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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

Mon, 08 Dec 2008 12:32:18 -0700

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/2008/Dec/08/t12287647651w867p6fozbr8cs.htm/, Retrieved Thu, 16 May 2024 20:34:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30824, Retrieved Thu, 16 May 2024 20:34:13 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

169

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

-     [(Partial) Autocorrelation Function] [] [2008-12-07 13:01:51] [a4ee3bef49b119f4bd2e925060c84f5e]
F         [(Partial) Autocorrelation Function] [] [2008-12-08 19:32:18] [3762bf489501725951ad2579179cae2a] [Current]

Feedback Forum

2008-12-14 16:23:04 [Tom Ardies] [reply] 
Met een beetje goede wil kan je er een AR proces in terug vinden en ook een seizonale als je de software meer lags laten vertonen.

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Boxplots

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=30824&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=30824&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30824&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	0.381128	2.8007	0.003531
2	0.252629	1.8564	0.034425
3	-0.089829	-0.6601	0.255996
4	-0.097421	-0.7159	0.238569
5	-0.034317	-0.2522	0.40093
6	0.062008	0.4557	0.32523
7	0.086425	0.6351	0.264026
8	0.143041	1.0511	0.148939
9	0.084146	0.6183	0.269475
10	-0.192641	-1.4156	0.081314
11	-0.38194	-2.8067	0.003474
12	-0.463262	-3.4043	0.000629
13	-0.319712	-2.3494	0.011246
14	-0.003996	-0.0294	0.488341
15	0.091677	0.6737	0.251692
16	0.125157	0.9197	0.180906
17	0.048941	0.3596	0.360259
18	0.008875	0.0652	0.474122

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.381128 & 2.8007 & 0.003531 \tabularnewline
2 & 0.252629 & 1.8564 & 0.034425 \tabularnewline
3 & -0.089829 & -0.6601 & 0.255996 \tabularnewline
4 & -0.097421 & -0.7159 & 0.238569 \tabularnewline
5 & -0.034317 & -0.2522 & 0.40093 \tabularnewline
6 & 0.062008 & 0.4557 & 0.32523 \tabularnewline
7 & 0.086425 & 0.6351 & 0.264026 \tabularnewline
8 & 0.143041 & 1.0511 & 0.148939 \tabularnewline
9 & 0.084146 & 0.6183 & 0.269475 \tabularnewline
10 & -0.192641 & -1.4156 & 0.081314 \tabularnewline
11 & -0.38194 & -2.8067 & 0.003474 \tabularnewline
12 & -0.463262 & -3.4043 & 0.000629 \tabularnewline
13 & -0.319712 & -2.3494 & 0.011246 \tabularnewline
14 & -0.003996 & -0.0294 & 0.488341 \tabularnewline
15 & 0.091677 & 0.6737 & 0.251692 \tabularnewline
16 & 0.125157 & 0.9197 & 0.180906 \tabularnewline
17 & 0.048941 & 0.3596 & 0.360259 \tabularnewline
18 & 0.008875 & 0.0652 & 0.474122 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30824&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]0.381128[/C][C]2.8007[/C][C]0.003531[/C][/ROW]
[ROW][C]2[/C][C]0.252629[/C][C]1.8564[/C][C]0.034425[/C][/ROW]
[ROW][C]3[/C][C]-0.089829[/C][C]-0.6601[/C][C]0.255996[/C][/ROW]
[ROW][C]4[/C][C]-0.097421[/C][C]-0.7159[/C][C]0.238569[/C][/ROW]
[ROW][C]5[/C][C]-0.034317[/C][C]-0.2522[/C][C]0.40093[/C][/ROW]
[ROW][C]6[/C][C]0.062008[/C][C]0.4557[/C][C]0.32523[/C][/ROW]
[ROW][C]7[/C][C]0.086425[/C][C]0.6351[/C][C]0.264026[/C][/ROW]
[ROW][C]8[/C][C]0.143041[/C][C]1.0511[/C][C]0.148939[/C][/ROW]
[ROW][C]9[/C][C]0.084146[/C][C]0.6183[/C][C]0.269475[/C][/ROW]
[ROW][C]10[/C][C]-0.192641[/C][C]-1.4156[/C][C]0.081314[/C][/ROW]
[ROW][C]11[/C][C]-0.38194[/C][C]-2.8067[/C][C]0.003474[/C][/ROW]
[ROW][C]12[/C][C]-0.463262[/C][C]-3.4043[/C][C]0.000629[/C][/ROW]
[ROW][C]13[/C][C]-0.319712[/C][C]-2.3494[/C][C]0.011246[/C][/ROW]
[ROW][C]14[/C][C]-0.003996[/C][C]-0.0294[/C][C]0.488341[/C][/ROW]
[ROW][C]15[/C][C]0.091677[/C][C]0.6737[/C][C]0.251692[/C][/ROW]
[ROW][C]16[/C][C]0.125157[/C][C]0.9197[/C][C]0.180906[/C][/ROW]
[ROW][C]17[/C][C]0.048941[/C][C]0.3596[/C][C]0.360259[/C][/ROW]
[ROW][C]18[/C][C]0.008875[/C][C]0.0652[/C][C]0.474122[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30824&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30824&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	0.381128	2.8007	0.003531
2	0.252629	1.8564	0.034425
3	-0.089829	-0.6601	0.255996
4	-0.097421	-0.7159	0.238569
5	-0.034317	-0.2522	0.40093
6	0.062008	0.4557	0.32523
7	0.086425	0.6351	0.264026
8	0.143041	1.0511	0.148939
9	0.084146	0.6183	0.269475
10	-0.192641	-1.4156	0.081314
11	-0.38194	-2.8067	0.003474
12	-0.463262	-3.4043	0.000629
13	-0.319712	-2.3494	0.011246
14	-0.003996	-0.0294	0.488341
15	0.091677	0.6737	0.251692
16	0.125157	0.9197	0.180906
17	0.048941	0.3596	0.360259
18	0.008875	0.0652	0.474122

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.381128	2.8007	0.003531
2	0.125618	0.9231	0.180031
3	-0.263766	-1.9383	0.028912
4	-0.022897	-0.1683	0.433506
5	0.119708	0.8797	0.191468
6	0.0577	0.424	0.336622
7	-0.009099	-0.0669	0.47347
8	0.099465	0.7309	0.233995
9	0.01989	0.1462	0.442169
10	-0.337024	-2.4766	0.008214
11	-0.301621	-2.2165	0.015447
12	-0.147106	-1.081	0.142249
13	-0.05741	-0.4219	0.337394
14	0.158019	1.1612	0.125335
15	0.04059	0.2983	0.383318
16	0.007196	0.0529	0.479011
17	0.047509	0.3491	0.364179
18	0.10999	0.8083	0.211244

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.381128 & 2.8007 & 0.003531 \tabularnewline
2 & 0.125618 & 0.9231 & 0.180031 \tabularnewline
3 & -0.263766 & -1.9383 & 0.028912 \tabularnewline
4 & -0.022897 & -0.1683 & 0.433506 \tabularnewline
5 & 0.119708 & 0.8797 & 0.191468 \tabularnewline
6 & 0.0577 & 0.424 & 0.336622 \tabularnewline
7 & -0.009099 & -0.0669 & 0.47347 \tabularnewline
8 & 0.099465 & 0.7309 & 0.233995 \tabularnewline
9 & 0.01989 & 0.1462 & 0.442169 \tabularnewline
10 & -0.337024 & -2.4766 & 0.008214 \tabularnewline
11 & -0.301621 & -2.2165 & 0.015447 \tabularnewline
12 & -0.147106 & -1.081 & 0.142249 \tabularnewline
13 & -0.05741 & -0.4219 & 0.337394 \tabularnewline
14 & 0.158019 & 1.1612 & 0.125335 \tabularnewline
15 & 0.04059 & 0.2983 & 0.383318 \tabularnewline
16 & 0.007196 & 0.0529 & 0.479011 \tabularnewline
17 & 0.047509 & 0.3491 & 0.364179 \tabularnewline
18 & 0.10999 & 0.8083 & 0.211244 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30824&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]0.381128[/C][C]2.8007[/C][C]0.003531[/C][/ROW]
[ROW][C]2[/C][C]0.125618[/C][C]0.9231[/C][C]0.180031[/C][/ROW]
[ROW][C]3[/C][C]-0.263766[/C][C]-1.9383[/C][C]0.028912[/C][/ROW]
[ROW][C]4[/C][C]-0.022897[/C][C]-0.1683[/C][C]0.433506[/C][/ROW]
[ROW][C]5[/C][C]0.119708[/C][C]0.8797[/C][C]0.191468[/C][/ROW]
[ROW][C]6[/C][C]0.0577[/C][C]0.424[/C][C]0.336622[/C][/ROW]
[ROW][C]7[/C][C]-0.009099[/C][C]-0.0669[/C][C]0.47347[/C][/ROW]
[ROW][C]8[/C][C]0.099465[/C][C]0.7309[/C][C]0.233995[/C][/ROW]
[ROW][C]9[/C][C]0.01989[/C][C]0.1462[/C][C]0.442169[/C][/ROW]
[ROW][C]10[/C][C]-0.337024[/C][C]-2.4766[/C][C]0.008214[/C][/ROW]
[ROW][C]11[/C][C]-0.301621[/C][C]-2.2165[/C][C]0.015447[/C][/ROW]
[ROW][C]12[/C][C]-0.147106[/C][C]-1.081[/C][C]0.142249[/C][/ROW]
[ROW][C]13[/C][C]-0.05741[/C][C]-0.4219[/C][C]0.337394[/C][/ROW]
[ROW][C]14[/C][C]0.158019[/C][C]1.1612[/C][C]0.125335[/C][/ROW]
[ROW][C]15[/C][C]0.04059[/C][C]0.2983[/C][C]0.383318[/C][/ROW]
[ROW][C]16[/C][C]0.007196[/C][C]0.0529[/C][C]0.479011[/C][/ROW]
[ROW][C]17[/C][C]0.047509[/C][C]0.3491[/C][C]0.364179[/C][/ROW]
[ROW][C]18[/C][C]0.10999[/C][C]0.8083[/C][C]0.211244[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30824&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30824&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	0.381128	2.8007	0.003531
2	0.125618	0.9231	0.180031
3	-0.263766	-1.9383	0.028912
4	-0.022897	-0.1683	0.433506
5	0.119708	0.8797	0.191468
6	0.0577	0.424	0.336622
7	-0.009099	-0.0669	0.47347
8	0.099465	0.7309	0.233995
9	0.01989	0.1462	0.442169
10	-0.337024	-2.4766	0.008214
11	-0.301621	-2.2165	0.015447
12	-0.147106	-1.081	0.142249
13	-0.05741	-0.4219	0.337394
14	0.158019	1.1612	0.125335
15	0.04059	0.2983	0.383318
16	0.007196	0.0529	0.479011
17	0.047509	0.3491	0.364179
18	0.10999	0.8083	0.211244

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x,par1,main='Autocorrelation',xlab='lags',ylab='ACF')
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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