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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 01 Feb 2018 09:30:33 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2018/Feb/01/t15174739152d0jzamspeio5ej.htm/, Retrieved Mon, 29 Apr 2024 03:31:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=313622, Retrieved Mon, 29 Apr 2024 03:31:08 +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] [vraag4.1] [2018-02-01 08:30:33] [cbdc27eb3c0ce1e50616f96e5af4492f] [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=313622&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=313622&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313622&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	-0.044222	-0.5916	0.277416
2	-0.033466	-0.4477	0.327439
3	-0.00829	-0.1109	0.455904
4	-0.086153	-1.1526	0.125296
5	0.067229	0.8995	0.184809
6	-0.012564	-0.1681	0.433349
7	-0.008216	-0.1099	0.456296
8	0.139672	1.8687	0.031651
9	-0.041014	-0.5487	0.291937
10	-0.124817	-1.6699	0.04834
11	-0.070356	-0.9413	0.17391
12	0.083063	1.1113	0.133962
13	0.039943	0.5344	0.296862
14	0.072734	0.9731	0.165906
15	0.060993	0.816	0.207784
16	0.011259	0.1506	0.440216
17	-0.018452	-0.2469	0.402648
18	-0.052426	-0.7014	0.241978
19	-0.027957	-0.374	0.354411
20	0.061701	0.8255	0.205092
21	0.062093	0.8307	0.203612
22	-0.077322	-1.0345	0.151151

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.044222 & -0.5916 & 0.277416 \tabularnewline
2 & -0.033466 & -0.4477 & 0.327439 \tabularnewline
3 & -0.00829 & -0.1109 & 0.455904 \tabularnewline
4 & -0.086153 & -1.1526 & 0.125296 \tabularnewline
5 & 0.067229 & 0.8995 & 0.184809 \tabularnewline
6 & -0.012564 & -0.1681 & 0.433349 \tabularnewline
7 & -0.008216 & -0.1099 & 0.456296 \tabularnewline
8 & 0.139672 & 1.8687 & 0.031651 \tabularnewline
9 & -0.041014 & -0.5487 & 0.291937 \tabularnewline
10 & -0.124817 & -1.6699 & 0.04834 \tabularnewline
11 & -0.070356 & -0.9413 & 0.17391 \tabularnewline
12 & 0.083063 & 1.1113 & 0.133962 \tabularnewline
13 & 0.039943 & 0.5344 & 0.296862 \tabularnewline
14 & 0.072734 & 0.9731 & 0.165906 \tabularnewline
15 & 0.060993 & 0.816 & 0.207784 \tabularnewline
16 & 0.011259 & 0.1506 & 0.440216 \tabularnewline
17 & -0.018452 & -0.2469 & 0.402648 \tabularnewline
18 & -0.052426 & -0.7014 & 0.241978 \tabularnewline
19 & -0.027957 & -0.374 & 0.354411 \tabularnewline
20 & 0.061701 & 0.8255 & 0.205092 \tabularnewline
21 & 0.062093 & 0.8307 & 0.203612 \tabularnewline
22 & -0.077322 & -1.0345 & 0.151151 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=313622&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]-0.044222[/C][C]-0.5916[/C][C]0.277416[/C][/ROW]
[ROW][C]2[/C][C]-0.033466[/C][C]-0.4477[/C][C]0.327439[/C][/ROW]
[ROW][C]3[/C][C]-0.00829[/C][C]-0.1109[/C][C]0.455904[/C][/ROW]
[ROW][C]4[/C][C]-0.086153[/C][C]-1.1526[/C][C]0.125296[/C][/ROW]
[ROW][C]5[/C][C]0.067229[/C][C]0.8995[/C][C]0.184809[/C][/ROW]
[ROW][C]6[/C][C]-0.012564[/C][C]-0.1681[/C][C]0.433349[/C][/ROW]
[ROW][C]7[/C][C]-0.008216[/C][C]-0.1099[/C][C]0.456296[/C][/ROW]
[ROW][C]8[/C][C]0.139672[/C][C]1.8687[/C][C]0.031651[/C][/ROW]
[ROW][C]9[/C][C]-0.041014[/C][C]-0.5487[/C][C]0.291937[/C][/ROW]
[ROW][C]10[/C][C]-0.124817[/C][C]-1.6699[/C][C]0.04834[/C][/ROW]
[ROW][C]11[/C][C]-0.070356[/C][C]-0.9413[/C][C]0.17391[/C][/ROW]
[ROW][C]12[/C][C]0.083063[/C][C]1.1113[/C][C]0.133962[/C][/ROW]
[ROW][C]13[/C][C]0.039943[/C][C]0.5344[/C][C]0.296862[/C][/ROW]
[ROW][C]14[/C][C]0.072734[/C][C]0.9731[/C][C]0.165906[/C][/ROW]
[ROW][C]15[/C][C]0.060993[/C][C]0.816[/C][C]0.207784[/C][/ROW]
[ROW][C]16[/C][C]0.011259[/C][C]0.1506[/C][C]0.440216[/C][/ROW]
[ROW][C]17[/C][C]-0.018452[/C][C]-0.2469[/C][C]0.402648[/C][/ROW]
[ROW][C]18[/C][C]-0.052426[/C][C]-0.7014[/C][C]0.241978[/C][/ROW]
[ROW][C]19[/C][C]-0.027957[/C][C]-0.374[/C][C]0.354411[/C][/ROW]
[ROW][C]20[/C][C]0.061701[/C][C]0.8255[/C][C]0.205092[/C][/ROW]
[ROW][C]21[/C][C]0.062093[/C][C]0.8307[/C][C]0.203612[/C][/ROW]
[ROW][C]22[/C][C]-0.077322[/C][C]-1.0345[/C][C]0.151151[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=313622&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313622&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	-0.044222	-0.5916	0.277416
2	-0.033466	-0.4477	0.327439
3	-0.00829	-0.1109	0.455904
4	-0.086153	-1.1526	0.125296
5	0.067229	0.8995	0.184809
6	-0.012564	-0.1681	0.433349
7	-0.008216	-0.1099	0.456296
8	0.139672	1.8687	0.031651
9	-0.041014	-0.5487	0.291937
10	-0.124817	-1.6699	0.04834
11	-0.070356	-0.9413	0.17391
12	0.083063	1.1113	0.133962
13	0.039943	0.5344	0.296862
14	0.072734	0.9731	0.165906
15	0.060993	0.816	0.207784
16	0.011259	0.1506	0.440216
17	-0.018452	-0.2469	0.402648
18	-0.052426	-0.7014	0.241978
19	-0.027957	-0.374	0.354411
20	0.061701	0.8255	0.205092
21	0.062093	0.8307	0.203612
22	-0.077322	-1.0345	0.151151

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.044222	-0.5916	0.277416
2	-0.035491	-0.4748	0.31774
3	-0.011429	-0.1529	0.439322
4	-0.088543	-1.1846	0.118869
5	0.05906	0.7902	0.215236
6	-0.013607	-0.182	0.427877
7	-0.006693	-0.0895	0.464376
8	0.13405	1.7935	0.037293
9	-0.020602	-0.2756	0.391572
10	-0.127659	-1.708	0.044688
11	-0.081455	-1.0898	0.138634
12	0.095793	1.2816	0.100816
13	0.019227	0.2572	0.398646
14	0.067984	0.9096	0.182136
15	0.081549	1.091	0.138359
16	0.024281	0.3249	0.372832
17	-0.018099	-0.2422	0.40447
18	-0.012751	-0.1706	0.432367
19	-0.017108	-0.2289	0.409607
20	0.00914	0.1223	0.451406
21	0.047298	0.6328	0.263834
22	-0.075458	-1.0096	0.157035

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.044222 & -0.5916 & 0.277416 \tabularnewline
2 & -0.035491 & -0.4748 & 0.31774 \tabularnewline
3 & -0.011429 & -0.1529 & 0.439322 \tabularnewline
4 & -0.088543 & -1.1846 & 0.118869 \tabularnewline
5 & 0.05906 & 0.7902 & 0.215236 \tabularnewline
6 & -0.013607 & -0.182 & 0.427877 \tabularnewline
7 & -0.006693 & -0.0895 & 0.464376 \tabularnewline
8 & 0.13405 & 1.7935 & 0.037293 \tabularnewline
9 & -0.020602 & -0.2756 & 0.391572 \tabularnewline
10 & -0.127659 & -1.708 & 0.044688 \tabularnewline
11 & -0.081455 & -1.0898 & 0.138634 \tabularnewline
12 & 0.095793 & 1.2816 & 0.100816 \tabularnewline
13 & 0.019227 & 0.2572 & 0.398646 \tabularnewline
14 & 0.067984 & 0.9096 & 0.182136 \tabularnewline
15 & 0.081549 & 1.091 & 0.138359 \tabularnewline
16 & 0.024281 & 0.3249 & 0.372832 \tabularnewline
17 & -0.018099 & -0.2422 & 0.40447 \tabularnewline
18 & -0.012751 & -0.1706 & 0.432367 \tabularnewline
19 & -0.017108 & -0.2289 & 0.409607 \tabularnewline
20 & 0.00914 & 0.1223 & 0.451406 \tabularnewline
21 & 0.047298 & 0.6328 & 0.263834 \tabularnewline
22 & -0.075458 & -1.0096 & 0.157035 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=313622&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]-0.044222[/C][C]-0.5916[/C][C]0.277416[/C][/ROW]
[ROW][C]2[/C][C]-0.035491[/C][C]-0.4748[/C][C]0.31774[/C][/ROW]
[ROW][C]3[/C][C]-0.011429[/C][C]-0.1529[/C][C]0.439322[/C][/ROW]
[ROW][C]4[/C][C]-0.088543[/C][C]-1.1846[/C][C]0.118869[/C][/ROW]
[ROW][C]5[/C][C]0.05906[/C][C]0.7902[/C][C]0.215236[/C][/ROW]
[ROW][C]6[/C][C]-0.013607[/C][C]-0.182[/C][C]0.427877[/C][/ROW]
[ROW][C]7[/C][C]-0.006693[/C][C]-0.0895[/C][C]0.464376[/C][/ROW]
[ROW][C]8[/C][C]0.13405[/C][C]1.7935[/C][C]0.037293[/C][/ROW]
[ROW][C]9[/C][C]-0.020602[/C][C]-0.2756[/C][C]0.391572[/C][/ROW]
[ROW][C]10[/C][C]-0.127659[/C][C]-1.708[/C][C]0.044688[/C][/ROW]
[ROW][C]11[/C][C]-0.081455[/C][C]-1.0898[/C][C]0.138634[/C][/ROW]
[ROW][C]12[/C][C]0.095793[/C][C]1.2816[/C][C]0.100816[/C][/ROW]
[ROW][C]13[/C][C]0.019227[/C][C]0.2572[/C][C]0.398646[/C][/ROW]
[ROW][C]14[/C][C]0.067984[/C][C]0.9096[/C][C]0.182136[/C][/ROW]
[ROW][C]15[/C][C]0.081549[/C][C]1.091[/C][C]0.138359[/C][/ROW]
[ROW][C]16[/C][C]0.024281[/C][C]0.3249[/C][C]0.372832[/C][/ROW]
[ROW][C]17[/C][C]-0.018099[/C][C]-0.2422[/C][C]0.40447[/C][/ROW]
[ROW][C]18[/C][C]-0.012751[/C][C]-0.1706[/C][C]0.432367[/C][/ROW]
[ROW][C]19[/C][C]-0.017108[/C][C]-0.2289[/C][C]0.409607[/C][/ROW]
[ROW][C]20[/C][C]0.00914[/C][C]0.1223[/C][C]0.451406[/C][/ROW]
[ROW][C]21[/C][C]0.047298[/C][C]0.6328[/C][C]0.263834[/C][/ROW]
[ROW][C]22[/C][C]-0.075458[/C][C]-1.0096[/C][C]0.157035[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=313622&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313622&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	-0.044222	-0.5916	0.277416
2	-0.035491	-0.4748	0.31774
3	-0.011429	-0.1529	0.439322
4	-0.088543	-1.1846	0.118869
5	0.05906	0.7902	0.215236
6	-0.013607	-0.182	0.427877
7	-0.006693	-0.0895	0.464376
8	0.13405	1.7935	0.037293
9	-0.020602	-0.2756	0.391572
10	-0.127659	-1.708	0.044688
11	-0.081455	-1.0898	0.138634
12	0.095793	1.2816	0.100816
13	0.019227	0.2572	0.398646
14	0.067984	0.9096	0.182136
15	0.081549	1.091	0.138359
16	0.024281	0.3249	0.372832
17	-0.018099	-0.2422	0.40447
18	-0.012751	-0.1706	0.432367
19	-0.017108	-0.2289	0.409607
20	0.00914	0.1223	0.451406
21	0.047298	0.6328	0.263834
22	-0.075458	-1.0096	0.157035

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 = 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