnewline
3 & -0.006337 & -0.0499 & 0.480181 \tabularnewline
4 & -0.131059 & -1.032 & 0.15305 \tabularnewline
5 & 0.216609 & 1.7056 & 0.046546 \tabularnewline
6 & -0.001855 & -0.0146 & 0.494196 \tabularnewline
7 & -0.125075 & -0.9848 & 0.164265 \tabularnewline
8 & -0.089179 & -0.7022 & 0.242593 \tabularnewline
9 & 0.29259 & 2.3039 & 0.012298 \tabularnewline
10 & -0.175512 & -1.382 & 0.085968 \tabularnewline
11 & 0.038871 & 0.3061 & 0.380287 \tabularnewline
12 & -0.064769 & -0.51 & 0.305933 \tabularnewline
13 & -0.159611 & -1.2568 & 0.106775 \tabularnewline
14 & 0.392086 & 3.0873 & 0.00151 \tabularnewline
15 & -0.229945 & -1.8106 & 0.037525 \tabularnewline
16 & -0.024 & -0.189 & 0.425365 \tabularnewline
17 & 0.029401 & 0.2315 & 0.408842 \tabularnewline
18 & 0.072629 & 0.5719 & 0.284736 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202142&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]-0.439783[/C][C]-3.4629[/C][C]0.000487[/C][/ROW]
[ROW][C]2[/C][C]-0.025308[/C][C]-0.1993[/C][C]0.42135[/C][/ROW]
[ROW][C]3[/C][C]-0.006337[/C][C]-0.0499[/C][C]0.480181[/C][/ROW]
[ROW][C]4[/C][C]-0.131059[/C][C]-1.032[/C][C]0.15305[/C][/ROW]
[ROW][C]5[/C][C]0.216609[/C][C]1.7056[/C][C]0.046546[/C][/ROW]
[ROW][C]6[/C][C]-0.001855[/C][C]-0.0146[/C][C]0.494196[/C][/ROW]
[ROW][C]7[/C][C]-0.125075[/C][C]-0.9848[/C][C]0.164265[/C][/ROW]
[ROW][C]8[/C][C]-0.089179[/C][C]-0.7022[/C][C]0.242593[/C][/ROW]
[ROW][C]9[/C][C]0.29259[/C][C]2.3039[/C][C]0.012298[/C][/ROW]
[ROW][C]10[/C][C]-0.175512[/C][C]-1.382[/C][C]0.085968[/C][/ROW]
[ROW][C]11[/C][C]0.038871[/C][C]0.3061[/C][C]0.380287[/C][/ROW]
[ROW][C]12[/C][C]-0.064769[/C][C]-0.51[/C][C]0.305933[/C][/ROW]
[ROW][C]13[/C][C]-0.159611[/C][C]-1.2568[/C][C]0.106775[/C][/ROW]
[ROW][C]14[/C][C]0.392086[/C][C]3.0873[/C][C]0.00151[/C][/ROW]
[ROW][C]15[/C][C]-0.229945[/C][C]-1.8106[/C][C]0.037525[/C][/ROW]
[ROW][C]16[/C][C]-0.024[/C][C]-0.189[/C][C]0.425365[/C][/ROW]
[ROW][C]17[/C][C]0.029401[/C][C]0.2315[/C][C]0.408842[/C][/ROW]
[ROW][C]18[/C][C]0.072629[/C][C]0.5719[/C][C]0.284736[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202142&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202142&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	-0.439783	-3.4629	0.000487
2	-0.025308	-0.1993	0.42135
3	-0.006337	-0.0499	0.480181
4	-0.131059	-1.032	0.15305
5	0.216609	1.7056	0.046546
6	-0.001855	-0.0146	0.494196
7	-0.125075	-0.9848	0.164265
8	-0.089179	-0.7022	0.242593
9	0.29259	2.3039	0.012298
10	-0.175512	-1.382	0.085968
11	0.038871	0.3061	0.380287
12	-0.064769	-0.51	0.305933
13	-0.159611	-1.2568	0.106775
14	0.392086	3.0873	0.00151
15	-0.229945	-1.8106	0.037525
16	-0.024	-0.189	0.425365
17	0.029401	0.2315	0.408842
18	0.072629	0.5719	0.284736

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.439783	-3.4629	0.000487
2	-0.271162	-2.1351	0.018355
3	-0.186994	-1.4724	0.072986
4	-0.314314	-2.4749	0.008038
5	-0.033771	-0.2659	0.395595
6	0.081607	0.6426	0.261436
7	-0.055168	-0.4344	0.332755
8	-0.243368	-1.9163	0.029971
9	0.21758	1.7132	0.045834
10	0.038677	0.3045	0.380866
11	-0.046663	-0.3674	0.357276
12	-0.077526	-0.6104	0.271902
13	-0.205119	-1.6151	0.055682
14	0.141673	1.1155	0.134464
15	-0.082508	-0.6497	0.259153
16	-0.122284	-0.9629	0.169678
17	-0.006352	-0.05	0.480134
18	0.169827	1.3372	0.093018

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.439783 & -3.4629 & 0.000487 \tabularnewline
2 & -0.271162 & -2.1351 & 0.018355 \tabularnewline
3 & -0.186994 & -1.4724 & 0.072986 \tabularnewline
4 & -0.314314 & -2.4749 & 0.008038 \tabularnewline
5 & -0.033771 & -0.2659 & 0.395595 \tabularnewline
6 & 0.081607 & 0.6426 & 0.261436 \tabularnewline
7 & -0.055168 & -0.4344 & 0.332755 \tabularnewline
8 & -0.243368 & -1.9163 & 0.029971 \tabularnewline
9 & 0.21758 & 1.7132 & 0.045834 \tabularnewline
10 & 0.038677 & 0.3045 & 0.380866 \tabularnewline
11 & -0.046663 & -0.3674 & 0.357276 \tabularnewline
12 & -0.077526 & -0.6104 & 0.271902 \tabularnewline
13 & -0.205119 & -1.6151 & 0.055682 \tabularnewline
14 & 0.141673 & 1.1155 & 0.134464 \tabularnewline
15 & -0.082508 & -0.6497 & 0.259153 \tabularnewline
16 & -0.122284 & -0.9629 & 0.169678 \tabularnewline
17 & -0.006352 & -0.05 & 0.480134 \tabularnewline
18 & 0.169827 & 1.3372 & 0.093018 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=202142&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]-0.439783[/C][C]-3.4629[/C][C]0.000487[/C][/ROW]
[ROW][C]2[/C][C]-0.271162[/C][C]-2.1351[/C][C]0.018355[/C][/ROW]
[ROW][C]3[/C][C]-0.186994[/C][C]-1.4724[/C][C]0.072986[/C][/ROW]
[ROW][C]4[/C][C]-0.314314[/C][C]-2.4749[/C][C]0.008038[/C][/ROW]
[ROW][C]5[/C][C]-0.033771[/C][C]-0.2659[/C][C]0.395595[/C][/ROW]
[ROW][C]6[/C][C]0.081607[/C][C]0.6426[/C][C]0.261436[/C][/ROW]
[ROW][C]7[/C][C]-0.055168[/C][C]-0.4344[/C][C]0.332755[/C][/ROW]
[ROW][C]8[/C][C]-0.243368[/C][C]-1.9163[/C][C]0.029971[/C][/ROW]
[ROW][C]9[/C][C]0.21758[/C][C]1.7132[/C][C]0.045834[/C][/ROW]
[ROW][C]10[/C][C]0.038677[/C][C]0.3045[/C][C]0.380866[/C][/ROW]
[ROW][C]11[/C][C]-0.046663[/C][C]-0.3674[/C][C]0.357276[/C][/ROW]
[ROW][C]12[/C][C]-0.077526[/C][C]-0.6104[/C][C]0.271902[/C][/ROW]
[ROW][C]13[/C][C]-0.205119[/C][C]-1.6151[/C][C]0.055682[/C][/ROW]
[ROW][C]14[/C][C]0.141673[/C][C]1.1155[/C][C]0.134464[/C][/ROW]
[ROW][C]15[/C][C]-0.082508[/C][C]-0.6497[/C][C]0.259153[/C][/ROW]
[ROW][C]16[/C][C]-0.122284[/C][C]-0.9629[/C][C]0.169678[/C][/ROW]
[ROW][C]17[/C][C]-0.006352[/C][C]-0.05[/C][C]0.480134[/C][/ROW]
[ROW][C]18[/C][C]0.169827[/C][C]1.3372[/C][C]0.093018[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=202142&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=202142&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	-0.439783	-3.4629	0.000487
2	-0.271162	-2.1351	0.018355
3	-0.186994	-1.4724	0.072986
4	-0.314314	-2.4749	0.008038
5	-0.033771	-0.2659	0.395595
6	0.081607	0.6426	0.261436
7	-0.055168	-0.4344	0.332755
8	-0.243368	-1.9163	0.029971
9	0.21758	1.7132	0.045834
10	0.038677	0.3045	0.380866
11	-0.046663	-0.3674	0.357276
12	-0.077526	-0.6104	0.271902
13	-0.205119	-1.6151	0.055682
14	0.141673	1.1155	0.134464
15	-0.082508	-0.6497	0.259153
16	-0.122284	-0.9629	0.169678
17	-0.006352	-0.05	0.480134
18	0.169827	1.3372	0.093018

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