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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 07 Dec 2007 05:49:17 -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/07/t1197031029vtviddfh71nmpks.htm/, Retrieved Mon, 29 Apr 2024 03:11:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2788, Retrieved Mon, 29 Apr 2024 03:11:09 +0000

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No (this computation is public)

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Estimated Impact

204

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-       [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2007-12-07 12:49:17] [9bb499d88394279c02e6a8b8cf177cf7] [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=2788&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=2788&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2788&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	8.3066	0
1	-0.155485	-1.2916	0.89959
2	-0.040116	-0.3332	0.630015
3	-0.13661	-1.1348	0.869799
4	-0.044283	-0.3678	0.642943
5	0.17863	1.4838	0.071207
6	-0.090745	-0.7538	0.773228
7	0.043887	0.3646	0.358281
8	-0.242644	-2.0156	0.976128
9	-0.03929	-0.3264	0.627434
10	0.052641	0.4373	0.331642
11	0.248724	2.0661	0.02129
12	0.020064	0.1667	0.434061
13	-0.193481	-1.6072	0.943709
14	-0.02784	-0.2313	0.5911
15	0.048723	0.4047	0.343467
16	-0.014573	-0.1211	0.547998
17	-0.116607	-0.9686	0.83194

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.3066 & 0 \tabularnewline
1 & -0.155485 & -1.2916 & 0.89959 \tabularnewline
2 & -0.040116 & -0.3332 & 0.630015 \tabularnewline
3 & -0.13661 & -1.1348 & 0.869799 \tabularnewline
4 & -0.044283 & -0.3678 & 0.642943 \tabularnewline
5 & 0.17863 & 1.4838 & 0.071207 \tabularnewline
6 & -0.090745 & -0.7538 & 0.773228 \tabularnewline
7 & 0.043887 & 0.3646 & 0.358281 \tabularnewline
8 & -0.242644 & -2.0156 & 0.976128 \tabularnewline
9 & -0.03929 & -0.3264 & 0.627434 \tabularnewline
10 & 0.052641 & 0.4373 & 0.331642 \tabularnewline
11 & 0.248724 & 2.0661 & 0.02129 \tabularnewline
12 & 0.020064 & 0.1667 & 0.434061 \tabularnewline
13 & -0.193481 & -1.6072 & 0.943709 \tabularnewline
14 & -0.02784 & -0.2313 & 0.5911 \tabularnewline
15 & 0.048723 & 0.4047 & 0.343467 \tabularnewline
16 & -0.014573 & -0.1211 & 0.547998 \tabularnewline
17 & -0.116607 & -0.9686 & 0.83194 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2788&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]8.3066[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.155485[/C][C]-1.2916[/C][C]0.89959[/C][/ROW]
[ROW][C]2[/C][C]-0.040116[/C][C]-0.3332[/C][C]0.630015[/C][/ROW]
[ROW][C]3[/C][C]-0.13661[/C][C]-1.1348[/C][C]0.869799[/C][/ROW]
[ROW][C]4[/C][C]-0.044283[/C][C]-0.3678[/C][C]0.642943[/C][/ROW]
[ROW][C]5[/C][C]0.17863[/C][C]1.4838[/C][C]0.071207[/C][/ROW]
[ROW][C]6[/C][C]-0.090745[/C][C]-0.7538[/C][C]0.773228[/C][/ROW]
[ROW][C]7[/C][C]0.043887[/C][C]0.3646[/C][C]0.358281[/C][/ROW]
[ROW][C]8[/C][C]-0.242644[/C][C]-2.0156[/C][C]0.976128[/C][/ROW]
[ROW][C]9[/C][C]-0.03929[/C][C]-0.3264[/C][C]0.627434[/C][/ROW]
[ROW][C]10[/C][C]0.052641[/C][C]0.4373[/C][C]0.331642[/C][/ROW]
[ROW][C]11[/C][C]0.248724[/C][C]2.0661[/C][C]0.02129[/C][/ROW]
[ROW][C]12[/C][C]0.020064[/C][C]0.1667[/C][C]0.434061[/C][/ROW]
[ROW][C]13[/C][C]-0.193481[/C][C]-1.6072[/C][C]0.943709[/C][/ROW]
[ROW][C]14[/C][C]-0.02784[/C][C]-0.2313[/C][C]0.5911[/C][/ROW]
[ROW][C]15[/C][C]0.048723[/C][C]0.4047[/C][C]0.343467[/C][/ROW]
[ROW][C]16[/C][C]-0.014573[/C][C]-0.1211[/C][C]0.547998[/C][/ROW]
[ROW][C]17[/C][C]-0.116607[/C][C]-0.9686[/C][C]0.83194[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2788&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2788&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	8.3066	0
1	-0.155485	-1.2916	0.89959
2	-0.040116	-0.3332	0.630015
3	-0.13661	-1.1348	0.869799
4	-0.044283	-0.3678	0.642943
5	0.17863	1.4838	0.071207
6	-0.090745	-0.7538	0.773228
7	0.043887	0.3646	0.358281
8	-0.242644	-2.0156	0.976128
9	-0.03929	-0.3264	0.627434
10	0.052641	0.4373	0.331642
11	0.248724	2.0661	0.02129
12	0.020064	0.1667	0.434061
13	-0.193481	-1.6072	0.943709
14	-0.02784	-0.2313	0.5911
15	0.048723	0.4047	0.343467
16	-0.014573	-0.1211	0.547998
17	-0.116607	-0.9686	0.83194

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.155485	-1.2916	0.89959
1	-0.065885	-0.5473	0.707024
2	-0.157991	-1.3124	0.903128
3	-0.101975	-0.8471	0.800056
4	0.142234	1.1815	0.120734
5	-0.071118	-0.5907	0.72169
6	0.020591	0.171	0.432344
7	-0.21606	-1.7947	0.961462
8	-0.128969	-1.0713	0.856115
9	-0.038068	-0.3162	0.623602
10	0.236084	1.9611	0.026955
11	0.057924	0.4812	0.315965
12	-0.106349	-0.8834	0.809957
13	-0.052522	-0.4363	0.668003
14	0.046776	0.3886	0.349402
15	-0.162758	-1.352	0.9096
16	-0.201507	-1.6738	0.950656
17	-0.050119	-0.4163	0.660765

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.155485 & -1.2916 & 0.89959 \tabularnewline
1 & -0.065885 & -0.5473 & 0.707024 \tabularnewline
2 & -0.157991 & -1.3124 & 0.903128 \tabularnewline
3 & -0.101975 & -0.8471 & 0.800056 \tabularnewline
4 & 0.142234 & 1.1815 & 0.120734 \tabularnewline
5 & -0.071118 & -0.5907 & 0.72169 \tabularnewline
6 & 0.020591 & 0.171 & 0.432344 \tabularnewline
7 & -0.21606 & -1.7947 & 0.961462 \tabularnewline
8 & -0.128969 & -1.0713 & 0.856115 \tabularnewline
9 & -0.038068 & -0.3162 & 0.623602 \tabularnewline
10 & 0.236084 & 1.9611 & 0.026955 \tabularnewline
11 & 0.057924 & 0.4812 & 0.315965 \tabularnewline
12 & -0.106349 & -0.8834 & 0.809957 \tabularnewline
13 & -0.052522 & -0.4363 & 0.668003 \tabularnewline
14 & 0.046776 & 0.3886 & 0.349402 \tabularnewline
15 & -0.162758 & -1.352 & 0.9096 \tabularnewline
16 & -0.201507 & -1.6738 & 0.950656 \tabularnewline
17 & -0.050119 & -0.4163 & 0.660765 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2788&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]-0.155485[/C][C]-1.2916[/C][C]0.89959[/C][/ROW]
[ROW][C]1[/C][C]-0.065885[/C][C]-0.5473[/C][C]0.707024[/C][/ROW]
[ROW][C]2[/C][C]-0.157991[/C][C]-1.3124[/C][C]0.903128[/C][/ROW]
[ROW][C]3[/C][C]-0.101975[/C][C]-0.8471[/C][C]0.800056[/C][/ROW]
[ROW][C]4[/C][C]0.142234[/C][C]1.1815[/C][C]0.120734[/C][/ROW]
[ROW][C]5[/C][C]-0.071118[/C][C]-0.5907[/C][C]0.72169[/C][/ROW]
[ROW][C]6[/C][C]0.020591[/C][C]0.171[/C][C]0.432344[/C][/ROW]
[ROW][C]7[/C][C]-0.21606[/C][C]-1.7947[/C][C]0.961462[/C][/ROW]
[ROW][C]8[/C][C]-0.128969[/C][C]-1.0713[/C][C]0.856115[/C][/ROW]
[ROW][C]9[/C][C]-0.038068[/C][C]-0.3162[/C][C]0.623602[/C][/ROW]
[ROW][C]10[/C][C]0.236084[/C][C]1.9611[/C][C]0.026955[/C][/ROW]
[ROW][C]11[/C][C]0.057924[/C][C]0.4812[/C][C]0.315965[/C][/ROW]
[ROW][C]12[/C][C]-0.106349[/C][C]-0.8834[/C][C]0.809957[/C][/ROW]
[ROW][C]13[/C][C]-0.052522[/C][C]-0.4363[/C][C]0.668003[/C][/ROW]
[ROW][C]14[/C][C]0.046776[/C][C]0.3886[/C][C]0.349402[/C][/ROW]
[ROW][C]15[/C][C]-0.162758[/C][C]-1.352[/C][C]0.9096[/C][/ROW]
[ROW][C]16[/C][C]-0.201507[/C][C]-1.6738[/C][C]0.950656[/C][/ROW]
[ROW][C]17[/C][C]-0.050119[/C][C]-0.4163[/C][C]0.660765[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2788&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2788&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	-0.155485	-1.2916	0.89959
1	-0.065885	-0.5473	0.707024
2	-0.157991	-1.3124	0.903128
3	-0.101975	-0.8471	0.800056
4	0.142234	1.1815	0.120734
5	-0.071118	-0.5907	0.72169
6	0.020591	0.171	0.432344
7	-0.21606	-1.7947	0.961462
8	-0.128969	-1.0713	0.856115
9	-0.038068	-0.3162	0.623602
10	0.236084	1.9611	0.026955
11	0.057924	0.4812	0.315965
12	-0.106349	-0.8834	0.809957
13	-0.052522	-0.4363	0.668003
14	0.046776	0.3886	0.349402
15	-0.162758	-1.352	0.9096
16	-0.201507	-1.6738	0.950656
17	-0.050119	-0.4163	0.660765

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; 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 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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