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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 15 Dec 2016 21:06:51 +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/15/t148183303248159d9q8tarce4.htm/, Retrieved Fri, 03 May 2024 09:53:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299994, Retrieved Fri, 03 May 2024 09:53:39 +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] [ACF N2142 d=1] [2016-12-15 20:06:51] [31f526a885cd288e1bc58dc4a6a7fb1f] [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=299994&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=299994&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299994&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	-0.152746	-1.7077	0.045083
2	-0.071484	-0.7992	0.212839
3	-0.089167	-0.9969	0.160366
4	-0.132877	-1.4856	0.06995
5	0.158432	1.7713	0.039472
6	-0.169964	-1.9003	0.029851
7	0.1833	2.0494	0.021259
8	-0.149952	-1.6765	0.048069
9	-0.12328	-1.3783	0.085284
10	-0.012097	-0.1353	0.446315
11	-0.044127	-0.4934	0.311314
12	0.296427	3.3142	0.000601
13	0.058249	0.6512	0.258041
14	-0.032919	-0.368	0.356732
15	-0.082927	-0.9272	0.177816
16	-0.162924	-1.8215	0.035458
17	0.140113	1.5665	0.059879
18	-0.120527	-1.3475	0.090123
19	0.147484	1.6489	0.050838
20	-0.064907	-0.7257	0.234694
21	-0.212662	-2.3776	0.00947

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.152746 & -1.7077 & 0.045083 \tabularnewline
2 & -0.071484 & -0.7992 & 0.212839 \tabularnewline
3 & -0.089167 & -0.9969 & 0.160366 \tabularnewline
4 & -0.132877 & -1.4856 & 0.06995 \tabularnewline
5 & 0.158432 & 1.7713 & 0.039472 \tabularnewline
6 & -0.169964 & -1.9003 & 0.029851 \tabularnewline
7 & 0.1833 & 2.0494 & 0.021259 \tabularnewline
8 & -0.149952 & -1.6765 & 0.048069 \tabularnewline
9 & -0.12328 & -1.3783 & 0.085284 \tabularnewline
10 & -0.012097 & -0.1353 & 0.446315 \tabularnewline
11 & -0.044127 & -0.4934 & 0.311314 \tabularnewline
12 & 0.296427 & 3.3142 & 0.000601 \tabularnewline
13 & 0.058249 & 0.6512 & 0.258041 \tabularnewline
14 & -0.032919 & -0.368 & 0.356732 \tabularnewline
15 & -0.082927 & -0.9272 & 0.177816 \tabularnewline
16 & -0.162924 & -1.8215 & 0.035458 \tabularnewline
17 & 0.140113 & 1.5665 & 0.059879 \tabularnewline
18 & -0.120527 & -1.3475 & 0.090123 \tabularnewline
19 & 0.147484 & 1.6489 & 0.050838 \tabularnewline
20 & -0.064907 & -0.7257 & 0.234694 \tabularnewline
21 & -0.212662 & -2.3776 & 0.00947 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299994&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]-0.152746[/C][C]-1.7077[/C][C]0.045083[/C][/ROW]
[ROW][C]2[/C][C]-0.071484[/C][C]-0.7992[/C][C]0.212839[/C][/ROW]
[ROW][C]3[/C][C]-0.089167[/C][C]-0.9969[/C][C]0.160366[/C][/ROW]
[ROW][C]4[/C][C]-0.132877[/C][C]-1.4856[/C][C]0.06995[/C][/ROW]
[ROW][C]5[/C][C]0.158432[/C][C]1.7713[/C][C]0.039472[/C][/ROW]
[ROW][C]6[/C][C]-0.169964[/C][C]-1.9003[/C][C]0.029851[/C][/ROW]
[ROW][C]7[/C][C]0.1833[/C][C]2.0494[/C][C]0.021259[/C][/ROW]
[ROW][C]8[/C][C]-0.149952[/C][C]-1.6765[/C][C]0.048069[/C][/ROW]
[ROW][C]9[/C][C]-0.12328[/C][C]-1.3783[/C][C]0.085284[/C][/ROW]
[ROW][C]10[/C][C]-0.012097[/C][C]-0.1353[/C][C]0.446315[/C][/ROW]
[ROW][C]11[/C][C]-0.044127[/C][C]-0.4934[/C][C]0.311314[/C][/ROW]
[ROW][C]12[/C][C]0.296427[/C][C]3.3142[/C][C]0.000601[/C][/ROW]
[ROW][C]13[/C][C]0.058249[/C][C]0.6512[/C][C]0.258041[/C][/ROW]
[ROW][C]14[/C][C]-0.032919[/C][C]-0.368[/C][C]0.356732[/C][/ROW]
[ROW][C]15[/C][C]-0.082927[/C][C]-0.9272[/C][C]0.177816[/C][/ROW]
[ROW][C]16[/C][C]-0.162924[/C][C]-1.8215[/C][C]0.035458[/C][/ROW]
[ROW][C]17[/C][C]0.140113[/C][C]1.5665[/C][C]0.059879[/C][/ROW]
[ROW][C]18[/C][C]-0.120527[/C][C]-1.3475[/C][C]0.090123[/C][/ROW]
[ROW][C]19[/C][C]0.147484[/C][C]1.6489[/C][C]0.050838[/C][/ROW]
[ROW][C]20[/C][C]-0.064907[/C][C]-0.7257[/C][C]0.234694[/C][/ROW]
[ROW][C]21[/C][C]-0.212662[/C][C]-2.3776[/C][C]0.00947[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299994&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299994&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	-0.152746	-1.7077	0.045083
2	-0.071484	-0.7992	0.212839
3	-0.089167	-0.9969	0.160366
4	-0.132877	-1.4856	0.06995
5	0.158432	1.7713	0.039472
6	-0.169964	-1.9003	0.029851
7	0.1833	2.0494	0.021259
8	-0.149952	-1.6765	0.048069
9	-0.12328	-1.3783	0.085284
10	-0.012097	-0.1353	0.446315
11	-0.044127	-0.4934	0.311314
12	0.296427	3.3142	0.000601
13	0.058249	0.6512	0.258041
14	-0.032919	-0.368	0.356732
15	-0.082927	-0.9272	0.177816
16	-0.162924	-1.8215	0.035458
17	0.140113	1.5665	0.059879
18	-0.120527	-1.3475	0.090123
19	0.147484	1.6489	0.050838
20	-0.064907	-0.7257	0.234694
21	-0.212662	-2.3776	0.00947

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.152746	-1.7077	0.045083
2	-0.097081	-1.0854	0.139918
3	-0.119875	-1.3402	0.091299
4	-0.184092	-2.0582	0.020824
5	0.087131	0.9741	0.165932
6	-0.184229	-2.0597	0.020749
7	0.13118	1.4666	0.072492
8	-0.156564	-1.7504	0.041248
9	-0.147489	-1.649	0.050832
10	-0.1422	-1.5898	0.057198
11	-0.068183	-0.7623	0.223657
12	0.14978	1.6746	0.048257
13	0.17209	1.924	0.028312
14	-0.001311	-0.0147	0.494165
15	-0.015966	-0.1785	0.42931
16	-0.139431	-1.5589	0.060775
17	0.03774	0.4219	0.336894
18	-0.149916	-1.6761	0.048108
19	0.084614	0.946	0.172983
20	-0.070077	-0.7835	0.217411
21	-0.131286	-1.4678	0.072332

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.152746 & -1.7077 & 0.045083 \tabularnewline
2 & -0.097081 & -1.0854 & 0.139918 \tabularnewline
3 & -0.119875 & -1.3402 & 0.091299 \tabularnewline
4 & -0.184092 & -2.0582 & 0.020824 \tabularnewline
5 & 0.087131 & 0.9741 & 0.165932 \tabularnewline
6 & -0.184229 & -2.0597 & 0.020749 \tabularnewline
7 & 0.13118 & 1.4666 & 0.072492 \tabularnewline
8 & -0.156564 & -1.7504 & 0.041248 \tabularnewline
9 & -0.147489 & -1.649 & 0.050832 \tabularnewline
10 & -0.1422 & -1.5898 & 0.057198 \tabularnewline
11 & -0.068183 & -0.7623 & 0.223657 \tabularnewline
12 & 0.14978 & 1.6746 & 0.048257 \tabularnewline
13 & 0.17209 & 1.924 & 0.028312 \tabularnewline
14 & -0.001311 & -0.0147 & 0.494165 \tabularnewline
15 & -0.015966 & -0.1785 & 0.42931 \tabularnewline
16 & -0.139431 & -1.5589 & 0.060775 \tabularnewline
17 & 0.03774 & 0.4219 & 0.336894 \tabularnewline
18 & -0.149916 & -1.6761 & 0.048108 \tabularnewline
19 & 0.084614 & 0.946 & 0.172983 \tabularnewline
20 & -0.070077 & -0.7835 & 0.217411 \tabularnewline
21 & -0.131286 & -1.4678 & 0.072332 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299994&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]-0.152746[/C][C]-1.7077[/C][C]0.045083[/C][/ROW]
[ROW][C]2[/C][C]-0.097081[/C][C]-1.0854[/C][C]0.139918[/C][/ROW]
[ROW][C]3[/C][C]-0.119875[/C][C]-1.3402[/C][C]0.091299[/C][/ROW]
[ROW][C]4[/C][C]-0.184092[/C][C]-2.0582[/C][C]0.020824[/C][/ROW]
[ROW][C]5[/C][C]0.087131[/C][C]0.9741[/C][C]0.165932[/C][/ROW]
[ROW][C]6[/C][C]-0.184229[/C][C]-2.0597[/C][C]0.020749[/C][/ROW]
[ROW][C]7[/C][C]0.13118[/C][C]1.4666[/C][C]0.072492[/C][/ROW]
[ROW][C]8[/C][C]-0.156564[/C][C]-1.7504[/C][C]0.041248[/C][/ROW]
[ROW][C]9[/C][C]-0.147489[/C][C]-1.649[/C][C]0.050832[/C][/ROW]
[ROW][C]10[/C][C]-0.1422[/C][C]-1.5898[/C][C]0.057198[/C][/ROW]
[ROW][C]11[/C][C]-0.068183[/C][C]-0.7623[/C][C]0.223657[/C][/ROW]
[ROW][C]12[/C][C]0.14978[/C][C]1.6746[/C][C]0.048257[/C][/ROW]
[ROW][C]13[/C][C]0.17209[/C][C]1.924[/C][C]0.028312[/C][/ROW]
[ROW][C]14[/C][C]-0.001311[/C][C]-0.0147[/C][C]0.494165[/C][/ROW]
[ROW][C]15[/C][C]-0.015966[/C][C]-0.1785[/C][C]0.42931[/C][/ROW]
[ROW][C]16[/C][C]-0.139431[/C][C]-1.5589[/C][C]0.060775[/C][/ROW]
[ROW][C]17[/C][C]0.03774[/C][C]0.4219[/C][C]0.336894[/C][/ROW]
[ROW][C]18[/C][C]-0.149916[/C][C]-1.6761[/C][C]0.048108[/C][/ROW]
[ROW][C]19[/C][C]0.084614[/C][C]0.946[/C][C]0.172983[/C][/ROW]
[ROW][C]20[/C][C]-0.070077[/C][C]-0.7835[/C][C]0.217411[/C][/ROW]
[ROW][C]21[/C][C]-0.131286[/C][C]-1.4678[/C][C]0.072332[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299994&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299994&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	-0.152746	-1.7077	0.045083
2	-0.097081	-1.0854	0.139918
3	-0.119875	-1.3402	0.091299
4	-0.184092	-2.0582	0.020824
5	0.087131	0.9741	0.165932
6	-0.184229	-2.0597	0.020749
7	0.13118	1.4666	0.072492
8	-0.156564	-1.7504	0.041248
9	-0.147489	-1.649	0.050832
10	-0.1422	-1.5898	0.057198
11	-0.068183	-0.7623	0.223657
12	0.14978	1.6746	0.048257
13	0.17209	1.924	0.028312
14	-0.001311	-0.0147	0.494165
15	-0.015966	-0.1785	0.42931
16	-0.139431	-1.5589	0.060775
17	0.03774	0.4219	0.336894
18	-0.149916	-1.6761	0.048108
19	0.084614	0.946	0.172983
20	-0.070077	-0.7835	0.217411
21	-0.131286	-1.4678	0.072332

Figure 1

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Postscript link

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Figure 2

PNG link

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Figure 3

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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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code