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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 15 Dec 2016 11:38:03 +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/15/t1481798471454khivh2k3v6zo.htm/, Retrieved Fri, 03 May 2024 06:49:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299839, Retrieved Fri, 03 May 2024 06:49:07 +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] [F1 Autocorrelatio...] [2016-12-15 10:38:03] [10299735033611e1e2dae6371997f8c9] [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=299839&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=299839&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299839&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	0.967426	9.7705	0
2	0.936806	9.4613	0
3	0.906182	9.152	0
4	0.876211	8.8493	0
5	0.84865	8.5709	0
6	0.819026	8.2718	0
7	0.789584	7.9744	0
8	0.760262	7.6783	0
9	0.732423	7.3971	0
10	0.704769	7.1178	0
11	0.675663	6.8239	0
12	0.648075	6.5452	0
13	0.622484	6.2868	0
14	0.595295	6.0122	0
15	0.568661	5.7432	0
16	0.544008	5.4942	0
17	0.518551	5.2371	0
18	0.491128	4.9601	1e-06
19	0.464443	4.6906	4e-06
20	0.436758	4.411	1.3e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.967426 & 9.7705 & 0 \tabularnewline
2 & 0.936806 & 9.4613 & 0 \tabularnewline
3 & 0.906182 & 9.152 & 0 \tabularnewline
4 & 0.876211 & 8.8493 & 0 \tabularnewline
5 & 0.84865 & 8.5709 & 0 \tabularnewline
6 & 0.819026 & 8.2718 & 0 \tabularnewline
7 & 0.789584 & 7.9744 & 0 \tabularnewline
8 & 0.760262 & 7.6783 & 0 \tabularnewline
9 & 0.732423 & 7.3971 & 0 \tabularnewline
10 & 0.704769 & 7.1178 & 0 \tabularnewline
11 & 0.675663 & 6.8239 & 0 \tabularnewline
12 & 0.648075 & 6.5452 & 0 \tabularnewline
13 & 0.622484 & 6.2868 & 0 \tabularnewline
14 & 0.595295 & 6.0122 & 0 \tabularnewline
15 & 0.568661 & 5.7432 & 0 \tabularnewline
16 & 0.544008 & 5.4942 & 0 \tabularnewline
17 & 0.518551 & 5.2371 & 0 \tabularnewline
18 & 0.491128 & 4.9601 & 1e-06 \tabularnewline
19 & 0.464443 & 4.6906 & 4e-06 \tabularnewline
20 & 0.436758 & 4.411 & 1.3e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299839&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]0.967426[/C][C]9.7705[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.936806[/C][C]9.4613[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.906182[/C][C]9.152[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.876211[/C][C]8.8493[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.84865[/C][C]8.5709[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.819026[/C][C]8.2718[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.789584[/C][C]7.9744[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.760262[/C][C]7.6783[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.732423[/C][C]7.3971[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.704769[/C][C]7.1178[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.675663[/C][C]6.8239[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.648075[/C][C]6.5452[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.622484[/C][C]6.2868[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.595295[/C][C]6.0122[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.568661[/C][C]5.7432[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.544008[/C][C]5.4942[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.518551[/C][C]5.2371[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.491128[/C][C]4.9601[/C][C]1e-06[/C][/ROW]
[ROW][C]19[/C][C]0.464443[/C][C]4.6906[/C][C]4e-06[/C][/ROW]
[ROW][C]20[/C][C]0.436758[/C][C]4.411[/C][C]1.3e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299839&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299839&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	0.967426	9.7705	0
2	0.936806	9.4613	0
3	0.906182	9.152	0
4	0.876211	8.8493	0
5	0.84865	8.5709	0
6	0.819026	8.2718	0
7	0.789584	7.9744	0
8	0.760262	7.6783	0
9	0.732423	7.3971	0
10	0.704769	7.1178	0
11	0.675663	6.8239	0
12	0.648075	6.5452	0
13	0.622484	6.2868	0
14	0.595295	6.0122	0
15	0.568661	5.7432	0
16	0.544008	5.4942	0
17	0.518551	5.2371	0
18	0.491128	4.9601	1e-06
19	0.464443	4.6906	4e-06
20	0.436758	4.411	1.3e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.967426	9.7705	0
2	0.013937	0.1408	0.444171
3	-0.015003	-0.1515	0.439932
4	-0.005841	-0.059	0.476538
5	0.022242	0.2246	0.411358
6	-0.044977	-0.4542	0.325307
7	-0.015096	-0.1525	0.439563
8	-0.01371	-0.1385	0.445075
9	0.007439	0.0751	0.47013
10	-0.014102	-0.1424	0.443513
11	-0.037755	-0.3813	0.351883
12	0.005731	0.0579	0.476977
13	0.017513	0.1769	0.42998
14	-0.040878	-0.4128	0.340293
15	-0.011034	-0.1114	0.455742
16	0.018384	0.1857	0.426537
17	-0.026009	-0.2627	0.396664
18	-0.052185	-0.527	0.299653
19	-0.006583	-0.0665	0.473561
20	-0.030236	-0.3054	0.380352

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.967426 & 9.7705 & 0 \tabularnewline
2 & 0.013937 & 0.1408 & 0.444171 \tabularnewline
3 & -0.015003 & -0.1515 & 0.439932 \tabularnewline
4 & -0.005841 & -0.059 & 0.476538 \tabularnewline
5 & 0.022242 & 0.2246 & 0.411358 \tabularnewline
6 & -0.044977 & -0.4542 & 0.325307 \tabularnewline
7 & -0.015096 & -0.1525 & 0.439563 \tabularnewline
8 & -0.01371 & -0.1385 & 0.445075 \tabularnewline
9 & 0.007439 & 0.0751 & 0.47013 \tabularnewline
10 & -0.014102 & -0.1424 & 0.443513 \tabularnewline
11 & -0.037755 & -0.3813 & 0.351883 \tabularnewline
12 & 0.005731 & 0.0579 & 0.476977 \tabularnewline
13 & 0.017513 & 0.1769 & 0.42998 \tabularnewline
14 & -0.040878 & -0.4128 & 0.340293 \tabularnewline
15 & -0.011034 & -0.1114 & 0.455742 \tabularnewline
16 & 0.018384 & 0.1857 & 0.426537 \tabularnewline
17 & -0.026009 & -0.2627 & 0.396664 \tabularnewline
18 & -0.052185 & -0.527 & 0.299653 \tabularnewline
19 & -0.006583 & -0.0665 & 0.473561 \tabularnewline
20 & -0.030236 & -0.3054 & 0.380352 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299839&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]0.967426[/C][C]9.7705[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.013937[/C][C]0.1408[/C][C]0.444171[/C][/ROW]
[ROW][C]3[/C][C]-0.015003[/C][C]-0.1515[/C][C]0.439932[/C][/ROW]
[ROW][C]4[/C][C]-0.005841[/C][C]-0.059[/C][C]0.476538[/C][/ROW]
[ROW][C]5[/C][C]0.022242[/C][C]0.2246[/C][C]0.411358[/C][/ROW]
[ROW][C]6[/C][C]-0.044977[/C][C]-0.4542[/C][C]0.325307[/C][/ROW]
[ROW][C]7[/C][C]-0.015096[/C][C]-0.1525[/C][C]0.439563[/C][/ROW]
[ROW][C]8[/C][C]-0.01371[/C][C]-0.1385[/C][C]0.445075[/C][/ROW]
[ROW][C]9[/C][C]0.007439[/C][C]0.0751[/C][C]0.47013[/C][/ROW]
[ROW][C]10[/C][C]-0.014102[/C][C]-0.1424[/C][C]0.443513[/C][/ROW]
[ROW][C]11[/C][C]-0.037755[/C][C]-0.3813[/C][C]0.351883[/C][/ROW]
[ROW][C]12[/C][C]0.005731[/C][C]0.0579[/C][C]0.476977[/C][/ROW]
[ROW][C]13[/C][C]0.017513[/C][C]0.1769[/C][C]0.42998[/C][/ROW]
[ROW][C]14[/C][C]-0.040878[/C][C]-0.4128[/C][C]0.340293[/C][/ROW]
[ROW][C]15[/C][C]-0.011034[/C][C]-0.1114[/C][C]0.455742[/C][/ROW]
[ROW][C]16[/C][C]0.018384[/C][C]0.1857[/C][C]0.426537[/C][/ROW]
[ROW][C]17[/C][C]-0.026009[/C][C]-0.2627[/C][C]0.396664[/C][/ROW]
[ROW][C]18[/C][C]-0.052185[/C][C]-0.527[/C][C]0.299653[/C][/ROW]
[ROW][C]19[/C][C]-0.006583[/C][C]-0.0665[/C][C]0.473561[/C][/ROW]
[ROW][C]20[/C][C]-0.030236[/C][C]-0.3054[/C][C]0.380352[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299839&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299839&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	0.967426	9.7705	0
2	0.013937	0.1408	0.444171
3	-0.015003	-0.1515	0.439932
4	-0.005841	-0.059	0.476538
5	0.022242	0.2246	0.411358
6	-0.044977	-0.4542	0.325307
7	-0.015096	-0.1525	0.439563
8	-0.01371	-0.1385	0.445075
9	0.007439	0.0751	0.47013
10	-0.014102	-0.1424	0.443513
11	-0.037755	-0.3813	0.351883
12	0.005731	0.0579	0.476977
13	0.017513	0.1769	0.42998
14	-0.040878	-0.4128	0.340293
15	-0.011034	-0.1114	0.455742
16	0.018384	0.1857	0.426537
17	-0.026009	-0.2627	0.396664
18	-0.052185	-0.527	0.299653
19	-0.006583	-0.0665	0.473561
20	-0.030236	-0.3054	0.380352

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):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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')

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Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code