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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 02 Jan 2012 09:18:42 -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/Jan/02/t1325513956bxng2nialfcnhgn.htm/, Retrieved Sat, 04 May 2024 13:22:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160929, Retrieved Sat, 04 May 2024 13:22:06 +0000

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No (this computation is public)

User-defined keywords

KDGP2W12

Estimated Impact

154

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

-     [Harrell-Davis Quantiles] [decielen] [2012-01-02 13:39:09] [da1dd7ba20267c8dec1286cd318791a0]
- RMPD    [(Partial) Autocorrelation Function] [autocorrelatie] [2012-01-02 14:18:42] [5f178b5bce8a01d64692a8a5c649399b] [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=160929&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=160929&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160929&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	0.946989	8.0911	0
2	0.907526	7.7539	0
3	0.867693	7.4136	0
4	0.81766	6.9861	0
5	0.782795	6.6882	0
6	0.74105	6.3315	0
7	0.698551	5.9684	0
8	0.66517	5.6832	0
9	0.633003	5.4084	0
10	0.594715	5.0812	1e-06
11	0.562596	4.8068	4e-06
12	0.523105	4.4694	1.4e-05
13	0.487338	4.1638	4.2e-05
14	0.450036	3.8451	0.000128
15	0.406917	3.4767	0.000429
16	0.369145	3.154	0.001169
17	0.332359	2.8397	0.002923
18	0.295899	2.5282	0.006814

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.946989 & 8.0911 & 0 \tabularnewline
2 & 0.907526 & 7.7539 & 0 \tabularnewline
3 & 0.867693 & 7.4136 & 0 \tabularnewline
4 & 0.81766 & 6.9861 & 0 \tabularnewline
5 & 0.782795 & 6.6882 & 0 \tabularnewline
6 & 0.74105 & 6.3315 & 0 \tabularnewline
7 & 0.698551 & 5.9684 & 0 \tabularnewline
8 & 0.66517 & 5.6832 & 0 \tabularnewline
9 & 0.633003 & 5.4084 & 0 \tabularnewline
10 & 0.594715 & 5.0812 & 1e-06 \tabularnewline
11 & 0.562596 & 4.8068 & 4e-06 \tabularnewline
12 & 0.523105 & 4.4694 & 1.4e-05 \tabularnewline
13 & 0.487338 & 4.1638 & 4.2e-05 \tabularnewline
14 & 0.450036 & 3.8451 & 0.000128 \tabularnewline
15 & 0.406917 & 3.4767 & 0.000429 \tabularnewline
16 & 0.369145 & 3.154 & 0.001169 \tabularnewline
17 & 0.332359 & 2.8397 & 0.002923 \tabularnewline
18 & 0.295899 & 2.5282 & 0.006814 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160929&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]0.946989[/C][C]8.0911[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.907526[/C][C]7.7539[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.867693[/C][C]7.4136[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.81766[/C][C]6.9861[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.782795[/C][C]6.6882[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.74105[/C][C]6.3315[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.698551[/C][C]5.9684[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.66517[/C][C]5.6832[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.633003[/C][C]5.4084[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.594715[/C][C]5.0812[/C][C]1e-06[/C][/ROW]
[ROW][C]11[/C][C]0.562596[/C][C]4.8068[/C][C]4e-06[/C][/ROW]
[ROW][C]12[/C][C]0.523105[/C][C]4.4694[/C][C]1.4e-05[/C][/ROW]
[ROW][C]13[/C][C]0.487338[/C][C]4.1638[/C][C]4.2e-05[/C][/ROW]
[ROW][C]14[/C][C]0.450036[/C][C]3.8451[/C][C]0.000128[/C][/ROW]
[ROW][C]15[/C][C]0.406917[/C][C]3.4767[/C][C]0.000429[/C][/ROW]
[ROW][C]16[/C][C]0.369145[/C][C]3.154[/C][C]0.001169[/C][/ROW]
[ROW][C]17[/C][C]0.332359[/C][C]2.8397[/C][C]0.002923[/C][/ROW]
[ROW][C]18[/C][C]0.295899[/C][C]2.5282[/C][C]0.006814[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160929&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160929&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	0.946989	8.0911	0
2	0.907526	7.7539	0
3	0.867693	7.4136	0
4	0.81766	6.9861	0
5	0.782795	6.6882	0
6	0.74105	6.3315	0
7	0.698551	5.9684	0
8	0.66517	5.6832	0
9	0.633003	5.4084	0
10	0.594715	5.0812	1e-06
11	0.562596	4.8068	4e-06
12	0.523105	4.4694	1.4e-05
13	0.487338	4.1638	4.2e-05
14	0.450036	3.8451	0.000128
15	0.406917	3.4767	0.000429
16	0.369145	3.154	0.001169
17	0.332359	2.8397	0.002923
18	0.295899	2.5282	0.006814

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.946989	8.0911	0
2	0.104047	0.889	0.188468
3	-0.008179	-0.0699	0.472238
4	-0.12006	-1.0258	0.154189
5	0.098069	0.8379	0.202411
6	-0.055888	-0.4775	0.317214
7	-0.034959	-0.2987	0.383013
8	0.040662	0.3474	0.364638
9	0.035109	0.3	0.382526
10	-0.086438	-0.7385	0.231282
11	0.011498	0.0982	0.461007
12	-0.069627	-0.5949	0.276876
13	0.009814	0.0838	0.466703
14	-0.060372	-0.5158	0.303769
15	-0.056852	-0.4857	0.314303
16	-0.004378	-0.0374	0.485133
17	0.002129	0.0182	0.492769
18	-0.022284	-0.1904	0.424764

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.946989 & 8.0911 & 0 \tabularnewline
2 & 0.104047 & 0.889 & 0.188468 \tabularnewline
3 & -0.008179 & -0.0699 & 0.472238 \tabularnewline
4 & -0.12006 & -1.0258 & 0.154189 \tabularnewline
5 & 0.098069 & 0.8379 & 0.202411 \tabularnewline
6 & -0.055888 & -0.4775 & 0.317214 \tabularnewline
7 & -0.034959 & -0.2987 & 0.383013 \tabularnewline
8 & 0.040662 & 0.3474 & 0.364638 \tabularnewline
9 & 0.035109 & 0.3 & 0.382526 \tabularnewline
10 & -0.086438 & -0.7385 & 0.231282 \tabularnewline
11 & 0.011498 & 0.0982 & 0.461007 \tabularnewline
12 & -0.069627 & -0.5949 & 0.276876 \tabularnewline
13 & 0.009814 & 0.0838 & 0.466703 \tabularnewline
14 & -0.060372 & -0.5158 & 0.303769 \tabularnewline
15 & -0.056852 & -0.4857 & 0.314303 \tabularnewline
16 & -0.004378 & -0.0374 & 0.485133 \tabularnewline
17 & 0.002129 & 0.0182 & 0.492769 \tabularnewline
18 & -0.022284 & -0.1904 & 0.424764 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160929&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]0.946989[/C][C]8.0911[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.104047[/C][C]0.889[/C][C]0.188468[/C][/ROW]
[ROW][C]3[/C][C]-0.008179[/C][C]-0.0699[/C][C]0.472238[/C][/ROW]
[ROW][C]4[/C][C]-0.12006[/C][C]-1.0258[/C][C]0.154189[/C][/ROW]
[ROW][C]5[/C][C]0.098069[/C][C]0.8379[/C][C]0.202411[/C][/ROW]
[ROW][C]6[/C][C]-0.055888[/C][C]-0.4775[/C][C]0.317214[/C][/ROW]
[ROW][C]7[/C][C]-0.034959[/C][C]-0.2987[/C][C]0.383013[/C][/ROW]
[ROW][C]8[/C][C]0.040662[/C][C]0.3474[/C][C]0.364638[/C][/ROW]
[ROW][C]9[/C][C]0.035109[/C][C]0.3[/C][C]0.382526[/C][/ROW]
[ROW][C]10[/C][C]-0.086438[/C][C]-0.7385[/C][C]0.231282[/C][/ROW]
[ROW][C]11[/C][C]0.011498[/C][C]0.0982[/C][C]0.461007[/C][/ROW]
[ROW][C]12[/C][C]-0.069627[/C][C]-0.5949[/C][C]0.276876[/C][/ROW]
[ROW][C]13[/C][C]0.009814[/C][C]0.0838[/C][C]0.466703[/C][/ROW]
[ROW][C]14[/C][C]-0.060372[/C][C]-0.5158[/C][C]0.303769[/C][/ROW]
[ROW][C]15[/C][C]-0.056852[/C][C]-0.4857[/C][C]0.314303[/C][/ROW]
[ROW][C]16[/C][C]-0.004378[/C][C]-0.0374[/C][C]0.485133[/C][/ROW]
[ROW][C]17[/C][C]0.002129[/C][C]0.0182[/C][C]0.492769[/C][/ROW]
[ROW][C]18[/C][C]-0.022284[/C][C]-0.1904[/C][C]0.424764[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160929&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160929&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	0.946989	8.0911	0
2	0.104047	0.889	0.188468
3	-0.008179	-0.0699	0.472238
4	-0.12006	-1.0258	0.154189
5	0.098069	0.8379	0.202411
6	-0.055888	-0.4775	0.317214
7	-0.034959	-0.2987	0.383013
8	0.040662	0.3474	0.364638
9	0.035109	0.3	0.382526
10	-0.086438	-0.7385	0.231282
11	0.011498	0.0982	0.461007
12	-0.069627	-0.5949	0.276876
13	0.009814	0.0838	0.466703
14	-0.060372	-0.5158	0.303769
15	-0.056852	-0.4857	0.314303
16	-0.004378	-0.0374	0.485133
17	0.002129	0.0182	0.492769
18	-0.022284	-0.1904	0.424764

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 = 0.1 ; par2 = 0.9 ; par3 = 0.1 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code