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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 18 Dec 2016 20:18:14 +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/18/t1482088718tmvl3uvm6vlw6nf.htm/, Retrieved Wed, 08 May 2024 23:22:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301226, Retrieved Wed, 08 May 2024 23:22:16 +0000

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-     [(Partial) Autocorrelation Function] [autocorrelation N247] [2016-12-16 08:48:05] [5ad8e5538a25411d3c3b0ec85050bd51]
- R P   [(Partial) Autocorrelation Function] [Autocorrelation N...] [2016-12-16 13:04:03] [d1d385d9b7e195437bdc484ddbefdda4]
- R         [(Partial) Autocorrelation Function] [autocorrelation m...] [2016-12-18 19:18:14] [b95f76f605693b3a3343a287ab24f42a] [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=301226&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=301226&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301226&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	-0.537238	-5.3992	0
2	-0.049132	-0.4938	0.311269
3	0.087357	0.8779	0.191033
4	0.140928	1.4163	0.07988
5	-0.168084	-1.6892	0.047131
6	-0.051185	-0.5144	0.304049
7	0.171744	1.726	0.043702
8	-0.03457	-0.3474	0.364498
9	-0.106483	-1.0701	0.143554
10	-0.005379	-0.0541	0.478499
11	0.288836	2.9028	0.002271
12	-0.38899	-3.9093	8.4e-05
13	0.178093	1.7898	0.03824
14	0.047818	0.4806	0.315931
15	-0.063343	-0.6366	0.262917
16	-0.009051	-0.091	0.463852
17	0.001721	0.0173	0.493117
18	0.01342	0.1349	0.446492
19	0.028751	0.2889	0.386607
20	-0.035482	-0.3566	0.36107

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.537238 & -5.3992 & 0 \tabularnewline
2 & -0.049132 & -0.4938 & 0.311269 \tabularnewline
3 & 0.087357 & 0.8779 & 0.191033 \tabularnewline
4 & 0.140928 & 1.4163 & 0.07988 \tabularnewline
5 & -0.168084 & -1.6892 & 0.047131 \tabularnewline
6 & -0.051185 & -0.5144 & 0.304049 \tabularnewline
7 & 0.171744 & 1.726 & 0.043702 \tabularnewline
8 & -0.03457 & -0.3474 & 0.364498 \tabularnewline
9 & -0.106483 & -1.0701 & 0.143554 \tabularnewline
10 & -0.005379 & -0.0541 & 0.478499 \tabularnewline
11 & 0.288836 & 2.9028 & 0.002271 \tabularnewline
12 & -0.38899 & -3.9093 & 8.4e-05 \tabularnewline
13 & 0.178093 & 1.7898 & 0.03824 \tabularnewline
14 & 0.047818 & 0.4806 & 0.315931 \tabularnewline
15 & -0.063343 & -0.6366 & 0.262917 \tabularnewline
16 & -0.009051 & -0.091 & 0.463852 \tabularnewline
17 & 0.001721 & 0.0173 & 0.493117 \tabularnewline
18 & 0.01342 & 0.1349 & 0.446492 \tabularnewline
19 & 0.028751 & 0.2889 & 0.386607 \tabularnewline
20 & -0.035482 & -0.3566 & 0.36107 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301226&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]-0.537238[/C][C]-5.3992[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.049132[/C][C]-0.4938[/C][C]0.311269[/C][/ROW]
[ROW][C]3[/C][C]0.087357[/C][C]0.8779[/C][C]0.191033[/C][/ROW]
[ROW][C]4[/C][C]0.140928[/C][C]1.4163[/C][C]0.07988[/C][/ROW]
[ROW][C]5[/C][C]-0.168084[/C][C]-1.6892[/C][C]0.047131[/C][/ROW]
[ROW][C]6[/C][C]-0.051185[/C][C]-0.5144[/C][C]0.304049[/C][/ROW]
[ROW][C]7[/C][C]0.171744[/C][C]1.726[/C][C]0.043702[/C][/ROW]
[ROW][C]8[/C][C]-0.03457[/C][C]-0.3474[/C][C]0.364498[/C][/ROW]
[ROW][C]9[/C][C]-0.106483[/C][C]-1.0701[/C][C]0.143554[/C][/ROW]
[ROW][C]10[/C][C]-0.005379[/C][C]-0.0541[/C][C]0.478499[/C][/ROW]
[ROW][C]11[/C][C]0.288836[/C][C]2.9028[/C][C]0.002271[/C][/ROW]
[ROW][C]12[/C][C]-0.38899[/C][C]-3.9093[/C][C]8.4e-05[/C][/ROW]
[ROW][C]13[/C][C]0.178093[/C][C]1.7898[/C][C]0.03824[/C][/ROW]
[ROW][C]14[/C][C]0.047818[/C][C]0.4806[/C][C]0.315931[/C][/ROW]
[ROW][C]15[/C][C]-0.063343[/C][C]-0.6366[/C][C]0.262917[/C][/ROW]
[ROW][C]16[/C][C]-0.009051[/C][C]-0.091[/C][C]0.463852[/C][/ROW]
[ROW][C]17[/C][C]0.001721[/C][C]0.0173[/C][C]0.493117[/C][/ROW]
[ROW][C]18[/C][C]0.01342[/C][C]0.1349[/C][C]0.446492[/C][/ROW]
[ROW][C]19[/C][C]0.028751[/C][C]0.2889[/C][C]0.386607[/C][/ROW]
[ROW][C]20[/C][C]-0.035482[/C][C]-0.3566[/C][C]0.36107[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301226&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301226&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	-0.537238	-5.3992	0
2	-0.049132	-0.4938	0.311269
3	0.087357	0.8779	0.191033
4	0.140928	1.4163	0.07988
5	-0.168084	-1.6892	0.047131
6	-0.051185	-0.5144	0.304049
7	0.171744	1.726	0.043702
8	-0.03457	-0.3474	0.364498
9	-0.106483	-1.0701	0.143554
10	-0.005379	-0.0541	0.478499
11	0.288836	2.9028	0.002271
12	-0.38899	-3.9093	8.4e-05
13	0.178093	1.7898	0.03824
14	0.047818	0.4806	0.315931
15	-0.063343	-0.6366	0.262917
16	-0.009051	-0.091	0.463852
17	0.001721	0.0173	0.493117
18	0.01342	0.1349	0.446492
19	0.028751	0.2889	0.386607
20	-0.035482	-0.3566	0.36107

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.537238	-5.3992	0
2	-0.474795	-4.7716	3e-06
3	-0.375038	-3.7691	0.000138
4	-0.028962	-0.2911	0.3858
5	0.008926	0.0897	0.464349
6	-0.140018	-1.4072	0.081224
7	-0.039347	-0.3954	0.346678
8	0.047501	0.4774	0.317062
9	0.013077	0.1314	0.447853
10	-0.13696	-1.3764	0.085866
11	0.240582	2.4178	0.008703
12	-0.086108	-0.8654	0.194441
13	-0.015483	-0.1556	0.438328
14	0.024448	0.2457	0.403209
15	-0.073838	-0.7421	0.229886
16	0.066325	0.6666	0.253286
17	0.011493	0.1155	0.454139
18	-0.141871	-1.4258	0.078507
19	0.020072	0.2017	0.420271
20	0.076756	0.7714	0.221139

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.537238 & -5.3992 & 0 \tabularnewline
2 & -0.474795 & -4.7716 & 3e-06 \tabularnewline
3 & -0.375038 & -3.7691 & 0.000138 \tabularnewline
4 & -0.028962 & -0.2911 & 0.3858 \tabularnewline
5 & 0.008926 & 0.0897 & 0.464349 \tabularnewline
6 & -0.140018 & -1.4072 & 0.081224 \tabularnewline
7 & -0.039347 & -0.3954 & 0.346678 \tabularnewline
8 & 0.047501 & 0.4774 & 0.317062 \tabularnewline
9 & 0.013077 & 0.1314 & 0.447853 \tabularnewline
10 & -0.13696 & -1.3764 & 0.085866 \tabularnewline
11 & 0.240582 & 2.4178 & 0.008703 \tabularnewline
12 & -0.086108 & -0.8654 & 0.194441 \tabularnewline
13 & -0.015483 & -0.1556 & 0.438328 \tabularnewline
14 & 0.024448 & 0.2457 & 0.403209 \tabularnewline
15 & -0.073838 & -0.7421 & 0.229886 \tabularnewline
16 & 0.066325 & 0.6666 & 0.253286 \tabularnewline
17 & 0.011493 & 0.1155 & 0.454139 \tabularnewline
18 & -0.141871 & -1.4258 & 0.078507 \tabularnewline
19 & 0.020072 & 0.2017 & 0.420271 \tabularnewline
20 & 0.076756 & 0.7714 & 0.221139 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301226&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]-0.537238[/C][C]-5.3992[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.474795[/C][C]-4.7716[/C][C]3e-06[/C][/ROW]
[ROW][C]3[/C][C]-0.375038[/C][C]-3.7691[/C][C]0.000138[/C][/ROW]
[ROW][C]4[/C][C]-0.028962[/C][C]-0.2911[/C][C]0.3858[/C][/ROW]
[ROW][C]5[/C][C]0.008926[/C][C]0.0897[/C][C]0.464349[/C][/ROW]
[ROW][C]6[/C][C]-0.140018[/C][C]-1.4072[/C][C]0.081224[/C][/ROW]
[ROW][C]7[/C][C]-0.039347[/C][C]-0.3954[/C][C]0.346678[/C][/ROW]
[ROW][C]8[/C][C]0.047501[/C][C]0.4774[/C][C]0.317062[/C][/ROW]
[ROW][C]9[/C][C]0.013077[/C][C]0.1314[/C][C]0.447853[/C][/ROW]
[ROW][C]10[/C][C]-0.13696[/C][C]-1.3764[/C][C]0.085866[/C][/ROW]
[ROW][C]11[/C][C]0.240582[/C][C]2.4178[/C][C]0.008703[/C][/ROW]
[ROW][C]12[/C][C]-0.086108[/C][C]-0.8654[/C][C]0.194441[/C][/ROW]
[ROW][C]13[/C][C]-0.015483[/C][C]-0.1556[/C][C]0.438328[/C][/ROW]
[ROW][C]14[/C][C]0.024448[/C][C]0.2457[/C][C]0.403209[/C][/ROW]
[ROW][C]15[/C][C]-0.073838[/C][C]-0.7421[/C][C]0.229886[/C][/ROW]
[ROW][C]16[/C][C]0.066325[/C][C]0.6666[/C][C]0.253286[/C][/ROW]
[ROW][C]17[/C][C]0.011493[/C][C]0.1155[/C][C]0.454139[/C][/ROW]
[ROW][C]18[/C][C]-0.141871[/C][C]-1.4258[/C][C]0.078507[/C][/ROW]
[ROW][C]19[/C][C]0.020072[/C][C]0.2017[/C][C]0.420271[/C][/ROW]
[ROW][C]20[/C][C]0.076756[/C][C]0.7714[/C][C]0.221139[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301226&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301226&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	-0.537238	-5.3992	0
2	-0.474795	-4.7716	3e-06
3	-0.375038	-3.7691	0.000138
4	-0.028962	-0.2911	0.3858
5	0.008926	0.0897	0.464349
6	-0.140018	-1.4072	0.081224
7	-0.039347	-0.3954	0.346678
8	0.047501	0.4774	0.317062
9	0.013077	0.1314	0.447853
10	-0.13696	-1.3764	0.085866
11	0.240582	2.4178	0.008703
12	-0.086108	-0.8654	0.194441
13	-0.015483	-0.1556	0.438328
14	0.024448	0.2457	0.403209
15	-0.073838	-0.7421	0.229886
16	0.066325	0.6666	0.253286
17	0.011493	0.1155	0.454139
18	-0.141871	-1.4258	0.078507
19	0.020072	0.2017	0.420271
20	0.076756	0.7714	0.221139

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = -0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; par3 = 1 ; par4 = 1 ; 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 <- '0'
par3 <- '0'
par2 <- '0.0'
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