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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

Fri, 11 Dec 2009 06:44:12 -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/2009/Dec/11/t1260540493sc1z0kbln4r5735.htm/, Retrieved Sun, 28 Apr 2024 21:25:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=66208, Retrieved Sun, 28 Apr 2024 21:25:42 +0000

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No (this computation is public)

User-defined keywords

uedap

Estimated Impact

107

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

-     [Bivariate Explorative Data Analysis] [shw-ws4p1] [2009-10-28 17:17:04] [2663058f2a5dda519058ac6b2228468f]
- RMPD    [(Partial) Autocorrelation Function] [Paper: univariate...] [2009-12-11 13:44:12] [682632737e024f9e62885141c5f654cd] [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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66208&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66208&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66208&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.956646	7.4102	0
2	0.905267	7.0122	0
3	0.845884	6.5522	0
4	0.781973	6.0571	0
5	0.716638	5.5511	0
6	0.656902	5.0883	2e-06
7	0.599922	4.647	9e-06
8	0.543316	4.2085	4.4e-05
9	0.487909	3.7793	0.000182
10	0.431233	3.3403	0.000722
11	0.371019	2.8739	0.0028
12	0.306459	2.3738	0.010412
13	0.23997	1.8588	0.033981
14	0.172127	1.3333	0.093738
15	0.107782	0.8349	0.20355
16	0.049698	0.385	0.350815
17	0.005875	0.0455	0.481926

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.956646 & 7.4102 & 0 \tabularnewline
2 & 0.905267 & 7.0122 & 0 \tabularnewline
3 & 0.845884 & 6.5522 & 0 \tabularnewline
4 & 0.781973 & 6.0571 & 0 \tabularnewline
5 & 0.716638 & 5.5511 & 0 \tabularnewline
6 & 0.656902 & 5.0883 & 2e-06 \tabularnewline
7 & 0.599922 & 4.647 & 9e-06 \tabularnewline
8 & 0.543316 & 4.2085 & 4.4e-05 \tabularnewline
9 & 0.487909 & 3.7793 & 0.000182 \tabularnewline
10 & 0.431233 & 3.3403 & 0.000722 \tabularnewline
11 & 0.371019 & 2.8739 & 0.0028 \tabularnewline
12 & 0.306459 & 2.3738 & 0.010412 \tabularnewline
13 & 0.23997 & 1.8588 & 0.033981 \tabularnewline
14 & 0.172127 & 1.3333 & 0.093738 \tabularnewline
15 & 0.107782 & 0.8349 & 0.20355 \tabularnewline
16 & 0.049698 & 0.385 & 0.350815 \tabularnewline
17 & 0.005875 & 0.0455 & 0.481926 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66208&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]0.956646[/C][C]7.4102[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.905267[/C][C]7.0122[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.845884[/C][C]6.5522[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.781973[/C][C]6.0571[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.716638[/C][C]5.5511[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.656902[/C][C]5.0883[/C][C]2e-06[/C][/ROW]
[ROW][C]7[/C][C]0.599922[/C][C]4.647[/C][C]9e-06[/C][/ROW]
[ROW][C]8[/C][C]0.543316[/C][C]4.2085[/C][C]4.4e-05[/C][/ROW]
[ROW][C]9[/C][C]0.487909[/C][C]3.7793[/C][C]0.000182[/C][/ROW]
[ROW][C]10[/C][C]0.431233[/C][C]3.3403[/C][C]0.000722[/C][/ROW]
[ROW][C]11[/C][C]0.371019[/C][C]2.8739[/C][C]0.0028[/C][/ROW]
[ROW][C]12[/C][C]0.306459[/C][C]2.3738[/C][C]0.010412[/C][/ROW]
[ROW][C]13[/C][C]0.23997[/C][C]1.8588[/C][C]0.033981[/C][/ROW]
[ROW][C]14[/C][C]0.172127[/C][C]1.3333[/C][C]0.093738[/C][/ROW]
[ROW][C]15[/C][C]0.107782[/C][C]0.8349[/C][C]0.20355[/C][/ROW]
[ROW][C]16[/C][C]0.049698[/C][C]0.385[/C][C]0.350815[/C][/ROW]
[ROW][C]17[/C][C]0.005875[/C][C]0.0455[/C][C]0.481926[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66208&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66208&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	0.956646	7.4102	0
2	0.905267	7.0122	0
3	0.845884	6.5522	0
4	0.781973	6.0571	0
5	0.716638	5.5511	0
6	0.656902	5.0883	2e-06
7	0.599922	4.647	9e-06
8	0.543316	4.2085	4.4e-05
9	0.487909	3.7793	0.000182
10	0.431233	3.3403	0.000722
11	0.371019	2.8739	0.0028
12	0.306459	2.3738	0.010412
13	0.23997	1.8588	0.033981
14	0.172127	1.3333	0.093738
15	0.107782	0.8349	0.20355
16	0.049698	0.385	0.350815
17	0.005875	0.0455	0.481926

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.956646	7.4102	0
2	-0.116769	-0.9045	0.184678
3	-0.114184	-0.8845	0.189988
4	-0.071972	-0.5575	0.289632
5	-0.038772	-0.3003	0.382484
6	0.038823	0.3007	0.382334
7	-0.009506	-0.0736	0.470774
8	-0.046356	-0.3591	0.3604
9	-0.033214	-0.2573	0.398924
10	-0.058479	-0.453	0.326099
11	-0.07792	-0.6036	0.274203
12	-0.086007	-0.6662	0.253915
13	-0.059087	-0.4577	0.324416
14	-0.05572	-0.4316	0.333788
15	-0.006661	-0.0516	0.479512
16	0.01268	0.0982	0.461042
17	0.100042	0.7749	0.220714

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.956646 & 7.4102 & 0 \tabularnewline
2 & -0.116769 & -0.9045 & 0.184678 \tabularnewline
3 & -0.114184 & -0.8845 & 0.189988 \tabularnewline
4 & -0.071972 & -0.5575 & 0.289632 \tabularnewline
5 & -0.038772 & -0.3003 & 0.382484 \tabularnewline
6 & 0.038823 & 0.3007 & 0.382334 \tabularnewline
7 & -0.009506 & -0.0736 & 0.470774 \tabularnewline
8 & -0.046356 & -0.3591 & 0.3604 \tabularnewline
9 & -0.033214 & -0.2573 & 0.398924 \tabularnewline
10 & -0.058479 & -0.453 & 0.326099 \tabularnewline
11 & -0.07792 & -0.6036 & 0.274203 \tabularnewline
12 & -0.086007 & -0.6662 & 0.253915 \tabularnewline
13 & -0.059087 & -0.4577 & 0.324416 \tabularnewline
14 & -0.05572 & -0.4316 & 0.333788 \tabularnewline
15 & -0.006661 & -0.0516 & 0.479512 \tabularnewline
16 & 0.01268 & 0.0982 & 0.461042 \tabularnewline
17 & 0.100042 & 0.7749 & 0.220714 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66208&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]0.956646[/C][C]7.4102[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.116769[/C][C]-0.9045[/C][C]0.184678[/C][/ROW]
[ROW][C]3[/C][C]-0.114184[/C][C]-0.8845[/C][C]0.189988[/C][/ROW]
[ROW][C]4[/C][C]-0.071972[/C][C]-0.5575[/C][C]0.289632[/C][/ROW]
[ROW][C]5[/C][C]-0.038772[/C][C]-0.3003[/C][C]0.382484[/C][/ROW]
[ROW][C]6[/C][C]0.038823[/C][C]0.3007[/C][C]0.382334[/C][/ROW]
[ROW][C]7[/C][C]-0.009506[/C][C]-0.0736[/C][C]0.470774[/C][/ROW]
[ROW][C]8[/C][C]-0.046356[/C][C]-0.3591[/C][C]0.3604[/C][/ROW]
[ROW][C]9[/C][C]-0.033214[/C][C]-0.2573[/C][C]0.398924[/C][/ROW]
[ROW][C]10[/C][C]-0.058479[/C][C]-0.453[/C][C]0.326099[/C][/ROW]
[ROW][C]11[/C][C]-0.07792[/C][C]-0.6036[/C][C]0.274203[/C][/ROW]
[ROW][C]12[/C][C]-0.086007[/C][C]-0.6662[/C][C]0.253915[/C][/ROW]
[ROW][C]13[/C][C]-0.059087[/C][C]-0.4577[/C][C]0.324416[/C][/ROW]
[ROW][C]14[/C][C]-0.05572[/C][C]-0.4316[/C][C]0.333788[/C][/ROW]
[ROW][C]15[/C][C]-0.006661[/C][C]-0.0516[/C][C]0.479512[/C][/ROW]
[ROW][C]16[/C][C]0.01268[/C][C]0.0982[/C][C]0.461042[/C][/ROW]
[ROW][C]17[/C][C]0.100042[/C][C]0.7749[/C][C]0.220714[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66208&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66208&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	0.956646	7.4102	0
2	-0.116769	-0.9045	0.184678
3	-0.114184	-0.8845	0.189988
4	-0.071972	-0.5575	0.289632
5	-0.038772	-0.3003	0.382484
6	0.038823	0.3007	0.382334
7	-0.009506	-0.0736	0.470774
8	-0.046356	-0.3591	0.3604
9	-0.033214	-0.2573	0.398924
10	-0.058479	-0.453	0.326099
11	-0.07792	-0.6036	0.274203
12	-0.086007	-0.6662	0.253915
13	-0.059087	-0.4577	0.324416
14	-0.05572	-0.4316	0.333788
15	-0.006661	-0.0516	0.479512
16	0.01268	0.0982	0.461042
17	0.100042	0.7749	0.220714

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 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code