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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 14 Dec 2016 14:16:47 +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/2016/Dec/14/t1481721622azdfa5b0ghwgcbl.htm/, Retrieved Fri, 01 Nov 2024 03:43:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299403, Retrieved Fri, 01 Nov 2024 03:43:44 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-14 13:16:47] [df90c754990be6fd2b18fcd529010a59] [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=299403&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=299403&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299403&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	-0.256829	-2.8714	0.002401
2	-0.202326	-2.2621	0.01271
3	0.015134	0.1692	0.432954
4	-0.136101	-1.5217	0.065311
5	0.189978	2.124	0.01782
6	-0.102285	-1.1436	0.127492
7	0.152728	1.7076	0.045101
8	-0.117553	-1.3143	0.095579
9	-0.07935	-0.8872	0.188349
10	-0.118591	-1.3259	0.093647
11	-0.139539	-1.5601	0.060633
12	0.633751	7.0856	0
13	-0.203964	-2.2804	0.012139
14	-0.037998	-0.4248	0.335847
15	-0.09887	-1.1054	0.135555
16	-0.106538	-1.1911	0.117928
17	0.24701	2.7617	0.003309
18	-0.129639	-1.4494	0.074864
19	0.127257	1.4228	0.078647
20	-0.03157	-0.353	0.362357
21	-0.082106	-0.918	0.1802

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.256829 & -2.8714 & 0.002401 \tabularnewline
2 & -0.202326 & -2.2621 & 0.01271 \tabularnewline
3 & 0.015134 & 0.1692 & 0.432954 \tabularnewline
4 & -0.136101 & -1.5217 & 0.065311 \tabularnewline
5 & 0.189978 & 2.124 & 0.01782 \tabularnewline
6 & -0.102285 & -1.1436 & 0.127492 \tabularnewline
7 & 0.152728 & 1.7076 & 0.045101 \tabularnewline
8 & -0.117553 & -1.3143 & 0.095579 \tabularnewline
9 & -0.07935 & -0.8872 & 0.188349 \tabularnewline
10 & -0.118591 & -1.3259 & 0.093647 \tabularnewline
11 & -0.139539 & -1.5601 & 0.060633 \tabularnewline
12 & 0.633751 & 7.0856 & 0 \tabularnewline
13 & -0.203964 & -2.2804 & 0.012139 \tabularnewline
14 & -0.037998 & -0.4248 & 0.335847 \tabularnewline
15 & -0.09887 & -1.1054 & 0.135555 \tabularnewline
16 & -0.106538 & -1.1911 & 0.117928 \tabularnewline
17 & 0.24701 & 2.7617 & 0.003309 \tabularnewline
18 & -0.129639 & -1.4494 & 0.074864 \tabularnewline
19 & 0.127257 & 1.4228 & 0.078647 \tabularnewline
20 & -0.03157 & -0.353 & 0.362357 \tabularnewline
21 & -0.082106 & -0.918 & 0.1802 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299403&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]-0.256829[/C][C]-2.8714[/C][C]0.002401[/C][/ROW]
[ROW][C]2[/C][C]-0.202326[/C][C]-2.2621[/C][C]0.01271[/C][/ROW]
[ROW][C]3[/C][C]0.015134[/C][C]0.1692[/C][C]0.432954[/C][/ROW]
[ROW][C]4[/C][C]-0.136101[/C][C]-1.5217[/C][C]0.065311[/C][/ROW]
[ROW][C]5[/C][C]0.189978[/C][C]2.124[/C][C]0.01782[/C][/ROW]
[ROW][C]6[/C][C]-0.102285[/C][C]-1.1436[/C][C]0.127492[/C][/ROW]
[ROW][C]7[/C][C]0.152728[/C][C]1.7076[/C][C]0.045101[/C][/ROW]
[ROW][C]8[/C][C]-0.117553[/C][C]-1.3143[/C][C]0.095579[/C][/ROW]
[ROW][C]9[/C][C]-0.07935[/C][C]-0.8872[/C][C]0.188349[/C][/ROW]
[ROW][C]10[/C][C]-0.118591[/C][C]-1.3259[/C][C]0.093647[/C][/ROW]
[ROW][C]11[/C][C]-0.139539[/C][C]-1.5601[/C][C]0.060633[/C][/ROW]
[ROW][C]12[/C][C]0.633751[/C][C]7.0856[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.203964[/C][C]-2.2804[/C][C]0.012139[/C][/ROW]
[ROW][C]14[/C][C]-0.037998[/C][C]-0.4248[/C][C]0.335847[/C][/ROW]
[ROW][C]15[/C][C]-0.09887[/C][C]-1.1054[/C][C]0.135555[/C][/ROW]
[ROW][C]16[/C][C]-0.106538[/C][C]-1.1911[/C][C]0.117928[/C][/ROW]
[ROW][C]17[/C][C]0.24701[/C][C]2.7617[/C][C]0.003309[/C][/ROW]
[ROW][C]18[/C][C]-0.129639[/C][C]-1.4494[/C][C]0.074864[/C][/ROW]
[ROW][C]19[/C][C]0.127257[/C][C]1.4228[/C][C]0.078647[/C][/ROW]
[ROW][C]20[/C][C]-0.03157[/C][C]-0.353[/C][C]0.362357[/C][/ROW]
[ROW][C]21[/C][C]-0.082106[/C][C]-0.918[/C][C]0.1802[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299403&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299403&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	-0.256829	-2.8714	0.002401
2	-0.202326	-2.2621	0.01271
3	0.015134	0.1692	0.432954
4	-0.136101	-1.5217	0.065311
5	0.189978	2.124	0.01782
6	-0.102285	-1.1436	0.127492
7	0.152728	1.7076	0.045101
8	-0.117553	-1.3143	0.095579
9	-0.07935	-0.8872	0.188349
10	-0.118591	-1.3259	0.093647
11	-0.139539	-1.5601	0.060633
12	0.633751	7.0856	0
13	-0.203964	-2.2804	0.012139
14	-0.037998	-0.4248	0.335847
15	-0.09887	-1.1054	0.135555
16	-0.106538	-1.1911	0.117928
17	0.24701	2.7617	0.003309
18	-0.129639	-1.4494	0.074864
19	0.127257	1.4228	0.078647
20	-0.03157	-0.353	0.362357
21	-0.082106	-0.918	0.1802

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.256829	-2.8714	0.002401
2	-0.287233	-3.2114	0.00084
3	-0.146473	-1.6376	0.052009
4	-0.281413	-3.1463	0.001034
5	0.022051	0.2465	0.402834
6	-0.166344	-1.8598	0.032634
7	0.153884	1.7205	0.04391
8	-0.117718	-1.3161	0.09527
9	-0.020011	-0.2237	0.411668
10	-0.352992	-3.9466	6.6e-05
11	-0.392993	-4.3938	1.2e-05
12	0.361402	4.0406	4.6e-05
13	0.015861	0.1773	0.429767
14	0.281834	3.151	0.001018
15	-0.148016	-1.6549	0.05023
16	0.04254	0.4756	0.317591
17	-0.053187	-0.5947	0.276576
18	-0.008731	-0.0976	0.461196
19	-0.075216	-0.8409	0.200995
20	0.1281	1.4322	0.07729
21	0.10013	1.1195	0.132538

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.256829 & -2.8714 & 0.002401 \tabularnewline
2 & -0.287233 & -3.2114 & 0.00084 \tabularnewline
3 & -0.146473 & -1.6376 & 0.052009 \tabularnewline
4 & -0.281413 & -3.1463 & 0.001034 \tabularnewline
5 & 0.022051 & 0.2465 & 0.402834 \tabularnewline
6 & -0.166344 & -1.8598 & 0.032634 \tabularnewline
7 & 0.153884 & 1.7205 & 0.04391 \tabularnewline
8 & -0.117718 & -1.3161 & 0.09527 \tabularnewline
9 & -0.020011 & -0.2237 & 0.411668 \tabularnewline
10 & -0.352992 & -3.9466 & 6.6e-05 \tabularnewline
11 & -0.392993 & -4.3938 & 1.2e-05 \tabularnewline
12 & 0.361402 & 4.0406 & 4.6e-05 \tabularnewline
13 & 0.015861 & 0.1773 & 0.429767 \tabularnewline
14 & 0.281834 & 3.151 & 0.001018 \tabularnewline
15 & -0.148016 & -1.6549 & 0.05023 \tabularnewline
16 & 0.04254 & 0.4756 & 0.317591 \tabularnewline
17 & -0.053187 & -0.5947 & 0.276576 \tabularnewline
18 & -0.008731 & -0.0976 & 0.461196 \tabularnewline
19 & -0.075216 & -0.8409 & 0.200995 \tabularnewline
20 & 0.1281 & 1.4322 & 0.07729 \tabularnewline
21 & 0.10013 & 1.1195 & 0.132538 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299403&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]-0.256829[/C][C]-2.8714[/C][C]0.002401[/C][/ROW]
[ROW][C]2[/C][C]-0.287233[/C][C]-3.2114[/C][C]0.00084[/C][/ROW]
[ROW][C]3[/C][C]-0.146473[/C][C]-1.6376[/C][C]0.052009[/C][/ROW]
[ROW][C]4[/C][C]-0.281413[/C][C]-3.1463[/C][C]0.001034[/C][/ROW]
[ROW][C]5[/C][C]0.022051[/C][C]0.2465[/C][C]0.402834[/C][/ROW]
[ROW][C]6[/C][C]-0.166344[/C][C]-1.8598[/C][C]0.032634[/C][/ROW]
[ROW][C]7[/C][C]0.153884[/C][C]1.7205[/C][C]0.04391[/C][/ROW]
[ROW][C]8[/C][C]-0.117718[/C][C]-1.3161[/C][C]0.09527[/C][/ROW]
[ROW][C]9[/C][C]-0.020011[/C][C]-0.2237[/C][C]0.411668[/C][/ROW]
[ROW][C]10[/C][C]-0.352992[/C][C]-3.9466[/C][C]6.6e-05[/C][/ROW]
[ROW][C]11[/C][C]-0.392993[/C][C]-4.3938[/C][C]1.2e-05[/C][/ROW]
[ROW][C]12[/C][C]0.361402[/C][C]4.0406[/C][C]4.6e-05[/C][/ROW]
[ROW][C]13[/C][C]0.015861[/C][C]0.1773[/C][C]0.429767[/C][/ROW]
[ROW][C]14[/C][C]0.281834[/C][C]3.151[/C][C]0.001018[/C][/ROW]
[ROW][C]15[/C][C]-0.148016[/C][C]-1.6549[/C][C]0.05023[/C][/ROW]
[ROW][C]16[/C][C]0.04254[/C][C]0.4756[/C][C]0.317591[/C][/ROW]
[ROW][C]17[/C][C]-0.053187[/C][C]-0.5947[/C][C]0.276576[/C][/ROW]
[ROW][C]18[/C][C]-0.008731[/C][C]-0.0976[/C][C]0.461196[/C][/ROW]
[ROW][C]19[/C][C]-0.075216[/C][C]-0.8409[/C][C]0.200995[/C][/ROW]
[ROW][C]20[/C][C]0.1281[/C][C]1.4322[/C][C]0.07729[/C][/ROW]
[ROW][C]21[/C][C]0.10013[/C][C]1.1195[/C][C]0.132538[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299403&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299403&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	-0.256829	-2.8714	0.002401
2	-0.287233	-3.2114	0.00084
3	-0.146473	-1.6376	0.052009
4	-0.281413	-3.1463	0.001034
5	0.022051	0.2465	0.402834
6	-0.166344	-1.8598	0.032634
7	0.153884	1.7205	0.04391
8	-0.117718	-1.3161	0.09527
9	-0.020011	-0.2237	0.411668
10	-0.352992	-3.9466	6.6e-05
11	-0.392993	-4.3938	1.2e-05
12	0.361402	4.0406	4.6e-05
13	0.015861	0.1773	0.429767
14	0.281834	3.151	0.001018
15	-0.148016	-1.6549	0.05023
16	0.04254	0.4756	0.317591
17	-0.053187	-0.5947	0.276576
18	-0.008731	-0.0976	0.461196
19	-0.075216	-0.8409	0.200995
20	0.1281	1.4322	0.07729
21	0.10013	1.1195	0.132538

Figure 1

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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 = 1 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 4 ; 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