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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 04 Dec 2016 16:57:20 +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/04/t1480867241bkymal31el0qkhu.htm/, Retrieved Sat, 18 May 2024 06:15:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297678, Retrieved Sat, 18 May 2024 06:15:19 +0000

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Estimated Impact

131

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [] [2016-12-04 15:57:20] [6deb082de88ded72ec069288c69f9f98] [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=297678&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=297678&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297678&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	-0.444617	-4.8705	2e-06
2	0.003857	0.0422	0.483186
3	-0.00106	-0.0116	0.495376
4	0.029439	0.3225	0.373821
5	0.010672	0.1169	0.453566
6	-0.095139	-1.0422	0.149709
7	0.042449	0.465	0.321384
8	0.025211	0.2762	0.391447
9	-0.045283	-0.496	0.310385
10	-0.031458	-0.3446	0.365497
11	0.164619	1.8033	0.036925
12	-0.057	-0.6244	0.266775
13	-0.063175	-0.692	0.245123
14	0.184503	2.0211	0.022746
15	-0.053873	-0.5901	0.2781
16	-0.024229	-0.2654	0.395574
17	-0.029159	-0.3194	0.374983
18	-0.06629	-0.7262	0.234575
19	0.084205	0.9224	0.17908
20	-0.147752	-1.6185	0.054086

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.444617 & -4.8705 & 2e-06 \tabularnewline
2 & 0.003857 & 0.0422 & 0.483186 \tabularnewline
3 & -0.00106 & -0.0116 & 0.495376 \tabularnewline
4 & 0.029439 & 0.3225 & 0.373821 \tabularnewline
5 & 0.010672 & 0.1169 & 0.453566 \tabularnewline
6 & -0.095139 & -1.0422 & 0.149709 \tabularnewline
7 & 0.042449 & 0.465 & 0.321384 \tabularnewline
8 & 0.025211 & 0.2762 & 0.391447 \tabularnewline
9 & -0.045283 & -0.496 & 0.310385 \tabularnewline
10 & -0.031458 & -0.3446 & 0.365497 \tabularnewline
11 & 0.164619 & 1.8033 & 0.036925 \tabularnewline
12 & -0.057 & -0.6244 & 0.266775 \tabularnewline
13 & -0.063175 & -0.692 & 0.245123 \tabularnewline
14 & 0.184503 & 2.0211 & 0.022746 \tabularnewline
15 & -0.053873 & -0.5901 & 0.2781 \tabularnewline
16 & -0.024229 & -0.2654 & 0.395574 \tabularnewline
17 & -0.029159 & -0.3194 & 0.374983 \tabularnewline
18 & -0.06629 & -0.7262 & 0.234575 \tabularnewline
19 & 0.084205 & 0.9224 & 0.17908 \tabularnewline
20 & -0.147752 & -1.6185 & 0.054086 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297678&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]-0.444617[/C][C]-4.8705[/C][C]2e-06[/C][/ROW]
[ROW][C]2[/C][C]0.003857[/C][C]0.0422[/C][C]0.483186[/C][/ROW]
[ROW][C]3[/C][C]-0.00106[/C][C]-0.0116[/C][C]0.495376[/C][/ROW]
[ROW][C]4[/C][C]0.029439[/C][C]0.3225[/C][C]0.373821[/C][/ROW]
[ROW][C]5[/C][C]0.010672[/C][C]0.1169[/C][C]0.453566[/C][/ROW]
[ROW][C]6[/C][C]-0.095139[/C][C]-1.0422[/C][C]0.149709[/C][/ROW]
[ROW][C]7[/C][C]0.042449[/C][C]0.465[/C][C]0.321384[/C][/ROW]
[ROW][C]8[/C][C]0.025211[/C][C]0.2762[/C][C]0.391447[/C][/ROW]
[ROW][C]9[/C][C]-0.045283[/C][C]-0.496[/C][C]0.310385[/C][/ROW]
[ROW][C]10[/C][C]-0.031458[/C][C]-0.3446[/C][C]0.365497[/C][/ROW]
[ROW][C]11[/C][C]0.164619[/C][C]1.8033[/C][C]0.036925[/C][/ROW]
[ROW][C]12[/C][C]-0.057[/C][C]-0.6244[/C][C]0.266775[/C][/ROW]
[ROW][C]13[/C][C]-0.063175[/C][C]-0.692[/C][C]0.245123[/C][/ROW]
[ROW][C]14[/C][C]0.184503[/C][C]2.0211[/C][C]0.022746[/C][/ROW]
[ROW][C]15[/C][C]-0.053873[/C][C]-0.5901[/C][C]0.2781[/C][/ROW]
[ROW][C]16[/C][C]-0.024229[/C][C]-0.2654[/C][C]0.395574[/C][/ROW]
[ROW][C]17[/C][C]-0.029159[/C][C]-0.3194[/C][C]0.374983[/C][/ROW]
[ROW][C]18[/C][C]-0.06629[/C][C]-0.7262[/C][C]0.234575[/C][/ROW]
[ROW][C]19[/C][C]0.084205[/C][C]0.9224[/C][C]0.17908[/C][/ROW]
[ROW][C]20[/C][C]-0.147752[/C][C]-1.6185[/C][C]0.054086[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297678&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297678&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	-0.444617	-4.8705	2e-06
2	0.003857	0.0422	0.483186
3	-0.00106	-0.0116	0.495376
4	0.029439	0.3225	0.373821
5	0.010672	0.1169	0.453566
6	-0.095139	-1.0422	0.149709
7	0.042449	0.465	0.321384
8	0.025211	0.2762	0.391447
9	-0.045283	-0.496	0.310385
10	-0.031458	-0.3446	0.365497
11	0.164619	1.8033	0.036925
12	-0.057	-0.6244	0.266775
13	-0.063175	-0.692	0.245123
14	0.184503	2.0211	0.022746
15	-0.053873	-0.5901	0.2781
16	-0.024229	-0.2654	0.395574
17	-0.029159	-0.3194	0.374983
18	-0.06629	-0.7262	0.234575
19	0.084205	0.9224	0.17908
20	-0.147752	-1.6185	0.054086

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.444617	-4.8705	2e-06
2	-0.241586	-2.6464	0.004613
3	-0.140762	-1.542	0.062857
4	-0.043937	-0.4813	0.315589
5	0.011988	0.1313	0.447871
6	-0.099827	-1.0936	0.138171
7	-0.067208	-0.7362	0.231516
8	-0.009143	-0.1002	0.460193
9	-0.047058	-0.5155	0.303577
10	-0.09029	-0.9891	0.162308
11	0.133784	1.4655	0.072695
12	0.103784	1.1369	0.128924
13	-0.009946	-0.109	0.45671
14	0.217069	2.3779	0.009496
15	0.176425	1.9326	0.027818
16	0.094679	1.0372	0.150875
17	0.067805	0.7428	0.229538
18	-0.091482	-1.0021	0.159148
19	-0.044785	-0.4906	0.312305
20	-0.165613	-1.8142	0.036073

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.444617 & -4.8705 & 2e-06 \tabularnewline
2 & -0.241586 & -2.6464 & 0.004613 \tabularnewline
3 & -0.140762 & -1.542 & 0.062857 \tabularnewline
4 & -0.043937 & -0.4813 & 0.315589 \tabularnewline
5 & 0.011988 & 0.1313 & 0.447871 \tabularnewline
6 & -0.099827 & -1.0936 & 0.138171 \tabularnewline
7 & -0.067208 & -0.7362 & 0.231516 \tabularnewline
8 & -0.009143 & -0.1002 & 0.460193 \tabularnewline
9 & -0.047058 & -0.5155 & 0.303577 \tabularnewline
10 & -0.09029 & -0.9891 & 0.162308 \tabularnewline
11 & 0.133784 & 1.4655 & 0.072695 \tabularnewline
12 & 0.103784 & 1.1369 & 0.128924 \tabularnewline
13 & -0.009946 & -0.109 & 0.45671 \tabularnewline
14 & 0.217069 & 2.3779 & 0.009496 \tabularnewline
15 & 0.176425 & 1.9326 & 0.027818 \tabularnewline
16 & 0.094679 & 1.0372 & 0.150875 \tabularnewline
17 & 0.067805 & 0.7428 & 0.229538 \tabularnewline
18 & -0.091482 & -1.0021 & 0.159148 \tabularnewline
19 & -0.044785 & -0.4906 & 0.312305 \tabularnewline
20 & -0.165613 & -1.8142 & 0.036073 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297678&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]-0.444617[/C][C]-4.8705[/C][C]2e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.241586[/C][C]-2.6464[/C][C]0.004613[/C][/ROW]
[ROW][C]3[/C][C]-0.140762[/C][C]-1.542[/C][C]0.062857[/C][/ROW]
[ROW][C]4[/C][C]-0.043937[/C][C]-0.4813[/C][C]0.315589[/C][/ROW]
[ROW][C]5[/C][C]0.011988[/C][C]0.1313[/C][C]0.447871[/C][/ROW]
[ROW][C]6[/C][C]-0.099827[/C][C]-1.0936[/C][C]0.138171[/C][/ROW]
[ROW][C]7[/C][C]-0.067208[/C][C]-0.7362[/C][C]0.231516[/C][/ROW]
[ROW][C]8[/C][C]-0.009143[/C][C]-0.1002[/C][C]0.460193[/C][/ROW]
[ROW][C]9[/C][C]-0.047058[/C][C]-0.5155[/C][C]0.303577[/C][/ROW]
[ROW][C]10[/C][C]-0.09029[/C][C]-0.9891[/C][C]0.162308[/C][/ROW]
[ROW][C]11[/C][C]0.133784[/C][C]1.4655[/C][C]0.072695[/C][/ROW]
[ROW][C]12[/C][C]0.103784[/C][C]1.1369[/C][C]0.128924[/C][/ROW]
[ROW][C]13[/C][C]-0.009946[/C][C]-0.109[/C][C]0.45671[/C][/ROW]
[ROW][C]14[/C][C]0.217069[/C][C]2.3779[/C][C]0.009496[/C][/ROW]
[ROW][C]15[/C][C]0.176425[/C][C]1.9326[/C][C]0.027818[/C][/ROW]
[ROW][C]16[/C][C]0.094679[/C][C]1.0372[/C][C]0.150875[/C][/ROW]
[ROW][C]17[/C][C]0.067805[/C][C]0.7428[/C][C]0.229538[/C][/ROW]
[ROW][C]18[/C][C]-0.091482[/C][C]-1.0021[/C][C]0.159148[/C][/ROW]
[ROW][C]19[/C][C]-0.044785[/C][C]-0.4906[/C][C]0.312305[/C][/ROW]
[ROW][C]20[/C][C]-0.165613[/C][C]-1.8142[/C][C]0.036073[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297678&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297678&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	-0.444617	-4.8705	2e-06
2	-0.241586	-2.6464	0.004613
3	-0.140762	-1.542	0.062857
4	-0.043937	-0.4813	0.315589
5	0.011988	0.1313	0.447871
6	-0.099827	-1.0936	0.138171
7	-0.067208	-0.7362	0.231516
8	-0.009143	-0.1002	0.460193
9	-0.047058	-0.5155	0.303577
10	-0.09029	-0.9891	0.162308
11	0.133784	1.4655	0.072695
12	0.103784	1.1369	0.128924
13	-0.009946	-0.109	0.45671
14	0.217069	2.3779	0.009496
15	0.176425	1.9326	0.027818
16	0.094679	1.0372	0.150875
17	0.067805	0.7428	0.229538
18	-0.091482	-1.0021	0.159148
19	-0.044785	-0.4906	0.312305
20	-0.165613	-1.8142	0.036073

Figure 1

PNG link

Postscript link

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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 = 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,'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