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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 10 Dec 2017 13:25:40 +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/2017/Dec/10/t1512909089v8x9ndv6nwoikix.htm/, Retrieved Wed, 15 May 2024 07:08:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308907, Retrieved Wed, 15 May 2024 07:08:35 +0000

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User-defined keywords

Estimated Impact

159

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [] [2017-12-10 12:25:40] [ca643b0c409f93e6a7ce1fd0961340ec] [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	2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308907&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308907&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308907&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	2 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.897899	13.0736	0
2	0.873485	12.7181	0
3	0.874663	12.7353	0
4	0.818223	11.9135	0
5	0.845393	12.3091	0
6	0.851708	12.4011	0
7	0.805071	11.722	0
8	0.787441	11.4653	0
9	0.795705	11.5856	0
10	0.76317	11.1119	0
11	0.785727	11.4404	0
12	0.811121	11.8101	0
13	0.738782	10.7568	0
14	0.729716	10.6248	0
15	0.70359	10.2444	0
16	0.660792	9.6213	0
17	0.695348	10.1244	0
18	0.683393	9.9504	0
19	0.648516	9.4425	0
20	0.646082	9.4071	0
21	0.630428	9.1792	0
22	0.61589	8.9675	0
23	0.646026	9.4063	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.897899 & 13.0736 & 0 \tabularnewline
2 & 0.873485 & 12.7181 & 0 \tabularnewline
3 & 0.874663 & 12.7353 & 0 \tabularnewline
4 & 0.818223 & 11.9135 & 0 \tabularnewline
5 & 0.845393 & 12.3091 & 0 \tabularnewline
6 & 0.851708 & 12.4011 & 0 \tabularnewline
7 & 0.805071 & 11.722 & 0 \tabularnewline
8 & 0.787441 & 11.4653 & 0 \tabularnewline
9 & 0.795705 & 11.5856 & 0 \tabularnewline
10 & 0.76317 & 11.1119 & 0 \tabularnewline
11 & 0.785727 & 11.4404 & 0 \tabularnewline
12 & 0.811121 & 11.8101 & 0 \tabularnewline
13 & 0.738782 & 10.7568 & 0 \tabularnewline
14 & 0.729716 & 10.6248 & 0 \tabularnewline
15 & 0.70359 & 10.2444 & 0 \tabularnewline
16 & 0.660792 & 9.6213 & 0 \tabularnewline
17 & 0.695348 & 10.1244 & 0 \tabularnewline
18 & 0.683393 & 9.9504 & 0 \tabularnewline
19 & 0.648516 & 9.4425 & 0 \tabularnewline
20 & 0.646082 & 9.4071 & 0 \tabularnewline
21 & 0.630428 & 9.1792 & 0 \tabularnewline
22 & 0.61589 & 8.9675 & 0 \tabularnewline
23 & 0.646026 & 9.4063 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308907&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]0.897899[/C][C]13.0736[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.873485[/C][C]12.7181[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.874663[/C][C]12.7353[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.818223[/C][C]11.9135[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.845393[/C][C]12.3091[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.851708[/C][C]12.4011[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.805071[/C][C]11.722[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.787441[/C][C]11.4653[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.795705[/C][C]11.5856[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.76317[/C][C]11.1119[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.785727[/C][C]11.4404[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.811121[/C][C]11.8101[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.738782[/C][C]10.7568[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.729716[/C][C]10.6248[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.70359[/C][C]10.2444[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.660792[/C][C]9.6213[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.695348[/C][C]10.1244[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.683393[/C][C]9.9504[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.648516[/C][C]9.4425[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.646082[/C][C]9.4071[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.630428[/C][C]9.1792[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.61589[/C][C]8.9675[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.646026[/C][C]9.4063[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308907&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308907&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	0.897899	13.0736	0
2	0.873485	12.7181	0
3	0.874663	12.7353	0
4	0.818223	11.9135	0
5	0.845393	12.3091	0
6	0.851708	12.4011	0
7	0.805071	11.722	0
8	0.787441	11.4653	0
9	0.795705	11.5856	0
10	0.76317	11.1119	0
11	0.785727	11.4404	0
12	0.811121	11.8101	0
13	0.738782	10.7568	0
14	0.729716	10.6248	0
15	0.70359	10.2444	0
16	0.660792	9.6213	0
17	0.695348	10.1244	0
18	0.683393	9.9504	0
19	0.648516	9.4425	0
20	0.646082	9.4071	0
21	0.630428	9.1792	0
22	0.61589	8.9675	0
23	0.646026	9.4063	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.897899	13.0736	0
2	0.347111	5.054	0
3	0.298839	4.3512	1.1e-05
4	-0.143674	-2.0919	0.018818
5	0.33494	4.8768	1e-06
6	0.154916	2.2556	0.012558
7	-0.126295	-1.8389	0.033666
8	-0.183931	-2.6781	0.003992
9	0.252996	3.6837	0.000146
10	-0.031754	-0.4623	0.322155
11	0.136255	1.9839	0.024278
12	0.15185	2.211	0.014053
13	-0.294424	-4.2869	1.4e-05
14	-0.14861	-2.1638	0.015799
15	-0.109033	-1.5875	0.05694
16	0.021605	0.3146	0.376699
17	0.101127	1.4724	0.071193
18	0.016954	0.2469	0.402629
19	0.007371	0.1073	0.457319
20	0.011861	0.1727	0.431525
21	0.036393	0.5299	0.298371
22	0.053485	0.7788	0.218496
23	0.060883	0.8865	0.188186

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.897899 & 13.0736 & 0 \tabularnewline
2 & 0.347111 & 5.054 & 0 \tabularnewline
3 & 0.298839 & 4.3512 & 1.1e-05 \tabularnewline
4 & -0.143674 & -2.0919 & 0.018818 \tabularnewline
5 & 0.33494 & 4.8768 & 1e-06 \tabularnewline
6 & 0.154916 & 2.2556 & 0.012558 \tabularnewline
7 & -0.126295 & -1.8389 & 0.033666 \tabularnewline
8 & -0.183931 & -2.6781 & 0.003992 \tabularnewline
9 & 0.252996 & 3.6837 & 0.000146 \tabularnewline
10 & -0.031754 & -0.4623 & 0.322155 \tabularnewline
11 & 0.136255 & 1.9839 & 0.024278 \tabularnewline
12 & 0.15185 & 2.211 & 0.014053 \tabularnewline
13 & -0.294424 & -4.2869 & 1.4e-05 \tabularnewline
14 & -0.14861 & -2.1638 & 0.015799 \tabularnewline
15 & -0.109033 & -1.5875 & 0.05694 \tabularnewline
16 & 0.021605 & 0.3146 & 0.376699 \tabularnewline
17 & 0.101127 & 1.4724 & 0.071193 \tabularnewline
18 & 0.016954 & 0.2469 & 0.402629 \tabularnewline
19 & 0.007371 & 0.1073 & 0.457319 \tabularnewline
20 & 0.011861 & 0.1727 & 0.431525 \tabularnewline
21 & 0.036393 & 0.5299 & 0.298371 \tabularnewline
22 & 0.053485 & 0.7788 & 0.218496 \tabularnewline
23 & 0.060883 & 0.8865 & 0.188186 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308907&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]0.897899[/C][C]13.0736[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.347111[/C][C]5.054[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.298839[/C][C]4.3512[/C][C]1.1e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.143674[/C][C]-2.0919[/C][C]0.018818[/C][/ROW]
[ROW][C]5[/C][C]0.33494[/C][C]4.8768[/C][C]1e-06[/C][/ROW]
[ROW][C]6[/C][C]0.154916[/C][C]2.2556[/C][C]0.012558[/C][/ROW]
[ROW][C]7[/C][C]-0.126295[/C][C]-1.8389[/C][C]0.033666[/C][/ROW]
[ROW][C]8[/C][C]-0.183931[/C][C]-2.6781[/C][C]0.003992[/C][/ROW]
[ROW][C]9[/C][C]0.252996[/C][C]3.6837[/C][C]0.000146[/C][/ROW]
[ROW][C]10[/C][C]-0.031754[/C][C]-0.4623[/C][C]0.322155[/C][/ROW]
[ROW][C]11[/C][C]0.136255[/C][C]1.9839[/C][C]0.024278[/C][/ROW]
[ROW][C]12[/C][C]0.15185[/C][C]2.211[/C][C]0.014053[/C][/ROW]
[ROW][C]13[/C][C]-0.294424[/C][C]-4.2869[/C][C]1.4e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.14861[/C][C]-2.1638[/C][C]0.015799[/C][/ROW]
[ROW][C]15[/C][C]-0.109033[/C][C]-1.5875[/C][C]0.05694[/C][/ROW]
[ROW][C]16[/C][C]0.021605[/C][C]0.3146[/C][C]0.376699[/C][/ROW]
[ROW][C]17[/C][C]0.101127[/C][C]1.4724[/C][C]0.071193[/C][/ROW]
[ROW][C]18[/C][C]0.016954[/C][C]0.2469[/C][C]0.402629[/C][/ROW]
[ROW][C]19[/C][C]0.007371[/C][C]0.1073[/C][C]0.457319[/C][/ROW]
[ROW][C]20[/C][C]0.011861[/C][C]0.1727[/C][C]0.431525[/C][/ROW]
[ROW][C]21[/C][C]0.036393[/C][C]0.5299[/C][C]0.298371[/C][/ROW]
[ROW][C]22[/C][C]0.053485[/C][C]0.7788[/C][C]0.218496[/C][/ROW]
[ROW][C]23[/C][C]0.060883[/C][C]0.8865[/C][C]0.188186[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308907&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308907&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	0.897899	13.0736	0
2	0.347111	5.054	0
3	0.298839	4.3512	1.1e-05
4	-0.143674	-2.0919	0.018818
5	0.33494	4.8768	1e-06
6	0.154916	2.2556	0.012558
7	-0.126295	-1.8389	0.033666
8	-0.183931	-2.6781	0.003992
9	0.252996	3.6837	0.000146
10	-0.031754	-0.4623	0.322155
11	0.136255	1.9839	0.024278
12	0.15185	2.211	0.014053
13	-0.294424	-4.2869	1.4e-05
14	-0.14861	-2.1638	0.015799
15	-0.109033	-1.5875	0.05694
16	0.021605	0.3146	0.376699
17	0.101127	1.4724	0.071193
18	0.016954	0.2469	0.402629
19	0.007371	0.1073	0.457319
20	0.011861	0.1727	0.431525
21	0.036393	0.5299	0.298371
22	0.053485	0.7788	0.218496
23	0.060883	0.8865	0.188186

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 = 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