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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 27 Dec 2010 10:49:12 +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/2010/Dec/27/t1293447863kzs4vh2u8ro2e7c.htm/, Retrieved Mon, 06 May 2024 23:54:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115907, Retrieved Mon, 06 May 2024 23:54:22 +0000

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Estimated Impact

115

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

-       [(Partial) Autocorrelation Function] [] [2010-12-27 10:49:12] [c984196f1244e05baf3e7c2e52d47a33] [Current]

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8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1
8.3
8.1
7.9
7.9
8.3
8.6

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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115907&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115907&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115907&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.561515	-3.8903	0.000154
2	0.019105	0.1324	0.447626
3	0.048227	0.3341	0.369869
4	0.055259	0.3828	0.351762
5	-0.034775	-0.2409	0.405319
6	0.006838	0.0474	0.481207
7	0.005109	0.0354	0.485955
8	-0.026041	-0.1804	0.428793
9	-0.015579	-0.1079	0.457248
10	-0.022164	-0.1536	0.439301
11	0.299309	2.0737	0.021749
12	-0.504178	-3.493	0.000518
13	0.272031	1.8847	0.032767
14	0.012569	0.0871	0.465485
15	-0.035463	-0.2457	0.403484
16	-0.04666	-0.3233	0.373948
17	0.035824	0.2482	0.402522

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.561515 & -3.8903 & 0.000154 \tabularnewline
2 & 0.019105 & 0.1324 & 0.447626 \tabularnewline
3 & 0.048227 & 0.3341 & 0.369869 \tabularnewline
4 & 0.055259 & 0.3828 & 0.351762 \tabularnewline
5 & -0.034775 & -0.2409 & 0.405319 \tabularnewline
6 & 0.006838 & 0.0474 & 0.481207 \tabularnewline
7 & 0.005109 & 0.0354 & 0.485955 \tabularnewline
8 & -0.026041 & -0.1804 & 0.428793 \tabularnewline
9 & -0.015579 & -0.1079 & 0.457248 \tabularnewline
10 & -0.022164 & -0.1536 & 0.439301 \tabularnewline
11 & 0.299309 & 2.0737 & 0.021749 \tabularnewline
12 & -0.504178 & -3.493 & 0.000518 \tabularnewline
13 & 0.272031 & 1.8847 & 0.032767 \tabularnewline
14 & 0.012569 & 0.0871 & 0.465485 \tabularnewline
15 & -0.035463 & -0.2457 & 0.403484 \tabularnewline
16 & -0.04666 & -0.3233 & 0.373948 \tabularnewline
17 & 0.035824 & 0.2482 & 0.402522 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115907&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]-0.561515[/C][C]-3.8903[/C][C]0.000154[/C][/ROW]
[ROW][C]2[/C][C]0.019105[/C][C]0.1324[/C][C]0.447626[/C][/ROW]
[ROW][C]3[/C][C]0.048227[/C][C]0.3341[/C][C]0.369869[/C][/ROW]
[ROW][C]4[/C][C]0.055259[/C][C]0.3828[/C][C]0.351762[/C][/ROW]
[ROW][C]5[/C][C]-0.034775[/C][C]-0.2409[/C][C]0.405319[/C][/ROW]
[ROW][C]6[/C][C]0.006838[/C][C]0.0474[/C][C]0.481207[/C][/ROW]
[ROW][C]7[/C][C]0.005109[/C][C]0.0354[/C][C]0.485955[/C][/ROW]
[ROW][C]8[/C][C]-0.026041[/C][C]-0.1804[/C][C]0.428793[/C][/ROW]
[ROW][C]9[/C][C]-0.015579[/C][C]-0.1079[/C][C]0.457248[/C][/ROW]
[ROW][C]10[/C][C]-0.022164[/C][C]-0.1536[/C][C]0.439301[/C][/ROW]
[ROW][C]11[/C][C]0.299309[/C][C]2.0737[/C][C]0.021749[/C][/ROW]
[ROW][C]12[/C][C]-0.504178[/C][C]-3.493[/C][C]0.000518[/C][/ROW]
[ROW][C]13[/C][C]0.272031[/C][C]1.8847[/C][C]0.032767[/C][/ROW]
[ROW][C]14[/C][C]0.012569[/C][C]0.0871[/C][C]0.465485[/C][/ROW]
[ROW][C]15[/C][C]-0.035463[/C][C]-0.2457[/C][C]0.403484[/C][/ROW]
[ROW][C]16[/C][C]-0.04666[/C][C]-0.3233[/C][C]0.373948[/C][/ROW]
[ROW][C]17[/C][C]0.035824[/C][C]0.2482[/C][C]0.402522[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115907&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115907&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	-0.561515	-3.8903	0.000154
2	0.019105	0.1324	0.447626
3	0.048227	0.3341	0.369869
4	0.055259	0.3828	0.351762
5	-0.034775	-0.2409	0.405319
6	0.006838	0.0474	0.481207
7	0.005109	0.0354	0.485955
8	-0.026041	-0.1804	0.428793
9	-0.015579	-0.1079	0.457248
10	-0.022164	-0.1536	0.439301
11	0.299309	2.0737	0.021749
12	-0.504178	-3.493	0.000518
13	0.272031	1.8847	0.032767
14	0.012569	0.0871	0.465485
15	-0.035463	-0.2457	0.403484
16	-0.04666	-0.3233	0.373948
17	0.035824	0.2482	0.402522

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.561515	-3.8903	0.000154
2	-0.43259	-2.9971	0.002153
3	-0.322171	-2.2321	0.015157
4	-0.134146	-0.9294	0.178668
5	-0.018677	-0.1294	0.448793
6	0.063355	0.4389	0.331339
7	0.099008	0.6859	0.248024
8	0.040621	0.2814	0.389795
9	-0.069312	-0.4802	0.316631
10	-0.213524	-1.4793	0.072792
11	0.335664	2.3255	0.012158
12	-0.1352	-0.9367	0.176803
13	-0.152869	-1.0591	0.147426
14	-0.126482	-0.8763	0.192618
15	-0.094183	-0.6525	0.258591
16	-0.06253	-0.4332	0.333397
17	-0.034735	-0.2406	0.405426

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.561515 & -3.8903 & 0.000154 \tabularnewline
2 & -0.43259 & -2.9971 & 0.002153 \tabularnewline
3 & -0.322171 & -2.2321 & 0.015157 \tabularnewline
4 & -0.134146 & -0.9294 & 0.178668 \tabularnewline
5 & -0.018677 & -0.1294 & 0.448793 \tabularnewline
6 & 0.063355 & 0.4389 & 0.331339 \tabularnewline
7 & 0.099008 & 0.6859 & 0.248024 \tabularnewline
8 & 0.040621 & 0.2814 & 0.389795 \tabularnewline
9 & -0.069312 & -0.4802 & 0.316631 \tabularnewline
10 & -0.213524 & -1.4793 & 0.072792 \tabularnewline
11 & 0.335664 & 2.3255 & 0.012158 \tabularnewline
12 & -0.1352 & -0.9367 & 0.176803 \tabularnewline
13 & -0.152869 & -1.0591 & 0.147426 \tabularnewline
14 & -0.126482 & -0.8763 & 0.192618 \tabularnewline
15 & -0.094183 & -0.6525 & 0.258591 \tabularnewline
16 & -0.06253 & -0.4332 & 0.333397 \tabularnewline
17 & -0.034735 & -0.2406 & 0.405426 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115907&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]-0.561515[/C][C]-3.8903[/C][C]0.000154[/C][/ROW]
[ROW][C]2[/C][C]-0.43259[/C][C]-2.9971[/C][C]0.002153[/C][/ROW]
[ROW][C]3[/C][C]-0.322171[/C][C]-2.2321[/C][C]0.015157[/C][/ROW]
[ROW][C]4[/C][C]-0.134146[/C][C]-0.9294[/C][C]0.178668[/C][/ROW]
[ROW][C]5[/C][C]-0.018677[/C][C]-0.1294[/C][C]0.448793[/C][/ROW]
[ROW][C]6[/C][C]0.063355[/C][C]0.4389[/C][C]0.331339[/C][/ROW]
[ROW][C]7[/C][C]0.099008[/C][C]0.6859[/C][C]0.248024[/C][/ROW]
[ROW][C]8[/C][C]0.040621[/C][C]0.2814[/C][C]0.389795[/C][/ROW]
[ROW][C]9[/C][C]-0.069312[/C][C]-0.4802[/C][C]0.316631[/C][/ROW]
[ROW][C]10[/C][C]-0.213524[/C][C]-1.4793[/C][C]0.072792[/C][/ROW]
[ROW][C]11[/C][C]0.335664[/C][C]2.3255[/C][C]0.012158[/C][/ROW]
[ROW][C]12[/C][C]-0.1352[/C][C]-0.9367[/C][C]0.176803[/C][/ROW]
[ROW][C]13[/C][C]-0.152869[/C][C]-1.0591[/C][C]0.147426[/C][/ROW]
[ROW][C]14[/C][C]-0.126482[/C][C]-0.8763[/C][C]0.192618[/C][/ROW]
[ROW][C]15[/C][C]-0.094183[/C][C]-0.6525[/C][C]0.258591[/C][/ROW]
[ROW][C]16[/C][C]-0.06253[/C][C]-0.4332[/C][C]0.333397[/C][/ROW]
[ROW][C]17[/C][C]-0.034735[/C][C]-0.2406[/C][C]0.405426[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115907&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115907&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	-0.561515	-3.8903	0.000154
2	-0.43259	-2.9971	0.002153
3	-0.322171	-2.2321	0.015157
4	-0.134146	-0.9294	0.178668
5	-0.018677	-0.1294	0.448793
6	0.063355	0.4389	0.331339
7	0.099008	0.6859	0.248024
8	0.040621	0.2814	0.389795
9	-0.069312	-0.4802	0.316631
10	-0.213524	-1.4793	0.072792
11	0.335664	2.3255	0.012158
12	-0.1352	-0.9367	0.176803
13	-0.152869	-1.0591	0.147426
14	-0.126482	-0.8763	0.192618
15	-0.094183	-0.6525	0.258591
16	-0.06253	-0.4332	0.333397
17	-0.034735	-0.2406	0.405426

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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)
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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Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code