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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 19 Nov 2016 15:57:51 +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/Nov/19/t1479567772c5ld8l3kkq3sfyk.htm/, Retrieved Sat, 04 May 2024 17:29:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296849, Retrieved Sat, 04 May 2024 17:29:32 +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] [] [2016-11-19 14:57:51] [219800a2f11ddd28e3280d87dbde8c8d] [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=296849&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=296849&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296849&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	-0.010686	-0.1278	0.449249
2	-0.046453	-0.5555	0.28971
3	-0.069856	-0.8354	0.202455
4	0.102809	1.2294	0.110467
5	-0.053159	-0.6357	0.262999
6	0.017229	0.206	0.41853
7	0.087617	1.0477	0.148261
8	-0.063741	-0.7622	0.223587
9	-0.025105	-0.3002	0.382225
10	-0.021366	-0.2555	0.399352
11	-0.06196	-0.7409	0.229975
12	-0.050466	-0.6035	0.273572
13	0.110052	1.316	0.095134
14	0.075017	0.8971	0.185594
15	-0.080436	-0.9619	0.168869
16	-0.073551	-0.8795	0.190291
17	-0.003895	-0.0466	0.481455
18	-0.013253	-0.1585	0.437151
19	-0.088527	-1.0586	0.145778
20	-0.163068	-1.95	0.026565
21	0.008133	0.0973	0.46133

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.010686 & -0.1278 & 0.449249 \tabularnewline
2 & -0.046453 & -0.5555 & 0.28971 \tabularnewline
3 & -0.069856 & -0.8354 & 0.202455 \tabularnewline
4 & 0.102809 & 1.2294 & 0.110467 \tabularnewline
5 & -0.053159 & -0.6357 & 0.262999 \tabularnewline
6 & 0.017229 & 0.206 & 0.41853 \tabularnewline
7 & 0.087617 & 1.0477 & 0.148261 \tabularnewline
8 & -0.063741 & -0.7622 & 0.223587 \tabularnewline
9 & -0.025105 & -0.3002 & 0.382225 \tabularnewline
10 & -0.021366 & -0.2555 & 0.399352 \tabularnewline
11 & -0.06196 & -0.7409 & 0.229975 \tabularnewline
12 & -0.050466 & -0.6035 & 0.273572 \tabularnewline
13 & 0.110052 & 1.316 & 0.095134 \tabularnewline
14 & 0.075017 & 0.8971 & 0.185594 \tabularnewline
15 & -0.080436 & -0.9619 & 0.168869 \tabularnewline
16 & -0.073551 & -0.8795 & 0.190291 \tabularnewline
17 & -0.003895 & -0.0466 & 0.481455 \tabularnewline
18 & -0.013253 & -0.1585 & 0.437151 \tabularnewline
19 & -0.088527 & -1.0586 & 0.145778 \tabularnewline
20 & -0.163068 & -1.95 & 0.026565 \tabularnewline
21 & 0.008133 & 0.0973 & 0.46133 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296849&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]-0.010686[/C][C]-0.1278[/C][C]0.449249[/C][/ROW]
[ROW][C]2[/C][C]-0.046453[/C][C]-0.5555[/C][C]0.28971[/C][/ROW]
[ROW][C]3[/C][C]-0.069856[/C][C]-0.8354[/C][C]0.202455[/C][/ROW]
[ROW][C]4[/C][C]0.102809[/C][C]1.2294[/C][C]0.110467[/C][/ROW]
[ROW][C]5[/C][C]-0.053159[/C][C]-0.6357[/C][C]0.262999[/C][/ROW]
[ROW][C]6[/C][C]0.017229[/C][C]0.206[/C][C]0.41853[/C][/ROW]
[ROW][C]7[/C][C]0.087617[/C][C]1.0477[/C][C]0.148261[/C][/ROW]
[ROW][C]8[/C][C]-0.063741[/C][C]-0.7622[/C][C]0.223587[/C][/ROW]
[ROW][C]9[/C][C]-0.025105[/C][C]-0.3002[/C][C]0.382225[/C][/ROW]
[ROW][C]10[/C][C]-0.021366[/C][C]-0.2555[/C][C]0.399352[/C][/ROW]
[ROW][C]11[/C][C]-0.06196[/C][C]-0.7409[/C][C]0.229975[/C][/ROW]
[ROW][C]12[/C][C]-0.050466[/C][C]-0.6035[/C][C]0.273572[/C][/ROW]
[ROW][C]13[/C][C]0.110052[/C][C]1.316[/C][C]0.095134[/C][/ROW]
[ROW][C]14[/C][C]0.075017[/C][C]0.8971[/C][C]0.185594[/C][/ROW]
[ROW][C]15[/C][C]-0.080436[/C][C]-0.9619[/C][C]0.168869[/C][/ROW]
[ROW][C]16[/C][C]-0.073551[/C][C]-0.8795[/C][C]0.190291[/C][/ROW]
[ROW][C]17[/C][C]-0.003895[/C][C]-0.0466[/C][C]0.481455[/C][/ROW]
[ROW][C]18[/C][C]-0.013253[/C][C]-0.1585[/C][C]0.437151[/C][/ROW]
[ROW][C]19[/C][C]-0.088527[/C][C]-1.0586[/C][C]0.145778[/C][/ROW]
[ROW][C]20[/C][C]-0.163068[/C][C]-1.95[/C][C]0.026565[/C][/ROW]
[ROW][C]21[/C][C]0.008133[/C][C]0.0973[/C][C]0.46133[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296849&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296849&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	-0.010686	-0.1278	0.449249
2	-0.046453	-0.5555	0.28971
3	-0.069856	-0.8354	0.202455
4	0.102809	1.2294	0.110467
5	-0.053159	-0.6357	0.262999
6	0.017229	0.206	0.41853
7	0.087617	1.0477	0.148261
8	-0.063741	-0.7622	0.223587
9	-0.025105	-0.3002	0.382225
10	-0.021366	-0.2555	0.399352
11	-0.06196	-0.7409	0.229975
12	-0.050466	-0.6035	0.273572
13	0.110052	1.316	0.095134
14	0.075017	0.8971	0.185594
15	-0.080436	-0.9619	0.168869
16	-0.073551	-0.8795	0.190291
17	-0.003895	-0.0466	0.481455
18	-0.013253	-0.1585	0.437151
19	-0.088527	-1.0586	0.145778
20	-0.163068	-1.95	0.026565
21	0.008133	0.0973	0.46133

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.010686	-0.1278	0.449249
2	-0.046573	-0.5569	0.289223
3	-0.071035	-0.8495	0.198522
4	0.099566	1.1906	0.117884
5	-0.058549	-0.7001	0.242488
6	0.02133	0.2551	0.399519
7	0.098858	1.1822	0.119551
8	-0.082287	-0.984	0.163385
9	-0.002442	-0.0292	0.48837
10	-0.021158	-0.253	0.400311
11	-0.095937	-1.1472	0.126599
12	-0.029187	-0.349	0.363792
13	0.096371	1.1524	0.125533
14	0.058125	0.6951	0.244068
15	-0.052235	-0.6246	0.266601
16	-0.055069	-0.6585	0.25563
17	-0.023868	-0.2854	0.387866
18	-0.023091	-0.2761	0.391423
19	-0.089696	-1.0726	0.142626
20	-0.203026	-2.4278	0.008216
21	-0.009959	-0.1191	0.452685

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.010686 & -0.1278 & 0.449249 \tabularnewline
2 & -0.046573 & -0.5569 & 0.289223 \tabularnewline
3 & -0.071035 & -0.8495 & 0.198522 \tabularnewline
4 & 0.099566 & 1.1906 & 0.117884 \tabularnewline
5 & -0.058549 & -0.7001 & 0.242488 \tabularnewline
6 & 0.02133 & 0.2551 & 0.399519 \tabularnewline
7 & 0.098858 & 1.1822 & 0.119551 \tabularnewline
8 & -0.082287 & -0.984 & 0.163385 \tabularnewline
9 & -0.002442 & -0.0292 & 0.48837 \tabularnewline
10 & -0.021158 & -0.253 & 0.400311 \tabularnewline
11 & -0.095937 & -1.1472 & 0.126599 \tabularnewline
12 & -0.029187 & -0.349 & 0.363792 \tabularnewline
13 & 0.096371 & 1.1524 & 0.125533 \tabularnewline
14 & 0.058125 & 0.6951 & 0.244068 \tabularnewline
15 & -0.052235 & -0.6246 & 0.266601 \tabularnewline
16 & -0.055069 & -0.6585 & 0.25563 \tabularnewline
17 & -0.023868 & -0.2854 & 0.387866 \tabularnewline
18 & -0.023091 & -0.2761 & 0.391423 \tabularnewline
19 & -0.089696 & -1.0726 & 0.142626 \tabularnewline
20 & -0.203026 & -2.4278 & 0.008216 \tabularnewline
21 & -0.009959 & -0.1191 & 0.452685 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296849&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]-0.010686[/C][C]-0.1278[/C][C]0.449249[/C][/ROW]
[ROW][C]2[/C][C]-0.046573[/C][C]-0.5569[/C][C]0.289223[/C][/ROW]
[ROW][C]3[/C][C]-0.071035[/C][C]-0.8495[/C][C]0.198522[/C][/ROW]
[ROW][C]4[/C][C]0.099566[/C][C]1.1906[/C][C]0.117884[/C][/ROW]
[ROW][C]5[/C][C]-0.058549[/C][C]-0.7001[/C][C]0.242488[/C][/ROW]
[ROW][C]6[/C][C]0.02133[/C][C]0.2551[/C][C]0.399519[/C][/ROW]
[ROW][C]7[/C][C]0.098858[/C][C]1.1822[/C][C]0.119551[/C][/ROW]
[ROW][C]8[/C][C]-0.082287[/C][C]-0.984[/C][C]0.163385[/C][/ROW]
[ROW][C]9[/C][C]-0.002442[/C][C]-0.0292[/C][C]0.48837[/C][/ROW]
[ROW][C]10[/C][C]-0.021158[/C][C]-0.253[/C][C]0.400311[/C][/ROW]
[ROW][C]11[/C][C]-0.095937[/C][C]-1.1472[/C][C]0.126599[/C][/ROW]
[ROW][C]12[/C][C]-0.029187[/C][C]-0.349[/C][C]0.363792[/C][/ROW]
[ROW][C]13[/C][C]0.096371[/C][C]1.1524[/C][C]0.125533[/C][/ROW]
[ROW][C]14[/C][C]0.058125[/C][C]0.6951[/C][C]0.244068[/C][/ROW]
[ROW][C]15[/C][C]-0.052235[/C][C]-0.6246[/C][C]0.266601[/C][/ROW]
[ROW][C]16[/C][C]-0.055069[/C][C]-0.6585[/C][C]0.25563[/C][/ROW]
[ROW][C]17[/C][C]-0.023868[/C][C]-0.2854[/C][C]0.387866[/C][/ROW]
[ROW][C]18[/C][C]-0.023091[/C][C]-0.2761[/C][C]0.391423[/C][/ROW]
[ROW][C]19[/C][C]-0.089696[/C][C]-1.0726[/C][C]0.142626[/C][/ROW]
[ROW][C]20[/C][C]-0.203026[/C][C]-2.4278[/C][C]0.008216[/C][/ROW]
[ROW][C]21[/C][C]-0.009959[/C][C]-0.1191[/C][C]0.452685[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296849&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296849&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	-0.010686	-0.1278	0.449249
2	-0.046573	-0.5569	0.289223
3	-0.071035	-0.8495	0.198522
4	0.099566	1.1906	0.117884
5	-0.058549	-0.7001	0.242488
6	0.02133	0.2551	0.399519
7	0.098858	1.1822	0.119551
8	-0.082287	-0.984	0.163385
9	-0.002442	-0.0292	0.48837
10	-0.021158	-0.253	0.400311
11	-0.095937	-1.1472	0.126599
12	-0.029187	-0.349	0.363792
13	0.096371	1.1524	0.125533
14	0.058125	0.6951	0.244068
15	-0.052235	-0.6246	0.266601
16	-0.055069	-0.6585	0.25563
17	-0.023868	-0.2854	0.387866
18	-0.023091	-0.2761	0.391423
19	-0.089696	-1.0726	0.142626
20	-0.203026	-2.4278	0.008216
21	-0.009959	-0.1191	0.452685

Figure 1

PNG link

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 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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