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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 06 Sep 2017 13:59:23 +0200

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/Sep/06/t1504699242oo77venzeol5an0.htm/, Retrieved Wed, 15 May 2024 22:17:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307649, Retrieved Wed, 15 May 2024 22:17:22 +0000

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-       [(Partial) Autocorrelation Function] [] [2017-09-06 11:59:23] [5a51f23852103e2c2ec1d52ada9b446b] [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=307649&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=307649&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307649&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	-0.191006	-2.2761	0.012168
2	-0.195982	-2.3354	0.010462
3	-0.048547	-0.5785	0.281919
4	-0.206647	-2.4625	0.007497
5	0.119397	1.4228	0.078497
6	0.025751	0.3069	0.379699
7	0.145582	1.7348	0.042472
8	-0.226139	-2.6948	0.003947
9	0.014075	0.1677	0.433518
10	-0.208276	-2.4819	0.007117
11	-0.1209	-1.4407	0.075937
12	0.782249	9.3216	0
13	-0.095929	-1.1431	0.127456
14	-0.195474	-2.3293	0.010626
15	-0.070343	-0.8382	0.201653
16	-0.147948	-1.763	0.040025
17	0.113196	1.3489	0.089761
18	0.019219	0.229	0.409589
19	0.136951	1.632	0.052451
20	-0.240152	-2.8617	0.002425
21	0.026131	0.3114	0.377983

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.191006 & -2.2761 & 0.012168 \tabularnewline
2 & -0.195982 & -2.3354 & 0.010462 \tabularnewline
3 & -0.048547 & -0.5785 & 0.281919 \tabularnewline
4 & -0.206647 & -2.4625 & 0.007497 \tabularnewline
5 & 0.119397 & 1.4228 & 0.078497 \tabularnewline
6 & 0.025751 & 0.3069 & 0.379699 \tabularnewline
7 & 0.145582 & 1.7348 & 0.042472 \tabularnewline
8 & -0.226139 & -2.6948 & 0.003947 \tabularnewline
9 & 0.014075 & 0.1677 & 0.433518 \tabularnewline
10 & -0.208276 & -2.4819 & 0.007117 \tabularnewline
11 & -0.1209 & -1.4407 & 0.075937 \tabularnewline
12 & 0.782249 & 9.3216 & 0 \tabularnewline
13 & -0.095929 & -1.1431 & 0.127456 \tabularnewline
14 & -0.195474 & -2.3293 & 0.010626 \tabularnewline
15 & -0.070343 & -0.8382 & 0.201653 \tabularnewline
16 & -0.147948 & -1.763 & 0.040025 \tabularnewline
17 & 0.113196 & 1.3489 & 0.089761 \tabularnewline
18 & 0.019219 & 0.229 & 0.409589 \tabularnewline
19 & 0.136951 & 1.632 & 0.052451 \tabularnewline
20 & -0.240152 & -2.8617 & 0.002425 \tabularnewline
21 & 0.026131 & 0.3114 & 0.377983 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307649&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]-0.191006[/C][C]-2.2761[/C][C]0.012168[/C][/ROW]
[ROW][C]2[/C][C]-0.195982[/C][C]-2.3354[/C][C]0.010462[/C][/ROW]
[ROW][C]3[/C][C]-0.048547[/C][C]-0.5785[/C][C]0.281919[/C][/ROW]
[ROW][C]4[/C][C]-0.206647[/C][C]-2.4625[/C][C]0.007497[/C][/ROW]
[ROW][C]5[/C][C]0.119397[/C][C]1.4228[/C][C]0.078497[/C][/ROW]
[ROW][C]6[/C][C]0.025751[/C][C]0.3069[/C][C]0.379699[/C][/ROW]
[ROW][C]7[/C][C]0.145582[/C][C]1.7348[/C][C]0.042472[/C][/ROW]
[ROW][C]8[/C][C]-0.226139[/C][C]-2.6948[/C][C]0.003947[/C][/ROW]
[ROW][C]9[/C][C]0.014075[/C][C]0.1677[/C][C]0.433518[/C][/ROW]
[ROW][C]10[/C][C]-0.208276[/C][C]-2.4819[/C][C]0.007117[/C][/ROW]
[ROW][C]11[/C][C]-0.1209[/C][C]-1.4407[/C][C]0.075937[/C][/ROW]
[ROW][C]12[/C][C]0.782249[/C][C]9.3216[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.095929[/C][C]-1.1431[/C][C]0.127456[/C][/ROW]
[ROW][C]14[/C][C]-0.195474[/C][C]-2.3293[/C][C]0.010626[/C][/ROW]
[ROW][C]15[/C][C]-0.070343[/C][C]-0.8382[/C][C]0.201653[/C][/ROW]
[ROW][C]16[/C][C]-0.147948[/C][C]-1.763[/C][C]0.040025[/C][/ROW]
[ROW][C]17[/C][C]0.113196[/C][C]1.3489[/C][C]0.089761[/C][/ROW]
[ROW][C]18[/C][C]0.019219[/C][C]0.229[/C][C]0.409589[/C][/ROW]
[ROW][C]19[/C][C]0.136951[/C][C]1.632[/C][C]0.052451[/C][/ROW]
[ROW][C]20[/C][C]-0.240152[/C][C]-2.8617[/C][C]0.002425[/C][/ROW]
[ROW][C]21[/C][C]0.026131[/C][C]0.3114[/C][C]0.377983[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307649&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307649&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	-0.191006	-2.2761	0.012168
2	-0.195982	-2.3354	0.010462
3	-0.048547	-0.5785	0.281919
4	-0.206647	-2.4625	0.007497
5	0.119397	1.4228	0.078497
6	0.025751	0.3069	0.379699
7	0.145582	1.7348	0.042472
8	-0.226139	-2.6948	0.003947
9	0.014075	0.1677	0.433518
10	-0.208276	-2.4819	0.007117
11	-0.1209	-1.4407	0.075937
12	0.782249	9.3216	0
13	-0.095929	-1.1431	0.127456
14	-0.195474	-2.3293	0.010626
15	-0.070343	-0.8382	0.201653
16	-0.147948	-1.763	0.040025
17	0.113196	1.3489	0.089761
18	0.019219	0.229	0.409589
19	0.136951	1.632	0.052451
20	-0.240152	-2.8617	0.002425
21	0.026131	0.3114	0.377983

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.191006	-2.2761	0.012168
2	-0.241267	-2.875	0.002331
3	-0.155489	-1.8529	0.032988
4	-0.343522	-4.0935	3.5e-05
5	-0.103846	-1.2375	0.108979
6	-0.156945	-1.8702	0.031756
7	0.077315	0.9213	0.179225
8	-0.303402	-3.6154	0.000208
9	-0.061961	-0.7383	0.230762
10	-0.523954	-6.2436	0
11	-0.672457	-8.0133	0
12	0.230868	2.7511	0.003357
13	0.114061	1.3592	0.088119
14	-0.107503	-1.281	0.101133
15	-0.045146	-0.538	0.295717
16	0.00556	0.0663	0.473633
17	0.152935	1.8224	0.035247
18	0.048751	0.5809	0.281102
19	0.084131	1.0025	0.158895
20	-0.023622	-0.2815	0.389373
21	-0.014861	-0.1771	0.429846

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.191006 & -2.2761 & 0.012168 \tabularnewline
2 & -0.241267 & -2.875 & 0.002331 \tabularnewline
3 & -0.155489 & -1.8529 & 0.032988 \tabularnewline
4 & -0.343522 & -4.0935 & 3.5e-05 \tabularnewline
5 & -0.103846 & -1.2375 & 0.108979 \tabularnewline
6 & -0.156945 & -1.8702 & 0.031756 \tabularnewline
7 & 0.077315 & 0.9213 & 0.179225 \tabularnewline
8 & -0.303402 & -3.6154 & 0.000208 \tabularnewline
9 & -0.061961 & -0.7383 & 0.230762 \tabularnewline
10 & -0.523954 & -6.2436 & 0 \tabularnewline
11 & -0.672457 & -8.0133 & 0 \tabularnewline
12 & 0.230868 & 2.7511 & 0.003357 \tabularnewline
13 & 0.114061 & 1.3592 & 0.088119 \tabularnewline
14 & -0.107503 & -1.281 & 0.101133 \tabularnewline
15 & -0.045146 & -0.538 & 0.295717 \tabularnewline
16 & 0.00556 & 0.0663 & 0.473633 \tabularnewline
17 & 0.152935 & 1.8224 & 0.035247 \tabularnewline
18 & 0.048751 & 0.5809 & 0.281102 \tabularnewline
19 & 0.084131 & 1.0025 & 0.158895 \tabularnewline
20 & -0.023622 & -0.2815 & 0.389373 \tabularnewline
21 & -0.014861 & -0.1771 & 0.429846 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307649&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]-0.191006[/C][C]-2.2761[/C][C]0.012168[/C][/ROW]
[ROW][C]2[/C][C]-0.241267[/C][C]-2.875[/C][C]0.002331[/C][/ROW]
[ROW][C]3[/C][C]-0.155489[/C][C]-1.8529[/C][C]0.032988[/C][/ROW]
[ROW][C]4[/C][C]-0.343522[/C][C]-4.0935[/C][C]3.5e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.103846[/C][C]-1.2375[/C][C]0.108979[/C][/ROW]
[ROW][C]6[/C][C]-0.156945[/C][C]-1.8702[/C][C]0.031756[/C][/ROW]
[ROW][C]7[/C][C]0.077315[/C][C]0.9213[/C][C]0.179225[/C][/ROW]
[ROW][C]8[/C][C]-0.303402[/C][C]-3.6154[/C][C]0.000208[/C][/ROW]
[ROW][C]9[/C][C]-0.061961[/C][C]-0.7383[/C][C]0.230762[/C][/ROW]
[ROW][C]10[/C][C]-0.523954[/C][C]-6.2436[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]-0.672457[/C][C]-8.0133[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.230868[/C][C]2.7511[/C][C]0.003357[/C][/ROW]
[ROW][C]13[/C][C]0.114061[/C][C]1.3592[/C][C]0.088119[/C][/ROW]
[ROW][C]14[/C][C]-0.107503[/C][C]-1.281[/C][C]0.101133[/C][/ROW]
[ROW][C]15[/C][C]-0.045146[/C][C]-0.538[/C][C]0.295717[/C][/ROW]
[ROW][C]16[/C][C]0.00556[/C][C]0.0663[/C][C]0.473633[/C][/ROW]
[ROW][C]17[/C][C]0.152935[/C][C]1.8224[/C][C]0.035247[/C][/ROW]
[ROW][C]18[/C][C]0.048751[/C][C]0.5809[/C][C]0.281102[/C][/ROW]
[ROW][C]19[/C][C]0.084131[/C][C]1.0025[/C][C]0.158895[/C][/ROW]
[ROW][C]20[/C][C]-0.023622[/C][C]-0.2815[/C][C]0.389373[/C][/ROW]
[ROW][C]21[/C][C]-0.014861[/C][C]-0.1771[/C][C]0.429846[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307649&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307649&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	-0.191006	-2.2761	0.012168
2	-0.241267	-2.875	0.002331
3	-0.155489	-1.8529	0.032988
4	-0.343522	-4.0935	3.5e-05
5	-0.103846	-1.2375	0.108979
6	-0.156945	-1.8702	0.031756
7	0.077315	0.9213	0.179225
8	-0.303402	-3.6154	0.000208
9	-0.061961	-0.7383	0.230762
10	-0.523954	-6.2436	0
11	-0.672457	-8.0133	0
12	0.230868	2.7511	0.003357
13	0.114061	1.3592	0.088119
14	-0.107503	-1.281	0.101133
15	-0.045146	-0.538	0.295717
16	0.00556	0.0663	0.473633
17	0.152935	1.8224	0.035247
18	0.048751	0.5809	0.281102
19	0.084131	1.0025	0.158895
20	-0.023622	-0.2815	0.389373
21	-0.014861	-0.1771	0.429846

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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