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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 21 Dec 2011 17:23:05 -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/21/t1324506195kej6a1ippc6xqbn.htm/, Retrieved Tue, 07 May 2024 16:11:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159098, Retrieved Tue, 07 May 2024 16:11:40 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

130

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

-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [Spectral Analysis] [] [2011-12-06 19:48:28] [b98453cac15ba1066b407e146608df68]
- R PD    [Spectral Analysis] [] [2011-12-14 15:31:08] [c53df38315e3cbde2dbe0de809195ef2]
- RMP         [(Partial) Autocorrelation Function] [] [2011-12-21 22:23:05] [204816f6f70a8d342ddc2b9d4f4a80d3] [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	'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159098&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159098&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159098&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.731409	8.4032	0
2	0.384271	4.4149	1e-05
3	-0.007567	-0.0869	0.465428
4	-0.429894	-4.9391	1e-06
5	-0.723453	-8.3118	0
6	-0.812956	-9.3401	0
7	-0.694459	-7.9787	0
8	-0.392573	-4.5103	7e-06
9	0.015044	0.1728	0.431522
10	0.395902	4.5486	6e-06
11	0.685506	7.8759	0
12	0.856625	9.8419	0
13	0.67103	7.7096	0
14	0.330539	3.7976	0.000111
15	-0.008702	-0.1	0.460257
16	-0.385948	-4.4342	1e-05
17	-0.665651	-7.6477	0
18	-0.736622	-8.4631	0
19	-0.633756	-7.2813	0
20	-0.356534	-4.0963	3.6e-05
21	0.012107	0.1391	0.44479

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.731409 & 8.4032 & 0 \tabularnewline
2 & 0.384271 & 4.4149 & 1e-05 \tabularnewline
3 & -0.007567 & -0.0869 & 0.465428 \tabularnewline
4 & -0.429894 & -4.9391 & 1e-06 \tabularnewline
5 & -0.723453 & -8.3118 & 0 \tabularnewline
6 & -0.812956 & -9.3401 & 0 \tabularnewline
7 & -0.694459 & -7.9787 & 0 \tabularnewline
8 & -0.392573 & -4.5103 & 7e-06 \tabularnewline
9 & 0.015044 & 0.1728 & 0.431522 \tabularnewline
10 & 0.395902 & 4.5486 & 6e-06 \tabularnewline
11 & 0.685506 & 7.8759 & 0 \tabularnewline
12 & 0.856625 & 9.8419 & 0 \tabularnewline
13 & 0.67103 & 7.7096 & 0 \tabularnewline
14 & 0.330539 & 3.7976 & 0.000111 \tabularnewline
15 & -0.008702 & -0.1 & 0.460257 \tabularnewline
16 & -0.385948 & -4.4342 & 1e-05 \tabularnewline
17 & -0.665651 & -7.6477 & 0 \tabularnewline
18 & -0.736622 & -8.4631 & 0 \tabularnewline
19 & -0.633756 & -7.2813 & 0 \tabularnewline
20 & -0.356534 & -4.0963 & 3.6e-05 \tabularnewline
21 & 0.012107 & 0.1391 & 0.44479 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159098&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]0.731409[/C][C]8.4032[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.384271[/C][C]4.4149[/C][C]1e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.007567[/C][C]-0.0869[/C][C]0.465428[/C][/ROW]
[ROW][C]4[/C][C]-0.429894[/C][C]-4.9391[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]-0.723453[/C][C]-8.3118[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]-0.812956[/C][C]-9.3401[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.694459[/C][C]-7.9787[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]-0.392573[/C][C]-4.5103[/C][C]7e-06[/C][/ROW]
[ROW][C]9[/C][C]0.015044[/C][C]0.1728[/C][C]0.431522[/C][/ROW]
[ROW][C]10[/C][C]0.395902[/C][C]4.5486[/C][C]6e-06[/C][/ROW]
[ROW][C]11[/C][C]0.685506[/C][C]7.8759[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.856625[/C][C]9.8419[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.67103[/C][C]7.7096[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.330539[/C][C]3.7976[/C][C]0.000111[/C][/ROW]
[ROW][C]15[/C][C]-0.008702[/C][C]-0.1[/C][C]0.460257[/C][/ROW]
[ROW][C]16[/C][C]-0.385948[/C][C]-4.4342[/C][C]1e-05[/C][/ROW]
[ROW][C]17[/C][C]-0.665651[/C][C]-7.6477[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]-0.736622[/C][C]-8.4631[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]-0.633756[/C][C]-7.2813[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]-0.356534[/C][C]-4.0963[/C][C]3.6e-05[/C][/ROW]
[ROW][C]21[/C][C]0.012107[/C][C]0.1391[/C][C]0.44479[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159098&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159098&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	0.731409	8.4032	0
2	0.384271	4.4149	1e-05
3	-0.007567	-0.0869	0.465428
4	-0.429894	-4.9391	1e-06
5	-0.723453	-8.3118	0
6	-0.812956	-9.3401	0
7	-0.694459	-7.9787	0
8	-0.392573	-4.5103	7e-06
9	0.015044	0.1728	0.431522
10	0.395902	4.5486	6e-06
11	0.685506	7.8759	0
12	0.856625	9.8419	0
13	0.67103	7.7096	0
14	0.330539	3.7976	0.000111
15	-0.008702	-0.1	0.460257
16	-0.385948	-4.4342	1e-05
17	-0.665651	-7.6477	0
18	-0.736622	-8.4631	0
19	-0.633756	-7.2813	0
20	-0.356534	-4.0963	3.6e-05
21	0.012107	0.1391	0.44479

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.731409	8.4032	0
2	-0.32403	-3.7228	0.000145
3	-0.342851	-3.9391	6.6e-05
4	-0.478405	-5.4965	0
5	-0.357558	-4.108	3.5e-05
6	-0.27966	-3.2131	0.000825
7	-0.212504	-2.4415	0.007976
8	-0.127621	-1.4663	0.072479
9	-0.031467	-0.3615	0.35914
10	-0.042357	-0.4866	0.313657
11	0.081657	0.9382	0.174936
12	0.404812	4.6509	4e-06
13	-0.165278	-1.8989	0.02988
14	-0.125468	-1.4415	0.075904
15	0.169704	1.9497	0.026663
16	0.104167	1.1968	0.116766
17	0.02743	0.3151	0.376575
18	0.056084	0.6444	0.260232
19	-0.040172	-0.4615	0.322584
20	0.017567	0.2018	0.420182
21	-0.008784	-0.1009	0.459884

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.731409 & 8.4032 & 0 \tabularnewline
2 & -0.32403 & -3.7228 & 0.000145 \tabularnewline
3 & -0.342851 & -3.9391 & 6.6e-05 \tabularnewline
4 & -0.478405 & -5.4965 & 0 \tabularnewline
5 & -0.357558 & -4.108 & 3.5e-05 \tabularnewline
6 & -0.27966 & -3.2131 & 0.000825 \tabularnewline
7 & -0.212504 & -2.4415 & 0.007976 \tabularnewline
8 & -0.127621 & -1.4663 & 0.072479 \tabularnewline
9 & -0.031467 & -0.3615 & 0.35914 \tabularnewline
10 & -0.042357 & -0.4866 & 0.313657 \tabularnewline
11 & 0.081657 & 0.9382 & 0.174936 \tabularnewline
12 & 0.404812 & 4.6509 & 4e-06 \tabularnewline
13 & -0.165278 & -1.8989 & 0.02988 \tabularnewline
14 & -0.125468 & -1.4415 & 0.075904 \tabularnewline
15 & 0.169704 & 1.9497 & 0.026663 \tabularnewline
16 & 0.104167 & 1.1968 & 0.116766 \tabularnewline
17 & 0.02743 & 0.3151 & 0.376575 \tabularnewline
18 & 0.056084 & 0.6444 & 0.260232 \tabularnewline
19 & -0.040172 & -0.4615 & 0.322584 \tabularnewline
20 & 0.017567 & 0.2018 & 0.420182 \tabularnewline
21 & -0.008784 & -0.1009 & 0.459884 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159098&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]0.731409[/C][C]8.4032[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.32403[/C][C]-3.7228[/C][C]0.000145[/C][/ROW]
[ROW][C]3[/C][C]-0.342851[/C][C]-3.9391[/C][C]6.6e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.478405[/C][C]-5.4965[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]-0.357558[/C][C]-4.108[/C][C]3.5e-05[/C][/ROW]
[ROW][C]6[/C][C]-0.27966[/C][C]-3.2131[/C][C]0.000825[/C][/ROW]
[ROW][C]7[/C][C]-0.212504[/C][C]-2.4415[/C][C]0.007976[/C][/ROW]
[ROW][C]8[/C][C]-0.127621[/C][C]-1.4663[/C][C]0.072479[/C][/ROW]
[ROW][C]9[/C][C]-0.031467[/C][C]-0.3615[/C][C]0.35914[/C][/ROW]
[ROW][C]10[/C][C]-0.042357[/C][C]-0.4866[/C][C]0.313657[/C][/ROW]
[ROW][C]11[/C][C]0.081657[/C][C]0.9382[/C][C]0.174936[/C][/ROW]
[ROW][C]12[/C][C]0.404812[/C][C]4.6509[/C][C]4e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.165278[/C][C]-1.8989[/C][C]0.02988[/C][/ROW]
[ROW][C]14[/C][C]-0.125468[/C][C]-1.4415[/C][C]0.075904[/C][/ROW]
[ROW][C]15[/C][C]0.169704[/C][C]1.9497[/C][C]0.026663[/C][/ROW]
[ROW][C]16[/C][C]0.104167[/C][C]1.1968[/C][C]0.116766[/C][/ROW]
[ROW][C]17[/C][C]0.02743[/C][C]0.3151[/C][C]0.376575[/C][/ROW]
[ROW][C]18[/C][C]0.056084[/C][C]0.6444[/C][C]0.260232[/C][/ROW]
[ROW][C]19[/C][C]-0.040172[/C][C]-0.4615[/C][C]0.322584[/C][/ROW]
[ROW][C]20[/C][C]0.017567[/C][C]0.2018[/C][C]0.420182[/C][/ROW]
[ROW][C]21[/C][C]-0.008784[/C][C]-0.1009[/C][C]0.459884[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159098&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159098&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	0.731409	8.4032	0
2	-0.32403	-3.7228	0.000145
3	-0.342851	-3.9391	6.6e-05
4	-0.478405	-5.4965	0
5	-0.357558	-4.108	3.5e-05
6	-0.27966	-3.2131	0.000825
7	-0.212504	-2.4415	0.007976
8	-0.127621	-1.4663	0.072479
9	-0.031467	-0.3615	0.35914
10	-0.042357	-0.4866	0.313657
11	0.081657	0.9382	0.174936
12	0.404812	4.6509	4e-06
13	-0.165278	-1.8989	0.02988
14	-0.125468	-1.4415	0.075904
15	0.169704	1.9497	0.026663
16	0.104167	1.1968	0.116766
17	0.02743	0.3151	0.376575
18	0.056084	0.6444	0.260232
19	-0.040172	-0.4615	0.322584
20	0.017567	0.2018	0.420182
21	-0.008784	-0.1009	0.459884

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 = 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)
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