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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 19 May 2011 19:19:32 +0000

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/2011/May/19/t1305832532mvev8bl4alqxi3d.htm/, Retrieved Sat, 11 May 2024 06:59:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122209, Retrieved Sat, 11 May 2024 06:59:54 +0000

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User-defined keywords

KDGP2W62

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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] [Verbetering opgav...] [2011-05-19 19:19:32] [764118764852521a1756ded753a212d7] [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	2 seconds
R Server	'Herman Ole Andreas Wold' @ www.yougetit.org

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122209&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122209&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122209&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	2 seconds
R Server	'Herman Ole Andreas Wold' @ www.yougetit.org

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.305928	2.5959	0.005714
2	-0.171317	-1.4537	0.075191
3	-0.358471	-3.0417	0.00164
4	-0.27799	-2.3588	0.010525
5	-0.034946	-0.2965	0.383841
6	0.078126	0.6629	0.25475
7	-0.000608	-0.0052	0.49795
8	-0.20267	-1.7197	0.044891
9	-0.263902	-2.2393	0.014114
10	-0.148672	-1.2615	0.105596
11	0.25639	2.1755	0.016437
12	0.783323	6.6467	0
13	0.221593	1.8803	0.032058
14	-0.167516	-1.4214	0.079756
15	-0.30422	-2.5814	0.005938
16	-0.222239	-1.8858	0.03168
17	-0.001939	-0.0165	0.49346
18	0.08541	0.7247	0.235483

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.305928 & 2.5959 & 0.005714 \tabularnewline
2 & -0.171317 & -1.4537 & 0.075191 \tabularnewline
3 & -0.358471 & -3.0417 & 0.00164 \tabularnewline
4 & -0.27799 & -2.3588 & 0.010525 \tabularnewline
5 & -0.034946 & -0.2965 & 0.383841 \tabularnewline
6 & 0.078126 & 0.6629 & 0.25475 \tabularnewline
7 & -0.000608 & -0.0052 & 0.49795 \tabularnewline
8 & -0.20267 & -1.7197 & 0.044891 \tabularnewline
9 & -0.263902 & -2.2393 & 0.014114 \tabularnewline
10 & -0.148672 & -1.2615 & 0.105596 \tabularnewline
11 & 0.25639 & 2.1755 & 0.016437 \tabularnewline
12 & 0.783323 & 6.6467 & 0 \tabularnewline
13 & 0.221593 & 1.8803 & 0.032058 \tabularnewline
14 & -0.167516 & -1.4214 & 0.079756 \tabularnewline
15 & -0.30422 & -2.5814 & 0.005938 \tabularnewline
16 & -0.222239 & -1.8858 & 0.03168 \tabularnewline
17 & -0.001939 & -0.0165 & 0.49346 \tabularnewline
18 & 0.08541 & 0.7247 & 0.235483 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122209&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]0.305928[/C][C]2.5959[/C][C]0.005714[/C][/ROW]
[ROW][C]2[/C][C]-0.171317[/C][C]-1.4537[/C][C]0.075191[/C][/ROW]
[ROW][C]3[/C][C]-0.358471[/C][C]-3.0417[/C][C]0.00164[/C][/ROW]
[ROW][C]4[/C][C]-0.27799[/C][C]-2.3588[/C][C]0.010525[/C][/ROW]
[ROW][C]5[/C][C]-0.034946[/C][C]-0.2965[/C][C]0.383841[/C][/ROW]
[ROW][C]6[/C][C]0.078126[/C][C]0.6629[/C][C]0.25475[/C][/ROW]
[ROW][C]7[/C][C]-0.000608[/C][C]-0.0052[/C][C]0.49795[/C][/ROW]
[ROW][C]8[/C][C]-0.20267[/C][C]-1.7197[/C][C]0.044891[/C][/ROW]
[ROW][C]9[/C][C]-0.263902[/C][C]-2.2393[/C][C]0.014114[/C][/ROW]
[ROW][C]10[/C][C]-0.148672[/C][C]-1.2615[/C][C]0.105596[/C][/ROW]
[ROW][C]11[/C][C]0.25639[/C][C]2.1755[/C][C]0.016437[/C][/ROW]
[ROW][C]12[/C][C]0.783323[/C][C]6.6467[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.221593[/C][C]1.8803[/C][C]0.032058[/C][/ROW]
[ROW][C]14[/C][C]-0.167516[/C][C]-1.4214[/C][C]0.079756[/C][/ROW]
[ROW][C]15[/C][C]-0.30422[/C][C]-2.5814[/C][C]0.005938[/C][/ROW]
[ROW][C]16[/C][C]-0.222239[/C][C]-1.8858[/C][C]0.03168[/C][/ROW]
[ROW][C]17[/C][C]-0.001939[/C][C]-0.0165[/C][C]0.49346[/C][/ROW]
[ROW][C]18[/C][C]0.08541[/C][C]0.7247[/C][C]0.235483[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122209&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122209&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	0.305928	2.5959	0.005714
2	-0.171317	-1.4537	0.075191
3	-0.358471	-3.0417	0.00164
4	-0.27799	-2.3588	0.010525
5	-0.034946	-0.2965	0.383841
6	0.078126	0.6629	0.25475
7	-0.000608	-0.0052	0.49795
8	-0.20267	-1.7197	0.044891
9	-0.263902	-2.2393	0.014114
10	-0.148672	-1.2615	0.105596
11	0.25639	2.1755	0.016437
12	0.783323	6.6467	0
13	0.221593	1.8803	0.032058
14	-0.167516	-1.4214	0.079756
15	-0.30422	-2.5814	0.005938
16	-0.222239	-1.8858	0.03168
17	-0.001939	-0.0165	0.49346
18	0.08541	0.7247	0.235483

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.305928	2.5959	0.005714
2	-0.292262	-2.4799	0.007741
3	-0.242865	-2.0608	0.021469
4	-0.15516	-1.3166	0.096078
5	-0.028943	-0.2456	0.403351
6	-0.084476	-0.7168	0.237907
7	-0.166498	-1.4128	0.081013
8	-0.299745	-2.5434	0.006563
9	-0.307646	-2.6105	0.005497
10	-0.356366	-3.0239	0.001728
11	-0.056624	-0.4805	0.316175
12	0.613591	5.2065	1e-06
13	-0.320711	-2.7213	0.004074
14	0.033038	0.2803	0.390013
15	0.164722	1.3977	0.083246
16	0.046911	0.3981	0.345883
17	0.038583	0.3274	0.372164
18	0.03496	0.2966	0.383795

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.305928 & 2.5959 & 0.005714 \tabularnewline
2 & -0.292262 & -2.4799 & 0.007741 \tabularnewline
3 & -0.242865 & -2.0608 & 0.021469 \tabularnewline
4 & -0.15516 & -1.3166 & 0.096078 \tabularnewline
5 & -0.028943 & -0.2456 & 0.403351 \tabularnewline
6 & -0.084476 & -0.7168 & 0.237907 \tabularnewline
7 & -0.166498 & -1.4128 & 0.081013 \tabularnewline
8 & -0.299745 & -2.5434 & 0.006563 \tabularnewline
9 & -0.307646 & -2.6105 & 0.005497 \tabularnewline
10 & -0.356366 & -3.0239 & 0.001728 \tabularnewline
11 & -0.056624 & -0.4805 & 0.316175 \tabularnewline
12 & 0.613591 & 5.2065 & 1e-06 \tabularnewline
13 & -0.320711 & -2.7213 & 0.004074 \tabularnewline
14 & 0.033038 & 0.2803 & 0.390013 \tabularnewline
15 & 0.164722 & 1.3977 & 0.083246 \tabularnewline
16 & 0.046911 & 0.3981 & 0.345883 \tabularnewline
17 & 0.038583 & 0.3274 & 0.372164 \tabularnewline
18 & 0.03496 & 0.2966 & 0.383795 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122209&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]0.305928[/C][C]2.5959[/C][C]0.005714[/C][/ROW]
[ROW][C]2[/C][C]-0.292262[/C][C]-2.4799[/C][C]0.007741[/C][/ROW]
[ROW][C]3[/C][C]-0.242865[/C][C]-2.0608[/C][C]0.021469[/C][/ROW]
[ROW][C]4[/C][C]-0.15516[/C][C]-1.3166[/C][C]0.096078[/C][/ROW]
[ROW][C]5[/C][C]-0.028943[/C][C]-0.2456[/C][C]0.403351[/C][/ROW]
[ROW][C]6[/C][C]-0.084476[/C][C]-0.7168[/C][C]0.237907[/C][/ROW]
[ROW][C]7[/C][C]-0.166498[/C][C]-1.4128[/C][C]0.081013[/C][/ROW]
[ROW][C]8[/C][C]-0.299745[/C][C]-2.5434[/C][C]0.006563[/C][/ROW]
[ROW][C]9[/C][C]-0.307646[/C][C]-2.6105[/C][C]0.005497[/C][/ROW]
[ROW][C]10[/C][C]-0.356366[/C][C]-3.0239[/C][C]0.001728[/C][/ROW]
[ROW][C]11[/C][C]-0.056624[/C][C]-0.4805[/C][C]0.316175[/C][/ROW]
[ROW][C]12[/C][C]0.613591[/C][C]5.2065[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.320711[/C][C]-2.7213[/C][C]0.004074[/C][/ROW]
[ROW][C]14[/C][C]0.033038[/C][C]0.2803[/C][C]0.390013[/C][/ROW]
[ROW][C]15[/C][C]0.164722[/C][C]1.3977[/C][C]0.083246[/C][/ROW]
[ROW][C]16[/C][C]0.046911[/C][C]0.3981[/C][C]0.345883[/C][/ROW]
[ROW][C]17[/C][C]0.038583[/C][C]0.3274[/C][C]0.372164[/C][/ROW]
[ROW][C]18[/C][C]0.03496[/C][C]0.2966[/C][C]0.383795[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122209&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122209&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	0.305928	2.5959	0.005714
2	-0.292262	-2.4799	0.007741
3	-0.242865	-2.0608	0.021469
4	-0.15516	-1.3166	0.096078
5	-0.028943	-0.2456	0.403351
6	-0.084476	-0.7168	0.237907
7	-0.166498	-1.4128	0.081013
8	-0.299745	-2.5434	0.006563
9	-0.307646	-2.6105	0.005497
10	-0.356366	-3.0239	0.001728
11	-0.056624	-0.4805	0.316175
12	0.613591	5.2065	1e-06
13	-0.320711	-2.7213	0.004074
14	0.033038	0.2803	0.390013
15	0.164722	1.3977	0.083246
16	0.046911	0.3981	0.345883
17	0.038583	0.3274	0.372164
18	0.03496	0.2966	0.383795

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):

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)
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,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),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,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code