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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 04 Dec 2016 15:39:17 +0000

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/04/t1480866045b9qet6kn2lj7x4v.htm/, Retrieved Sun, 19 May 2024 02:55:22 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 19 May 2024 02:55:22 +0200

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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	'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.484789	5.2884	0
2	0.266062	2.9024	0.002207
3	0.231137	2.5214	0.006505
4	0.089292	0.9741	0.166002
5	0.007516	0.082	0.467398
6	-0.00786	-0.0857	0.465908
7	0.03402	0.3711	0.355607
8	0.084928	0.9265	0.178044
9	0.007591	0.0828	0.46707
10	0.009362	0.1021	0.459415
11	0.105488	1.1507	0.126073
12	0.08065	0.8798	0.190373
13	-0.011116	-0.1213	0.451842
14	-0.075746	-0.8263	0.205145
15	-0.184989	-2.018	0.02292
16	-0.151689	-1.6547	0.050307
17	-0.066448	-0.7249	0.234981
18	-0.08393	-0.9156	0.180871
19	-0.074141	-0.8088	0.210129
20	-0.036892	-0.4024	0.34404

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.484789 & 5.2884 & 0 \tabularnewline
2 & 0.266062 & 2.9024 & 0.002207 \tabularnewline
3 & 0.231137 & 2.5214 & 0.006505 \tabularnewline
4 & 0.089292 & 0.9741 & 0.166002 \tabularnewline
5 & 0.007516 & 0.082 & 0.467398 \tabularnewline
6 & -0.00786 & -0.0857 & 0.465908 \tabularnewline
7 & 0.03402 & 0.3711 & 0.355607 \tabularnewline
8 & 0.084928 & 0.9265 & 0.178044 \tabularnewline
9 & 0.007591 & 0.0828 & 0.46707 \tabularnewline
10 & 0.009362 & 0.1021 & 0.459415 \tabularnewline
11 & 0.105488 & 1.1507 & 0.126073 \tabularnewline
12 & 0.08065 & 0.8798 & 0.190373 \tabularnewline
13 & -0.011116 & -0.1213 & 0.451842 \tabularnewline
14 & -0.075746 & -0.8263 & 0.205145 \tabularnewline
15 & -0.184989 & -2.018 & 0.02292 \tabularnewline
16 & -0.151689 & -1.6547 & 0.050307 \tabularnewline
17 & -0.066448 & -0.7249 & 0.234981 \tabularnewline
18 & -0.08393 & -0.9156 & 0.180871 \tabularnewline
19 & -0.074141 & -0.8088 & 0.210129 \tabularnewline
20 & -0.036892 & -0.4024 & 0.34404 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.484789[/C][C]5.2884[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.266062[/C][C]2.9024[/C][C]0.002207[/C][/ROW]
[ROW][C]3[/C][C]0.231137[/C][C]2.5214[/C][C]0.006505[/C][/ROW]
[ROW][C]4[/C][C]0.089292[/C][C]0.9741[/C][C]0.166002[/C][/ROW]
[ROW][C]5[/C][C]0.007516[/C][C]0.082[/C][C]0.467398[/C][/ROW]
[ROW][C]6[/C][C]-0.00786[/C][C]-0.0857[/C][C]0.465908[/C][/ROW]
[ROW][C]7[/C][C]0.03402[/C][C]0.3711[/C][C]0.355607[/C][/ROW]
[ROW][C]8[/C][C]0.084928[/C][C]0.9265[/C][C]0.178044[/C][/ROW]
[ROW][C]9[/C][C]0.007591[/C][C]0.0828[/C][C]0.46707[/C][/ROW]
[ROW][C]10[/C][C]0.009362[/C][C]0.1021[/C][C]0.459415[/C][/ROW]
[ROW][C]11[/C][C]0.105488[/C][C]1.1507[/C][C]0.126073[/C][/ROW]
[ROW][C]12[/C][C]0.08065[/C][C]0.8798[/C][C]0.190373[/C][/ROW]
[ROW][C]13[/C][C]-0.011116[/C][C]-0.1213[/C][C]0.451842[/C][/ROW]
[ROW][C]14[/C][C]-0.075746[/C][C]-0.8263[/C][C]0.205145[/C][/ROW]
[ROW][C]15[/C][C]-0.184989[/C][C]-2.018[/C][C]0.02292[/C][/ROW]
[ROW][C]16[/C][C]-0.151689[/C][C]-1.6547[/C][C]0.050307[/C][/ROW]
[ROW][C]17[/C][C]-0.066448[/C][C]-0.7249[/C][C]0.234981[/C][/ROW]
[ROW][C]18[/C][C]-0.08393[/C][C]-0.9156[/C][C]0.180871[/C][/ROW]
[ROW][C]19[/C][C]-0.074141[/C][C]-0.8088[/C][C]0.210129[/C][/ROW]
[ROW][C]20[/C][C]-0.036892[/C][C]-0.4024[/C][C]0.34404[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.484789	5.2884	0
2	0.266062	2.9024	0.002207
3	0.231137	2.5214	0.006505
4	0.089292	0.9741	0.166002
5	0.007516	0.082	0.467398
6	-0.00786	-0.0857	0.465908
7	0.03402	0.3711	0.355607
8	0.084928	0.9265	0.178044
9	0.007591	0.0828	0.46707
10	0.009362	0.1021	0.459415
11	0.105488	1.1507	0.126073
12	0.08065	0.8798	0.190373
13	-0.011116	-0.1213	0.451842
14	-0.075746	-0.8263	0.205145
15	-0.184989	-2.018	0.02292
16	-0.151689	-1.6547	0.050307
17	-0.066448	-0.7249	0.234981
18	-0.08393	-0.9156	0.180871
19	-0.074141	-0.8088	0.210129
20	-0.036892	-0.4024	0.34404

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.484789	5.2884	0
2	0.040579	0.4427	0.329406
3	0.114852	1.2529	0.106351
4	-0.092085	-1.0045	0.158581
5	-0.038139	-0.416	0.339062
6	-0.01162	-0.1268	0.449672
7	0.073841	0.8055	0.211067
8	0.079887	0.8715	0.192629
9	-0.086141	-0.9397	0.174642
10	0.005892	0.0643	0.474431
11	0.109224	1.1915	0.117915
12	0.012457	0.1359	0.446068
13	-0.084324	-0.9199	0.179752
14	-0.109434	-1.1938	0.117469
15	-0.170366	-1.8585	0.032786
16	0.042376	0.4623	0.322365
17	0.108732	1.1861	0.118968
18	-0.041786	-0.4558	0.32467
19	-0.080423	-0.8773	0.191043
20	-0.018116	-0.1976	0.421837

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.484789 & 5.2884 & 0 \tabularnewline
2 & 0.040579 & 0.4427 & 0.329406 \tabularnewline
3 & 0.114852 & 1.2529 & 0.106351 \tabularnewline
4 & -0.092085 & -1.0045 & 0.158581 \tabularnewline
5 & -0.038139 & -0.416 & 0.339062 \tabularnewline
6 & -0.01162 & -0.1268 & 0.449672 \tabularnewline
7 & 0.073841 & 0.8055 & 0.211067 \tabularnewline
8 & 0.079887 & 0.8715 & 0.192629 \tabularnewline
9 & -0.086141 & -0.9397 & 0.174642 \tabularnewline
10 & 0.005892 & 0.0643 & 0.474431 \tabularnewline
11 & 0.109224 & 1.1915 & 0.117915 \tabularnewline
12 & 0.012457 & 0.1359 & 0.446068 \tabularnewline
13 & -0.084324 & -0.9199 & 0.179752 \tabularnewline
14 & -0.109434 & -1.1938 & 0.117469 \tabularnewline
15 & -0.170366 & -1.8585 & 0.032786 \tabularnewline
16 & 0.042376 & 0.4623 & 0.322365 \tabularnewline
17 & 0.108732 & 1.1861 & 0.118968 \tabularnewline
18 & -0.041786 & -0.4558 & 0.32467 \tabularnewline
19 & -0.080423 & -0.8773 & 0.191043 \tabularnewline
20 & -0.018116 & -0.1976 & 0.421837 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.484789[/C][C]5.2884[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.040579[/C][C]0.4427[/C][C]0.329406[/C][/ROW]
[ROW][C]3[/C][C]0.114852[/C][C]1.2529[/C][C]0.106351[/C][/ROW]
[ROW][C]4[/C][C]-0.092085[/C][C]-1.0045[/C][C]0.158581[/C][/ROW]
[ROW][C]5[/C][C]-0.038139[/C][C]-0.416[/C][C]0.339062[/C][/ROW]
[ROW][C]6[/C][C]-0.01162[/C][C]-0.1268[/C][C]0.449672[/C][/ROW]
[ROW][C]7[/C][C]0.073841[/C][C]0.8055[/C][C]0.211067[/C][/ROW]
[ROW][C]8[/C][C]0.079887[/C][C]0.8715[/C][C]0.192629[/C][/ROW]
[ROW][C]9[/C][C]-0.086141[/C][C]-0.9397[/C][C]0.174642[/C][/ROW]
[ROW][C]10[/C][C]0.005892[/C][C]0.0643[/C][C]0.474431[/C][/ROW]
[ROW][C]11[/C][C]0.109224[/C][C]1.1915[/C][C]0.117915[/C][/ROW]
[ROW][C]12[/C][C]0.012457[/C][C]0.1359[/C][C]0.446068[/C][/ROW]
[ROW][C]13[/C][C]-0.084324[/C][C]-0.9199[/C][C]0.179752[/C][/ROW]
[ROW][C]14[/C][C]-0.109434[/C][C]-1.1938[/C][C]0.117469[/C][/ROW]
[ROW][C]15[/C][C]-0.170366[/C][C]-1.8585[/C][C]0.032786[/C][/ROW]
[ROW][C]16[/C][C]0.042376[/C][C]0.4623[/C][C]0.322365[/C][/ROW]
[ROW][C]17[/C][C]0.108732[/C][C]1.1861[/C][C]0.118968[/C][/ROW]
[ROW][C]18[/C][C]-0.041786[/C][C]-0.4558[/C][C]0.32467[/C][/ROW]
[ROW][C]19[/C][C]-0.080423[/C][C]-0.8773[/C][C]0.191043[/C][/ROW]
[ROW][C]20[/C][C]-0.018116[/C][C]-0.1976[/C][C]0.421837[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.484789	5.2884	0
2	0.040579	0.4427	0.329406
3	0.114852	1.2529	0.106351
4	-0.092085	-1.0045	0.158581
5	-0.038139	-0.416	0.339062
6	-0.01162	-0.1268	0.449672
7	0.073841	0.8055	0.211067
8	0.079887	0.8715	0.192629
9	-0.086141	-0.9397	0.174642
10	0.005892	0.0643	0.474431
11	0.109224	1.1915	0.117915
12	0.012457	0.1359	0.446068
13	-0.084324	-0.9199	0.179752
14	-0.109434	-1.1938	0.117469
15	-0.170366	-1.8585	0.032786
16	0.042376	0.4623	0.322365
17	0.108732	1.1861	0.118968
18	-0.041786	-0.4558	0.32467
19	-0.080423	-0.8773	0.191043
20	-0.018116	-0.1976	0.421837

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 = 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,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),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,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),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