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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 21 Dec 2008 04:10:38 -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/2008/Dec/21/t1229857894l1eromyi464kccg.htm/, Retrieved Sun, 19 May 2024 10:07:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35495, Retrieved Sun, 19 May 2024 10:07:41 +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)

-     [Standard Deviation-Mean Plot] [] [2008-12-21 10:26:45] [339926f84f7378398edd9a77d1fc8e74]
- RMPD    [(Partial) Autocorrelation Function] [] [2008-12-21 11:10:38] [76e580e81b2082744334eb1f6d9ccc3e] [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	'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35495&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35495&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35495&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.047797	0.4381	0.331232
2	-0.202038	-1.8517	0.03379
3	0.031852	0.2919	0.385531
4	0.03521	0.3227	0.373862
5	0.110322	1.0111	0.157432
6	-0.073058	-0.6696	0.252479
7	0.009788	0.0897	0.464368
8	-0.095398	-0.8743	0.192213
9	-0.147575	-1.3525	0.089915
10	0.230705	2.1144	0.018721
11	0.172982	1.5854	0.058316
12	0.006594	0.0604	0.475977
13	-0.110491	-1.0127	0.157064
14	-0.074412	-0.682	0.24856
15	0.064139	0.5878	0.279107
16	-0.006557	-0.0601	0.476112
17	0.006638	0.0608	0.475816
18	-0.025617	-0.2348	0.407475
19	-0.082331	-0.7546	0.226306

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.047797 & 0.4381 & 0.331232 \tabularnewline
2 & -0.202038 & -1.8517 & 0.03379 \tabularnewline
3 & 0.031852 & 0.2919 & 0.385531 \tabularnewline
4 & 0.03521 & 0.3227 & 0.373862 \tabularnewline
5 & 0.110322 & 1.0111 & 0.157432 \tabularnewline
6 & -0.073058 & -0.6696 & 0.252479 \tabularnewline
7 & 0.009788 & 0.0897 & 0.464368 \tabularnewline
8 & -0.095398 & -0.8743 & 0.192213 \tabularnewline
9 & -0.147575 & -1.3525 & 0.089915 \tabularnewline
10 & 0.230705 & 2.1144 & 0.018721 \tabularnewline
11 & 0.172982 & 1.5854 & 0.058316 \tabularnewline
12 & 0.006594 & 0.0604 & 0.475977 \tabularnewline
13 & -0.110491 & -1.0127 & 0.157064 \tabularnewline
14 & -0.074412 & -0.682 & 0.24856 \tabularnewline
15 & 0.064139 & 0.5878 & 0.279107 \tabularnewline
16 & -0.006557 & -0.0601 & 0.476112 \tabularnewline
17 & 0.006638 & 0.0608 & 0.475816 \tabularnewline
18 & -0.025617 & -0.2348 & 0.407475 \tabularnewline
19 & -0.082331 & -0.7546 & 0.226306 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35495&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]0.047797[/C][C]0.4381[/C][C]0.331232[/C][/ROW]
[ROW][C]2[/C][C]-0.202038[/C][C]-1.8517[/C][C]0.03379[/C][/ROW]
[ROW][C]3[/C][C]0.031852[/C][C]0.2919[/C][C]0.385531[/C][/ROW]
[ROW][C]4[/C][C]0.03521[/C][C]0.3227[/C][C]0.373862[/C][/ROW]
[ROW][C]5[/C][C]0.110322[/C][C]1.0111[/C][C]0.157432[/C][/ROW]
[ROW][C]6[/C][C]-0.073058[/C][C]-0.6696[/C][C]0.252479[/C][/ROW]
[ROW][C]7[/C][C]0.009788[/C][C]0.0897[/C][C]0.464368[/C][/ROW]
[ROW][C]8[/C][C]-0.095398[/C][C]-0.8743[/C][C]0.192213[/C][/ROW]
[ROW][C]9[/C][C]-0.147575[/C][C]-1.3525[/C][C]0.089915[/C][/ROW]
[ROW][C]10[/C][C]0.230705[/C][C]2.1144[/C][C]0.018721[/C][/ROW]
[ROW][C]11[/C][C]0.172982[/C][C]1.5854[/C][C]0.058316[/C][/ROW]
[ROW][C]12[/C][C]0.006594[/C][C]0.0604[/C][C]0.475977[/C][/ROW]
[ROW][C]13[/C][C]-0.110491[/C][C]-1.0127[/C][C]0.157064[/C][/ROW]
[ROW][C]14[/C][C]-0.074412[/C][C]-0.682[/C][C]0.24856[/C][/ROW]
[ROW][C]15[/C][C]0.064139[/C][C]0.5878[/C][C]0.279107[/C][/ROW]
[ROW][C]16[/C][C]-0.006557[/C][C]-0.0601[/C][C]0.476112[/C][/ROW]
[ROW][C]17[/C][C]0.006638[/C][C]0.0608[/C][C]0.475816[/C][/ROW]
[ROW][C]18[/C][C]-0.025617[/C][C]-0.2348[/C][C]0.407475[/C][/ROW]
[ROW][C]19[/C][C]-0.082331[/C][C]-0.7546[/C][C]0.226306[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35495&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35495&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	0.047797	0.4381	0.331232
2	-0.202038	-1.8517	0.03379
3	0.031852	0.2919	0.385531
4	0.03521	0.3227	0.373862
5	0.110322	1.0111	0.157432
6	-0.073058	-0.6696	0.252479
7	0.009788	0.0897	0.464368
8	-0.095398	-0.8743	0.192213
9	-0.147575	-1.3525	0.089915
10	0.230705	2.1144	0.018721
11	0.172982	1.5854	0.058316
12	0.006594	0.0604	0.475977
13	-0.110491	-1.0127	0.157064
14	-0.074412	-0.682	0.24856
15	0.064139	0.5878	0.279107
16	-0.006557	-0.0601	0.476112
17	0.006638	0.0608	0.475816
18	-0.025617	-0.2348	0.407475
19	-0.082331	-0.7546	0.226306

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.047797	0.4381	0.331232
2	-0.204791	-1.8769	0.031999
3	0.055734	0.5108	0.305412
4	-0.012253	-0.1123	0.455426
5	0.132868	1.2178	0.113363
6	-0.092567	-0.8484	0.199316
7	0.076355	0.6998	0.242993
8	-0.163235	-1.4961	0.069191
9	-0.106577	-0.9768	0.165738
10	0.197379	1.809	0.037014
11	0.136937	1.2551	0.10647
12	0.085986	0.7881	0.216436
13	-0.064741	-0.5934	0.277266
14	-0.073539	-0.674	0.251082
15	-0.051829	-0.475	0.318003
16	-0.025218	-0.2311	0.408889
17	0.018125	0.1661	0.434231
18	0.024567	0.2252	0.411201
19	0.013503	0.1238	0.450902

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.047797 & 0.4381 & 0.331232 \tabularnewline
2 & -0.204791 & -1.8769 & 0.031999 \tabularnewline
3 & 0.055734 & 0.5108 & 0.305412 \tabularnewline
4 & -0.012253 & -0.1123 & 0.455426 \tabularnewline
5 & 0.132868 & 1.2178 & 0.113363 \tabularnewline
6 & -0.092567 & -0.8484 & 0.199316 \tabularnewline
7 & 0.076355 & 0.6998 & 0.242993 \tabularnewline
8 & -0.163235 & -1.4961 & 0.069191 \tabularnewline
9 & -0.106577 & -0.9768 & 0.165738 \tabularnewline
10 & 0.197379 & 1.809 & 0.037014 \tabularnewline
11 & 0.136937 & 1.2551 & 0.10647 \tabularnewline
12 & 0.085986 & 0.7881 & 0.216436 \tabularnewline
13 & -0.064741 & -0.5934 & 0.277266 \tabularnewline
14 & -0.073539 & -0.674 & 0.251082 \tabularnewline
15 & -0.051829 & -0.475 & 0.318003 \tabularnewline
16 & -0.025218 & -0.2311 & 0.408889 \tabularnewline
17 & 0.018125 & 0.1661 & 0.434231 \tabularnewline
18 & 0.024567 & 0.2252 & 0.411201 \tabularnewline
19 & 0.013503 & 0.1238 & 0.450902 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35495&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]0.047797[/C][C]0.4381[/C][C]0.331232[/C][/ROW]
[ROW][C]2[/C][C]-0.204791[/C][C]-1.8769[/C][C]0.031999[/C][/ROW]
[ROW][C]3[/C][C]0.055734[/C][C]0.5108[/C][C]0.305412[/C][/ROW]
[ROW][C]4[/C][C]-0.012253[/C][C]-0.1123[/C][C]0.455426[/C][/ROW]
[ROW][C]5[/C][C]0.132868[/C][C]1.2178[/C][C]0.113363[/C][/ROW]
[ROW][C]6[/C][C]-0.092567[/C][C]-0.8484[/C][C]0.199316[/C][/ROW]
[ROW][C]7[/C][C]0.076355[/C][C]0.6998[/C][C]0.242993[/C][/ROW]
[ROW][C]8[/C][C]-0.163235[/C][C]-1.4961[/C][C]0.069191[/C][/ROW]
[ROW][C]9[/C][C]-0.106577[/C][C]-0.9768[/C][C]0.165738[/C][/ROW]
[ROW][C]10[/C][C]0.197379[/C][C]1.809[/C][C]0.037014[/C][/ROW]
[ROW][C]11[/C][C]0.136937[/C][C]1.2551[/C][C]0.10647[/C][/ROW]
[ROW][C]12[/C][C]0.085986[/C][C]0.7881[/C][C]0.216436[/C][/ROW]
[ROW][C]13[/C][C]-0.064741[/C][C]-0.5934[/C][C]0.277266[/C][/ROW]
[ROW][C]14[/C][C]-0.073539[/C][C]-0.674[/C][C]0.251082[/C][/ROW]
[ROW][C]15[/C][C]-0.051829[/C][C]-0.475[/C][C]0.318003[/C][/ROW]
[ROW][C]16[/C][C]-0.025218[/C][C]-0.2311[/C][C]0.408889[/C][/ROW]
[ROW][C]17[/C][C]0.018125[/C][C]0.1661[/C][C]0.434231[/C][/ROW]
[ROW][C]18[/C][C]0.024567[/C][C]0.2252[/C][C]0.411201[/C][/ROW]
[ROW][C]19[/C][C]0.013503[/C][C]0.1238[/C][C]0.450902[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35495&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35495&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	0.047797	0.4381	0.331232
2	-0.204791	-1.8769	0.031999
3	0.055734	0.5108	0.305412
4	-0.012253	-0.1123	0.455426
5	0.132868	1.2178	0.113363
6	-0.092567	-0.8484	0.199316
7	0.076355	0.6998	0.242993
8	-0.163235	-1.4961	0.069191
9	-0.106577	-0.9768	0.165738
10	0.197379	1.809	0.037014
11	0.136937	1.2551	0.10647
12	0.085986	0.7881	0.216436
13	-0.064741	-0.5934	0.277266
14	-0.073539	-0.674	0.251082
15	-0.051829	-0.475	0.318003
16	-0.025218	-0.2311	0.408889
17	0.018125	0.1661	0.434231
18	0.024567	0.2252	0.411201
19	0.013503	0.1238	0.450902

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.8 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.8 ; 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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