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rwasp_autocorrelation.wasp

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(Partial) Autocorrelation Function

Date of computation

Mon, 22 Nov 2010 14:56:30 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/22/t1290437667vmel6pk8y0hd27g.htm/, Retrieved Fri, 03 May 2024 17:03:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=98561, Retrieved Fri, 03 May 2024 17:03:21 +0000

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

-       [(Partial) Autocorrelation Function] [] [2010-11-22 14:56:30] [9b9a58c480cb5dafe4bfceb51e1cfd12] [Current]

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1.8651746813703E-14
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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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98561&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98561&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98561&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.250134	-3.5374	0.000251
2	-0.112684	-1.5936	0.056304
3	0.012257	0.1733	0.431282
4	-0.091686	-1.2966	0.098124
5	-0.022753	-0.3218	0.373978
6	-0.032484	-0.4594	0.323226
7	0.067692	0.9573	0.169784
8	-0.114209	-1.6152	0.053927
9	0.055057	0.7786	0.218561
10	0.045548	0.6441	0.260109
11	-0.100759	-1.4249	0.077866
12	0.054693	0.7735	0.220076
13	0.021179	0.2995	0.382429
14	0.03579	0.5061	0.306657
15	-0.090668	-1.2822	0.100622
16	0.077999	1.1031	0.135661
17	0.044315	0.6267	0.265782
18	-0.169081	-2.3912	0.008861
19	0.054474	0.7704	0.220994
20	0.022023	0.3115	0.377889
21	0.022458	0.3176	0.37556
22	-0.045492	-0.6434	0.260364
23	0.045281	0.6404	0.261331

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.250134 & -3.5374 & 0.000251 \tabularnewline
2 & -0.112684 & -1.5936 & 0.056304 \tabularnewline
3 & 0.012257 & 0.1733 & 0.431282 \tabularnewline
4 & -0.091686 & -1.2966 & 0.098124 \tabularnewline
5 & -0.022753 & -0.3218 & 0.373978 \tabularnewline
6 & -0.032484 & -0.4594 & 0.323226 \tabularnewline
7 & 0.067692 & 0.9573 & 0.169784 \tabularnewline
8 & -0.114209 & -1.6152 & 0.053927 \tabularnewline
9 & 0.055057 & 0.7786 & 0.218561 \tabularnewline
10 & 0.045548 & 0.6441 & 0.260109 \tabularnewline
11 & -0.100759 & -1.4249 & 0.077866 \tabularnewline
12 & 0.054693 & 0.7735 & 0.220076 \tabularnewline
13 & 0.021179 & 0.2995 & 0.382429 \tabularnewline
14 & 0.03579 & 0.5061 & 0.306657 \tabularnewline
15 & -0.090668 & -1.2822 & 0.100622 \tabularnewline
16 & 0.077999 & 1.1031 & 0.135661 \tabularnewline
17 & 0.044315 & 0.6267 & 0.265782 \tabularnewline
18 & -0.169081 & -2.3912 & 0.008861 \tabularnewline
19 & 0.054474 & 0.7704 & 0.220994 \tabularnewline
20 & 0.022023 & 0.3115 & 0.377889 \tabularnewline
21 & 0.022458 & 0.3176 & 0.37556 \tabularnewline
22 & -0.045492 & -0.6434 & 0.260364 \tabularnewline
23 & 0.045281 & 0.6404 & 0.261331 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98561&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]-0.250134[/C][C]-3.5374[/C][C]0.000251[/C][/ROW]
[ROW][C]2[/C][C]-0.112684[/C][C]-1.5936[/C][C]0.056304[/C][/ROW]
[ROW][C]3[/C][C]0.012257[/C][C]0.1733[/C][C]0.431282[/C][/ROW]
[ROW][C]4[/C][C]-0.091686[/C][C]-1.2966[/C][C]0.098124[/C][/ROW]
[ROW][C]5[/C][C]-0.022753[/C][C]-0.3218[/C][C]0.373978[/C][/ROW]
[ROW][C]6[/C][C]-0.032484[/C][C]-0.4594[/C][C]0.323226[/C][/ROW]
[ROW][C]7[/C][C]0.067692[/C][C]0.9573[/C][C]0.169784[/C][/ROW]
[ROW][C]8[/C][C]-0.114209[/C][C]-1.6152[/C][C]0.053927[/C][/ROW]
[ROW][C]9[/C][C]0.055057[/C][C]0.7786[/C][C]0.218561[/C][/ROW]
[ROW][C]10[/C][C]0.045548[/C][C]0.6441[/C][C]0.260109[/C][/ROW]
[ROW][C]11[/C][C]-0.100759[/C][C]-1.4249[/C][C]0.077866[/C][/ROW]
[ROW][C]12[/C][C]0.054693[/C][C]0.7735[/C][C]0.220076[/C][/ROW]
[ROW][C]13[/C][C]0.021179[/C][C]0.2995[/C][C]0.382429[/C][/ROW]
[ROW][C]14[/C][C]0.03579[/C][C]0.5061[/C][C]0.306657[/C][/ROW]
[ROW][C]15[/C][C]-0.090668[/C][C]-1.2822[/C][C]0.100622[/C][/ROW]
[ROW][C]16[/C][C]0.077999[/C][C]1.1031[/C][C]0.135661[/C][/ROW]
[ROW][C]17[/C][C]0.044315[/C][C]0.6267[/C][C]0.265782[/C][/ROW]
[ROW][C]18[/C][C]-0.169081[/C][C]-2.3912[/C][C]0.008861[/C][/ROW]
[ROW][C]19[/C][C]0.054474[/C][C]0.7704[/C][C]0.220994[/C][/ROW]
[ROW][C]20[/C][C]0.022023[/C][C]0.3115[/C][C]0.377889[/C][/ROW]
[ROW][C]21[/C][C]0.022458[/C][C]0.3176[/C][C]0.37556[/C][/ROW]
[ROW][C]22[/C][C]-0.045492[/C][C]-0.6434[/C][C]0.260364[/C][/ROW]
[ROW][C]23[/C][C]0.045281[/C][C]0.6404[/C][C]0.261331[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98561&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98561&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	-0.250134	-3.5374	0.000251
2	-0.112684	-1.5936	0.056304
3	0.012257	0.1733	0.431282
4	-0.091686	-1.2966	0.098124
5	-0.022753	-0.3218	0.373978
6	-0.032484	-0.4594	0.323226
7	0.067692	0.9573	0.169784
8	-0.114209	-1.6152	0.053927
9	0.055057	0.7786	0.218561
10	0.045548	0.6441	0.260109
11	-0.100759	-1.4249	0.077866
12	0.054693	0.7735	0.220076
13	0.021179	0.2995	0.382429
14	0.03579	0.5061	0.306657
15	-0.090668	-1.2822	0.100622
16	0.077999	1.1031	0.135661
17	0.044315	0.6267	0.265782
18	-0.169081	-2.3912	0.008861
19	0.054474	0.7704	0.220994
20	0.022023	0.3115	0.377889
21	0.022458	0.3176	0.37556
22	-0.045492	-0.6434	0.260364
23	0.045281	0.6404	0.261331

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.250134	-3.5374	0.000251
2	-0.186947	-2.6438	0.004424
3	-0.075122	-1.0624	0.144672
4	-0.144787	-2.0476	0.020954
5	-0.112497	-1.591	0.0566
6	-0.126628	-1.7908	0.03742
7	-0.013781	-0.1949	0.42284
8	-0.16268	-2.3006	0.011221
9	-0.049296	-0.6972	0.243259
10	-0.020302	-0.2871	0.38716
11	-0.121898	-1.7239	0.043136
12	-0.045712	-0.6465	0.259359
13	-0.024916	-0.3524	0.362466
14	0.022679	0.3207	0.374374
15	-0.09513	-1.3453	0.090019
16	0.018888	0.2671	0.394829
17	0.055517	0.7851	0.216652
18	-0.127114	-1.7977	0.036869
19	-0.058973	-0.834	0.202635
20	-0.015527	-0.2196	0.413208
21	0.022176	0.3136	0.377069
22	-0.067421	-0.9535	0.170748
23	-0.009145	-0.1293	0.448615

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.250134 & -3.5374 & 0.000251 \tabularnewline
2 & -0.186947 & -2.6438 & 0.004424 \tabularnewline
3 & -0.075122 & -1.0624 & 0.144672 \tabularnewline
4 & -0.144787 & -2.0476 & 0.020954 \tabularnewline
5 & -0.112497 & -1.591 & 0.0566 \tabularnewline
6 & -0.126628 & -1.7908 & 0.03742 \tabularnewline
7 & -0.013781 & -0.1949 & 0.42284 \tabularnewline
8 & -0.16268 & -2.3006 & 0.011221 \tabularnewline
9 & -0.049296 & -0.6972 & 0.243259 \tabularnewline
10 & -0.020302 & -0.2871 & 0.38716 \tabularnewline
11 & -0.121898 & -1.7239 & 0.043136 \tabularnewline
12 & -0.045712 & -0.6465 & 0.259359 \tabularnewline
13 & -0.024916 & -0.3524 & 0.362466 \tabularnewline
14 & 0.022679 & 0.3207 & 0.374374 \tabularnewline
15 & -0.09513 & -1.3453 & 0.090019 \tabularnewline
16 & 0.018888 & 0.2671 & 0.394829 \tabularnewline
17 & 0.055517 & 0.7851 & 0.216652 \tabularnewline
18 & -0.127114 & -1.7977 & 0.036869 \tabularnewline
19 & -0.058973 & -0.834 & 0.202635 \tabularnewline
20 & -0.015527 & -0.2196 & 0.413208 \tabularnewline
21 & 0.022176 & 0.3136 & 0.377069 \tabularnewline
22 & -0.067421 & -0.9535 & 0.170748 \tabularnewline
23 & -0.009145 & -0.1293 & 0.448615 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98561&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]-0.250134[/C][C]-3.5374[/C][C]0.000251[/C][/ROW]
[ROW][C]2[/C][C]-0.186947[/C][C]-2.6438[/C][C]0.004424[/C][/ROW]
[ROW][C]3[/C][C]-0.075122[/C][C]-1.0624[/C][C]0.144672[/C][/ROW]
[ROW][C]4[/C][C]-0.144787[/C][C]-2.0476[/C][C]0.020954[/C][/ROW]
[ROW][C]5[/C][C]-0.112497[/C][C]-1.591[/C][C]0.0566[/C][/ROW]
[ROW][C]6[/C][C]-0.126628[/C][C]-1.7908[/C][C]0.03742[/C][/ROW]
[ROW][C]7[/C][C]-0.013781[/C][C]-0.1949[/C][C]0.42284[/C][/ROW]
[ROW][C]8[/C][C]-0.16268[/C][C]-2.3006[/C][C]0.011221[/C][/ROW]
[ROW][C]9[/C][C]-0.049296[/C][C]-0.6972[/C][C]0.243259[/C][/ROW]
[ROW][C]10[/C][C]-0.020302[/C][C]-0.2871[/C][C]0.38716[/C][/ROW]
[ROW][C]11[/C][C]-0.121898[/C][C]-1.7239[/C][C]0.043136[/C][/ROW]
[ROW][C]12[/C][C]-0.045712[/C][C]-0.6465[/C][C]0.259359[/C][/ROW]
[ROW][C]13[/C][C]-0.024916[/C][C]-0.3524[/C][C]0.362466[/C][/ROW]
[ROW][C]14[/C][C]0.022679[/C][C]0.3207[/C][C]0.374374[/C][/ROW]
[ROW][C]15[/C][C]-0.09513[/C][C]-1.3453[/C][C]0.090019[/C][/ROW]
[ROW][C]16[/C][C]0.018888[/C][C]0.2671[/C][C]0.394829[/C][/ROW]
[ROW][C]17[/C][C]0.055517[/C][C]0.7851[/C][C]0.216652[/C][/ROW]
[ROW][C]18[/C][C]-0.127114[/C][C]-1.7977[/C][C]0.036869[/C][/ROW]
[ROW][C]19[/C][C]-0.058973[/C][C]-0.834[/C][C]0.202635[/C][/ROW]
[ROW][C]20[/C][C]-0.015527[/C][C]-0.2196[/C][C]0.413208[/C][/ROW]
[ROW][C]21[/C][C]0.022176[/C][C]0.3136[/C][C]0.377069[/C][/ROW]
[ROW][C]22[/C][C]-0.067421[/C][C]-0.9535[/C][C]0.170748[/C][/ROW]
[ROW][C]23[/C][C]-0.009145[/C][C]-0.1293[/C][C]0.448615[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98561&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98561&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	-0.250134	-3.5374	0.000251
2	-0.186947	-2.6438	0.004424
3	-0.075122	-1.0624	0.144672
4	-0.144787	-2.0476	0.020954
5	-0.112497	-1.591	0.0566
6	-0.126628	-1.7908	0.03742
7	-0.013781	-0.1949	0.42284
8	-0.16268	-2.3006	0.011221
9	-0.049296	-0.6972	0.243259
10	-0.020302	-0.2871	0.38716
11	-0.121898	-1.7239	0.043136
12	-0.045712	-0.6465	0.259359
13	-0.024916	-0.3524	0.362466
14	0.022679	0.3207	0.374374
15	-0.09513	-1.3453	0.090019
16	0.018888	0.2671	0.394829
17	0.055517	0.7851	0.216652
18	-0.127114	-1.7977	0.036869
19	-0.058973	-0.834	0.202635
20	-0.015527	-0.2196	0.413208
21	0.022176	0.3136	0.377069
22	-0.067421	-0.9535	0.170748
23	-0.009145	-0.1293	0.448615

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code