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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 13 Dec 2016 13:01:25 +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/13/t14816305845l5yh6l907qu90v.htm/, Retrieved Fri, 01 Nov 2024 03:35:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299081, Retrieved Fri, 01 Nov 2024 03:35:52 +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] [Autocorrelation] [2016-12-13 12:01:25] [36884fbde1107444791dd71ee0072a5a] [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=299081&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=299081&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299081&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	-0.51401	-5.7468	0
2	0.184829	2.0664	0.020426
3	-0.252	-2.8175	0.002814
4	0.301302	3.3687	0.000502
5	-0.36149	-4.0416	4.6e-05
6	0.206682	2.3108	0.011242
7	-0.162714	-1.8192	0.035638
8	0.186767	2.0881	0.019408
9	-0.077417	-0.8655	0.194198
10	-0.001338	-0.015	0.494043
11	0.023788	0.266	0.395355
12	0.142688	1.5953	0.056585
13	-0.195703	-2.188	0.015263
14	0.023094	0.2582	0.398337
15	-0.009669	-0.1081	0.457044
16	0.052252	0.5842	0.280072
17	-0.037157	-0.4154	0.33927
18	0.122368	1.3681	0.086865
19	-0.116619	-1.3038	0.097342
20	0.073038	0.8166	0.207857
21	-0.098874	-1.1054	0.135545

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.51401 & -5.7468 & 0 \tabularnewline
2 & 0.184829 & 2.0664 & 0.020426 \tabularnewline
3 & -0.252 & -2.8175 & 0.002814 \tabularnewline
4 & 0.301302 & 3.3687 & 0.000502 \tabularnewline
5 & -0.36149 & -4.0416 & 4.6e-05 \tabularnewline
6 & 0.206682 & 2.3108 & 0.011242 \tabularnewline
7 & -0.162714 & -1.8192 & 0.035638 \tabularnewline
8 & 0.186767 & 2.0881 & 0.019408 \tabularnewline
9 & -0.077417 & -0.8655 & 0.194198 \tabularnewline
10 & -0.001338 & -0.015 & 0.494043 \tabularnewline
11 & 0.023788 & 0.266 & 0.395355 \tabularnewline
12 & 0.142688 & 1.5953 & 0.056585 \tabularnewline
13 & -0.195703 & -2.188 & 0.015263 \tabularnewline
14 & 0.023094 & 0.2582 & 0.398337 \tabularnewline
15 & -0.009669 & -0.1081 & 0.457044 \tabularnewline
16 & 0.052252 & 0.5842 & 0.280072 \tabularnewline
17 & -0.037157 & -0.4154 & 0.33927 \tabularnewline
18 & 0.122368 & 1.3681 & 0.086865 \tabularnewline
19 & -0.116619 & -1.3038 & 0.097342 \tabularnewline
20 & 0.073038 & 0.8166 & 0.207857 \tabularnewline
21 & -0.098874 & -1.1054 & 0.135545 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299081&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]-0.51401[/C][C]-5.7468[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.184829[/C][C]2.0664[/C][C]0.020426[/C][/ROW]
[ROW][C]3[/C][C]-0.252[/C][C]-2.8175[/C][C]0.002814[/C][/ROW]
[ROW][C]4[/C][C]0.301302[/C][C]3.3687[/C][C]0.000502[/C][/ROW]
[ROW][C]5[/C][C]-0.36149[/C][C]-4.0416[/C][C]4.6e-05[/C][/ROW]
[ROW][C]6[/C][C]0.206682[/C][C]2.3108[/C][C]0.011242[/C][/ROW]
[ROW][C]7[/C][C]-0.162714[/C][C]-1.8192[/C][C]0.035638[/C][/ROW]
[ROW][C]8[/C][C]0.186767[/C][C]2.0881[/C][C]0.019408[/C][/ROW]
[ROW][C]9[/C][C]-0.077417[/C][C]-0.8655[/C][C]0.194198[/C][/ROW]
[ROW][C]10[/C][C]-0.001338[/C][C]-0.015[/C][C]0.494043[/C][/ROW]
[ROW][C]11[/C][C]0.023788[/C][C]0.266[/C][C]0.395355[/C][/ROW]
[ROW][C]12[/C][C]0.142688[/C][C]1.5953[/C][C]0.056585[/C][/ROW]
[ROW][C]13[/C][C]-0.195703[/C][C]-2.188[/C][C]0.015263[/C][/ROW]
[ROW][C]14[/C][C]0.023094[/C][C]0.2582[/C][C]0.398337[/C][/ROW]
[ROW][C]15[/C][C]-0.009669[/C][C]-0.1081[/C][C]0.457044[/C][/ROW]
[ROW][C]16[/C][C]0.052252[/C][C]0.5842[/C][C]0.280072[/C][/ROW]
[ROW][C]17[/C][C]-0.037157[/C][C]-0.4154[/C][C]0.33927[/C][/ROW]
[ROW][C]18[/C][C]0.122368[/C][C]1.3681[/C][C]0.086865[/C][/ROW]
[ROW][C]19[/C][C]-0.116619[/C][C]-1.3038[/C][C]0.097342[/C][/ROW]
[ROW][C]20[/C][C]0.073038[/C][C]0.8166[/C][C]0.207857[/C][/ROW]
[ROW][C]21[/C][C]-0.098874[/C][C]-1.1054[/C][C]0.135545[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299081&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299081&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	-0.51401	-5.7468	0
2	0.184829	2.0664	0.020426
3	-0.252	-2.8175	0.002814
4	0.301302	3.3687	0.000502
5	-0.36149	-4.0416	4.6e-05
6	0.206682	2.3108	0.011242
7	-0.162714	-1.8192	0.035638
8	0.186767	2.0881	0.019408
9	-0.077417	-0.8655	0.194198
10	-0.001338	-0.015	0.494043
11	0.023788	0.266	0.395355
12	0.142688	1.5953	0.056585
13	-0.195703	-2.188	0.015263
14	0.023094	0.2582	0.398337
15	-0.009669	-0.1081	0.457044
16	0.052252	0.5842	0.280072
17	-0.037157	-0.4154	0.33927
18	0.122368	1.3681	0.086865
19	-0.116619	-1.3038	0.097342
20	0.073038	0.8166	0.207857
21	-0.098874	-1.1054	0.135545

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.51401	-5.7468	0
2	-0.107881	-1.2061	0.11502
3	-0.27804	-3.1086	0.001164
4	0.084241	0.9418	0.174046
5	-0.246166	-2.7522	0.0034
6	-0.147121	-1.6449	0.051256
7	-0.152126	-1.7008	0.045732
8	-0.078557	-0.8783	0.190736
9	0.079598	0.8899	0.187606
10	-0.132998	-1.487	0.069771
11	0.02832	0.3166	0.376028
12	0.201728	2.2554	0.012924
13	-0.029885	-0.3341	0.369421
14	-0.024148	-0.27	0.393809
15	-0.067246	-0.7518	0.226782
16	-0.00444	-0.0496	0.480246
17	0.089299	0.9984	0.160008
18	0.159752	1.7861	0.038255
19	0.025183	0.2816	0.389377
20	-0.018147	-0.2029	0.419774
21	-0.046296	-0.5176	0.302824

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.51401 & -5.7468 & 0 \tabularnewline
2 & -0.107881 & -1.2061 & 0.11502 \tabularnewline
3 & -0.27804 & -3.1086 & 0.001164 \tabularnewline
4 & 0.084241 & 0.9418 & 0.174046 \tabularnewline
5 & -0.246166 & -2.7522 & 0.0034 \tabularnewline
6 & -0.147121 & -1.6449 & 0.051256 \tabularnewline
7 & -0.152126 & -1.7008 & 0.045732 \tabularnewline
8 & -0.078557 & -0.8783 & 0.190736 \tabularnewline
9 & 0.079598 & 0.8899 & 0.187606 \tabularnewline
10 & -0.132998 & -1.487 & 0.069771 \tabularnewline
11 & 0.02832 & 0.3166 & 0.376028 \tabularnewline
12 & 0.201728 & 2.2554 & 0.012924 \tabularnewline
13 & -0.029885 & -0.3341 & 0.369421 \tabularnewline
14 & -0.024148 & -0.27 & 0.393809 \tabularnewline
15 & -0.067246 & -0.7518 & 0.226782 \tabularnewline
16 & -0.00444 & -0.0496 & 0.480246 \tabularnewline
17 & 0.089299 & 0.9984 & 0.160008 \tabularnewline
18 & 0.159752 & 1.7861 & 0.038255 \tabularnewline
19 & 0.025183 & 0.2816 & 0.389377 \tabularnewline
20 & -0.018147 & -0.2029 & 0.419774 \tabularnewline
21 & -0.046296 & -0.5176 & 0.302824 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299081&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]-0.51401[/C][C]-5.7468[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.107881[/C][C]-1.2061[/C][C]0.11502[/C][/ROW]
[ROW][C]3[/C][C]-0.27804[/C][C]-3.1086[/C][C]0.001164[/C][/ROW]
[ROW][C]4[/C][C]0.084241[/C][C]0.9418[/C][C]0.174046[/C][/ROW]
[ROW][C]5[/C][C]-0.246166[/C][C]-2.7522[/C][C]0.0034[/C][/ROW]
[ROW][C]6[/C][C]-0.147121[/C][C]-1.6449[/C][C]0.051256[/C][/ROW]
[ROW][C]7[/C][C]-0.152126[/C][C]-1.7008[/C][C]0.045732[/C][/ROW]
[ROW][C]8[/C][C]-0.078557[/C][C]-0.8783[/C][C]0.190736[/C][/ROW]
[ROW][C]9[/C][C]0.079598[/C][C]0.8899[/C][C]0.187606[/C][/ROW]
[ROW][C]10[/C][C]-0.132998[/C][C]-1.487[/C][C]0.069771[/C][/ROW]
[ROW][C]11[/C][C]0.02832[/C][C]0.3166[/C][C]0.376028[/C][/ROW]
[ROW][C]12[/C][C]0.201728[/C][C]2.2554[/C][C]0.012924[/C][/ROW]
[ROW][C]13[/C][C]-0.029885[/C][C]-0.3341[/C][C]0.369421[/C][/ROW]
[ROW][C]14[/C][C]-0.024148[/C][C]-0.27[/C][C]0.393809[/C][/ROW]
[ROW][C]15[/C][C]-0.067246[/C][C]-0.7518[/C][C]0.226782[/C][/ROW]
[ROW][C]16[/C][C]-0.00444[/C][C]-0.0496[/C][C]0.480246[/C][/ROW]
[ROW][C]17[/C][C]0.089299[/C][C]0.9984[/C][C]0.160008[/C][/ROW]
[ROW][C]18[/C][C]0.159752[/C][C]1.7861[/C][C]0.038255[/C][/ROW]
[ROW][C]19[/C][C]0.025183[/C][C]0.2816[/C][C]0.389377[/C][/ROW]
[ROW][C]20[/C][C]-0.018147[/C][C]-0.2029[/C][C]0.419774[/C][/ROW]
[ROW][C]21[/C][C]-0.046296[/C][C]-0.5176[/C][C]0.302824[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299081&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299081&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	-0.51401	-5.7468	0
2	-0.107881	-1.2061	0.11502
3	-0.27804	-3.1086	0.001164
4	0.084241	0.9418	0.174046
5	-0.246166	-2.7522	0.0034
6	-0.147121	-1.6449	0.051256
7	-0.152126	-1.7008	0.045732
8	-0.078557	-0.8783	0.190736
9	0.079598	0.8899	0.187606
10	-0.132998	-1.487	0.069771
11	0.02832	0.3166	0.376028
12	0.201728	2.2554	0.012924
13	-0.029885	-0.3341	0.369421
14	-0.024148	-0.27	0.393809
15	-0.067246	-0.7518	0.226782
16	-0.00444	-0.0496	0.480246
17	0.089299	0.9984	0.160008
18	0.159752	1.7861	0.038255
19	0.025183	0.2816	0.389377
20	-0.018147	-0.2029	0.419774
21	-0.046296	-0.5176	0.302824

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

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Figure 3

PNG link

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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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '1'
par3 <- '0'
par2 <- '1'
par1 <- 'Default'
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