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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 19 Dec 2016 15:16:38 +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/19/t1482157069cx6mrfoj5y14tw3.htm/, Retrieved Fri, 01 Nov 2024 03:33:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301364, Retrieved Fri, 01 Nov 2024 03:33:46 +0000

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No (this computation is public)

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Estimated Impact

107

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

-       [(Partial) Autocorrelation Function] [auto 0 1] [2016-12-19 14:16:38] [06fd994a2f2098873ec640c3e39346e5] [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=301364&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=301364&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301364&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	0.296847	3.1695	0.000981
2	0.114327	1.2207	0.112362
3	0.131994	1.4093	0.080733
4	0.056069	0.5987	0.275297
5	0.135411	1.4458	0.075489
6	0.168159	1.7954	0.037616
7	0.046198	0.4933	0.311389
8	0.054193	0.5786	0.281991
9	0.252182	2.6926	0.00408
10	0.044019	0.47	0.319629
11	0.115517	1.2334	0.109984
12	-0.174793	-1.8663	0.032286
13	-0.24736	-2.6411	0.004712
14	0.081293	0.868	0.193618
15	0.176926	1.8891	0.030713
16	0.080056	0.8548	0.197238
17	0.169974	1.8148	0.03609
18	0.036576	0.3905	0.34844
19	-0.123903	-1.3229	0.094254
20	0.047967	0.5121	0.304769
21	-0.041404	-0.4421	0.329637

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.296847 & 3.1695 & 0.000981 \tabularnewline
2 & 0.114327 & 1.2207 & 0.112362 \tabularnewline
3 & 0.131994 & 1.4093 & 0.080733 \tabularnewline
4 & 0.056069 & 0.5987 & 0.275297 \tabularnewline
5 & 0.135411 & 1.4458 & 0.075489 \tabularnewline
6 & 0.168159 & 1.7954 & 0.037616 \tabularnewline
7 & 0.046198 & 0.4933 & 0.311389 \tabularnewline
8 & 0.054193 & 0.5786 & 0.281991 \tabularnewline
9 & 0.252182 & 2.6926 & 0.00408 \tabularnewline
10 & 0.044019 & 0.47 & 0.319629 \tabularnewline
11 & 0.115517 & 1.2334 & 0.109984 \tabularnewline
12 & -0.174793 & -1.8663 & 0.032286 \tabularnewline
13 & -0.24736 & -2.6411 & 0.004712 \tabularnewline
14 & 0.081293 & 0.868 & 0.193618 \tabularnewline
15 & 0.176926 & 1.8891 & 0.030713 \tabularnewline
16 & 0.080056 & 0.8548 & 0.197238 \tabularnewline
17 & 0.169974 & 1.8148 & 0.03609 \tabularnewline
18 & 0.036576 & 0.3905 & 0.34844 \tabularnewline
19 & -0.123903 & -1.3229 & 0.094254 \tabularnewline
20 & 0.047967 & 0.5121 & 0.304769 \tabularnewline
21 & -0.041404 & -0.4421 & 0.329637 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301364&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]0.296847[/C][C]3.1695[/C][C]0.000981[/C][/ROW]
[ROW][C]2[/C][C]0.114327[/C][C]1.2207[/C][C]0.112362[/C][/ROW]
[ROW][C]3[/C][C]0.131994[/C][C]1.4093[/C][C]0.080733[/C][/ROW]
[ROW][C]4[/C][C]0.056069[/C][C]0.5987[/C][C]0.275297[/C][/ROW]
[ROW][C]5[/C][C]0.135411[/C][C]1.4458[/C][C]0.075489[/C][/ROW]
[ROW][C]6[/C][C]0.168159[/C][C]1.7954[/C][C]0.037616[/C][/ROW]
[ROW][C]7[/C][C]0.046198[/C][C]0.4933[/C][C]0.311389[/C][/ROW]
[ROW][C]8[/C][C]0.054193[/C][C]0.5786[/C][C]0.281991[/C][/ROW]
[ROW][C]9[/C][C]0.252182[/C][C]2.6926[/C][C]0.00408[/C][/ROW]
[ROW][C]10[/C][C]0.044019[/C][C]0.47[/C][C]0.319629[/C][/ROW]
[ROW][C]11[/C][C]0.115517[/C][C]1.2334[/C][C]0.109984[/C][/ROW]
[ROW][C]12[/C][C]-0.174793[/C][C]-1.8663[/C][C]0.032286[/C][/ROW]
[ROW][C]13[/C][C]-0.24736[/C][C]-2.6411[/C][C]0.004712[/C][/ROW]
[ROW][C]14[/C][C]0.081293[/C][C]0.868[/C][C]0.193618[/C][/ROW]
[ROW][C]15[/C][C]0.176926[/C][C]1.8891[/C][C]0.030713[/C][/ROW]
[ROW][C]16[/C][C]0.080056[/C][C]0.8548[/C][C]0.197238[/C][/ROW]
[ROW][C]17[/C][C]0.169974[/C][C]1.8148[/C][C]0.03609[/C][/ROW]
[ROW][C]18[/C][C]0.036576[/C][C]0.3905[/C][C]0.34844[/C][/ROW]
[ROW][C]19[/C][C]-0.123903[/C][C]-1.3229[/C][C]0.094254[/C][/ROW]
[ROW][C]20[/C][C]0.047967[/C][C]0.5121[/C][C]0.304769[/C][/ROW]
[ROW][C]21[/C][C]-0.041404[/C][C]-0.4421[/C][C]0.329637[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301364&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301364&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	0.296847	3.1695	0.000981
2	0.114327	1.2207	0.112362
3	0.131994	1.4093	0.080733
4	0.056069	0.5987	0.275297
5	0.135411	1.4458	0.075489
6	0.168159	1.7954	0.037616
7	0.046198	0.4933	0.311389
8	0.054193	0.5786	0.281991
9	0.252182	2.6926	0.00408
10	0.044019	0.47	0.319629
11	0.115517	1.2334	0.109984
12	-0.174793	-1.8663	0.032286
13	-0.24736	-2.6411	0.004712
14	0.081293	0.868	0.193618
15	0.176926	1.8891	0.030713
16	0.080056	0.8548	0.197238
17	0.169974	1.8148	0.03609
18	0.036576	0.3905	0.34844
19	-0.123903	-1.3229	0.094254
20	0.047967	0.5121	0.304769
21	-0.041404	-0.4421	0.329637

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.296847	3.1695	0.000981
2	0.028742	0.3069	0.379747
3	0.099327	1.0605	0.145574
4	-0.012312	-0.1315	0.447823
5	0.123304	1.3165	0.095319
6	0.095816	1.023	0.15423
7	-0.042787	-0.4568	0.324329
8	0.022497	0.2402	0.405303
9	0.236185	2.5218	0.006529
10	-0.11551	-1.2333	0.109998
11	0.101439	1.0831	0.140531
12	-0.346659	-3.7013	0.000166
13	-0.119087	-1.2715	0.10307
14	0.183822	1.9627	0.026059
15	0.165615	1.7683	0.039845
16	0.012542	0.1339	0.446856
17	0.176944	1.8892	0.0307
18	-0.105324	-1.1246	0.13157
19	-0.132015	-1.4095	0.080699
20	-0.056595	-0.6043	0.273433
21	0.058069	0.62	0.268245

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.296847 & 3.1695 & 0.000981 \tabularnewline
2 & 0.028742 & 0.3069 & 0.379747 \tabularnewline
3 & 0.099327 & 1.0605 & 0.145574 \tabularnewline
4 & -0.012312 & -0.1315 & 0.447823 \tabularnewline
5 & 0.123304 & 1.3165 & 0.095319 \tabularnewline
6 & 0.095816 & 1.023 & 0.15423 \tabularnewline
7 & -0.042787 & -0.4568 & 0.324329 \tabularnewline
8 & 0.022497 & 0.2402 & 0.405303 \tabularnewline
9 & 0.236185 & 2.5218 & 0.006529 \tabularnewline
10 & -0.11551 & -1.2333 & 0.109998 \tabularnewline
11 & 0.101439 & 1.0831 & 0.140531 \tabularnewline
12 & -0.346659 & -3.7013 & 0.000166 \tabularnewline
13 & -0.119087 & -1.2715 & 0.10307 \tabularnewline
14 & 0.183822 & 1.9627 & 0.026059 \tabularnewline
15 & 0.165615 & 1.7683 & 0.039845 \tabularnewline
16 & 0.012542 & 0.1339 & 0.446856 \tabularnewline
17 & 0.176944 & 1.8892 & 0.0307 \tabularnewline
18 & -0.105324 & -1.1246 & 0.13157 \tabularnewline
19 & -0.132015 & -1.4095 & 0.080699 \tabularnewline
20 & -0.056595 & -0.6043 & 0.273433 \tabularnewline
21 & 0.058069 & 0.62 & 0.268245 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301364&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]0.296847[/C][C]3.1695[/C][C]0.000981[/C][/ROW]
[ROW][C]2[/C][C]0.028742[/C][C]0.3069[/C][C]0.379747[/C][/ROW]
[ROW][C]3[/C][C]0.099327[/C][C]1.0605[/C][C]0.145574[/C][/ROW]
[ROW][C]4[/C][C]-0.012312[/C][C]-0.1315[/C][C]0.447823[/C][/ROW]
[ROW][C]5[/C][C]0.123304[/C][C]1.3165[/C][C]0.095319[/C][/ROW]
[ROW][C]6[/C][C]0.095816[/C][C]1.023[/C][C]0.15423[/C][/ROW]
[ROW][C]7[/C][C]-0.042787[/C][C]-0.4568[/C][C]0.324329[/C][/ROW]
[ROW][C]8[/C][C]0.022497[/C][C]0.2402[/C][C]0.405303[/C][/ROW]
[ROW][C]9[/C][C]0.236185[/C][C]2.5218[/C][C]0.006529[/C][/ROW]
[ROW][C]10[/C][C]-0.11551[/C][C]-1.2333[/C][C]0.109998[/C][/ROW]
[ROW][C]11[/C][C]0.101439[/C][C]1.0831[/C][C]0.140531[/C][/ROW]
[ROW][C]12[/C][C]-0.346659[/C][C]-3.7013[/C][C]0.000166[/C][/ROW]
[ROW][C]13[/C][C]-0.119087[/C][C]-1.2715[/C][C]0.10307[/C][/ROW]
[ROW][C]14[/C][C]0.183822[/C][C]1.9627[/C][C]0.026059[/C][/ROW]
[ROW][C]15[/C][C]0.165615[/C][C]1.7683[/C][C]0.039845[/C][/ROW]
[ROW][C]16[/C][C]0.012542[/C][C]0.1339[/C][C]0.446856[/C][/ROW]
[ROW][C]17[/C][C]0.176944[/C][C]1.8892[/C][C]0.0307[/C][/ROW]
[ROW][C]18[/C][C]-0.105324[/C][C]-1.1246[/C][C]0.13157[/C][/ROW]
[ROW][C]19[/C][C]-0.132015[/C][C]-1.4095[/C][C]0.080699[/C][/ROW]
[ROW][C]20[/C][C]-0.056595[/C][C]-0.6043[/C][C]0.273433[/C][/ROW]
[ROW][C]21[/C][C]0.058069[/C][C]0.62[/C][C]0.268245[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301364&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301364&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	0.296847	3.1695	0.000981
2	0.028742	0.3069	0.379747
3	0.099327	1.0605	0.145574
4	-0.012312	-0.1315	0.447823
5	0.123304	1.3165	0.095319
6	0.095816	1.023	0.15423
7	-0.042787	-0.4568	0.324329
8	0.022497	0.2402	0.405303
9	0.236185	2.5218	0.006529
10	-0.11551	-1.2333	0.109998
11	0.101439	1.0831	0.140531
12	-0.346659	-3.7013	0.000166
13	-0.119087	-1.2715	0.10307
14	0.183822	1.9627	0.026059
15	0.165615	1.7683	0.039845
16	0.012542	0.1339	0.446856
17	0.176944	1.8892	0.0307
18	-0.105324	-1.1246	0.13157
19	-0.132015	-1.4095	0.080699
20	-0.056595	-0.6043	0.273433
21	0.058069	0.62	0.268245

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):

Parameters (R input):

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