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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 20 Oct 2016 21:51:01 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/20/t1476996734q2033z0s3oxeey8.htm/, Retrieved Sat, 04 May 2024 22:30:27 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 22:30:27 +0200

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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	'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.698694	5.4121	1e-06
2	0.630815	4.8863	4e-06
3	0.612272	4.7426	7e-06
4	0.7776	6.0233	0
5	0.512599	3.9706	9.7e-05
6	0.427628	3.3124	0.000785
7	0.397964	3.0826	0.001549
8	0.545522	4.2256	4.1e-05
9	0.287005	2.2231	0.014993
10	0.237116	1.8367	0.035605
11	0.176853	1.3699	0.087912
12	0.301917	2.3386	0.011352
13	0.096296	0.7459	0.229318
14	0.039016	0.3022	0.381765
15	-0.006074	-0.047	0.481317
16	0.120223	0.9312	0.17773
17	-0.068368	-0.5296	0.299179

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.698694 & 5.4121 & 1e-06 \tabularnewline
2 & 0.630815 & 4.8863 & 4e-06 \tabularnewline
3 & 0.612272 & 4.7426 & 7e-06 \tabularnewline
4 & 0.7776 & 6.0233 & 0 \tabularnewline
5 & 0.512599 & 3.9706 & 9.7e-05 \tabularnewline
6 & 0.427628 & 3.3124 & 0.000785 \tabularnewline
7 & 0.397964 & 3.0826 & 0.001549 \tabularnewline
8 & 0.545522 & 4.2256 & 4.1e-05 \tabularnewline
9 & 0.287005 & 2.2231 & 0.014993 \tabularnewline
10 & 0.237116 & 1.8367 & 0.035605 \tabularnewline
11 & 0.176853 & 1.3699 & 0.087912 \tabularnewline
12 & 0.301917 & 2.3386 & 0.011352 \tabularnewline
13 & 0.096296 & 0.7459 & 0.229318 \tabularnewline
14 & 0.039016 & 0.3022 & 0.381765 \tabularnewline
15 & -0.006074 & -0.047 & 0.481317 \tabularnewline
16 & 0.120223 & 0.9312 & 0.17773 \tabularnewline
17 & -0.068368 & -0.5296 & 0.299179 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.698694[/C][C]5.4121[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.630815[/C][C]4.8863[/C][C]4e-06[/C][/ROW]
[ROW][C]3[/C][C]0.612272[/C][C]4.7426[/C][C]7e-06[/C][/ROW]
[ROW][C]4[/C][C]0.7776[/C][C]6.0233[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.512599[/C][C]3.9706[/C][C]9.7e-05[/C][/ROW]
[ROW][C]6[/C][C]0.427628[/C][C]3.3124[/C][C]0.000785[/C][/ROW]
[ROW][C]7[/C][C]0.397964[/C][C]3.0826[/C][C]0.001549[/C][/ROW]
[ROW][C]8[/C][C]0.545522[/C][C]4.2256[/C][C]4.1e-05[/C][/ROW]
[ROW][C]9[/C][C]0.287005[/C][C]2.2231[/C][C]0.014993[/C][/ROW]
[ROW][C]10[/C][C]0.237116[/C][C]1.8367[/C][C]0.035605[/C][/ROW]
[ROW][C]11[/C][C]0.176853[/C][C]1.3699[/C][C]0.087912[/C][/ROW]
[ROW][C]12[/C][C]0.301917[/C][C]2.3386[/C][C]0.011352[/C][/ROW]
[ROW][C]13[/C][C]0.096296[/C][C]0.7459[/C][C]0.229318[/C][/ROW]
[ROW][C]14[/C][C]0.039016[/C][C]0.3022[/C][C]0.381765[/C][/ROW]
[ROW][C]15[/C][C]-0.006074[/C][C]-0.047[/C][C]0.481317[/C][/ROW]
[ROW][C]16[/C][C]0.120223[/C][C]0.9312[/C][C]0.17773[/C][/ROW]
[ROW][C]17[/C][C]-0.068368[/C][C]-0.5296[/C][C]0.299179[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.698694	5.4121	1e-06
2	0.630815	4.8863	4e-06
3	0.612272	4.7426	7e-06
4	0.7776	6.0233	0
5	0.512599	3.9706	9.7e-05
6	0.427628	3.3124	0.000785
7	0.397964	3.0826	0.001549
8	0.545522	4.2256	4.1e-05
9	0.287005	2.2231	0.014993
10	0.237116	1.8367	0.035605
11	0.176853	1.3699	0.087912
12	0.301917	2.3386	0.011352
13	0.096296	0.7459	0.229318
14	0.039016	0.3022	0.381765
15	-0.006074	-0.047	0.481317
16	0.120223	0.9312	0.17773
17	-0.068368	-0.5296	0.299179

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.698694	5.4121	1e-06
2	0.27869	2.1587	0.017441
3	0.211065	1.6349	0.053653
4	0.551773	4.274	3.5e-05
5	-0.490895	-3.8025	0.000169
6	-0.149054	-1.1546	0.126422
7	-0.000904	-0.007	0.497219
8	0.177382	1.374	0.087278
9	-0.250074	-1.9371	0.028725
10	0.092016	0.7128	0.23938
11	-0.178927	-1.386	0.085444
12	0.0116	0.0899	0.46435
13	0.050073	0.3879	0.349744
14	-0.11735	-0.909	0.183496
15	0.018315	0.1419	0.44383
16	0.056926	0.4409	0.330418
17	-0.126357	-0.9788	0.165815

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.698694 & 5.4121 & 1e-06 \tabularnewline
2 & 0.27869 & 2.1587 & 0.017441 \tabularnewline
3 & 0.211065 & 1.6349 & 0.053653 \tabularnewline
4 & 0.551773 & 4.274 & 3.5e-05 \tabularnewline
5 & -0.490895 & -3.8025 & 0.000169 \tabularnewline
6 & -0.149054 & -1.1546 & 0.126422 \tabularnewline
7 & -0.000904 & -0.007 & 0.497219 \tabularnewline
8 & 0.177382 & 1.374 & 0.087278 \tabularnewline
9 & -0.250074 & -1.9371 & 0.028725 \tabularnewline
10 & 0.092016 & 0.7128 & 0.23938 \tabularnewline
11 & -0.178927 & -1.386 & 0.085444 \tabularnewline
12 & 0.0116 & 0.0899 & 0.46435 \tabularnewline
13 & 0.050073 & 0.3879 & 0.349744 \tabularnewline
14 & -0.11735 & -0.909 & 0.183496 \tabularnewline
15 & 0.018315 & 0.1419 & 0.44383 \tabularnewline
16 & 0.056926 & 0.4409 & 0.330418 \tabularnewline
17 & -0.126357 & -0.9788 & 0.165815 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.698694[/C][C]5.4121[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.27869[/C][C]2.1587[/C][C]0.017441[/C][/ROW]
[ROW][C]3[/C][C]0.211065[/C][C]1.6349[/C][C]0.053653[/C][/ROW]
[ROW][C]4[/C][C]0.551773[/C][C]4.274[/C][C]3.5e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.490895[/C][C]-3.8025[/C][C]0.000169[/C][/ROW]
[ROW][C]6[/C][C]-0.149054[/C][C]-1.1546[/C][C]0.126422[/C][/ROW]
[ROW][C]7[/C][C]-0.000904[/C][C]-0.007[/C][C]0.497219[/C][/ROW]
[ROW][C]8[/C][C]0.177382[/C][C]1.374[/C][C]0.087278[/C][/ROW]
[ROW][C]9[/C][C]-0.250074[/C][C]-1.9371[/C][C]0.028725[/C][/ROW]
[ROW][C]10[/C][C]0.092016[/C][C]0.7128[/C][C]0.23938[/C][/ROW]
[ROW][C]11[/C][C]-0.178927[/C][C]-1.386[/C][C]0.085444[/C][/ROW]
[ROW][C]12[/C][C]0.0116[/C][C]0.0899[/C][C]0.46435[/C][/ROW]
[ROW][C]13[/C][C]0.050073[/C][C]0.3879[/C][C]0.349744[/C][/ROW]
[ROW][C]14[/C][C]-0.11735[/C][C]-0.909[/C][C]0.183496[/C][/ROW]
[ROW][C]15[/C][C]0.018315[/C][C]0.1419[/C][C]0.44383[/C][/ROW]
[ROW][C]16[/C][C]0.056926[/C][C]0.4409[/C][C]0.330418[/C][/ROW]
[ROW][C]17[/C][C]-0.126357[/C][C]-0.9788[/C][C]0.165815[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.698694	5.4121	1e-06
2	0.27869	2.1587	0.017441
3	0.211065	1.6349	0.053653
4	0.551773	4.274	3.5e-05
5	-0.490895	-3.8025	0.000169
6	-0.149054	-1.1546	0.126422
7	-0.000904	-0.007	0.497219
8	0.177382	1.374	0.087278
9	-0.250074	-1.9371	0.028725
10	0.092016	0.7128	0.23938
11	-0.178927	-1.386	0.085444
12	0.0116	0.0899	0.46435
13	0.050073	0.3879	0.349744
14	-0.11735	-0.909	0.183496
15	0.018315	0.1419	0.44383
16	0.056926	0.4409	0.330418
17	-0.126357	-0.9788	0.165815

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

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 ; par8 = ;

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 (par8 != '') par8 <- as.numeric(par8)
x <- na.omit(x)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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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