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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 16 Aug 2011 06:32:40 -0400

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/Aug/16/t1313490828i1b7xed257a9v2h.htm/, Retrieved Mon, 13 May 2024 23:35:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123828, Retrieved Mon, 13 May 2024 23:35:20 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

S�bastien Delforge

Estimated Impact

166

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

-       [(Partial) Autocorrelation Function] [Tijdreeks 2 - sta...] [2011-08-16 10:32:40] [923770d86edf74ed976a539eae527e37] [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	'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123828&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123828&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123828&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' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.051927	0.5396	0.295278
2	-0.087052	-0.9047	0.183826
3	0.126941	1.3192	0.094944
4	-0.049181	-0.5111	0.305163
5	-0.182339	-1.8949	0.030388
6	-0.399601	-4.1528	3.3e-05
7	-0.178583	-1.8559	0.033098
8	-0.077055	-0.8008	0.21251
9	0.106832	1.1102	0.134682
10	-0.110436	-1.1477	0.126817
11	0.121356	1.2612	0.104982
12	0.77	8.0021	0
13	0.032404	0.3367	0.36848
14	-0.041925	-0.4357	0.331961
15	0.091813	0.9542	0.171069
16	-0.037635	-0.3911	0.348242
17	-0.191177	-1.9868	0.02474
18	-0.339207	-3.5251	0.000311
19	-0.190921	-1.9841	0.02489
20	-0.096072	-0.9984	0.160156

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.051927 & 0.5396 & 0.295278 \tabularnewline
2 & -0.087052 & -0.9047 & 0.183826 \tabularnewline
3 & 0.126941 & 1.3192 & 0.094944 \tabularnewline
4 & -0.049181 & -0.5111 & 0.305163 \tabularnewline
5 & -0.182339 & -1.8949 & 0.030388 \tabularnewline
6 & -0.399601 & -4.1528 & 3.3e-05 \tabularnewline
7 & -0.178583 & -1.8559 & 0.033098 \tabularnewline
8 & -0.077055 & -0.8008 & 0.21251 \tabularnewline
9 & 0.106832 & 1.1102 & 0.134682 \tabularnewline
10 & -0.110436 & -1.1477 & 0.126817 \tabularnewline
11 & 0.121356 & 1.2612 & 0.104982 \tabularnewline
12 & 0.77 & 8.0021 & 0 \tabularnewline
13 & 0.032404 & 0.3367 & 0.36848 \tabularnewline
14 & -0.041925 & -0.4357 & 0.331961 \tabularnewline
15 & 0.091813 & 0.9542 & 0.171069 \tabularnewline
16 & -0.037635 & -0.3911 & 0.348242 \tabularnewline
17 & -0.191177 & -1.9868 & 0.02474 \tabularnewline
18 & -0.339207 & -3.5251 & 0.000311 \tabularnewline
19 & -0.190921 & -1.9841 & 0.02489 \tabularnewline
20 & -0.096072 & -0.9984 & 0.160156 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123828&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]0.051927[/C][C]0.5396[/C][C]0.295278[/C][/ROW]
[ROW][C]2[/C][C]-0.087052[/C][C]-0.9047[/C][C]0.183826[/C][/ROW]
[ROW][C]3[/C][C]0.126941[/C][C]1.3192[/C][C]0.094944[/C][/ROW]
[ROW][C]4[/C][C]-0.049181[/C][C]-0.5111[/C][C]0.305163[/C][/ROW]
[ROW][C]5[/C][C]-0.182339[/C][C]-1.8949[/C][C]0.030388[/C][/ROW]
[ROW][C]6[/C][C]-0.399601[/C][C]-4.1528[/C][C]3.3e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.178583[/C][C]-1.8559[/C][C]0.033098[/C][/ROW]
[ROW][C]8[/C][C]-0.077055[/C][C]-0.8008[/C][C]0.21251[/C][/ROW]
[ROW][C]9[/C][C]0.106832[/C][C]1.1102[/C][C]0.134682[/C][/ROW]
[ROW][C]10[/C][C]-0.110436[/C][C]-1.1477[/C][C]0.126817[/C][/ROW]
[ROW][C]11[/C][C]0.121356[/C][C]1.2612[/C][C]0.104982[/C][/ROW]
[ROW][C]12[/C][C]0.77[/C][C]8.0021[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.032404[/C][C]0.3367[/C][C]0.36848[/C][/ROW]
[ROW][C]14[/C][C]-0.041925[/C][C]-0.4357[/C][C]0.331961[/C][/ROW]
[ROW][C]15[/C][C]0.091813[/C][C]0.9542[/C][C]0.171069[/C][/ROW]
[ROW][C]16[/C][C]-0.037635[/C][C]-0.3911[/C][C]0.348242[/C][/ROW]
[ROW][C]17[/C][C]-0.191177[/C][C]-1.9868[/C][C]0.02474[/C][/ROW]
[ROW][C]18[/C][C]-0.339207[/C][C]-3.5251[/C][C]0.000311[/C][/ROW]
[ROW][C]19[/C][C]-0.190921[/C][C]-1.9841[/C][C]0.02489[/C][/ROW]
[ROW][C]20[/C][C]-0.096072[/C][C]-0.9984[/C][C]0.160156[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123828&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123828&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	0.051927	0.5396	0.295278
2	-0.087052	-0.9047	0.183826
3	0.126941	1.3192	0.094944
4	-0.049181	-0.5111	0.305163
5	-0.182339	-1.8949	0.030388
6	-0.399601	-4.1528	3.3e-05
7	-0.178583	-1.8559	0.033098
8	-0.077055	-0.8008	0.21251
9	0.106832	1.1102	0.134682
10	-0.110436	-1.1477	0.126817
11	0.121356	1.2612	0.104982
12	0.77	8.0021	0
13	0.032404	0.3367	0.36848
14	-0.041925	-0.4357	0.331961
15	0.091813	0.9542	0.171069
16	-0.037635	-0.3911	0.348242
17	-0.191177	-1.9868	0.02474
18	-0.339207	-3.5251	0.000311
19	-0.190921	-1.9841	0.02489
20	-0.096072	-0.9984	0.160156

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.051927	0.5396	0.295278
2	-0.089991	-0.9352	0.175881
3	0.138028	1.4344	0.077169
4	-0.075871	-0.7885	0.216074
5	-0.154086	-1.6013	0.056115
6	-0.42998	-4.4685	1e-05
7	-0.215059	-2.235	0.013739
8	-0.176553	-1.8348	0.034644
9	0.197629	2.0538	0.021204
10	-0.197499	-2.0525	0.021271
11	0.041647	0.4328	0.33301
12	0.659758	6.8564	0
13	0.036889	0.3834	0.351102
14	0.007522	0.0782	0.468917
15	-0.097105	-1.0091	0.157582
16	-0.052398	-0.5445	0.293597
17	-0.028618	-0.2974	0.383364
18	0.082964	0.8622	0.195248
19	-0.034964	-0.3634	0.358526
20	-0.044103	-0.4583	0.323816

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.051927 & 0.5396 & 0.295278 \tabularnewline
2 & -0.089991 & -0.9352 & 0.175881 \tabularnewline
3 & 0.138028 & 1.4344 & 0.077169 \tabularnewline
4 & -0.075871 & -0.7885 & 0.216074 \tabularnewline
5 & -0.154086 & -1.6013 & 0.056115 \tabularnewline
6 & -0.42998 & -4.4685 & 1e-05 \tabularnewline
7 & -0.215059 & -2.235 & 0.013739 \tabularnewline
8 & -0.176553 & -1.8348 & 0.034644 \tabularnewline
9 & 0.197629 & 2.0538 & 0.021204 \tabularnewline
10 & -0.197499 & -2.0525 & 0.021271 \tabularnewline
11 & 0.041647 & 0.4328 & 0.33301 \tabularnewline
12 & 0.659758 & 6.8564 & 0 \tabularnewline
13 & 0.036889 & 0.3834 & 0.351102 \tabularnewline
14 & 0.007522 & 0.0782 & 0.468917 \tabularnewline
15 & -0.097105 & -1.0091 & 0.157582 \tabularnewline
16 & -0.052398 & -0.5445 & 0.293597 \tabularnewline
17 & -0.028618 & -0.2974 & 0.383364 \tabularnewline
18 & 0.082964 & 0.8622 & 0.195248 \tabularnewline
19 & -0.034964 & -0.3634 & 0.358526 \tabularnewline
20 & -0.044103 & -0.4583 & 0.323816 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123828&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]0.051927[/C][C]0.5396[/C][C]0.295278[/C][/ROW]
[ROW][C]2[/C][C]-0.089991[/C][C]-0.9352[/C][C]0.175881[/C][/ROW]
[ROW][C]3[/C][C]0.138028[/C][C]1.4344[/C][C]0.077169[/C][/ROW]
[ROW][C]4[/C][C]-0.075871[/C][C]-0.7885[/C][C]0.216074[/C][/ROW]
[ROW][C]5[/C][C]-0.154086[/C][C]-1.6013[/C][C]0.056115[/C][/ROW]
[ROW][C]6[/C][C]-0.42998[/C][C]-4.4685[/C][C]1e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.215059[/C][C]-2.235[/C][C]0.013739[/C][/ROW]
[ROW][C]8[/C][C]-0.176553[/C][C]-1.8348[/C][C]0.034644[/C][/ROW]
[ROW][C]9[/C][C]0.197629[/C][C]2.0538[/C][C]0.021204[/C][/ROW]
[ROW][C]10[/C][C]-0.197499[/C][C]-2.0525[/C][C]0.021271[/C][/ROW]
[ROW][C]11[/C][C]0.041647[/C][C]0.4328[/C][C]0.33301[/C][/ROW]
[ROW][C]12[/C][C]0.659758[/C][C]6.8564[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.036889[/C][C]0.3834[/C][C]0.351102[/C][/ROW]
[ROW][C]14[/C][C]0.007522[/C][C]0.0782[/C][C]0.468917[/C][/ROW]
[ROW][C]15[/C][C]-0.097105[/C][C]-1.0091[/C][C]0.157582[/C][/ROW]
[ROW][C]16[/C][C]-0.052398[/C][C]-0.5445[/C][C]0.293597[/C][/ROW]
[ROW][C]17[/C][C]-0.028618[/C][C]-0.2974[/C][C]0.383364[/C][/ROW]
[ROW][C]18[/C][C]0.082964[/C][C]0.8622[/C][C]0.195248[/C][/ROW]
[ROW][C]19[/C][C]-0.034964[/C][C]-0.3634[/C][C]0.358526[/C][/ROW]
[ROW][C]20[/C][C]-0.044103[/C][C]-0.4583[/C][C]0.323816[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123828&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123828&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	0.051927	0.5396	0.295278
2	-0.089991	-0.9352	0.175881
3	0.138028	1.4344	0.077169
4	-0.075871	-0.7885	0.216074
5	-0.154086	-1.6013	0.056115
6	-0.42998	-4.4685	1e-05
7	-0.215059	-2.235	0.013739
8	-0.176553	-1.8348	0.034644
9	0.197629	2.0538	0.021204
10	-0.197499	-2.0525	0.021271
11	0.041647	0.4328	0.33301
12	0.659758	6.8564	0
13	0.036889	0.3834	0.351102
14	0.007522	0.0782	0.468917
15	-0.097105	-1.0091	0.157582
16	-0.052398	-0.5445	0.293597
17	-0.028618	-0.2974	0.383364
18	0.082964	0.8622	0.195248
19	-0.034964	-0.3634	0.358526
20	-0.044103	-0.4583	0.323816

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):

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)
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