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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 07 Jun 2009 11:20:59 -0600

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/Jun/07/t1244395304q91l54bbm10t14m.htm/, Retrieved Mon, 13 May 2024 18:43:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42208, Retrieved Mon, 13 May 2024 18:43:38 +0000

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Estimated Impact

101

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

-       [(Partial) Autocorrelation Function] [Thomas Van den Bo...] [2009-06-07 17:20:59] [50e97696ebad247f45d73cd9926afb25] [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	'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=42208&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=42208&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42208&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	0.240626	2.308	0.01162
2	0.185818	1.7823	0.038999
3	0.065004	0.6235	0.26725
4	-0.099151	-0.951	0.172041
5	-0.029265	-0.2807	0.389784
6	-0.154864	-1.4854	0.070428
7	0.032904	0.3156	0.376507
8	-0.21861	-2.0968	0.019376
9	-0.152282	-1.4606	0.073761
10	-0.296301	-2.842	0.002761
11	-0.338643	-3.2482	0.000811
12	-0.111057	-1.0652	0.144782
13	-0.141921	-1.3613	0.088378
14	0.044155	0.4235	0.336451
15	-0.010736	-0.103	0.459103
16	0.067969	0.6519	0.258034
17	-0.016667	-0.1599	0.436669
18	0.125313	1.202	0.116233
19	0.09907	0.9502	0.172239

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.240626 & 2.308 & 0.01162 \tabularnewline
2 & 0.185818 & 1.7823 & 0.038999 \tabularnewline
3 & 0.065004 & 0.6235 & 0.26725 \tabularnewline
4 & -0.099151 & -0.951 & 0.172041 \tabularnewline
5 & -0.029265 & -0.2807 & 0.389784 \tabularnewline
6 & -0.154864 & -1.4854 & 0.070428 \tabularnewline
7 & 0.032904 & 0.3156 & 0.376507 \tabularnewline
8 & -0.21861 & -2.0968 & 0.019376 \tabularnewline
9 & -0.152282 & -1.4606 & 0.073761 \tabularnewline
10 & -0.296301 & -2.842 & 0.002761 \tabularnewline
11 & -0.338643 & -3.2482 & 0.000811 \tabularnewline
12 & -0.111057 & -1.0652 & 0.144782 \tabularnewline
13 & -0.141921 & -1.3613 & 0.088378 \tabularnewline
14 & 0.044155 & 0.4235 & 0.336451 \tabularnewline
15 & -0.010736 & -0.103 & 0.459103 \tabularnewline
16 & 0.067969 & 0.6519 & 0.258034 \tabularnewline
17 & -0.016667 & -0.1599 & 0.436669 \tabularnewline
18 & 0.125313 & 1.202 & 0.116233 \tabularnewline
19 & 0.09907 & 0.9502 & 0.172239 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42208&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]0.240626[/C][C]2.308[/C][C]0.01162[/C][/ROW]
[ROW][C]2[/C][C]0.185818[/C][C]1.7823[/C][C]0.038999[/C][/ROW]
[ROW][C]3[/C][C]0.065004[/C][C]0.6235[/C][C]0.26725[/C][/ROW]
[ROW][C]4[/C][C]-0.099151[/C][C]-0.951[/C][C]0.172041[/C][/ROW]
[ROW][C]5[/C][C]-0.029265[/C][C]-0.2807[/C][C]0.389784[/C][/ROW]
[ROW][C]6[/C][C]-0.154864[/C][C]-1.4854[/C][C]0.070428[/C][/ROW]
[ROW][C]7[/C][C]0.032904[/C][C]0.3156[/C][C]0.376507[/C][/ROW]
[ROW][C]8[/C][C]-0.21861[/C][C]-2.0968[/C][C]0.019376[/C][/ROW]
[ROW][C]9[/C][C]-0.152282[/C][C]-1.4606[/C][C]0.073761[/C][/ROW]
[ROW][C]10[/C][C]-0.296301[/C][C]-2.842[/C][C]0.002761[/C][/ROW]
[ROW][C]11[/C][C]-0.338643[/C][C]-3.2482[/C][C]0.000811[/C][/ROW]
[ROW][C]12[/C][C]-0.111057[/C][C]-1.0652[/C][C]0.144782[/C][/ROW]
[ROW][C]13[/C][C]-0.141921[/C][C]-1.3613[/C][C]0.088378[/C][/ROW]
[ROW][C]14[/C][C]0.044155[/C][C]0.4235[/C][C]0.336451[/C][/ROW]
[ROW][C]15[/C][C]-0.010736[/C][C]-0.103[/C][C]0.459103[/C][/ROW]
[ROW][C]16[/C][C]0.067969[/C][C]0.6519[/C][C]0.258034[/C][/ROW]
[ROW][C]17[/C][C]-0.016667[/C][C]-0.1599[/C][C]0.436669[/C][/ROW]
[ROW][C]18[/C][C]0.125313[/C][C]1.202[/C][C]0.116233[/C][/ROW]
[ROW][C]19[/C][C]0.09907[/C][C]0.9502[/C][C]0.172239[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42208&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42208&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	0.240626	2.308	0.01162
2	0.185818	1.7823	0.038999
3	0.065004	0.6235	0.26725
4	-0.099151	-0.951	0.172041
5	-0.029265	-0.2807	0.389784
6	-0.154864	-1.4854	0.070428
7	0.032904	0.3156	0.376507
8	-0.21861	-2.0968	0.019376
9	-0.152282	-1.4606	0.073761
10	-0.296301	-2.842	0.002761
11	-0.338643	-3.2482	0.000811
12	-0.111057	-1.0652	0.144782
13	-0.141921	-1.3613	0.088378
14	0.044155	0.4235	0.336451
15	-0.010736	-0.103	0.459103
16	0.067969	0.6519	0.258034
17	-0.016667	-0.1599	0.436669
18	0.125313	1.202	0.116233
19	0.09907	0.9502	0.172239

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.240626	2.308	0.01162
2	0.135779	1.3023	0.098024
3	-0.006823	-0.0654	0.473981
4	-0.147706	-1.4167	0.079968
5	0.013473	0.1292	0.44873
6	-0.121459	-1.165	0.123518
7	0.115248	1.1054	0.13593
8	-0.249661	-2.3947	0.009332
9	-0.07161	-0.6869	0.246949
10	-0.273876	-2.6269	0.005047
11	-0.189029	-1.8131	0.036539
12	-0.023941	-0.2296	0.409441
13	-0.058052	-0.5568	0.289502
14	-0.038454	-0.3688	0.356549
15	-0.085652	-0.8215	0.206729
16	-0.052269	-0.5013	0.308664
17	-0.148714	-1.4264	0.078566
18	0.103078	0.9887	0.162705
19	-0.140625	-1.3488	0.090352

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.240626 & 2.308 & 0.01162 \tabularnewline
2 & 0.135779 & 1.3023 & 0.098024 \tabularnewline
3 & -0.006823 & -0.0654 & 0.473981 \tabularnewline
4 & -0.147706 & -1.4167 & 0.079968 \tabularnewline
5 & 0.013473 & 0.1292 & 0.44873 \tabularnewline
6 & -0.121459 & -1.165 & 0.123518 \tabularnewline
7 & 0.115248 & 1.1054 & 0.13593 \tabularnewline
8 & -0.249661 & -2.3947 & 0.009332 \tabularnewline
9 & -0.07161 & -0.6869 & 0.246949 \tabularnewline
10 & -0.273876 & -2.6269 & 0.005047 \tabularnewline
11 & -0.189029 & -1.8131 & 0.036539 \tabularnewline
12 & -0.023941 & -0.2296 & 0.409441 \tabularnewline
13 & -0.058052 & -0.5568 & 0.289502 \tabularnewline
14 & -0.038454 & -0.3688 & 0.356549 \tabularnewline
15 & -0.085652 & -0.8215 & 0.206729 \tabularnewline
16 & -0.052269 & -0.5013 & 0.308664 \tabularnewline
17 & -0.148714 & -1.4264 & 0.078566 \tabularnewline
18 & 0.103078 & 0.9887 & 0.162705 \tabularnewline
19 & -0.140625 & -1.3488 & 0.090352 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42208&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]0.240626[/C][C]2.308[/C][C]0.01162[/C][/ROW]
[ROW][C]2[/C][C]0.135779[/C][C]1.3023[/C][C]0.098024[/C][/ROW]
[ROW][C]3[/C][C]-0.006823[/C][C]-0.0654[/C][C]0.473981[/C][/ROW]
[ROW][C]4[/C][C]-0.147706[/C][C]-1.4167[/C][C]0.079968[/C][/ROW]
[ROW][C]5[/C][C]0.013473[/C][C]0.1292[/C][C]0.44873[/C][/ROW]
[ROW][C]6[/C][C]-0.121459[/C][C]-1.165[/C][C]0.123518[/C][/ROW]
[ROW][C]7[/C][C]0.115248[/C][C]1.1054[/C][C]0.13593[/C][/ROW]
[ROW][C]8[/C][C]-0.249661[/C][C]-2.3947[/C][C]0.009332[/C][/ROW]
[ROW][C]9[/C][C]-0.07161[/C][C]-0.6869[/C][C]0.246949[/C][/ROW]
[ROW][C]10[/C][C]-0.273876[/C][C]-2.6269[/C][C]0.005047[/C][/ROW]
[ROW][C]11[/C][C]-0.189029[/C][C]-1.8131[/C][C]0.036539[/C][/ROW]
[ROW][C]12[/C][C]-0.023941[/C][C]-0.2296[/C][C]0.409441[/C][/ROW]
[ROW][C]13[/C][C]-0.058052[/C][C]-0.5568[/C][C]0.289502[/C][/ROW]
[ROW][C]14[/C][C]-0.038454[/C][C]-0.3688[/C][C]0.356549[/C][/ROW]
[ROW][C]15[/C][C]-0.085652[/C][C]-0.8215[/C][C]0.206729[/C][/ROW]
[ROW][C]16[/C][C]-0.052269[/C][C]-0.5013[/C][C]0.308664[/C][/ROW]
[ROW][C]17[/C][C]-0.148714[/C][C]-1.4264[/C][C]0.078566[/C][/ROW]
[ROW][C]18[/C][C]0.103078[/C][C]0.9887[/C][C]0.162705[/C][/ROW]
[ROW][C]19[/C][C]-0.140625[/C][C]-1.3488[/C][C]0.090352[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42208&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42208&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	0.240626	2.308	0.01162
2	0.135779	1.3023	0.098024
3	-0.006823	-0.0654	0.473981
4	-0.147706	-1.4167	0.079968
5	0.013473	0.1292	0.44873
6	-0.121459	-1.165	0.123518
7	0.115248	1.1054	0.13593
8	-0.249661	-2.3947	0.009332
9	-0.07161	-0.6869	0.246949
10	-0.273876	-2.6269	0.005047
11	-0.189029	-1.8131	0.036539
12	-0.023941	-0.2296	0.409441
13	-0.058052	-0.5568	0.289502
14	-0.038454	-0.3688	0.356549
15	-0.085652	-0.8215	0.206729
16	-0.052269	-0.5013	0.308664
17	-0.148714	-1.4264	0.078566
18	0.103078	0.9887	0.162705
19	-0.140625	-1.3488	0.090352

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

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')

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