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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 12 Mar 2016 17:19:30 +0000

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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/Mar/12/t1457803203m9n2505lb58kyme.htm/, Retrieved Sat, 18 May 2024 13:48:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293931, Retrieved Sat, 18 May 2024 13:48:48 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-03-12 17:19:30] [6bb7048e855cced252efb5418d255fa6] [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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293931&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293931&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293931&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.703247	6.4454	0
2	0.207372	1.9006	0.030392
3	-0.167396	-1.5342	0.064368
4	-0.26279	-2.4085	0.009103
5	-0.194266	-1.7805	0.039307
6	-0.139313	-1.2768	0.102591
7	-0.216927	-1.9882	0.025025
8	-0.309307	-2.8348	0.002871
9	-0.249787	-2.2893	0.012284
10	0.052681	0.4828	0.315236
11	0.465893	4.27	2.6e-05
12	0.718156	6.582	0
13	0.473562	4.3403	2e-05
14	0.04597	0.4213	0.337297
15	-0.286111	-2.6222	0.005185
16	-0.378354	-3.4677	0.000415
17	-0.318016	-2.9147	0.002282
18	-0.258563	-2.3698	0.010046
19	-0.314008	-2.8779	0.002537

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.703247 & 6.4454 & 0 \tabularnewline
2 & 0.207372 & 1.9006 & 0.030392 \tabularnewline
3 & -0.167396 & -1.5342 & 0.064368 \tabularnewline
4 & -0.26279 & -2.4085 & 0.009103 \tabularnewline
5 & -0.194266 & -1.7805 & 0.039307 \tabularnewline
6 & -0.139313 & -1.2768 & 0.102591 \tabularnewline
7 & -0.216927 & -1.9882 & 0.025025 \tabularnewline
8 & -0.309307 & -2.8348 & 0.002871 \tabularnewline
9 & -0.249787 & -2.2893 & 0.012284 \tabularnewline
10 & 0.052681 & 0.4828 & 0.315236 \tabularnewline
11 & 0.465893 & 4.27 & 2.6e-05 \tabularnewline
12 & 0.718156 & 6.582 & 0 \tabularnewline
13 & 0.473562 & 4.3403 & 2e-05 \tabularnewline
14 & 0.04597 & 0.4213 & 0.337297 \tabularnewline
15 & -0.286111 & -2.6222 & 0.005185 \tabularnewline
16 & -0.378354 & -3.4677 & 0.000415 \tabularnewline
17 & -0.318016 & -2.9147 & 0.002282 \tabularnewline
18 & -0.258563 & -2.3698 & 0.010046 \tabularnewline
19 & -0.314008 & -2.8779 & 0.002537 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293931&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]0.703247[/C][C]6.4454[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.207372[/C][C]1.9006[/C][C]0.030392[/C][/ROW]
[ROW][C]3[/C][C]-0.167396[/C][C]-1.5342[/C][C]0.064368[/C][/ROW]
[ROW][C]4[/C][C]-0.26279[/C][C]-2.4085[/C][C]0.009103[/C][/ROW]
[ROW][C]5[/C][C]-0.194266[/C][C]-1.7805[/C][C]0.039307[/C][/ROW]
[ROW][C]6[/C][C]-0.139313[/C][C]-1.2768[/C][C]0.102591[/C][/ROW]
[ROW][C]7[/C][C]-0.216927[/C][C]-1.9882[/C][C]0.025025[/C][/ROW]
[ROW][C]8[/C][C]-0.309307[/C][C]-2.8348[/C][C]0.002871[/C][/ROW]
[ROW][C]9[/C][C]-0.249787[/C][C]-2.2893[/C][C]0.012284[/C][/ROW]
[ROW][C]10[/C][C]0.052681[/C][C]0.4828[/C][C]0.315236[/C][/ROW]
[ROW][C]11[/C][C]0.465893[/C][C]4.27[/C][C]2.6e-05[/C][/ROW]
[ROW][C]12[/C][C]0.718156[/C][C]6.582[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.473562[/C][C]4.3403[/C][C]2e-05[/C][/ROW]
[ROW][C]14[/C][C]0.04597[/C][C]0.4213[/C][C]0.337297[/C][/ROW]
[ROW][C]15[/C][C]-0.286111[/C][C]-2.6222[/C][C]0.005185[/C][/ROW]
[ROW][C]16[/C][C]-0.378354[/C][C]-3.4677[/C][C]0.000415[/C][/ROW]
[ROW][C]17[/C][C]-0.318016[/C][C]-2.9147[/C][C]0.002282[/C][/ROW]
[ROW][C]18[/C][C]-0.258563[/C][C]-2.3698[/C][C]0.010046[/C][/ROW]
[ROW][C]19[/C][C]-0.314008[/C][C]-2.8779[/C][C]0.002537[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293931&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293931&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	0.703247	6.4454	0
2	0.207372	1.9006	0.030392
3	-0.167396	-1.5342	0.064368
4	-0.26279	-2.4085	0.009103
5	-0.194266	-1.7805	0.039307
6	-0.139313	-1.2768	0.102591
7	-0.216927	-1.9882	0.025025
8	-0.309307	-2.8348	0.002871
9	-0.249787	-2.2893	0.012284
10	0.052681	0.4828	0.315236
11	0.465893	4.27	2.6e-05
12	0.718156	6.582	0
13	0.473562	4.3403	2e-05
14	0.04597	0.4213	0.337297
15	-0.286111	-2.6222	0.005185
16	-0.378354	-3.4677	0.000415
17	-0.318016	-2.9147	0.002282
18	-0.258563	-2.3698	0.010046
19	-0.314008	-2.8779	0.002537

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.703247	6.4454	0
2	-0.568184	-5.2075	1e-06
3	0.010177	0.0933	0.462953
4	0.104554	0.9583	0.170343
5	-0.123093	-1.1282	0.13123
6	-0.159576	-1.4625	0.073663
7	-0.259545	-2.3788	0.009819
8	-0.015592	-0.1429	0.443355
9	0.110661	1.0142	0.156693
10	0.31165	2.8563	0.0027
11	0.347615	3.1859	0.001013
12	0.199291	1.8265	0.035661
13	-0.649035	-5.9485	0
14	0.235999	2.163	0.016693
15	-0.171534	-1.5721	0.059839
16	-0.247358	-2.2671	0.012977
17	-0.002453	-0.0225	0.491059
18	-0.066305	-0.6077	0.272514
19	-0.081052	-0.7429	0.229821

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.703247 & 6.4454 & 0 \tabularnewline
2 & -0.568184 & -5.2075 & 1e-06 \tabularnewline
3 & 0.010177 & 0.0933 & 0.462953 \tabularnewline
4 & 0.104554 & 0.9583 & 0.170343 \tabularnewline
5 & -0.123093 & -1.1282 & 0.13123 \tabularnewline
6 & -0.159576 & -1.4625 & 0.073663 \tabularnewline
7 & -0.259545 & -2.3788 & 0.009819 \tabularnewline
8 & -0.015592 & -0.1429 & 0.443355 \tabularnewline
9 & 0.110661 & 1.0142 & 0.156693 \tabularnewline
10 & 0.31165 & 2.8563 & 0.0027 \tabularnewline
11 & 0.347615 & 3.1859 & 0.001013 \tabularnewline
12 & 0.199291 & 1.8265 & 0.035661 \tabularnewline
13 & -0.649035 & -5.9485 & 0 \tabularnewline
14 & 0.235999 & 2.163 & 0.016693 \tabularnewline
15 & -0.171534 & -1.5721 & 0.059839 \tabularnewline
16 & -0.247358 & -2.2671 & 0.012977 \tabularnewline
17 & -0.002453 & -0.0225 & 0.491059 \tabularnewline
18 & -0.066305 & -0.6077 & 0.272514 \tabularnewline
19 & -0.081052 & -0.7429 & 0.229821 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293931&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]0.703247[/C][C]6.4454[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.568184[/C][C]-5.2075[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.010177[/C][C]0.0933[/C][C]0.462953[/C][/ROW]
[ROW][C]4[/C][C]0.104554[/C][C]0.9583[/C][C]0.170343[/C][/ROW]
[ROW][C]5[/C][C]-0.123093[/C][C]-1.1282[/C][C]0.13123[/C][/ROW]
[ROW][C]6[/C][C]-0.159576[/C][C]-1.4625[/C][C]0.073663[/C][/ROW]
[ROW][C]7[/C][C]-0.259545[/C][C]-2.3788[/C][C]0.009819[/C][/ROW]
[ROW][C]8[/C][C]-0.015592[/C][C]-0.1429[/C][C]0.443355[/C][/ROW]
[ROW][C]9[/C][C]0.110661[/C][C]1.0142[/C][C]0.156693[/C][/ROW]
[ROW][C]10[/C][C]0.31165[/C][C]2.8563[/C][C]0.0027[/C][/ROW]
[ROW][C]11[/C][C]0.347615[/C][C]3.1859[/C][C]0.001013[/C][/ROW]
[ROW][C]12[/C][C]0.199291[/C][C]1.8265[/C][C]0.035661[/C][/ROW]
[ROW][C]13[/C][C]-0.649035[/C][C]-5.9485[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.235999[/C][C]2.163[/C][C]0.016693[/C][/ROW]
[ROW][C]15[/C][C]-0.171534[/C][C]-1.5721[/C][C]0.059839[/C][/ROW]
[ROW][C]16[/C][C]-0.247358[/C][C]-2.2671[/C][C]0.012977[/C][/ROW]
[ROW][C]17[/C][C]-0.002453[/C][C]-0.0225[/C][C]0.491059[/C][/ROW]
[ROW][C]18[/C][C]-0.066305[/C][C]-0.6077[/C][C]0.272514[/C][/ROW]
[ROW][C]19[/C][C]-0.081052[/C][C]-0.7429[/C][C]0.229821[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293931&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293931&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	0.703247	6.4454	0
2	-0.568184	-5.2075	1e-06
3	0.010177	0.0933	0.462953
4	0.104554	0.9583	0.170343
5	-0.123093	-1.1282	0.13123
6	-0.159576	-1.4625	0.073663
7	-0.259545	-2.3788	0.009819
8	-0.015592	-0.1429	0.443355
9	0.110661	1.0142	0.156693
10	0.31165	2.8563	0.0027
11	0.347615	3.1859	0.001013
12	0.199291	1.8265	0.035661
13	-0.649035	-5.9485	0
14	0.235999	2.163	0.016693
15	-0.171534	-1.5721	0.059839
16	-0.247358	-2.2671	0.012977
17	-0.002453	-0.0225	0.491059
18	-0.066305	-0.6077	0.272514
19	-0.081052	-0.7429	0.229821

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code