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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Dec 2016 19:37:14 +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/22/t14824330354r6pnhxxpvj2jt5.htm/, Retrieved Mon, 29 Apr 2024 00:10:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302636, Retrieved Mon, 29 Apr 2024 00:10:28 +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] [P A] [2016-12-22 18:37:14] [695928fec7566687630f1ba48b31beaa] [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=302636&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=302636&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302636&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	0.362398	3.8523	9.7e-05
2	0.334655	3.5574	0.000274
3	0.183887	1.9547	0.026542
4	0.12858	1.3668	0.087196
5	0.024733	0.2629	0.396547
6	0.012231	0.13	0.448393
7	0.109976	1.1691	0.12242
8	-0.022488	-0.2391	0.405749
9	-0.015572	-0.1655	0.43441
10	-0.175239	-1.8628	0.032542
11	-0.087651	-0.9317	0.176727
12	-0.365329	-3.8835	8.7e-05
13	-0.051082	-0.543	0.294095
14	-0.12922	-1.3736	0.086137
15	-0.045169	-0.4802	0.316022
16	-0.080372	-0.8544	0.197354
17	-0.053813	-0.572	0.284217
18	-0.058351	-0.6203	0.26816
19	-0.193849	-2.0606	0.020817
20	-0.070336	-0.7477	0.228102
21	-0.191478	-2.0354	0.022073

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.362398 & 3.8523 & 9.7e-05 \tabularnewline
2 & 0.334655 & 3.5574 & 0.000274 \tabularnewline
3 & 0.183887 & 1.9547 & 0.026542 \tabularnewline
4 & 0.12858 & 1.3668 & 0.087196 \tabularnewline
5 & 0.024733 & 0.2629 & 0.396547 \tabularnewline
6 & 0.012231 & 0.13 & 0.448393 \tabularnewline
7 & 0.109976 & 1.1691 & 0.12242 \tabularnewline
8 & -0.022488 & -0.2391 & 0.405749 \tabularnewline
9 & -0.015572 & -0.1655 & 0.43441 \tabularnewline
10 & -0.175239 & -1.8628 & 0.032542 \tabularnewline
11 & -0.087651 & -0.9317 & 0.176727 \tabularnewline
12 & -0.365329 & -3.8835 & 8.7e-05 \tabularnewline
13 & -0.051082 & -0.543 & 0.294095 \tabularnewline
14 & -0.12922 & -1.3736 & 0.086137 \tabularnewline
15 & -0.045169 & -0.4802 & 0.316022 \tabularnewline
16 & -0.080372 & -0.8544 & 0.197354 \tabularnewline
17 & -0.053813 & -0.572 & 0.284217 \tabularnewline
18 & -0.058351 & -0.6203 & 0.26816 \tabularnewline
19 & -0.193849 & -2.0606 & 0.020817 \tabularnewline
20 & -0.070336 & -0.7477 & 0.228102 \tabularnewline
21 & -0.191478 & -2.0354 & 0.022073 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302636&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]0.362398[/C][C]3.8523[/C][C]9.7e-05[/C][/ROW]
[ROW][C]2[/C][C]0.334655[/C][C]3.5574[/C][C]0.000274[/C][/ROW]
[ROW][C]3[/C][C]0.183887[/C][C]1.9547[/C][C]0.026542[/C][/ROW]
[ROW][C]4[/C][C]0.12858[/C][C]1.3668[/C][C]0.087196[/C][/ROW]
[ROW][C]5[/C][C]0.024733[/C][C]0.2629[/C][C]0.396547[/C][/ROW]
[ROW][C]6[/C][C]0.012231[/C][C]0.13[/C][C]0.448393[/C][/ROW]
[ROW][C]7[/C][C]0.109976[/C][C]1.1691[/C][C]0.12242[/C][/ROW]
[ROW][C]8[/C][C]-0.022488[/C][C]-0.2391[/C][C]0.405749[/C][/ROW]
[ROW][C]9[/C][C]-0.015572[/C][C]-0.1655[/C][C]0.43441[/C][/ROW]
[ROW][C]10[/C][C]-0.175239[/C][C]-1.8628[/C][C]0.032542[/C][/ROW]
[ROW][C]11[/C][C]-0.087651[/C][C]-0.9317[/C][C]0.176727[/C][/ROW]
[ROW][C]12[/C][C]-0.365329[/C][C]-3.8835[/C][C]8.7e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.051082[/C][C]-0.543[/C][C]0.294095[/C][/ROW]
[ROW][C]14[/C][C]-0.12922[/C][C]-1.3736[/C][C]0.086137[/C][/ROW]
[ROW][C]15[/C][C]-0.045169[/C][C]-0.4802[/C][C]0.316022[/C][/ROW]
[ROW][C]16[/C][C]-0.080372[/C][C]-0.8544[/C][C]0.197354[/C][/ROW]
[ROW][C]17[/C][C]-0.053813[/C][C]-0.572[/C][C]0.284217[/C][/ROW]
[ROW][C]18[/C][C]-0.058351[/C][C]-0.6203[/C][C]0.26816[/C][/ROW]
[ROW][C]19[/C][C]-0.193849[/C][C]-2.0606[/C][C]0.020817[/C][/ROW]
[ROW][C]20[/C][C]-0.070336[/C][C]-0.7477[/C][C]0.228102[/C][/ROW]
[ROW][C]21[/C][C]-0.191478[/C][C]-2.0354[/C][C]0.022073[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302636&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302636&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	0.362398	3.8523	9.7e-05
2	0.334655	3.5574	0.000274
3	0.183887	1.9547	0.026542
4	0.12858	1.3668	0.087196
5	0.024733	0.2629	0.396547
6	0.012231	0.13	0.448393
7	0.109976	1.1691	0.12242
8	-0.022488	-0.2391	0.405749
9	-0.015572	-0.1655	0.43441
10	-0.175239	-1.8628	0.032542
11	-0.087651	-0.9317	0.176727
12	-0.365329	-3.8835	8.7e-05
13	-0.051082	-0.543	0.294095
14	-0.12922	-1.3736	0.086137
15	-0.045169	-0.4802	0.316022
16	-0.080372	-0.8544	0.197354
17	-0.053813	-0.572	0.284217
18	-0.058351	-0.6203	0.26816
19	-0.193849	-2.0606	0.020817
20	-0.070336	-0.7477	0.228102
21	-0.191478	-2.0354	0.022073

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.362398	3.8523	9.7e-05
2	0.234062	2.4881	0.00715
3	0.007516	0.0799	0.468229
4	-0.003038	-0.0323	0.487148
5	-0.067253	-0.7149	0.238071
6	-0.012003	-0.1276	0.449349
7	0.146966	1.5623	0.06051
8	-0.095012	-1.01	0.15733
9	-0.052415	-0.5572	0.289255
10	-0.188528	-2.0041	0.023727
11	0.021697	0.2306	0.409005
12	-0.300728	-3.1968	0.000901
13	0.249478	2.652	0.004576
14	-0.049814	-0.5295	0.298737
15	0.037826	0.4021	0.344186
16	-0.092299	-0.9812	0.164306
17	0.018568	0.1974	0.421941
18	-0.071166	-0.7565	0.225462
19	-0.066937	-0.7116	0.239104
20	-0.043943	-0.4671	0.320657
21	-0.121772	-1.2945	0.099073

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.362398 & 3.8523 & 9.7e-05 \tabularnewline
2 & 0.234062 & 2.4881 & 0.00715 \tabularnewline
3 & 0.007516 & 0.0799 & 0.468229 \tabularnewline
4 & -0.003038 & -0.0323 & 0.487148 \tabularnewline
5 & -0.067253 & -0.7149 & 0.238071 \tabularnewline
6 & -0.012003 & -0.1276 & 0.449349 \tabularnewline
7 & 0.146966 & 1.5623 & 0.06051 \tabularnewline
8 & -0.095012 & -1.01 & 0.15733 \tabularnewline
9 & -0.052415 & -0.5572 & 0.289255 \tabularnewline
10 & -0.188528 & -2.0041 & 0.023727 \tabularnewline
11 & 0.021697 & 0.2306 & 0.409005 \tabularnewline
12 & -0.300728 & -3.1968 & 0.000901 \tabularnewline
13 & 0.249478 & 2.652 & 0.004576 \tabularnewline
14 & -0.049814 & -0.5295 & 0.298737 \tabularnewline
15 & 0.037826 & 0.4021 & 0.344186 \tabularnewline
16 & -0.092299 & -0.9812 & 0.164306 \tabularnewline
17 & 0.018568 & 0.1974 & 0.421941 \tabularnewline
18 & -0.071166 & -0.7565 & 0.225462 \tabularnewline
19 & -0.066937 & -0.7116 & 0.239104 \tabularnewline
20 & -0.043943 & -0.4671 & 0.320657 \tabularnewline
21 & -0.121772 & -1.2945 & 0.099073 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302636&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]0.362398[/C][C]3.8523[/C][C]9.7e-05[/C][/ROW]
[ROW][C]2[/C][C]0.234062[/C][C]2.4881[/C][C]0.00715[/C][/ROW]
[ROW][C]3[/C][C]0.007516[/C][C]0.0799[/C][C]0.468229[/C][/ROW]
[ROW][C]4[/C][C]-0.003038[/C][C]-0.0323[/C][C]0.487148[/C][/ROW]
[ROW][C]5[/C][C]-0.067253[/C][C]-0.7149[/C][C]0.238071[/C][/ROW]
[ROW][C]6[/C][C]-0.012003[/C][C]-0.1276[/C][C]0.449349[/C][/ROW]
[ROW][C]7[/C][C]0.146966[/C][C]1.5623[/C][C]0.06051[/C][/ROW]
[ROW][C]8[/C][C]-0.095012[/C][C]-1.01[/C][C]0.15733[/C][/ROW]
[ROW][C]9[/C][C]-0.052415[/C][C]-0.5572[/C][C]0.289255[/C][/ROW]
[ROW][C]10[/C][C]-0.188528[/C][C]-2.0041[/C][C]0.023727[/C][/ROW]
[ROW][C]11[/C][C]0.021697[/C][C]0.2306[/C][C]0.409005[/C][/ROW]
[ROW][C]12[/C][C]-0.300728[/C][C]-3.1968[/C][C]0.000901[/C][/ROW]
[ROW][C]13[/C][C]0.249478[/C][C]2.652[/C][C]0.004576[/C][/ROW]
[ROW][C]14[/C][C]-0.049814[/C][C]-0.5295[/C][C]0.298737[/C][/ROW]
[ROW][C]15[/C][C]0.037826[/C][C]0.4021[/C][C]0.344186[/C][/ROW]
[ROW][C]16[/C][C]-0.092299[/C][C]-0.9812[/C][C]0.164306[/C][/ROW]
[ROW][C]17[/C][C]0.018568[/C][C]0.1974[/C][C]0.421941[/C][/ROW]
[ROW][C]18[/C][C]-0.071166[/C][C]-0.7565[/C][C]0.225462[/C][/ROW]
[ROW][C]19[/C][C]-0.066937[/C][C]-0.7116[/C][C]0.239104[/C][/ROW]
[ROW][C]20[/C][C]-0.043943[/C][C]-0.4671[/C][C]0.320657[/C][/ROW]
[ROW][C]21[/C][C]-0.121772[/C][C]-1.2945[/C][C]0.099073[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302636&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302636&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	0.362398	3.8523	9.7e-05
2	0.234062	2.4881	0.00715
3	0.007516	0.0799	0.468229
4	-0.003038	-0.0323	0.487148
5	-0.067253	-0.7149	0.238071
6	-0.012003	-0.1276	0.449349
7	0.146966	1.5623	0.06051
8	-0.095012	-1.01	0.15733
9	-0.052415	-0.5572	0.289255
10	-0.188528	-2.0041	0.023727
11	0.021697	0.2306	0.409005
12	-0.300728	-3.1968	0.000901
13	0.249478	2.652	0.004576
14	-0.049814	-0.5295	0.298737
15	0.037826	0.4021	0.344186
16	-0.092299	-0.9812	0.164306
17	0.018568	0.1974	0.421941
18	-0.071166	-0.7565	0.225462
19	-0.066937	-0.7116	0.239104
20	-0.043943	-0.4671	0.320657
21	-0.121772	-1.2945	0.099073

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 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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