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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

Sat, 03 Dec 2011 09:02:10 -0500

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/Dec/03/t1322920989pvea312sfs7zkz5.htm/, Retrieved Mon, 29 Apr 2024 04:56:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150460, Retrieved Mon, 29 Apr 2024 04:56:39 +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] [] [2011-12-03 14:02:10] [ce4468323d272130d499477f5e05a6d2] [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	'AstonUniversity' @ aston.wessa.net

\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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150460&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150460&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150460&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	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.476601	-6.2687	0
2	0.134078	1.7635	0.039788
3	-0.11087	-1.4583	0.07329
4	0.054074	0.7112	0.238947
5	-0.119919	-1.5773	0.058278
6	0.04241	0.5578	0.288847
7	0.028307	0.3723	0.355056
8	0.04048	0.5324	0.297554
9	0.020648	0.2716	0.393136
10	-0.134915	-1.7745	0.038867
11	0.259373	3.4115	0.000402
12	-0.460273	-6.0539	0
13	0.241658	3.1785	0.000877
14	-0.201002	-2.6438	0.004476
15	0.287357	3.7796	0.000108
16	-0.077429	-1.0184	0.15495
17	-0.03339	-0.4392	0.330541
18	0.016697	0.2196	0.413216
19	0.023399	0.3078	0.379313
20	-0.085477	-1.1243	0.131227
21	0.007425	0.0977	0.461157
22	0.098774	1.2992	0.097807

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.476601 & -6.2687 & 0 \tabularnewline
2 & 0.134078 & 1.7635 & 0.039788 \tabularnewline
3 & -0.11087 & -1.4583 & 0.07329 \tabularnewline
4 & 0.054074 & 0.7112 & 0.238947 \tabularnewline
5 & -0.119919 & -1.5773 & 0.058278 \tabularnewline
6 & 0.04241 & 0.5578 & 0.288847 \tabularnewline
7 & 0.028307 & 0.3723 & 0.355056 \tabularnewline
8 & 0.04048 & 0.5324 & 0.297554 \tabularnewline
9 & 0.020648 & 0.2716 & 0.393136 \tabularnewline
10 & -0.134915 & -1.7745 & 0.038867 \tabularnewline
11 & 0.259373 & 3.4115 & 0.000402 \tabularnewline
12 & -0.460273 & -6.0539 & 0 \tabularnewline
13 & 0.241658 & 3.1785 & 0.000877 \tabularnewline
14 & -0.201002 & -2.6438 & 0.004476 \tabularnewline
15 & 0.287357 & 3.7796 & 0.000108 \tabularnewline
16 & -0.077429 & -1.0184 & 0.15495 \tabularnewline
17 & -0.03339 & -0.4392 & 0.330541 \tabularnewline
18 & 0.016697 & 0.2196 & 0.413216 \tabularnewline
19 & 0.023399 & 0.3078 & 0.379313 \tabularnewline
20 & -0.085477 & -1.1243 & 0.131227 \tabularnewline
21 & 0.007425 & 0.0977 & 0.461157 \tabularnewline
22 & 0.098774 & 1.2992 & 0.097807 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150460&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]-0.476601[/C][C]-6.2687[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.134078[/C][C]1.7635[/C][C]0.039788[/C][/ROW]
[ROW][C]3[/C][C]-0.11087[/C][C]-1.4583[/C][C]0.07329[/C][/ROW]
[ROW][C]4[/C][C]0.054074[/C][C]0.7112[/C][C]0.238947[/C][/ROW]
[ROW][C]5[/C][C]-0.119919[/C][C]-1.5773[/C][C]0.058278[/C][/ROW]
[ROW][C]6[/C][C]0.04241[/C][C]0.5578[/C][C]0.288847[/C][/ROW]
[ROW][C]7[/C][C]0.028307[/C][C]0.3723[/C][C]0.355056[/C][/ROW]
[ROW][C]8[/C][C]0.04048[/C][C]0.5324[/C][C]0.297554[/C][/ROW]
[ROW][C]9[/C][C]0.020648[/C][C]0.2716[/C][C]0.393136[/C][/ROW]
[ROW][C]10[/C][C]-0.134915[/C][C]-1.7745[/C][C]0.038867[/C][/ROW]
[ROW][C]11[/C][C]0.259373[/C][C]3.4115[/C][C]0.000402[/C][/ROW]
[ROW][C]12[/C][C]-0.460273[/C][C]-6.0539[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.241658[/C][C]3.1785[/C][C]0.000877[/C][/ROW]
[ROW][C]14[/C][C]-0.201002[/C][C]-2.6438[/C][C]0.004476[/C][/ROW]
[ROW][C]15[/C][C]0.287357[/C][C]3.7796[/C][C]0.000108[/C][/ROW]
[ROW][C]16[/C][C]-0.077429[/C][C]-1.0184[/C][C]0.15495[/C][/ROW]
[ROW][C]17[/C][C]-0.03339[/C][C]-0.4392[/C][C]0.330541[/C][/ROW]
[ROW][C]18[/C][C]0.016697[/C][C]0.2196[/C][C]0.413216[/C][/ROW]
[ROW][C]19[/C][C]0.023399[/C][C]0.3078[/C][C]0.379313[/C][/ROW]
[ROW][C]20[/C][C]-0.085477[/C][C]-1.1243[/C][C]0.131227[/C][/ROW]
[ROW][C]21[/C][C]0.007425[/C][C]0.0977[/C][C]0.461157[/C][/ROW]
[ROW][C]22[/C][C]0.098774[/C][C]1.2992[/C][C]0.097807[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150460&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150460&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	-0.476601	-6.2687	0
2	0.134078	1.7635	0.039788
3	-0.11087	-1.4583	0.07329
4	0.054074	0.7112	0.238947
5	-0.119919	-1.5773	0.058278
6	0.04241	0.5578	0.288847
7	0.028307	0.3723	0.355056
8	0.04048	0.5324	0.297554
9	0.020648	0.2716	0.393136
10	-0.134915	-1.7745	0.038867
11	0.259373	3.4115	0.000402
12	-0.460273	-6.0539	0
13	0.241658	3.1785	0.000877
14	-0.201002	-2.6438	0.004476
15	0.287357	3.7796	0.000108
16	-0.077429	-1.0184	0.15495
17	-0.03339	-0.4392	0.330541
18	0.016697	0.2196	0.413216
19	0.023399	0.3078	0.379313
20	-0.085477	-1.1243	0.131227
21	0.007425	0.0977	0.461157
22	0.098774	1.2992	0.097807

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.476601	-6.2687	0
2	-0.120425	-1.5839	0.057517
3	-0.126919	-1.6694	0.048427
4	-0.056155	-0.7386	0.230576
5	-0.157267	-2.0685	0.020039
6	-0.123443	-1.6236	0.053137
7	-0.016353	-0.2151	0.414974
8	0.049571	0.652	0.25763
9	0.084238	1.108	0.134705
10	-0.126571	-1.6648	0.048883
11	0.198623	2.6125	0.00489
12	-0.336844	-4.4305	8e-06
13	-0.163924	-2.1561	0.016229
14	-0.269417	-3.5436	0.000254
15	0.050418	0.6631	0.254062
16	0.147639	1.9419	0.026888
17	-0.131242	-1.7262	0.043047
18	-0.042428	-0.5581	0.288764
19	-0.007794	-0.1025	0.459234
20	0.012396	0.163	0.435338
21	-0.006005	-0.079	0.468568
22	-0.034993	-0.4603	0.322952

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.476601 & -6.2687 & 0 \tabularnewline
2 & -0.120425 & -1.5839 & 0.057517 \tabularnewline
3 & -0.126919 & -1.6694 & 0.048427 \tabularnewline
4 & -0.056155 & -0.7386 & 0.230576 \tabularnewline
5 & -0.157267 & -2.0685 & 0.020039 \tabularnewline
6 & -0.123443 & -1.6236 & 0.053137 \tabularnewline
7 & -0.016353 & -0.2151 & 0.414974 \tabularnewline
8 & 0.049571 & 0.652 & 0.25763 \tabularnewline
9 & 0.084238 & 1.108 & 0.134705 \tabularnewline
10 & -0.126571 & -1.6648 & 0.048883 \tabularnewline
11 & 0.198623 & 2.6125 & 0.00489 \tabularnewline
12 & -0.336844 & -4.4305 & 8e-06 \tabularnewline
13 & -0.163924 & -2.1561 & 0.016229 \tabularnewline
14 & -0.269417 & -3.5436 & 0.000254 \tabularnewline
15 & 0.050418 & 0.6631 & 0.254062 \tabularnewline
16 & 0.147639 & 1.9419 & 0.026888 \tabularnewline
17 & -0.131242 & -1.7262 & 0.043047 \tabularnewline
18 & -0.042428 & -0.5581 & 0.288764 \tabularnewline
19 & -0.007794 & -0.1025 & 0.459234 \tabularnewline
20 & 0.012396 & 0.163 & 0.435338 \tabularnewline
21 & -0.006005 & -0.079 & 0.468568 \tabularnewline
22 & -0.034993 & -0.4603 & 0.322952 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150460&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]-0.476601[/C][C]-6.2687[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.120425[/C][C]-1.5839[/C][C]0.057517[/C][/ROW]
[ROW][C]3[/C][C]-0.126919[/C][C]-1.6694[/C][C]0.048427[/C][/ROW]
[ROW][C]4[/C][C]-0.056155[/C][C]-0.7386[/C][C]0.230576[/C][/ROW]
[ROW][C]5[/C][C]-0.157267[/C][C]-2.0685[/C][C]0.020039[/C][/ROW]
[ROW][C]6[/C][C]-0.123443[/C][C]-1.6236[/C][C]0.053137[/C][/ROW]
[ROW][C]7[/C][C]-0.016353[/C][C]-0.2151[/C][C]0.414974[/C][/ROW]
[ROW][C]8[/C][C]0.049571[/C][C]0.652[/C][C]0.25763[/C][/ROW]
[ROW][C]9[/C][C]0.084238[/C][C]1.108[/C][C]0.134705[/C][/ROW]
[ROW][C]10[/C][C]-0.126571[/C][C]-1.6648[/C][C]0.048883[/C][/ROW]
[ROW][C]11[/C][C]0.198623[/C][C]2.6125[/C][C]0.00489[/C][/ROW]
[ROW][C]12[/C][C]-0.336844[/C][C]-4.4305[/C][C]8e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.163924[/C][C]-2.1561[/C][C]0.016229[/C][/ROW]
[ROW][C]14[/C][C]-0.269417[/C][C]-3.5436[/C][C]0.000254[/C][/ROW]
[ROW][C]15[/C][C]0.050418[/C][C]0.6631[/C][C]0.254062[/C][/ROW]
[ROW][C]16[/C][C]0.147639[/C][C]1.9419[/C][C]0.026888[/C][/ROW]
[ROW][C]17[/C][C]-0.131242[/C][C]-1.7262[/C][C]0.043047[/C][/ROW]
[ROW][C]18[/C][C]-0.042428[/C][C]-0.5581[/C][C]0.288764[/C][/ROW]
[ROW][C]19[/C][C]-0.007794[/C][C]-0.1025[/C][C]0.459234[/C][/ROW]
[ROW][C]20[/C][C]0.012396[/C][C]0.163[/C][C]0.435338[/C][/ROW]
[ROW][C]21[/C][C]-0.006005[/C][C]-0.079[/C][C]0.468568[/C][/ROW]
[ROW][C]22[/C][C]-0.034993[/C][C]-0.4603[/C][C]0.322952[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150460&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150460&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	-0.476601	-6.2687	0
2	-0.120425	-1.5839	0.057517
3	-0.126919	-1.6694	0.048427
4	-0.056155	-0.7386	0.230576
5	-0.157267	-2.0685	0.020039
6	-0.123443	-1.6236	0.053137
7	-0.016353	-0.2151	0.414974
8	0.049571	0.652	0.25763
9	0.084238	1.108	0.134705
10	-0.126571	-1.6648	0.048883
11	0.198623	2.6125	0.00489
12	-0.336844	-4.4305	8e-06
13	-0.163924	-2.1561	0.016229
14	-0.269417	-3.5436	0.000254
15	0.050418	0.6631	0.254062
16	0.147639	1.9419	0.026888
17	-0.131242	-1.7262	0.043047
18	-0.042428	-0.5581	0.288764
19	-0.007794	-0.1025	0.459234
20	0.012396	0.163	0.435338
21	-0.006005	-0.079	0.468568
22	-0.034993	-0.4603	0.322952

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code