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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 13:40:06 +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/t1481892050sbsfr390y1zkl0q.htm/, Retrieved Thu, 02 May 2024 19:03:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300221, Retrieved Thu, 02 May 2024 19:03:10 +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] [] [2016-12-16 12:40:06] [85f5800284aab30c091766186b093bb4] [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=300221&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=300221&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300221&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	-0.489256	-5.47	0
2	0.086623	0.9685	0.167338
3	-0.098422	-1.1004	0.136638
4	0.155056	1.7336	0.042729
5	-0.18724	-2.0934	0.019167
6	0.045999	0.5143	0.303981
7	-0.052826	-0.5906	0.277924
8	0.055406	0.6195	0.26837
9	0.088728	0.992	0.161555
10	-0.16198	-1.811	0.036272
11	0.132484	1.4812	0.070533
12	0.123828	1.3844	0.084345
13	-0.142695	-1.5954	0.056576
14	-0.086045	-0.962	0.16895
15	0.072848	0.8145	0.208463
16	-0.013998	-0.1565	0.437947
17	0.020718	0.2316	0.4086
18	0.037693	0.4214	0.337087
19	-0.02512	-0.2808	0.389645
20	0.021577	0.2412	0.404882
21	-0.09069	-1.0139	0.156284

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.489256 & -5.47 & 0 \tabularnewline
2 & 0.086623 & 0.9685 & 0.167338 \tabularnewline
3 & -0.098422 & -1.1004 & 0.136638 \tabularnewline
4 & 0.155056 & 1.7336 & 0.042729 \tabularnewline
5 & -0.18724 & -2.0934 & 0.019167 \tabularnewline
6 & 0.045999 & 0.5143 & 0.303981 \tabularnewline
7 & -0.052826 & -0.5906 & 0.277924 \tabularnewline
8 & 0.055406 & 0.6195 & 0.26837 \tabularnewline
9 & 0.088728 & 0.992 & 0.161555 \tabularnewline
10 & -0.16198 & -1.811 & 0.036272 \tabularnewline
11 & 0.132484 & 1.4812 & 0.070533 \tabularnewline
12 & 0.123828 & 1.3844 & 0.084345 \tabularnewline
13 & -0.142695 & -1.5954 & 0.056576 \tabularnewline
14 & -0.086045 & -0.962 & 0.16895 \tabularnewline
15 & 0.072848 & 0.8145 & 0.208463 \tabularnewline
16 & -0.013998 & -0.1565 & 0.437947 \tabularnewline
17 & 0.020718 & 0.2316 & 0.4086 \tabularnewline
18 & 0.037693 & 0.4214 & 0.337087 \tabularnewline
19 & -0.02512 & -0.2808 & 0.389645 \tabularnewline
20 & 0.021577 & 0.2412 & 0.404882 \tabularnewline
21 & -0.09069 & -1.0139 & 0.156284 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300221&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]-0.489256[/C][C]-5.47[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.086623[/C][C]0.9685[/C][C]0.167338[/C][/ROW]
[ROW][C]3[/C][C]-0.098422[/C][C]-1.1004[/C][C]0.136638[/C][/ROW]
[ROW][C]4[/C][C]0.155056[/C][C]1.7336[/C][C]0.042729[/C][/ROW]
[ROW][C]5[/C][C]-0.18724[/C][C]-2.0934[/C][C]0.019167[/C][/ROW]
[ROW][C]6[/C][C]0.045999[/C][C]0.5143[/C][C]0.303981[/C][/ROW]
[ROW][C]7[/C][C]-0.052826[/C][C]-0.5906[/C][C]0.277924[/C][/ROW]
[ROW][C]8[/C][C]0.055406[/C][C]0.6195[/C][C]0.26837[/C][/ROW]
[ROW][C]9[/C][C]0.088728[/C][C]0.992[/C][C]0.161555[/C][/ROW]
[ROW][C]10[/C][C]-0.16198[/C][C]-1.811[/C][C]0.036272[/C][/ROW]
[ROW][C]11[/C][C]0.132484[/C][C]1.4812[/C][C]0.070533[/C][/ROW]
[ROW][C]12[/C][C]0.123828[/C][C]1.3844[/C][C]0.084345[/C][/ROW]
[ROW][C]13[/C][C]-0.142695[/C][C]-1.5954[/C][C]0.056576[/C][/ROW]
[ROW][C]14[/C][C]-0.086045[/C][C]-0.962[/C][C]0.16895[/C][/ROW]
[ROW][C]15[/C][C]0.072848[/C][C]0.8145[/C][C]0.208463[/C][/ROW]
[ROW][C]16[/C][C]-0.013998[/C][C]-0.1565[/C][C]0.437947[/C][/ROW]
[ROW][C]17[/C][C]0.020718[/C][C]0.2316[/C][C]0.4086[/C][/ROW]
[ROW][C]18[/C][C]0.037693[/C][C]0.4214[/C][C]0.337087[/C][/ROW]
[ROW][C]19[/C][C]-0.02512[/C][C]-0.2808[/C][C]0.389645[/C][/ROW]
[ROW][C]20[/C][C]0.021577[/C][C]0.2412[/C][C]0.404882[/C][/ROW]
[ROW][C]21[/C][C]-0.09069[/C][C]-1.0139[/C][C]0.156284[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300221&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300221&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	-0.489256	-5.47	0
2	0.086623	0.9685	0.167338
3	-0.098422	-1.1004	0.136638
4	0.155056	1.7336	0.042729
5	-0.18724	-2.0934	0.019167
6	0.045999	0.5143	0.303981
7	-0.052826	-0.5906	0.277924
8	0.055406	0.6195	0.26837
9	0.088728	0.992	0.161555
10	-0.16198	-1.811	0.036272
11	0.132484	1.4812	0.070533
12	0.123828	1.3844	0.084345
13	-0.142695	-1.5954	0.056576
14	-0.086045	-0.962	0.16895
15	0.072848	0.8145	0.208463
16	-0.013998	-0.1565	0.437947
17	0.020718	0.2316	0.4086
18	0.037693	0.4214	0.337087
19	-0.02512	-0.2808	0.389645
20	0.021577	0.2412	0.404882
21	-0.09069	-1.0139	0.156284

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.489256	-5.47	0
2	-0.200818	-2.2452	0.013256
3	-0.199713	-2.2329	0.013669
4	0.033008	0.369	0.35636
5	-0.127945	-1.4305	0.077539
6	-0.142753	-1.596	0.056504
7	-0.160699	-1.7967	0.037402
8	-0.114215	-1.277	0.101991
9	0.113511	1.2691	0.103382
10	-0.10113	-1.1307	0.130179
11	0.0094	0.1051	0.458236
12	0.261839	2.9275	0.002031
13	0.07582	0.8477	0.199115
14	-0.069079	-0.7723	0.220689
15	-0.065961	-0.7375	0.231109
16	-0.043719	-0.4888	0.312922
17	0.078433	0.8769	0.191109
18	0.153195	1.7128	0.044617
19	0.088308	0.9873	0.162698
20	-0.018388	-0.2056	0.418727
21	-0.193894	-2.1678	0.016035

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.489256 & -5.47 & 0 \tabularnewline
2 & -0.200818 & -2.2452 & 0.013256 \tabularnewline
3 & -0.199713 & -2.2329 & 0.013669 \tabularnewline
4 & 0.033008 & 0.369 & 0.35636 \tabularnewline
5 & -0.127945 & -1.4305 & 0.077539 \tabularnewline
6 & -0.142753 & -1.596 & 0.056504 \tabularnewline
7 & -0.160699 & -1.7967 & 0.037402 \tabularnewline
8 & -0.114215 & -1.277 & 0.101991 \tabularnewline
9 & 0.113511 & 1.2691 & 0.103382 \tabularnewline
10 & -0.10113 & -1.1307 & 0.130179 \tabularnewline
11 & 0.0094 & 0.1051 & 0.458236 \tabularnewline
12 & 0.261839 & 2.9275 & 0.002031 \tabularnewline
13 & 0.07582 & 0.8477 & 0.199115 \tabularnewline
14 & -0.069079 & -0.7723 & 0.220689 \tabularnewline
15 & -0.065961 & -0.7375 & 0.231109 \tabularnewline
16 & -0.043719 & -0.4888 & 0.312922 \tabularnewline
17 & 0.078433 & 0.8769 & 0.191109 \tabularnewline
18 & 0.153195 & 1.7128 & 0.044617 \tabularnewline
19 & 0.088308 & 0.9873 & 0.162698 \tabularnewline
20 & -0.018388 & -0.2056 & 0.418727 \tabularnewline
21 & -0.193894 & -2.1678 & 0.016035 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300221&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]-0.489256[/C][C]-5.47[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.200818[/C][C]-2.2452[/C][C]0.013256[/C][/ROW]
[ROW][C]3[/C][C]-0.199713[/C][C]-2.2329[/C][C]0.013669[/C][/ROW]
[ROW][C]4[/C][C]0.033008[/C][C]0.369[/C][C]0.35636[/C][/ROW]
[ROW][C]5[/C][C]-0.127945[/C][C]-1.4305[/C][C]0.077539[/C][/ROW]
[ROW][C]6[/C][C]-0.142753[/C][C]-1.596[/C][C]0.056504[/C][/ROW]
[ROW][C]7[/C][C]-0.160699[/C][C]-1.7967[/C][C]0.037402[/C][/ROW]
[ROW][C]8[/C][C]-0.114215[/C][C]-1.277[/C][C]0.101991[/C][/ROW]
[ROW][C]9[/C][C]0.113511[/C][C]1.2691[/C][C]0.103382[/C][/ROW]
[ROW][C]10[/C][C]-0.10113[/C][C]-1.1307[/C][C]0.130179[/C][/ROW]
[ROW][C]11[/C][C]0.0094[/C][C]0.1051[/C][C]0.458236[/C][/ROW]
[ROW][C]12[/C][C]0.261839[/C][C]2.9275[/C][C]0.002031[/C][/ROW]
[ROW][C]13[/C][C]0.07582[/C][C]0.8477[/C][C]0.199115[/C][/ROW]
[ROW][C]14[/C][C]-0.069079[/C][C]-0.7723[/C][C]0.220689[/C][/ROW]
[ROW][C]15[/C][C]-0.065961[/C][C]-0.7375[/C][C]0.231109[/C][/ROW]
[ROW][C]16[/C][C]-0.043719[/C][C]-0.4888[/C][C]0.312922[/C][/ROW]
[ROW][C]17[/C][C]0.078433[/C][C]0.8769[/C][C]0.191109[/C][/ROW]
[ROW][C]18[/C][C]0.153195[/C][C]1.7128[/C][C]0.044617[/C][/ROW]
[ROW][C]19[/C][C]0.088308[/C][C]0.9873[/C][C]0.162698[/C][/ROW]
[ROW][C]20[/C][C]-0.018388[/C][C]-0.2056[/C][C]0.418727[/C][/ROW]
[ROW][C]21[/C][C]-0.193894[/C][C]-2.1678[/C][C]0.016035[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300221&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300221&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	-0.489256	-5.47	0
2	-0.200818	-2.2452	0.013256
3	-0.199713	-2.2329	0.013669
4	0.033008	0.369	0.35636
5	-0.127945	-1.4305	0.077539
6	-0.142753	-1.596	0.056504
7	-0.160699	-1.7967	0.037402
8	-0.114215	-1.277	0.101991
9	0.113511	1.2691	0.103382
10	-0.10113	-1.1307	0.130179
11	0.0094	0.1051	0.458236
12	0.261839	2.9275	0.002031
13	0.07582	0.8477	0.199115
14	-0.069079	-0.7723	0.220689
15	-0.065961	-0.7375	0.231109
16	-0.043719	-0.4888	0.312922
17	0.078433	0.8769	0.191109
18	0.153195	1.7128	0.044617
19	0.088308	0.9873	0.162698
20	-0.018388	-0.2056	0.418727
21	-0.193894	-2.1678	0.016035

Figure 1

PNG link

Postscript link

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Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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,'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