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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 18 Dec 2010 12:54:47 +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/Dec/18/t1292676966p9a8u1xw8l5sp2s.htm/, Retrieved Tue, 30 Apr 2024 02:04:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111927, Retrieved Tue, 30 Apr 2024 02:04:41 +0000

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Estimated Impact

173

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

-     [Spectral Analysis] [Spectraalanalyse ...] [2008-12-11 17:29:14] [12d343c4448a5f9e527bb31caeac580b]
- RMPD  [(Partial) Autocorrelation Function] [Paper PACF d=1] [2009-12-27 10:10:23] [83058a88a37d754675a5cd22dab372fc]
-   PD      [(Partial) Autocorrelation Function] [paper lambda 1] [2010-12-18 12:54:47] [912a7c71b856221ca57f8714938acfc7] [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	'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 & 1 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111927&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111927&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111927&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.524655	4.6336	7e-06
2	0.292442	2.5828	0.005836
3	0.517634	4.5716	9e-06
4	0.701026	6.1913	0
5	0.428469	3.7841	0.000151
6	0.148726	1.3135	0.096431
7	0.36224	3.1992	0.000996
8	0.504316	4.454	1.4e-05
9	0.194349	1.7164	0.045025
10	-0.03001	-0.265	0.395837
11	0.120488	1.0641	0.145278
12	0.238902	2.1099	0.019036
13	-0.01358	-0.1199	0.452421
14	-0.165715	-1.4636	0.073667
15	-0.010753	-0.095	0.462293
16	0.125332	1.1069	0.13587
17	-0.106694	-0.9423	0.174475
18	-0.235073	-2.0761	0.020589

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.524655 & 4.6336 & 7e-06 \tabularnewline
2 & 0.292442 & 2.5828 & 0.005836 \tabularnewline
3 & 0.517634 & 4.5716 & 9e-06 \tabularnewline
4 & 0.701026 & 6.1913 & 0 \tabularnewline
5 & 0.428469 & 3.7841 & 0.000151 \tabularnewline
6 & 0.148726 & 1.3135 & 0.096431 \tabularnewline
7 & 0.36224 & 3.1992 & 0.000996 \tabularnewline
8 & 0.504316 & 4.454 & 1.4e-05 \tabularnewline
9 & 0.194349 & 1.7164 & 0.045025 \tabularnewline
10 & -0.03001 & -0.265 & 0.395837 \tabularnewline
11 & 0.120488 & 1.0641 & 0.145278 \tabularnewline
12 & 0.238902 & 2.1099 & 0.019036 \tabularnewline
13 & -0.01358 & -0.1199 & 0.452421 \tabularnewline
14 & -0.165715 & -1.4636 & 0.073667 \tabularnewline
15 & -0.010753 & -0.095 & 0.462293 \tabularnewline
16 & 0.125332 & 1.1069 & 0.13587 \tabularnewline
17 & -0.106694 & -0.9423 & 0.174475 \tabularnewline
18 & -0.235073 & -2.0761 & 0.020589 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111927&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]0.524655[/C][C]4.6336[/C][C]7e-06[/C][/ROW]
[ROW][C]2[/C][C]0.292442[/C][C]2.5828[/C][C]0.005836[/C][/ROW]
[ROW][C]3[/C][C]0.517634[/C][C]4.5716[/C][C]9e-06[/C][/ROW]
[ROW][C]4[/C][C]0.701026[/C][C]6.1913[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.428469[/C][C]3.7841[/C][C]0.000151[/C][/ROW]
[ROW][C]6[/C][C]0.148726[/C][C]1.3135[/C][C]0.096431[/C][/ROW]
[ROW][C]7[/C][C]0.36224[/C][C]3.1992[/C][C]0.000996[/C][/ROW]
[ROW][C]8[/C][C]0.504316[/C][C]4.454[/C][C]1.4e-05[/C][/ROW]
[ROW][C]9[/C][C]0.194349[/C][C]1.7164[/C][C]0.045025[/C][/ROW]
[ROW][C]10[/C][C]-0.03001[/C][C]-0.265[/C][C]0.395837[/C][/ROW]
[ROW][C]11[/C][C]0.120488[/C][C]1.0641[/C][C]0.145278[/C][/ROW]
[ROW][C]12[/C][C]0.238902[/C][C]2.1099[/C][C]0.019036[/C][/ROW]
[ROW][C]13[/C][C]-0.01358[/C][C]-0.1199[/C][C]0.452421[/C][/ROW]
[ROW][C]14[/C][C]-0.165715[/C][C]-1.4636[/C][C]0.073667[/C][/ROW]
[ROW][C]15[/C][C]-0.010753[/C][C]-0.095[/C][C]0.462293[/C][/ROW]
[ROW][C]16[/C][C]0.125332[/C][C]1.1069[/C][C]0.13587[/C][/ROW]
[ROW][C]17[/C][C]-0.106694[/C][C]-0.9423[/C][C]0.174475[/C][/ROW]
[ROW][C]18[/C][C]-0.235073[/C][C]-2.0761[/C][C]0.020589[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111927&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111927&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	0.524655	4.6336	7e-06
2	0.292442	2.5828	0.005836
3	0.517634	4.5716	9e-06
4	0.701026	6.1913	0
5	0.428469	3.7841	0.000151
6	0.148726	1.3135	0.096431
7	0.36224	3.1992	0.000996
8	0.504316	4.454	1.4e-05
9	0.194349	1.7164	0.045025
10	-0.03001	-0.265	0.395837
11	0.120488	1.0641	0.145278
12	0.238902	2.1099	0.019036
13	-0.01358	-0.1199	0.452421
14	-0.165715	-1.4636	0.073667
15	-0.010753	-0.095	0.462293
16	0.125332	1.1069	0.13587
17	-0.106694	-0.9423	0.174475
18	-0.235073	-2.0761	0.020589

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.524655	4.6336	7e-06
2	0.023704	0.2094	0.41736
3	0.490665	4.3334	2.2e-05
4	0.456485	4.0316	6.4e-05
5	-0.040338	-0.3563	0.361307
6	-0.338389	-2.9886	0.001873
7	-0.006042	-0.0534	0.47879
8	0.041662	0.368	0.356953
9	-0.181556	-1.6035	0.056438
10	-0.176627	-1.5599	0.061413
11	-0.138955	-1.2272	0.111716
12	-0.037079	-0.3275	0.372093
13	-0.013645	-0.1205	0.452193
14	0.111746	0.9869	0.163367
15	0.067152	0.5931	0.277424
16	0.188743	1.6669	0.049769
17	0.00428	0.0378	0.484974
18	-0.000686	-0.0061	0.497592

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.524655 & 4.6336 & 7e-06 \tabularnewline
2 & 0.023704 & 0.2094 & 0.41736 \tabularnewline
3 & 0.490665 & 4.3334 & 2.2e-05 \tabularnewline
4 & 0.456485 & 4.0316 & 6.4e-05 \tabularnewline
5 & -0.040338 & -0.3563 & 0.361307 \tabularnewline
6 & -0.338389 & -2.9886 & 0.001873 \tabularnewline
7 & -0.006042 & -0.0534 & 0.47879 \tabularnewline
8 & 0.041662 & 0.368 & 0.356953 \tabularnewline
9 & -0.181556 & -1.6035 & 0.056438 \tabularnewline
10 & -0.176627 & -1.5599 & 0.061413 \tabularnewline
11 & -0.138955 & -1.2272 & 0.111716 \tabularnewline
12 & -0.037079 & -0.3275 & 0.372093 \tabularnewline
13 & -0.013645 & -0.1205 & 0.452193 \tabularnewline
14 & 0.111746 & 0.9869 & 0.163367 \tabularnewline
15 & 0.067152 & 0.5931 & 0.277424 \tabularnewline
16 & 0.188743 & 1.6669 & 0.049769 \tabularnewline
17 & 0.00428 & 0.0378 & 0.484974 \tabularnewline
18 & -0.000686 & -0.0061 & 0.497592 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111927&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]0.524655[/C][C]4.6336[/C][C]7e-06[/C][/ROW]
[ROW][C]2[/C][C]0.023704[/C][C]0.2094[/C][C]0.41736[/C][/ROW]
[ROW][C]3[/C][C]0.490665[/C][C]4.3334[/C][C]2.2e-05[/C][/ROW]
[ROW][C]4[/C][C]0.456485[/C][C]4.0316[/C][C]6.4e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.040338[/C][C]-0.3563[/C][C]0.361307[/C][/ROW]
[ROW][C]6[/C][C]-0.338389[/C][C]-2.9886[/C][C]0.001873[/C][/ROW]
[ROW][C]7[/C][C]-0.006042[/C][C]-0.0534[/C][C]0.47879[/C][/ROW]
[ROW][C]8[/C][C]0.041662[/C][C]0.368[/C][C]0.356953[/C][/ROW]
[ROW][C]9[/C][C]-0.181556[/C][C]-1.6035[/C][C]0.056438[/C][/ROW]
[ROW][C]10[/C][C]-0.176627[/C][C]-1.5599[/C][C]0.061413[/C][/ROW]
[ROW][C]11[/C][C]-0.138955[/C][C]-1.2272[/C][C]0.111716[/C][/ROW]
[ROW][C]12[/C][C]-0.037079[/C][C]-0.3275[/C][C]0.372093[/C][/ROW]
[ROW][C]13[/C][C]-0.013645[/C][C]-0.1205[/C][C]0.452193[/C][/ROW]
[ROW][C]14[/C][C]0.111746[/C][C]0.9869[/C][C]0.163367[/C][/ROW]
[ROW][C]15[/C][C]0.067152[/C][C]0.5931[/C][C]0.277424[/C][/ROW]
[ROW][C]16[/C][C]0.188743[/C][C]1.6669[/C][C]0.049769[/C][/ROW]
[ROW][C]17[/C][C]0.00428[/C][C]0.0378[/C][C]0.484974[/C][/ROW]
[ROW][C]18[/C][C]-0.000686[/C][C]-0.0061[/C][C]0.497592[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111927&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111927&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	0.524655	4.6336	7e-06
2	0.023704	0.2094	0.41736
3	0.490665	4.3334	2.2e-05
4	0.456485	4.0316	6.4e-05
5	-0.040338	-0.3563	0.361307
6	-0.338389	-2.9886	0.001873
7	-0.006042	-0.0534	0.47879
8	0.041662	0.368	0.356953
9	-0.181556	-1.6035	0.056438
10	-0.176627	-1.5599	0.061413
11	-0.138955	-1.2272	0.111716
12	-0.037079	-0.3275	0.372093
13	-0.013645	-0.1205	0.452193
14	0.111746	0.9869	0.163367
15	0.067152	0.5931	0.277424
16	0.188743	1.6669	0.049769
17	0.00428	0.0378	0.484974
18	-0.000686	-0.0061	0.497592

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = -1.0 ; par3 = 1 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 0.98 ;

Parameters (R input):

par1 = Default ; par2 = -1.0 ; par3 = 1 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 0.98 ; 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 (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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