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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 17 Dec 2016 20:39:07 +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/17/t1482003557yq8rou4qfsekg8s.htm/, Retrieved Thu, 02 May 2024 06:07:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300922, Retrieved Thu, 02 May 2024 06:07:16 +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] [] [2016-12-17 19:39:07] [94ac3c9a028ddd47e8862e80eac9f626] [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=300922&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=300922&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300922&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	0.32443	3.4487	0.000396
2	0.214881	2.2842	0.012113
3	0.264761	2.8145	0.002883
4	-0.112579	-1.1967	0.116959
5	-0.059766	-0.6353	0.263253
6	-0.037614	-0.3998	0.345012
7	-0.070206	-0.7463	0.228519
8	0.066342	0.7052	0.241061
9	-0.082192	-0.8737	0.192065
10	-0.078106	-0.8303	0.204067
11	-0.020925	-0.2224	0.412186
12	-0.362483	-3.8532	9.7e-05
13	-0.210248	-2.235	0.013693
14	-0.006922	-0.0736	0.470738
15	-0.138886	-1.4764	0.071312
16	-0.085651	-0.9105	0.182253
17	-0.007158	-0.0761	0.469739
18	-0.082362	-0.8755	0.191574
19	-0.084978	-0.9033	0.184135
20	-0.022288	-0.2369	0.406571
21	-0.028042	-0.2981	0.383092

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.32443 & 3.4487 & 0.000396 \tabularnewline
2 & 0.214881 & 2.2842 & 0.012113 \tabularnewline
3 & 0.264761 & 2.8145 & 0.002883 \tabularnewline
4 & -0.112579 & -1.1967 & 0.116959 \tabularnewline
5 & -0.059766 & -0.6353 & 0.263253 \tabularnewline
6 & -0.037614 & -0.3998 & 0.345012 \tabularnewline
7 & -0.070206 & -0.7463 & 0.228519 \tabularnewline
8 & 0.066342 & 0.7052 & 0.241061 \tabularnewline
9 & -0.082192 & -0.8737 & 0.192065 \tabularnewline
10 & -0.078106 & -0.8303 & 0.204067 \tabularnewline
11 & -0.020925 & -0.2224 & 0.412186 \tabularnewline
12 & -0.362483 & -3.8532 & 9.7e-05 \tabularnewline
13 & -0.210248 & -2.235 & 0.013693 \tabularnewline
14 & -0.006922 & -0.0736 & 0.470738 \tabularnewline
15 & -0.138886 & -1.4764 & 0.071312 \tabularnewline
16 & -0.085651 & -0.9105 & 0.182253 \tabularnewline
17 & -0.007158 & -0.0761 & 0.469739 \tabularnewline
18 & -0.082362 & -0.8755 & 0.191574 \tabularnewline
19 & -0.084978 & -0.9033 & 0.184135 \tabularnewline
20 & -0.022288 & -0.2369 & 0.406571 \tabularnewline
21 & -0.028042 & -0.2981 & 0.383092 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300922&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]0.32443[/C][C]3.4487[/C][C]0.000396[/C][/ROW]
[ROW][C]2[/C][C]0.214881[/C][C]2.2842[/C][C]0.012113[/C][/ROW]
[ROW][C]3[/C][C]0.264761[/C][C]2.8145[/C][C]0.002883[/C][/ROW]
[ROW][C]4[/C][C]-0.112579[/C][C]-1.1967[/C][C]0.116959[/C][/ROW]
[ROW][C]5[/C][C]-0.059766[/C][C]-0.6353[/C][C]0.263253[/C][/ROW]
[ROW][C]6[/C][C]-0.037614[/C][C]-0.3998[/C][C]0.345012[/C][/ROW]
[ROW][C]7[/C][C]-0.070206[/C][C]-0.7463[/C][C]0.228519[/C][/ROW]
[ROW][C]8[/C][C]0.066342[/C][C]0.7052[/C][C]0.241061[/C][/ROW]
[ROW][C]9[/C][C]-0.082192[/C][C]-0.8737[/C][C]0.192065[/C][/ROW]
[ROW][C]10[/C][C]-0.078106[/C][C]-0.8303[/C][C]0.204067[/C][/ROW]
[ROW][C]11[/C][C]-0.020925[/C][C]-0.2224[/C][C]0.412186[/C][/ROW]
[ROW][C]12[/C][C]-0.362483[/C][C]-3.8532[/C][C]9.7e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.210248[/C][C]-2.235[/C][C]0.013693[/C][/ROW]
[ROW][C]14[/C][C]-0.006922[/C][C]-0.0736[/C][C]0.470738[/C][/ROW]
[ROW][C]15[/C][C]-0.138886[/C][C]-1.4764[/C][C]0.071312[/C][/ROW]
[ROW][C]16[/C][C]-0.085651[/C][C]-0.9105[/C][C]0.182253[/C][/ROW]
[ROW][C]17[/C][C]-0.007158[/C][C]-0.0761[/C][C]0.469739[/C][/ROW]
[ROW][C]18[/C][C]-0.082362[/C][C]-0.8755[/C][C]0.191574[/C][/ROW]
[ROW][C]19[/C][C]-0.084978[/C][C]-0.9033[/C][C]0.184135[/C][/ROW]
[ROW][C]20[/C][C]-0.022288[/C][C]-0.2369[/C][C]0.406571[/C][/ROW]
[ROW][C]21[/C][C]-0.028042[/C][C]-0.2981[/C][C]0.383092[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300922&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300922&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	0.32443	3.4487	0.000396
2	0.214881	2.2842	0.012113
3	0.264761	2.8145	0.002883
4	-0.112579	-1.1967	0.116959
5	-0.059766	-0.6353	0.263253
6	-0.037614	-0.3998	0.345012
7	-0.070206	-0.7463	0.228519
8	0.066342	0.7052	0.241061
9	-0.082192	-0.8737	0.192065
10	-0.078106	-0.8303	0.204067
11	-0.020925	-0.2224	0.412186
12	-0.362483	-3.8532	9.7e-05
13	-0.210248	-2.235	0.013693
14	-0.006922	-0.0736	0.470738
15	-0.138886	-1.4764	0.071312
16	-0.085651	-0.9105	0.182253
17	-0.007158	-0.0761	0.469739
18	-0.082362	-0.8755	0.191574
19	-0.084978	-0.9033	0.184135
20	-0.022288	-0.2369	0.406571
21	-0.028042	-0.2981	0.383092

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.32443	3.4487	0.000396
2	0.122522	1.3024	0.09771
3	0.185903	1.9762	0.025286
4	-0.302271	-3.2132	0.000855
5	-0.008853	-0.0941	0.462594
6	-0.014835	-0.1577	0.437487
7	0.080154	0.852	0.197995
8	0.076914	0.8176	0.207652
9	-0.17188	-1.8271	0.035161
10	-0.061126	-0.6498	0.258579
11	-0.007748	-0.0824	0.467252
12	-0.317737	-3.3776	0.000502
13	-0.010872	-0.1156	0.454097
14	0.177656	1.8885	0.030761
15	0.021736	0.2311	0.408846
16	-0.233556	-2.4827	0.007254
17	-0.079391	-0.8439	0.200244
18	-0.001294	-0.0138	0.494527
19	-0.0173	-0.1839	0.42721
20	0.086414	0.9186	0.180133
21	-0.062872	-0.6683	0.252639

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.32443 & 3.4487 & 0.000396 \tabularnewline
2 & 0.122522 & 1.3024 & 0.09771 \tabularnewline
3 & 0.185903 & 1.9762 & 0.025286 \tabularnewline
4 & -0.302271 & -3.2132 & 0.000855 \tabularnewline
5 & -0.008853 & -0.0941 & 0.462594 \tabularnewline
6 & -0.014835 & -0.1577 & 0.437487 \tabularnewline
7 & 0.080154 & 0.852 & 0.197995 \tabularnewline
8 & 0.076914 & 0.8176 & 0.207652 \tabularnewline
9 & -0.17188 & -1.8271 & 0.035161 \tabularnewline
10 & -0.061126 & -0.6498 & 0.258579 \tabularnewline
11 & -0.007748 & -0.0824 & 0.467252 \tabularnewline
12 & -0.317737 & -3.3776 & 0.000502 \tabularnewline
13 & -0.010872 & -0.1156 & 0.454097 \tabularnewline
14 & 0.177656 & 1.8885 & 0.030761 \tabularnewline
15 & 0.021736 & 0.2311 & 0.408846 \tabularnewline
16 & -0.233556 & -2.4827 & 0.007254 \tabularnewline
17 & -0.079391 & -0.8439 & 0.200244 \tabularnewline
18 & -0.001294 & -0.0138 & 0.494527 \tabularnewline
19 & -0.0173 & -0.1839 & 0.42721 \tabularnewline
20 & 0.086414 & 0.9186 & 0.180133 \tabularnewline
21 & -0.062872 & -0.6683 & 0.252639 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300922&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]0.32443[/C][C]3.4487[/C][C]0.000396[/C][/ROW]
[ROW][C]2[/C][C]0.122522[/C][C]1.3024[/C][C]0.09771[/C][/ROW]
[ROW][C]3[/C][C]0.185903[/C][C]1.9762[/C][C]0.025286[/C][/ROW]
[ROW][C]4[/C][C]-0.302271[/C][C]-3.2132[/C][C]0.000855[/C][/ROW]
[ROW][C]5[/C][C]-0.008853[/C][C]-0.0941[/C][C]0.462594[/C][/ROW]
[ROW][C]6[/C][C]-0.014835[/C][C]-0.1577[/C][C]0.437487[/C][/ROW]
[ROW][C]7[/C][C]0.080154[/C][C]0.852[/C][C]0.197995[/C][/ROW]
[ROW][C]8[/C][C]0.076914[/C][C]0.8176[/C][C]0.207652[/C][/ROW]
[ROW][C]9[/C][C]-0.17188[/C][C]-1.8271[/C][C]0.035161[/C][/ROW]
[ROW][C]10[/C][C]-0.061126[/C][C]-0.6498[/C][C]0.258579[/C][/ROW]
[ROW][C]11[/C][C]-0.007748[/C][C]-0.0824[/C][C]0.467252[/C][/ROW]
[ROW][C]12[/C][C]-0.317737[/C][C]-3.3776[/C][C]0.000502[/C][/ROW]
[ROW][C]13[/C][C]-0.010872[/C][C]-0.1156[/C][C]0.454097[/C][/ROW]
[ROW][C]14[/C][C]0.177656[/C][C]1.8885[/C][C]0.030761[/C][/ROW]
[ROW][C]15[/C][C]0.021736[/C][C]0.2311[/C][C]0.408846[/C][/ROW]
[ROW][C]16[/C][C]-0.233556[/C][C]-2.4827[/C][C]0.007254[/C][/ROW]
[ROW][C]17[/C][C]-0.079391[/C][C]-0.8439[/C][C]0.200244[/C][/ROW]
[ROW][C]18[/C][C]-0.001294[/C][C]-0.0138[/C][C]0.494527[/C][/ROW]
[ROW][C]19[/C][C]-0.0173[/C][C]-0.1839[/C][C]0.42721[/C][/ROW]
[ROW][C]20[/C][C]0.086414[/C][C]0.9186[/C][C]0.180133[/C][/ROW]
[ROW][C]21[/C][C]-0.062872[/C][C]-0.6683[/C][C]0.252639[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300922&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300922&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	0.32443	3.4487	0.000396
2	0.122522	1.3024	0.09771
3	0.185903	1.9762	0.025286
4	-0.302271	-3.2132	0.000855
5	-0.008853	-0.0941	0.462594
6	-0.014835	-0.1577	0.437487
7	0.080154	0.852	0.197995
8	0.076914	0.8176	0.207652
9	-0.17188	-1.8271	0.035161
10	-0.061126	-0.6498	0.258579
11	-0.007748	-0.0824	0.467252
12	-0.317737	-3.3776	0.000502
13	-0.010872	-0.1156	0.454097
14	0.177656	1.8885	0.030761
15	0.021736	0.2311	0.408846
16	-0.233556	-2.4827	0.007254
17	-0.079391	-0.8439	0.200244
18	-0.001294	-0.0138	0.494527
19	-0.0173	-0.1839	0.42721
20	0.086414	0.9186	0.180133
21	-0.062872	-0.6683	0.252639

Figure 1

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Postscript link

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Figure 2

PNG link

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Figure 3

PNG link

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Parameters (Session):

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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