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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 07 Dec 2016 19:58:05 +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/07/t14811371221ujiqjucj1vtyxk.htm/, Retrieved Fri, 01 Nov 2024 03:41:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298306, Retrieved Fri, 01 Nov 2024 03:41:51 +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] [N2596] [2016-12-07 18:58:05] [85f5800284aab30c091766186b093bb4] [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=298306&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=298306&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298306&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	-0.374044	-4.1819	2.7e-05
2	-0.107156	-1.198	0.116584
3	0.043922	0.4911	0.312123
4	-0.103363	-1.1556	0.125018
5	-0.021962	-0.2455	0.403219
6	0.221216	2.4733	0.007366
7	-0.164239	-1.8362	0.034349
8	-0.0073	-0.0816	0.467543
9	0.076515	0.8555	0.196965
10	-0.119663	-1.3379	0.091684
11	0.113914	1.2736	0.102585
12	0.128028	1.4314	0.077406
13	-0.149628	-1.6729	0.048425
14	-0.078746	-0.8804	0.190163
15	0.01507	0.1685	0.433236
16	0.00192	0.0215	0.491454
17	0.057101	0.6384	0.262188
18	0.077787	0.8697	0.193069
19	-0.062578	-0.6996	0.242725
20	-0.070867	-0.7923	0.21484
21	-0.023186	-0.2592	0.397945

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.374044 & -4.1819 & 2.7e-05 \tabularnewline
2 & -0.107156 & -1.198 & 0.116584 \tabularnewline
3 & 0.043922 & 0.4911 & 0.312123 \tabularnewline
4 & -0.103363 & -1.1556 & 0.125018 \tabularnewline
5 & -0.021962 & -0.2455 & 0.403219 \tabularnewline
6 & 0.221216 & 2.4733 & 0.007366 \tabularnewline
7 & -0.164239 & -1.8362 & 0.034349 \tabularnewline
8 & -0.0073 & -0.0816 & 0.467543 \tabularnewline
9 & 0.076515 & 0.8555 & 0.196965 \tabularnewline
10 & -0.119663 & -1.3379 & 0.091684 \tabularnewline
11 & 0.113914 & 1.2736 & 0.102585 \tabularnewline
12 & 0.128028 & 1.4314 & 0.077406 \tabularnewline
13 & -0.149628 & -1.6729 & 0.048425 \tabularnewline
14 & -0.078746 & -0.8804 & 0.190163 \tabularnewline
15 & 0.01507 & 0.1685 & 0.433236 \tabularnewline
16 & 0.00192 & 0.0215 & 0.491454 \tabularnewline
17 & 0.057101 & 0.6384 & 0.262188 \tabularnewline
18 & 0.077787 & 0.8697 & 0.193069 \tabularnewline
19 & -0.062578 & -0.6996 & 0.242725 \tabularnewline
20 & -0.070867 & -0.7923 & 0.21484 \tabularnewline
21 & -0.023186 & -0.2592 & 0.397945 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298306&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]-0.374044[/C][C]-4.1819[/C][C]2.7e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.107156[/C][C]-1.198[/C][C]0.116584[/C][/ROW]
[ROW][C]3[/C][C]0.043922[/C][C]0.4911[/C][C]0.312123[/C][/ROW]
[ROW][C]4[/C][C]-0.103363[/C][C]-1.1556[/C][C]0.125018[/C][/ROW]
[ROW][C]5[/C][C]-0.021962[/C][C]-0.2455[/C][C]0.403219[/C][/ROW]
[ROW][C]6[/C][C]0.221216[/C][C]2.4733[/C][C]0.007366[/C][/ROW]
[ROW][C]7[/C][C]-0.164239[/C][C]-1.8362[/C][C]0.034349[/C][/ROW]
[ROW][C]8[/C][C]-0.0073[/C][C]-0.0816[/C][C]0.467543[/C][/ROW]
[ROW][C]9[/C][C]0.076515[/C][C]0.8555[/C][C]0.196965[/C][/ROW]
[ROW][C]10[/C][C]-0.119663[/C][C]-1.3379[/C][C]0.091684[/C][/ROW]
[ROW][C]11[/C][C]0.113914[/C][C]1.2736[/C][C]0.102585[/C][/ROW]
[ROW][C]12[/C][C]0.128028[/C][C]1.4314[/C][C]0.077406[/C][/ROW]
[ROW][C]13[/C][C]-0.149628[/C][C]-1.6729[/C][C]0.048425[/C][/ROW]
[ROW][C]14[/C][C]-0.078746[/C][C]-0.8804[/C][C]0.190163[/C][/ROW]
[ROW][C]15[/C][C]0.01507[/C][C]0.1685[/C][C]0.433236[/C][/ROW]
[ROW][C]16[/C][C]0.00192[/C][C]0.0215[/C][C]0.491454[/C][/ROW]
[ROW][C]17[/C][C]0.057101[/C][C]0.6384[/C][C]0.262188[/C][/ROW]
[ROW][C]18[/C][C]0.077787[/C][C]0.8697[/C][C]0.193069[/C][/ROW]
[ROW][C]19[/C][C]-0.062578[/C][C]-0.6996[/C][C]0.242725[/C][/ROW]
[ROW][C]20[/C][C]-0.070867[/C][C]-0.7923[/C][C]0.21484[/C][/ROW]
[ROW][C]21[/C][C]-0.023186[/C][C]-0.2592[/C][C]0.397945[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298306&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298306&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	-0.374044	-4.1819	2.7e-05
2	-0.107156	-1.198	0.116584
3	0.043922	0.4911	0.312123
4	-0.103363	-1.1556	0.125018
5	-0.021962	-0.2455	0.403219
6	0.221216	2.4733	0.007366
7	-0.164239	-1.8362	0.034349
8	-0.0073	-0.0816	0.467543
9	0.076515	0.8555	0.196965
10	-0.119663	-1.3379	0.091684
11	0.113914	1.2736	0.102585
12	0.128028	1.4314	0.077406
13	-0.149628	-1.6729	0.048425
14	-0.078746	-0.8804	0.190163
15	0.01507	0.1685	0.433236
16	0.00192	0.0215	0.491454
17	0.057101	0.6384	0.262188
18	0.077787	0.8697	0.193069
19	-0.062578	-0.6996	0.242725
20	-0.070867	-0.7923	0.21484
21	-0.023186	-0.2592	0.397945

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.374044	-4.1819	2.7e-05
2	-0.287255	-3.2116	0.000839
3	-0.145883	-1.631	0.052702
4	-0.224321	-2.508	0.006712
5	-0.234967	-2.627	0.004846
6	0.066905	0.748	0.227928
7	-0.087641	-0.9799	0.164526
8	-0.087649	-0.9799	0.164502
9	-0.006996	-0.0782	0.468889
10	-0.106316	-1.1887	0.118415
11	0.0285	0.3186	0.375264
12	0.171124	1.9132	0.029003
13	0.087743	0.981	0.164245
14	-0.064962	-0.7263	0.234508
15	-0.108233	-1.2101	0.114266
16	-0.047859	-0.5351	0.296773
17	-0.057307	-0.6407	0.261441
18	0.022961	0.2567	0.398913
19	0.05882	0.6576	0.255994
20	-0.040247	-0.45	0.326755
21	-0.122181	-1.366	0.087191

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.374044 & -4.1819 & 2.7e-05 \tabularnewline
2 & -0.287255 & -3.2116 & 0.000839 \tabularnewline
3 & -0.145883 & -1.631 & 0.052702 \tabularnewline
4 & -0.224321 & -2.508 & 0.006712 \tabularnewline
5 & -0.234967 & -2.627 & 0.004846 \tabularnewline
6 & 0.066905 & 0.748 & 0.227928 \tabularnewline
7 & -0.087641 & -0.9799 & 0.164526 \tabularnewline
8 & -0.087649 & -0.9799 & 0.164502 \tabularnewline
9 & -0.006996 & -0.0782 & 0.468889 \tabularnewline
10 & -0.106316 & -1.1887 & 0.118415 \tabularnewline
11 & 0.0285 & 0.3186 & 0.375264 \tabularnewline
12 & 0.171124 & 1.9132 & 0.029003 \tabularnewline
13 & 0.087743 & 0.981 & 0.164245 \tabularnewline
14 & -0.064962 & -0.7263 & 0.234508 \tabularnewline
15 & -0.108233 & -1.2101 & 0.114266 \tabularnewline
16 & -0.047859 & -0.5351 & 0.296773 \tabularnewline
17 & -0.057307 & -0.6407 & 0.261441 \tabularnewline
18 & 0.022961 & 0.2567 & 0.398913 \tabularnewline
19 & 0.05882 & 0.6576 & 0.255994 \tabularnewline
20 & -0.040247 & -0.45 & 0.326755 \tabularnewline
21 & -0.122181 & -1.366 & 0.087191 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298306&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]-0.374044[/C][C]-4.1819[/C][C]2.7e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.287255[/C][C]-3.2116[/C][C]0.000839[/C][/ROW]
[ROW][C]3[/C][C]-0.145883[/C][C]-1.631[/C][C]0.052702[/C][/ROW]
[ROW][C]4[/C][C]-0.224321[/C][C]-2.508[/C][C]0.006712[/C][/ROW]
[ROW][C]5[/C][C]-0.234967[/C][C]-2.627[/C][C]0.004846[/C][/ROW]
[ROW][C]6[/C][C]0.066905[/C][C]0.748[/C][C]0.227928[/C][/ROW]
[ROW][C]7[/C][C]-0.087641[/C][C]-0.9799[/C][C]0.164526[/C][/ROW]
[ROW][C]8[/C][C]-0.087649[/C][C]-0.9799[/C][C]0.164502[/C][/ROW]
[ROW][C]9[/C][C]-0.006996[/C][C]-0.0782[/C][C]0.468889[/C][/ROW]
[ROW][C]10[/C][C]-0.106316[/C][C]-1.1887[/C][C]0.118415[/C][/ROW]
[ROW][C]11[/C][C]0.0285[/C][C]0.3186[/C][C]0.375264[/C][/ROW]
[ROW][C]12[/C][C]0.171124[/C][C]1.9132[/C][C]0.029003[/C][/ROW]
[ROW][C]13[/C][C]0.087743[/C][C]0.981[/C][C]0.164245[/C][/ROW]
[ROW][C]14[/C][C]-0.064962[/C][C]-0.7263[/C][C]0.234508[/C][/ROW]
[ROW][C]15[/C][C]-0.108233[/C][C]-1.2101[/C][C]0.114266[/C][/ROW]
[ROW][C]16[/C][C]-0.047859[/C][C]-0.5351[/C][C]0.296773[/C][/ROW]
[ROW][C]17[/C][C]-0.057307[/C][C]-0.6407[/C][C]0.261441[/C][/ROW]
[ROW][C]18[/C][C]0.022961[/C][C]0.2567[/C][C]0.398913[/C][/ROW]
[ROW][C]19[/C][C]0.05882[/C][C]0.6576[/C][C]0.255994[/C][/ROW]
[ROW][C]20[/C][C]-0.040247[/C][C]-0.45[/C][C]0.326755[/C][/ROW]
[ROW][C]21[/C][C]-0.122181[/C][C]-1.366[/C][C]0.087191[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298306&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298306&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	-0.374044	-4.1819	2.7e-05
2	-0.287255	-3.2116	0.000839
3	-0.145883	-1.631	0.052702
4	-0.224321	-2.508	0.006712
5	-0.234967	-2.627	0.004846
6	0.066905	0.748	0.227928
7	-0.087641	-0.9799	0.164526
8	-0.087649	-0.9799	0.164502
9	-0.006996	-0.0782	0.468889
10	-0.106316	-1.1887	0.118415
11	0.0285	0.3186	0.375264
12	0.171124	1.9132	0.029003
13	0.087743	0.981	0.164245
14	-0.064962	-0.7263	0.234508
15	-0.108233	-1.2101	0.114266
16	-0.047859	-0.5351	0.296773
17	-0.057307	-0.6407	0.261441
18	0.022961	0.2567	0.398913
19	0.05882	0.6576	0.255994
20	-0.040247	-0.45	0.326755
21	-0.122181	-1.366	0.087191

Figure 1

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Postscript link

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Figure 2

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Figure 3

PNG link

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Parameters (Session):

par1 = -1.0 ; par2 = 1 ; par3 = 0 ; par4 = 1 ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; 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