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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 16 Oct 2014 18:18:10 +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/2014/Oct/16/t1413479925ncu6km01z4obq8c.htm/, Retrieved Sun, 12 May 2024 18:50:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=242803, Retrieved Sun, 12 May 2024 18:50:37 +0000

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-       [(Partial) Autocorrelation Function] [] [2014-10-16 17:18:10] [d67845bcf6d8dd3cd224f69460cf281c] [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	'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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=242803&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=242803&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=242803&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.257099	2.3563	0.010392
2	0.457004	4.1885	3.4e-05
3	0.348218	3.1915	0.000996
4	0.413406	3.7889	0.000142
5	0.375681	3.4432	0.000449
6	0.20742	1.901	0.030363
7	0.319604	2.9292	0.002187
8	0.31912	2.9248	0.002215
9	0.199671	1.83	0.035398
10	0.25193	2.309	0.0117
11	0.023646	0.2167	0.414477
12	0.597416	5.4754	0
13	-0.023872	-0.2188	0.413673
14	0.136249	1.2487	0.107614
15	0.003325	0.0305	0.487882
16	0.038942	0.3569	0.361028
17	0.005073	0.0465	0.481513
18	-0.116212	-1.0651	0.144942
19	-0.057347	-0.5256	0.300278

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.257099 & 2.3563 & 0.010392 \tabularnewline
2 & 0.457004 & 4.1885 & 3.4e-05 \tabularnewline
3 & 0.348218 & 3.1915 & 0.000996 \tabularnewline
4 & 0.413406 & 3.7889 & 0.000142 \tabularnewline
5 & 0.375681 & 3.4432 & 0.000449 \tabularnewline
6 & 0.20742 & 1.901 & 0.030363 \tabularnewline
7 & 0.319604 & 2.9292 & 0.002187 \tabularnewline
8 & 0.31912 & 2.9248 & 0.002215 \tabularnewline
9 & 0.199671 & 1.83 & 0.035398 \tabularnewline
10 & 0.25193 & 2.309 & 0.0117 \tabularnewline
11 & 0.023646 & 0.2167 & 0.414477 \tabularnewline
12 & 0.597416 & 5.4754 & 0 \tabularnewline
13 & -0.023872 & -0.2188 & 0.413673 \tabularnewline
14 & 0.136249 & 1.2487 & 0.107614 \tabularnewline
15 & 0.003325 & 0.0305 & 0.487882 \tabularnewline
16 & 0.038942 & 0.3569 & 0.361028 \tabularnewline
17 & 0.005073 & 0.0465 & 0.481513 \tabularnewline
18 & -0.116212 & -1.0651 & 0.144942 \tabularnewline
19 & -0.057347 & -0.5256 & 0.300278 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=242803&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]0.257099[/C][C]2.3563[/C][C]0.010392[/C][/ROW]
[ROW][C]2[/C][C]0.457004[/C][C]4.1885[/C][C]3.4e-05[/C][/ROW]
[ROW][C]3[/C][C]0.348218[/C][C]3.1915[/C][C]0.000996[/C][/ROW]
[ROW][C]4[/C][C]0.413406[/C][C]3.7889[/C][C]0.000142[/C][/ROW]
[ROW][C]5[/C][C]0.375681[/C][C]3.4432[/C][C]0.000449[/C][/ROW]
[ROW][C]6[/C][C]0.20742[/C][C]1.901[/C][C]0.030363[/C][/ROW]
[ROW][C]7[/C][C]0.319604[/C][C]2.9292[/C][C]0.002187[/C][/ROW]
[ROW][C]8[/C][C]0.31912[/C][C]2.9248[/C][C]0.002215[/C][/ROW]
[ROW][C]9[/C][C]0.199671[/C][C]1.83[/C][C]0.035398[/C][/ROW]
[ROW][C]10[/C][C]0.25193[/C][C]2.309[/C][C]0.0117[/C][/ROW]
[ROW][C]11[/C][C]0.023646[/C][C]0.2167[/C][C]0.414477[/C][/ROW]
[ROW][C]12[/C][C]0.597416[/C][C]5.4754[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.023872[/C][C]-0.2188[/C][C]0.413673[/C][/ROW]
[ROW][C]14[/C][C]0.136249[/C][C]1.2487[/C][C]0.107614[/C][/ROW]
[ROW][C]15[/C][C]0.003325[/C][C]0.0305[/C][C]0.487882[/C][/ROW]
[ROW][C]16[/C][C]0.038942[/C][C]0.3569[/C][C]0.361028[/C][/ROW]
[ROW][C]17[/C][C]0.005073[/C][C]0.0465[/C][C]0.481513[/C][/ROW]
[ROW][C]18[/C][C]-0.116212[/C][C]-1.0651[/C][C]0.144942[/C][/ROW]
[ROW][C]19[/C][C]-0.057347[/C][C]-0.5256[/C][C]0.300278[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=242803&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=242803&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	0.257099	2.3563	0.010392
2	0.457004	4.1885	3.4e-05
3	0.348218	3.1915	0.000996
4	0.413406	3.7889	0.000142
5	0.375681	3.4432	0.000449
6	0.20742	1.901	0.030363
7	0.319604	2.9292	0.002187
8	0.31912	2.9248	0.002215
9	0.199671	1.83	0.035398
10	0.25193	2.309	0.0117
11	0.023646	0.2167	0.414477
12	0.597416	5.4754	0
13	-0.023872	-0.2188	0.413673
14	0.136249	1.2487	0.107614
15	0.003325	0.0305	0.487882
16	0.038942	0.3569	0.361028
17	0.005073	0.0465	0.481513
18	-0.116212	-1.0651	0.144942
19	-0.057347	-0.5256	0.300278

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.257099	2.3563	0.010392
2	0.418572	3.8363	0.00012
3	0.22367	2.05	0.021743
4	0.219257	2.0095	0.023846
5	0.165331	1.5153	0.066728
6	-0.132664	-1.2159	0.113717
7	0.010272	0.0941	0.462608
8	0.137171	1.2572	0.106084
9	-0.0724	-0.6636	0.254395
10	0.020215	0.1853	0.42673
11	-0.242147	-2.2193	0.014581
12	0.583329	5.3463	0
13	-0.375783	-3.4441	0.000448
14	-0.285701	-2.6185	0.005238
15	-0.207333	-1.9002	0.030416
16	-0.166258	-1.5238	0.06566
17	-0.085931	-0.7876	0.216582
18	0.129253	1.1846	0.119753
19	-0.034865	-0.3195	0.375054

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.257099 & 2.3563 & 0.010392 \tabularnewline
2 & 0.418572 & 3.8363 & 0.00012 \tabularnewline
3 & 0.22367 & 2.05 & 0.021743 \tabularnewline
4 & 0.219257 & 2.0095 & 0.023846 \tabularnewline
5 & 0.165331 & 1.5153 & 0.066728 \tabularnewline
6 & -0.132664 & -1.2159 & 0.113717 \tabularnewline
7 & 0.010272 & 0.0941 & 0.462608 \tabularnewline
8 & 0.137171 & 1.2572 & 0.106084 \tabularnewline
9 & -0.0724 & -0.6636 & 0.254395 \tabularnewline
10 & 0.020215 & 0.1853 & 0.42673 \tabularnewline
11 & -0.242147 & -2.2193 & 0.014581 \tabularnewline
12 & 0.583329 & 5.3463 & 0 \tabularnewline
13 & -0.375783 & -3.4441 & 0.000448 \tabularnewline
14 & -0.285701 & -2.6185 & 0.005238 \tabularnewline
15 & -0.207333 & -1.9002 & 0.030416 \tabularnewline
16 & -0.166258 & -1.5238 & 0.06566 \tabularnewline
17 & -0.085931 & -0.7876 & 0.216582 \tabularnewline
18 & 0.129253 & 1.1846 & 0.119753 \tabularnewline
19 & -0.034865 & -0.3195 & 0.375054 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=242803&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]0.257099[/C][C]2.3563[/C][C]0.010392[/C][/ROW]
[ROW][C]2[/C][C]0.418572[/C][C]3.8363[/C][C]0.00012[/C][/ROW]
[ROW][C]3[/C][C]0.22367[/C][C]2.05[/C][C]0.021743[/C][/ROW]
[ROW][C]4[/C][C]0.219257[/C][C]2.0095[/C][C]0.023846[/C][/ROW]
[ROW][C]5[/C][C]0.165331[/C][C]1.5153[/C][C]0.066728[/C][/ROW]
[ROW][C]6[/C][C]-0.132664[/C][C]-1.2159[/C][C]0.113717[/C][/ROW]
[ROW][C]7[/C][C]0.010272[/C][C]0.0941[/C][C]0.462608[/C][/ROW]
[ROW][C]8[/C][C]0.137171[/C][C]1.2572[/C][C]0.106084[/C][/ROW]
[ROW][C]9[/C][C]-0.0724[/C][C]-0.6636[/C][C]0.254395[/C][/ROW]
[ROW][C]10[/C][C]0.020215[/C][C]0.1853[/C][C]0.42673[/C][/ROW]
[ROW][C]11[/C][C]-0.242147[/C][C]-2.2193[/C][C]0.014581[/C][/ROW]
[ROW][C]12[/C][C]0.583329[/C][C]5.3463[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.375783[/C][C]-3.4441[/C][C]0.000448[/C][/ROW]
[ROW][C]14[/C][C]-0.285701[/C][C]-2.6185[/C][C]0.005238[/C][/ROW]
[ROW][C]15[/C][C]-0.207333[/C][C]-1.9002[/C][C]0.030416[/C][/ROW]
[ROW][C]16[/C][C]-0.166258[/C][C]-1.5238[/C][C]0.06566[/C][/ROW]
[ROW][C]17[/C][C]-0.085931[/C][C]-0.7876[/C][C]0.216582[/C][/ROW]
[ROW][C]18[/C][C]0.129253[/C][C]1.1846[/C][C]0.119753[/C][/ROW]
[ROW][C]19[/C][C]-0.034865[/C][C]-0.3195[/C][C]0.375054[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=242803&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=242803&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	0.257099	2.3563	0.010392
2	0.418572	3.8363	0.00012
3	0.22367	2.05	0.021743
4	0.219257	2.0095	0.023846
5	0.165331	1.5153	0.066728
6	-0.132664	-1.2159	0.113717
7	0.010272	0.0941	0.462608
8	0.137171	1.2572	0.106084
9	-0.0724	-0.6636	0.254395
10	0.020215	0.1853	0.42673
11	-0.242147	-2.2193	0.014581
12	0.583329	5.3463	0
13	-0.375783	-3.4441	0.000448
14	-0.285701	-2.6185	0.005238
15	-0.207333	-1.9002	0.030416
16	-0.166258	-1.5238	0.06566
17	-0.085931	-0.7876	0.216582
18	0.129253	1.1846	0.119753
19	-0.034865	-0.3195	0.375054

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '1'
par2 <- '1'
par1 <- 'Default'
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)
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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code