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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 17 Dec 2007 15:45:30 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/17/t1197930501kxzei484qji3p4p.htm/, Retrieved Fri, 03 May 2024 17:30:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4441, Retrieved Fri, 03 May 2024 17:30:12 +0000

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Estimated Impact

181

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-       [(Partial) Autocorrelation Function] [] [2007-12-17 22:45:30] [ba3202e2798d2e4685d19d988e9c69df] [Current]

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Summary of compuational 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 compuational 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=4441&T=0

[TABLE]
[ROW][C]Summary of compuational 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=4441&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4441&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 compuational 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
0	1	7.6811	0
1	-0.341573	-2.6237	0.994472
2	-0.17333	-1.3314	0.905906
3	-0.044424	-0.3412	0.632928
4	0.165696	1.2727	0.104053
5	0.061154	0.4697	0.320138
6	-0.168819	-1.2967	0.900113
7	0.044327	0.3405	0.367351
8	0.097078	0.7457	0.229413
9	0.003794	0.0291	0.488424
10	-0.142595	-1.0953	0.86108
11	0.117757	0.9045	0.184702
12	-0.004268	-0.0328	0.513022
13	0.048767	0.3746	0.354655
14	-0.002981	-0.0229	0.509097
15	-0.189476	-1.4554	0.924569
16	0.235845	1.8116	0.037572
17	-0.100919	-0.7752	0.779334

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & -0.341573 & -2.6237 & 0.994472 \tabularnewline
2 & -0.17333 & -1.3314 & 0.905906 \tabularnewline
3 & -0.044424 & -0.3412 & 0.632928 \tabularnewline
4 & 0.165696 & 1.2727 & 0.104053 \tabularnewline
5 & 0.061154 & 0.4697 & 0.320138 \tabularnewline
6 & -0.168819 & -1.2967 & 0.900113 \tabularnewline
7 & 0.044327 & 0.3405 & 0.367351 \tabularnewline
8 & 0.097078 & 0.7457 & 0.229413 \tabularnewline
9 & 0.003794 & 0.0291 & 0.488424 \tabularnewline
10 & -0.142595 & -1.0953 & 0.86108 \tabularnewline
11 & 0.117757 & 0.9045 & 0.184702 \tabularnewline
12 & -0.004268 & -0.0328 & 0.513022 \tabularnewline
13 & 0.048767 & 0.3746 & 0.354655 \tabularnewline
14 & -0.002981 & -0.0229 & 0.509097 \tabularnewline
15 & -0.189476 & -1.4554 & 0.924569 \tabularnewline
16 & 0.235845 & 1.8116 & 0.037572 \tabularnewline
17 & -0.100919 & -0.7752 & 0.779334 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4441&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]0[/C][C]1[/C][C]7.6811[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.341573[/C][C]-2.6237[/C][C]0.994472[/C][/ROW]
[ROW][C]2[/C][C]-0.17333[/C][C]-1.3314[/C][C]0.905906[/C][/ROW]
[ROW][C]3[/C][C]-0.044424[/C][C]-0.3412[/C][C]0.632928[/C][/ROW]
[ROW][C]4[/C][C]0.165696[/C][C]1.2727[/C][C]0.104053[/C][/ROW]
[ROW][C]5[/C][C]0.061154[/C][C]0.4697[/C][C]0.320138[/C][/ROW]
[ROW][C]6[/C][C]-0.168819[/C][C]-1.2967[/C][C]0.900113[/C][/ROW]
[ROW][C]7[/C][C]0.044327[/C][C]0.3405[/C][C]0.367351[/C][/ROW]
[ROW][C]8[/C][C]0.097078[/C][C]0.7457[/C][C]0.229413[/C][/ROW]
[ROW][C]9[/C][C]0.003794[/C][C]0.0291[/C][C]0.488424[/C][/ROW]
[ROW][C]10[/C][C]-0.142595[/C][C]-1.0953[/C][C]0.86108[/C][/ROW]
[ROW][C]11[/C][C]0.117757[/C][C]0.9045[/C][C]0.184702[/C][/ROW]
[ROW][C]12[/C][C]-0.004268[/C][C]-0.0328[/C][C]0.513022[/C][/ROW]
[ROW][C]13[/C][C]0.048767[/C][C]0.3746[/C][C]0.354655[/C][/ROW]
[ROW][C]14[/C][C]-0.002981[/C][C]-0.0229[/C][C]0.509097[/C][/ROW]
[ROW][C]15[/C][C]-0.189476[/C][C]-1.4554[/C][C]0.924569[/C][/ROW]
[ROW][C]16[/C][C]0.235845[/C][C]1.8116[/C][C]0.037572[/C][/ROW]
[ROW][C]17[/C][C]-0.100919[/C][C]-0.7752[/C][C]0.779334[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4441&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4441&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
0	1	7.6811	0
1	-0.341573	-2.6237	0.994472
2	-0.17333	-1.3314	0.905906
3	-0.044424	-0.3412	0.632928
4	0.165696	1.2727	0.104053
5	0.061154	0.4697	0.320138
6	-0.168819	-1.2967	0.900113
7	0.044327	0.3405	0.367351
8	0.097078	0.7457	0.229413
9	0.003794	0.0291	0.488424
10	-0.142595	-1.0953	0.86108
11	0.117757	0.9045	0.184702
12	-0.004268	-0.0328	0.513022
13	0.048767	0.3746	0.354655
14	-0.002981	-0.0229	0.509097
15	-0.189476	-1.4554	0.924569
16	0.235845	1.8116	0.037572
17	-0.100919	-0.7752	0.779334

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.341573	-2.6237	0.994472
1	-0.328307	-2.5218	0.992802
2	-0.298442	-2.2924	0.987266
3	-0.057288	-0.44	0.66924
4	0.079441	0.6102	0.272037
5	-0.06373	-0.4895	0.686856
6	0.019174	0.1473	0.441707
7	0.095629	0.7345	0.232764
8	0.083871	0.6442	0.260963
9	-0.054136	-0.4158	0.660477
10	0.093757	0.7202	0.237133
11	0.006265	0.0481	0.480891
12	0.083143	0.6386	0.262767
13	0.151406	1.163	0.124761
14	-0.147883	-1.1359	0.869706
15	0.104298	0.8011	0.213137
16	-0.04545	-0.3491	0.635873
17	-0.118233	-0.9082	0.816256

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.341573 & -2.6237 & 0.994472 \tabularnewline
1 & -0.328307 & -2.5218 & 0.992802 \tabularnewline
2 & -0.298442 & -2.2924 & 0.987266 \tabularnewline
3 & -0.057288 & -0.44 & 0.66924 \tabularnewline
4 & 0.079441 & 0.6102 & 0.272037 \tabularnewline
5 & -0.06373 & -0.4895 & 0.686856 \tabularnewline
6 & 0.019174 & 0.1473 & 0.441707 \tabularnewline
7 & 0.095629 & 0.7345 & 0.232764 \tabularnewline
8 & 0.083871 & 0.6442 & 0.260963 \tabularnewline
9 & -0.054136 & -0.4158 & 0.660477 \tabularnewline
10 & 0.093757 & 0.7202 & 0.237133 \tabularnewline
11 & 0.006265 & 0.0481 & 0.480891 \tabularnewline
12 & 0.083143 & 0.6386 & 0.262767 \tabularnewline
13 & 0.151406 & 1.163 & 0.124761 \tabularnewline
14 & -0.147883 & -1.1359 & 0.869706 \tabularnewline
15 & 0.104298 & 0.8011 & 0.213137 \tabularnewline
16 & -0.04545 & -0.3491 & 0.635873 \tabularnewline
17 & -0.118233 & -0.9082 & 0.816256 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4441&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]0[/C][C]-0.341573[/C][C]-2.6237[/C][C]0.994472[/C][/ROW]
[ROW][C]1[/C][C]-0.328307[/C][C]-2.5218[/C][C]0.992802[/C][/ROW]
[ROW][C]2[/C][C]-0.298442[/C][C]-2.2924[/C][C]0.987266[/C][/ROW]
[ROW][C]3[/C][C]-0.057288[/C][C]-0.44[/C][C]0.66924[/C][/ROW]
[ROW][C]4[/C][C]0.079441[/C][C]0.6102[/C][C]0.272037[/C][/ROW]
[ROW][C]5[/C][C]-0.06373[/C][C]-0.4895[/C][C]0.686856[/C][/ROW]
[ROW][C]6[/C][C]0.019174[/C][C]0.1473[/C][C]0.441707[/C][/ROW]
[ROW][C]7[/C][C]0.095629[/C][C]0.7345[/C][C]0.232764[/C][/ROW]
[ROW][C]8[/C][C]0.083871[/C][C]0.6442[/C][C]0.260963[/C][/ROW]
[ROW][C]9[/C][C]-0.054136[/C][C]-0.4158[/C][C]0.660477[/C][/ROW]
[ROW][C]10[/C][C]0.093757[/C][C]0.7202[/C][C]0.237133[/C][/ROW]
[ROW][C]11[/C][C]0.006265[/C][C]0.0481[/C][C]0.480891[/C][/ROW]
[ROW][C]12[/C][C]0.083143[/C][C]0.6386[/C][C]0.262767[/C][/ROW]
[ROW][C]13[/C][C]0.151406[/C][C]1.163[/C][C]0.124761[/C][/ROW]
[ROW][C]14[/C][C]-0.147883[/C][C]-1.1359[/C][C]0.869706[/C][/ROW]
[ROW][C]15[/C][C]0.104298[/C][C]0.8011[/C][C]0.213137[/C][/ROW]
[ROW][C]16[/C][C]-0.04545[/C][C]-0.3491[/C][C]0.635873[/C][/ROW]
[ROW][C]17[/C][C]-0.118233[/C][C]-0.9082[/C][C]0.816256[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4441&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4441&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
0	-0.341573	-2.6237	0.994472
1	-0.328307	-2.5218	0.992802
2	-0.298442	-2.2924	0.987266
3	-0.057288	-0.44	0.66924
4	0.079441	0.6102	0.272037
5	-0.06373	-0.4895	0.686856
6	0.019174	0.1473	0.441707
7	0.095629	0.7345	0.232764
8	0.083871	0.6442	0.260963
9	-0.054136	-0.4158	0.660477
10	0.093757	0.7202	0.237133
11	0.006265	0.0481	0.480891
12	0.083143	0.6386	0.262767
13	0.151406	1.163	0.124761
14	-0.147883	-1.1359	0.869706
15	0.104298	0.8011	0.213137
16	-0.04545	-0.3491	0.635873
17	-0.118233	-0.9082	0.816256

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 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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