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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 21:13:21 +0100

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/2016/Dec/16/t1481919223ksonudedpxtlex7.htm/, Retrieved Thu, 02 May 2024 17:59:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300534, Retrieved Thu, 02 May 2024 17:59:55 +0000

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [N2099 - r0481974] [2016-12-16 20:13:21] [ee2f08b6fcfe19fae25bd9410e008f6d] [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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300534&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300534&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300534&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.298908	-3.1915	0.000915
2	0.110321	1.1779	0.120644
3	-0.092497	-0.9876	0.16272
4	0.08897	0.9499	0.172075
5	-0.100553	-1.0736	0.142632
6	-0.016344	-0.1745	0.430888
7	0.091144	0.9731	0.16627
8	-0.069756	-0.7448	0.228967
9	0.02924	0.3122	0.377732
10	-0.084567	-0.9029	0.184234
11	0.093391	0.9971	0.160404
12	-0.497696	-5.3139	0
13	0.2183	2.3308	0.010761
14	0.013929	0.1487	0.44102
15	-0.046631	-0.4979	0.309763
16	-0.001953	-0.0209	0.491699
17	0.113558	1.2125	0.113919
18	0.089212	0.9525	0.171424
19	-0.1239	-1.3229	0.094259
20	0.097187	1.0377	0.150809
21	0.012847	0.1372	0.445571

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.298908 & -3.1915 & 0.000915 \tabularnewline
2 & 0.110321 & 1.1779 & 0.120644 \tabularnewline
3 & -0.092497 & -0.9876 & 0.16272 \tabularnewline
4 & 0.08897 & 0.9499 & 0.172075 \tabularnewline
5 & -0.100553 & -1.0736 & 0.142632 \tabularnewline
6 & -0.016344 & -0.1745 & 0.430888 \tabularnewline
7 & 0.091144 & 0.9731 & 0.16627 \tabularnewline
8 & -0.069756 & -0.7448 & 0.228967 \tabularnewline
9 & 0.02924 & 0.3122 & 0.377732 \tabularnewline
10 & -0.084567 & -0.9029 & 0.184234 \tabularnewline
11 & 0.093391 & 0.9971 & 0.160404 \tabularnewline
12 & -0.497696 & -5.3139 & 0 \tabularnewline
13 & 0.2183 & 2.3308 & 0.010761 \tabularnewline
14 & 0.013929 & 0.1487 & 0.44102 \tabularnewline
15 & -0.046631 & -0.4979 & 0.309763 \tabularnewline
16 & -0.001953 & -0.0209 & 0.491699 \tabularnewline
17 & 0.113558 & 1.2125 & 0.113919 \tabularnewline
18 & 0.089212 & 0.9525 & 0.171424 \tabularnewline
19 & -0.1239 & -1.3229 & 0.094259 \tabularnewline
20 & 0.097187 & 1.0377 & 0.150809 \tabularnewline
21 & 0.012847 & 0.1372 & 0.445571 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300534&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]-0.298908[/C][C]-3.1915[/C][C]0.000915[/C][/ROW]
[ROW][C]2[/C][C]0.110321[/C][C]1.1779[/C][C]0.120644[/C][/ROW]
[ROW][C]3[/C][C]-0.092497[/C][C]-0.9876[/C][C]0.16272[/C][/ROW]
[ROW][C]4[/C][C]0.08897[/C][C]0.9499[/C][C]0.172075[/C][/ROW]
[ROW][C]5[/C][C]-0.100553[/C][C]-1.0736[/C][C]0.142632[/C][/ROW]
[ROW][C]6[/C][C]-0.016344[/C][C]-0.1745[/C][C]0.430888[/C][/ROW]
[ROW][C]7[/C][C]0.091144[/C][C]0.9731[/C][C]0.16627[/C][/ROW]
[ROW][C]8[/C][C]-0.069756[/C][C]-0.7448[/C][C]0.228967[/C][/ROW]
[ROW][C]9[/C][C]0.02924[/C][C]0.3122[/C][C]0.377732[/C][/ROW]
[ROW][C]10[/C][C]-0.084567[/C][C]-0.9029[/C][C]0.184234[/C][/ROW]
[ROW][C]11[/C][C]0.093391[/C][C]0.9971[/C][C]0.160404[/C][/ROW]
[ROW][C]12[/C][C]-0.497696[/C][C]-5.3139[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.2183[/C][C]2.3308[/C][C]0.010761[/C][/ROW]
[ROW][C]14[/C][C]0.013929[/C][C]0.1487[/C][C]0.44102[/C][/ROW]
[ROW][C]15[/C][C]-0.046631[/C][C]-0.4979[/C][C]0.309763[/C][/ROW]
[ROW][C]16[/C][C]-0.001953[/C][C]-0.0209[/C][C]0.491699[/C][/ROW]
[ROW][C]17[/C][C]0.113558[/C][C]1.2125[/C][C]0.113919[/C][/ROW]
[ROW][C]18[/C][C]0.089212[/C][C]0.9525[/C][C]0.171424[/C][/ROW]
[ROW][C]19[/C][C]-0.1239[/C][C]-1.3229[/C][C]0.094259[/C][/ROW]
[ROW][C]20[/C][C]0.097187[/C][C]1.0377[/C][C]0.150809[/C][/ROW]
[ROW][C]21[/C][C]0.012847[/C][C]0.1372[/C][C]0.445571[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300534&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300534&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	-0.298908	-3.1915	0.000915
2	0.110321	1.1779	0.120644
3	-0.092497	-0.9876	0.16272
4	0.08897	0.9499	0.172075
5	-0.100553	-1.0736	0.142632
6	-0.016344	-0.1745	0.430888
7	0.091144	0.9731	0.16627
8	-0.069756	-0.7448	0.228967
9	0.02924	0.3122	0.377732
10	-0.084567	-0.9029	0.184234
11	0.093391	0.9971	0.160404
12	-0.497696	-5.3139	0
13	0.2183	2.3308	0.010761
14	0.013929	0.1487	0.44102
15	-0.046631	-0.4979	0.309763
16	-0.001953	-0.0209	0.491699
17	0.113558	1.2125	0.113919
18	0.089212	0.9525	0.171424
19	-0.1239	-1.3229	0.094259
20	0.097187	1.0377	0.150809
21	0.012847	0.1372	0.445571

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.298908	-3.1915	0.000915
2	0.023033	0.2459	0.403092
3	-0.058666	-0.6264	0.266159
4	0.048396	0.5167	0.303172
5	-0.060822	-0.6494	0.258693
6	-0.078675	-0.84	0.201329
7	0.088994	0.9502	0.172011
8	-0.03073	-0.3281	0.371718
9	-0.0043	-0.0459	0.481731
10	-0.072436	-0.7734	0.220441
11	0.031703	0.3385	0.367805
12	-0.493644	-5.2707	0
13	-0.076436	-0.8161	0.20807
14	0.136599	1.4585	0.07373
15	-0.119766	-1.2788	0.10179
16	0.000743	0.0079	0.496841
17	0.11036	1.1783	0.12056
18	0.13004	1.3884	0.083855
19	-0.003937	-0.042	0.483271
20	0.032263	0.3445	0.36556
21	0.065943	0.7041	0.24141

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.298908 & -3.1915 & 0.000915 \tabularnewline
2 & 0.023033 & 0.2459 & 0.403092 \tabularnewline
3 & -0.058666 & -0.6264 & 0.266159 \tabularnewline
4 & 0.048396 & 0.5167 & 0.303172 \tabularnewline
5 & -0.060822 & -0.6494 & 0.258693 \tabularnewline
6 & -0.078675 & -0.84 & 0.201329 \tabularnewline
7 & 0.088994 & 0.9502 & 0.172011 \tabularnewline
8 & -0.03073 & -0.3281 & 0.371718 \tabularnewline
9 & -0.0043 & -0.0459 & 0.481731 \tabularnewline
10 & -0.072436 & -0.7734 & 0.220441 \tabularnewline
11 & 0.031703 & 0.3385 & 0.367805 \tabularnewline
12 & -0.493644 & -5.2707 & 0 \tabularnewline
13 & -0.076436 & -0.8161 & 0.20807 \tabularnewline
14 & 0.136599 & 1.4585 & 0.07373 \tabularnewline
15 & -0.119766 & -1.2788 & 0.10179 \tabularnewline
16 & 0.000743 & 0.0079 & 0.496841 \tabularnewline
17 & 0.11036 & 1.1783 & 0.12056 \tabularnewline
18 & 0.13004 & 1.3884 & 0.083855 \tabularnewline
19 & -0.003937 & -0.042 & 0.483271 \tabularnewline
20 & 0.032263 & 0.3445 & 0.36556 \tabularnewline
21 & 0.065943 & 0.7041 & 0.24141 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300534&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]-0.298908[/C][C]-3.1915[/C][C]0.000915[/C][/ROW]
[ROW][C]2[/C][C]0.023033[/C][C]0.2459[/C][C]0.403092[/C][/ROW]
[ROW][C]3[/C][C]-0.058666[/C][C]-0.6264[/C][C]0.266159[/C][/ROW]
[ROW][C]4[/C][C]0.048396[/C][C]0.5167[/C][C]0.303172[/C][/ROW]
[ROW][C]5[/C][C]-0.060822[/C][C]-0.6494[/C][C]0.258693[/C][/ROW]
[ROW][C]6[/C][C]-0.078675[/C][C]-0.84[/C][C]0.201329[/C][/ROW]
[ROW][C]7[/C][C]0.088994[/C][C]0.9502[/C][C]0.172011[/C][/ROW]
[ROW][C]8[/C][C]-0.03073[/C][C]-0.3281[/C][C]0.371718[/C][/ROW]
[ROW][C]9[/C][C]-0.0043[/C][C]-0.0459[/C][C]0.481731[/C][/ROW]
[ROW][C]10[/C][C]-0.072436[/C][C]-0.7734[/C][C]0.220441[/C][/ROW]
[ROW][C]11[/C][C]0.031703[/C][C]0.3385[/C][C]0.367805[/C][/ROW]
[ROW][C]12[/C][C]-0.493644[/C][C]-5.2707[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.076436[/C][C]-0.8161[/C][C]0.20807[/C][/ROW]
[ROW][C]14[/C][C]0.136599[/C][C]1.4585[/C][C]0.07373[/C][/ROW]
[ROW][C]15[/C][C]-0.119766[/C][C]-1.2788[/C][C]0.10179[/C][/ROW]
[ROW][C]16[/C][C]0.000743[/C][C]0.0079[/C][C]0.496841[/C][/ROW]
[ROW][C]17[/C][C]0.11036[/C][C]1.1783[/C][C]0.12056[/C][/ROW]
[ROW][C]18[/C][C]0.13004[/C][C]1.3884[/C][C]0.083855[/C][/ROW]
[ROW][C]19[/C][C]-0.003937[/C][C]-0.042[/C][C]0.483271[/C][/ROW]
[ROW][C]20[/C][C]0.032263[/C][C]0.3445[/C][C]0.36556[/C][/ROW]
[ROW][C]21[/C][C]0.065943[/C][C]0.7041[/C][C]0.24141[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300534&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300534&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	-0.298908	-3.1915	0.000915
2	0.023033	0.2459	0.403092
3	-0.058666	-0.6264	0.266159
4	0.048396	0.5167	0.303172
5	-0.060822	-0.6494	0.258693
6	-0.078675	-0.84	0.201329
7	0.088994	0.9502	0.172011
8	-0.03073	-0.3281	0.371718
9	-0.0043	-0.0459	0.481731
10	-0.072436	-0.7734	0.220441
11	0.031703	0.3385	0.367805
12	-0.493644	-5.2707	0
13	-0.076436	-0.8161	0.20807
14	0.136599	1.4585	0.07373
15	-0.119766	-1.2788	0.10179
16	0.000743	0.0079	0.496841
17	0.11036	1.1783	0.12056
18	0.13004	1.3884	0.083855
19	-0.003937	-0.042	0.483271
20	0.032263	0.3445	0.36556
21	0.065943	0.7041	0.24141

Figure 1

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Postscript link

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Figure 2

PNG link

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Figure 3

PNG link

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Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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,'ACF(k)',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,'PACF(k)',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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code