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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

Tue, 24 Nov 2009 07:31:17 -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/Nov/24/t1259073219pnq8swxk6v3p9vi.htm/, Retrieved Fri, 19 Apr 2024 12:24:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59087, Retrieved Fri, 19 Apr 2024 12:24:33 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

113

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

-       [(Partial) Autocorrelation Function] [] [2009-11-24 14:31:17] [4c719cde102be108d35939b6cdb81c0f] [Current]

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8,7
8,2
8,3
8,5
8,6
8,5
8,2
8,1
7,9
8,6
8,7
8,7
8,5
8,4
8,5
8,7
8,7
8,6
8,5
8,3
8
8,2
8,1
8,1
8
7,9
7,9
8
8
7,9
8
7,7
7,2
7,5
7,3
7
7
7
7,2
7,3
7,1
6,8
6,4
6,1
6,5
7,7
7,9
7,5
6,9
6,6
6,9
7,7
8
8
7,7
7,3
7,4
8,1
8,3
8,2

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=59087&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=59087&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59087&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	0.862289	6.6793	0
2	0.666135	5.1599	1e-06
3	0.543873	4.2128	4.3e-05
4	0.553114	4.2844	3.4e-05
5	0.645308	4.9985	3e-06
6	0.699257	5.4164	1e-06
7	0.630142	4.8811	4e-06
8	0.477969	3.7023	0.000233
9	0.358381	2.776	0.003665
10	0.295938	2.2923	0.012705
11	0.311176	2.4104	0.009509
12	0.322443	2.4976	0.007631
13	0.242214	1.8762	0.032748
14	0.140878	1.0912	0.139765
15	0.056574	0.4382	0.3314
16	-0.001897	-0.0147	0.494162
17	-0.03469	-0.2687	0.394537

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.862289 & 6.6793 & 0 \tabularnewline
2 & 0.666135 & 5.1599 & 1e-06 \tabularnewline
3 & 0.543873 & 4.2128 & 4.3e-05 \tabularnewline
4 & 0.553114 & 4.2844 & 3.4e-05 \tabularnewline
5 & 0.645308 & 4.9985 & 3e-06 \tabularnewline
6 & 0.699257 & 5.4164 & 1e-06 \tabularnewline
7 & 0.630142 & 4.8811 & 4e-06 \tabularnewline
8 & 0.477969 & 3.7023 & 0.000233 \tabularnewline
9 & 0.358381 & 2.776 & 0.003665 \tabularnewline
10 & 0.295938 & 2.2923 & 0.012705 \tabularnewline
11 & 0.311176 & 2.4104 & 0.009509 \tabularnewline
12 & 0.322443 & 2.4976 & 0.007631 \tabularnewline
13 & 0.242214 & 1.8762 & 0.032748 \tabularnewline
14 & 0.140878 & 1.0912 & 0.139765 \tabularnewline
15 & 0.056574 & 0.4382 & 0.3314 \tabularnewline
16 & -0.001897 & -0.0147 & 0.494162 \tabularnewline
17 & -0.03469 & -0.2687 & 0.394537 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59087&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]0.862289[/C][C]6.6793[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.666135[/C][C]5.1599[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.543873[/C][C]4.2128[/C][C]4.3e-05[/C][/ROW]
[ROW][C]4[/C][C]0.553114[/C][C]4.2844[/C][C]3.4e-05[/C][/ROW]
[ROW][C]5[/C][C]0.645308[/C][C]4.9985[/C][C]3e-06[/C][/ROW]
[ROW][C]6[/C][C]0.699257[/C][C]5.4164[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.630142[/C][C]4.8811[/C][C]4e-06[/C][/ROW]
[ROW][C]8[/C][C]0.477969[/C][C]3.7023[/C][C]0.000233[/C][/ROW]
[ROW][C]9[/C][C]0.358381[/C][C]2.776[/C][C]0.003665[/C][/ROW]
[ROW][C]10[/C][C]0.295938[/C][C]2.2923[/C][C]0.012705[/C][/ROW]
[ROW][C]11[/C][C]0.311176[/C][C]2.4104[/C][C]0.009509[/C][/ROW]
[ROW][C]12[/C][C]0.322443[/C][C]2.4976[/C][C]0.007631[/C][/ROW]
[ROW][C]13[/C][C]0.242214[/C][C]1.8762[/C][C]0.032748[/C][/ROW]
[ROW][C]14[/C][C]0.140878[/C][C]1.0912[/C][C]0.139765[/C][/ROW]
[ROW][C]15[/C][C]0.056574[/C][C]0.4382[/C][C]0.3314[/C][/ROW]
[ROW][C]16[/C][C]-0.001897[/C][C]-0.0147[/C][C]0.494162[/C][/ROW]
[ROW][C]17[/C][C]-0.03469[/C][C]-0.2687[/C][C]0.394537[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59087&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59087&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	0.862289	6.6793	0
2	0.666135	5.1599	1e-06
3	0.543873	4.2128	4.3e-05
4	0.553114	4.2844	3.4e-05
5	0.645308	4.9985	3e-06
6	0.699257	5.4164	1e-06
7	0.630142	4.8811	4e-06
8	0.477969	3.7023	0.000233
9	0.358381	2.776	0.003665
10	0.295938	2.2923	0.012705
11	0.311176	2.4104	0.009509
12	0.322443	2.4976	0.007631
13	0.242214	1.8762	0.032748
14	0.140878	1.0912	0.139765
15	0.056574	0.4382	0.3314
16	-0.001897	-0.0147	0.494162
17	-0.03469	-0.2687	0.394537

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.862289	6.6793	0
2	-0.301834	-2.338	0.01137
3	0.241816	1.8731	0.032964
4	0.347485	2.6916	0.0046
5	0.259027	2.0064	0.024663
6	0.00439	0.034	0.486494
7	-0.194981	-1.5103	0.068106
8	-0.142481	-1.1037	0.137076
9	0.002366	0.0183	0.492719
10	-0.232406	-1.8002	0.038427
11	0.02072	0.1605	0.436516
12	-0.110345	-0.8547	0.198051
13	-0.258346	-2.0011	0.024953
14	0.16065	1.2444	0.109098
15	-0.035728	-0.2767	0.391463
16	-0.149794	-1.1603	0.125262
17	-0.035599	-0.2757	0.391844

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.862289 & 6.6793 & 0 \tabularnewline
2 & -0.301834 & -2.338 & 0.01137 \tabularnewline
3 & 0.241816 & 1.8731 & 0.032964 \tabularnewline
4 & 0.347485 & 2.6916 & 0.0046 \tabularnewline
5 & 0.259027 & 2.0064 & 0.024663 \tabularnewline
6 & 0.00439 & 0.034 & 0.486494 \tabularnewline
7 & -0.194981 & -1.5103 & 0.068106 \tabularnewline
8 & -0.142481 & -1.1037 & 0.137076 \tabularnewline
9 & 0.002366 & 0.0183 & 0.492719 \tabularnewline
10 & -0.232406 & -1.8002 & 0.038427 \tabularnewline
11 & 0.02072 & 0.1605 & 0.436516 \tabularnewline
12 & -0.110345 & -0.8547 & 0.198051 \tabularnewline
13 & -0.258346 & -2.0011 & 0.024953 \tabularnewline
14 & 0.16065 & 1.2444 & 0.109098 \tabularnewline
15 & -0.035728 & -0.2767 & 0.391463 \tabularnewline
16 & -0.149794 & -1.1603 & 0.125262 \tabularnewline
17 & -0.035599 & -0.2757 & 0.391844 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59087&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]0.862289[/C][C]6.6793[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.301834[/C][C]-2.338[/C][C]0.01137[/C][/ROW]
[ROW][C]3[/C][C]0.241816[/C][C]1.8731[/C][C]0.032964[/C][/ROW]
[ROW][C]4[/C][C]0.347485[/C][C]2.6916[/C][C]0.0046[/C][/ROW]
[ROW][C]5[/C][C]0.259027[/C][C]2.0064[/C][C]0.024663[/C][/ROW]
[ROW][C]6[/C][C]0.00439[/C][C]0.034[/C][C]0.486494[/C][/ROW]
[ROW][C]7[/C][C]-0.194981[/C][C]-1.5103[/C][C]0.068106[/C][/ROW]
[ROW][C]8[/C][C]-0.142481[/C][C]-1.1037[/C][C]0.137076[/C][/ROW]
[ROW][C]9[/C][C]0.002366[/C][C]0.0183[/C][C]0.492719[/C][/ROW]
[ROW][C]10[/C][C]-0.232406[/C][C]-1.8002[/C][C]0.038427[/C][/ROW]
[ROW][C]11[/C][C]0.02072[/C][C]0.1605[/C][C]0.436516[/C][/ROW]
[ROW][C]12[/C][C]-0.110345[/C][C]-0.8547[/C][C]0.198051[/C][/ROW]
[ROW][C]13[/C][C]-0.258346[/C][C]-2.0011[/C][C]0.024953[/C][/ROW]
[ROW][C]14[/C][C]0.16065[/C][C]1.2444[/C][C]0.109098[/C][/ROW]
[ROW][C]15[/C][C]-0.035728[/C][C]-0.2767[/C][C]0.391463[/C][/ROW]
[ROW][C]16[/C][C]-0.149794[/C][C]-1.1603[/C][C]0.125262[/C][/ROW]
[ROW][C]17[/C][C]-0.035599[/C][C]-0.2757[/C][C]0.391844[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59087&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59087&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	0.862289	6.6793	0
2	-0.301834	-2.338	0.01137
3	0.241816	1.8731	0.032964
4	0.347485	2.6916	0.0046
5	0.259027	2.0064	0.024663
6	0.00439	0.034	0.486494
7	-0.194981	-1.5103	0.068106
8	-0.142481	-1.1037	0.137076
9	0.002366	0.0183	0.492719
10	-0.232406	-1.8002	0.038427
11	0.02072	0.1605	0.436516
12	-0.110345	-0.8547	0.198051
13	-0.258346	-2.0011	0.024953
14	0.16065	1.2444	0.109098
15	-0.035728	-0.2767	0.391463
16	-0.149794	-1.1603	0.125262
17	-0.035599	-0.2757	0.391844

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