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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, 29 Dec 2010 18:35:21 +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/29/t1293647583olqlxoelhwf89mf.htm/, Retrieved Fri, 03 May 2024 12:54:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117023, Retrieved Fri, 03 May 2024 12:54:54 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

124

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

-     [Univariate Explorative Data Analysis] [] [2010-12-26 15:53:52] [70635d2e8be5a44e0387ac70a19b85b5]
-   PD  [Univariate Explorative Data Analysis] [] [2010-12-27 12:40:14] [70635d2e8be5a44e0387ac70a19b85b5]
-    D    [Univariate Explorative Data Analysis] [] [2010-12-27 15:32:59] [70635d2e8be5a44e0387ac70a19b85b5]
- RMPD      [(Partial) Autocorrelation Function] [] [2010-12-29 13:40:49] [70635d2e8be5a44e0387ac70a19b85b5]
-   P         [(Partial) Autocorrelation Function] [] [2010-12-29 13:46:42] [70635d2e8be5a44e0387ac70a19b85b5]
-   P             [(Partial) Autocorrelation Function] [] [2010-12-29 18:35:21] [5e4b6b538311b7e958647ef5010fb0e5] [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	3 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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117023&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]3 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=117023&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117023&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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.098457	-1.1312	0.130015
2	0.067332	0.7736	0.220278
3	0.191665	2.2021	0.014699
4	-0.012521	-0.1439	0.442915
5	0.152758	1.7551	0.040785
6	0.19897	2.286	0.011924
7	-0.150357	-1.7275	0.043211
8	0.106526	1.2239	0.111586
9	0.192562	2.2124	0.01433
10	-0.075313	-0.8653	0.194226
11	0.096207	1.1053	0.135514
12	-0.383417	-4.4051	1.1e-05
13	-0.009097	-0.1045	0.458461
14	-0.009757	-0.1121	0.455459
15	-0.037447	-0.4302	0.333866
16	-0.143208	-1.6453	0.05114
17	0.051441	0.591	0.277762
18	-0.148109	-1.7016	0.045588
19	-0.112806	-1.296	0.098611
20	0.036406	0.4183	0.338215
21	-0.207971	-2.3894	0.009145

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.098457 & -1.1312 & 0.130015 \tabularnewline
2 & 0.067332 & 0.7736 & 0.220278 \tabularnewline
3 & 0.191665 & 2.2021 & 0.014699 \tabularnewline
4 & -0.012521 & -0.1439 & 0.442915 \tabularnewline
5 & 0.152758 & 1.7551 & 0.040785 \tabularnewline
6 & 0.19897 & 2.286 & 0.011924 \tabularnewline
7 & -0.150357 & -1.7275 & 0.043211 \tabularnewline
8 & 0.106526 & 1.2239 & 0.111586 \tabularnewline
9 & 0.192562 & 2.2124 & 0.01433 \tabularnewline
10 & -0.075313 & -0.8653 & 0.194226 \tabularnewline
11 & 0.096207 & 1.1053 & 0.135514 \tabularnewline
12 & -0.383417 & -4.4051 & 1.1e-05 \tabularnewline
13 & -0.009097 & -0.1045 & 0.458461 \tabularnewline
14 & -0.009757 & -0.1121 & 0.455459 \tabularnewline
15 & -0.037447 & -0.4302 & 0.333866 \tabularnewline
16 & -0.143208 & -1.6453 & 0.05114 \tabularnewline
17 & 0.051441 & 0.591 & 0.277762 \tabularnewline
18 & -0.148109 & -1.7016 & 0.045588 \tabularnewline
19 & -0.112806 & -1.296 & 0.098611 \tabularnewline
20 & 0.036406 & 0.4183 & 0.338215 \tabularnewline
21 & -0.207971 & -2.3894 & 0.009145 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117023&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]-0.098457[/C][C]-1.1312[/C][C]0.130015[/C][/ROW]
[ROW][C]2[/C][C]0.067332[/C][C]0.7736[/C][C]0.220278[/C][/ROW]
[ROW][C]3[/C][C]0.191665[/C][C]2.2021[/C][C]0.014699[/C][/ROW]
[ROW][C]4[/C][C]-0.012521[/C][C]-0.1439[/C][C]0.442915[/C][/ROW]
[ROW][C]5[/C][C]0.152758[/C][C]1.7551[/C][C]0.040785[/C][/ROW]
[ROW][C]6[/C][C]0.19897[/C][C]2.286[/C][C]0.011924[/C][/ROW]
[ROW][C]7[/C][C]-0.150357[/C][C]-1.7275[/C][C]0.043211[/C][/ROW]
[ROW][C]8[/C][C]0.106526[/C][C]1.2239[/C][C]0.111586[/C][/ROW]
[ROW][C]9[/C][C]0.192562[/C][C]2.2124[/C][C]0.01433[/C][/ROW]
[ROW][C]10[/C][C]-0.075313[/C][C]-0.8653[/C][C]0.194226[/C][/ROW]
[ROW][C]11[/C][C]0.096207[/C][C]1.1053[/C][C]0.135514[/C][/ROW]
[ROW][C]12[/C][C]-0.383417[/C][C]-4.4051[/C][C]1.1e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.009097[/C][C]-0.1045[/C][C]0.458461[/C][/ROW]
[ROW][C]14[/C][C]-0.009757[/C][C]-0.1121[/C][C]0.455459[/C][/ROW]
[ROW][C]15[/C][C]-0.037447[/C][C]-0.4302[/C][C]0.333866[/C][/ROW]
[ROW][C]16[/C][C]-0.143208[/C][C]-1.6453[/C][C]0.05114[/C][/ROW]
[ROW][C]17[/C][C]0.051441[/C][C]0.591[/C][C]0.277762[/C][/ROW]
[ROW][C]18[/C][C]-0.148109[/C][C]-1.7016[/C][C]0.045588[/C][/ROW]
[ROW][C]19[/C][C]-0.112806[/C][C]-1.296[/C][C]0.098611[/C][/ROW]
[ROW][C]20[/C][C]0.036406[/C][C]0.4183[/C][C]0.338215[/C][/ROW]
[ROW][C]21[/C][C]-0.207971[/C][C]-2.3894[/C][C]0.009145[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117023&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117023&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	-0.098457	-1.1312	0.130015
2	0.067332	0.7736	0.220278
3	0.191665	2.2021	0.014699
4	-0.012521	-0.1439	0.442915
5	0.152758	1.7551	0.040785
6	0.19897	2.286	0.011924
7	-0.150357	-1.7275	0.043211
8	0.106526	1.2239	0.111586
9	0.192562	2.2124	0.01433
10	-0.075313	-0.8653	0.194226
11	0.096207	1.1053	0.135514
12	-0.383417	-4.4051	1.1e-05
13	-0.009097	-0.1045	0.458461
14	-0.009757	-0.1121	0.455459
15	-0.037447	-0.4302	0.333866
16	-0.143208	-1.6453	0.05114
17	0.051441	0.591	0.277762
18	-0.148109	-1.7016	0.045588
19	-0.112806	-1.296	0.098611
20	0.036406	0.4183	0.338215
21	-0.207971	-2.3894	0.009145

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.098457	-1.1312	0.130015
2	0.058203	0.6687	0.252427
3	0.206331	2.3706	0.009604
4	0.023981	0.2755	0.391675
5	0.13259	1.5233	0.065033
6	0.203883	2.3424	0.010327
7	-0.137829	-1.5835	0.057847
8	-0.004043	-0.0465	0.48151
9	0.171046	1.9652	0.025747
10	-0.029369	-0.3374	0.368168
11	-0.014902	-0.1712	0.43216
12	-0.485753	-5.5809	0
13	-0.091507	-1.0513	0.147513
14	-0.090548	-1.0403	0.150048
15	0.078027	0.8965	0.18582
16	-0.081218	-0.9331	0.176229
17	0.166988	1.9185	0.028601
18	0.054202	0.6227	0.267266
19	-0.22553	-2.5911	0.005321
20	0.061957	0.7118	0.238913
21	0.064073	0.7361	0.231476

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.098457 & -1.1312 & 0.130015 \tabularnewline
2 & 0.058203 & 0.6687 & 0.252427 \tabularnewline
3 & 0.206331 & 2.3706 & 0.009604 \tabularnewline
4 & 0.023981 & 0.2755 & 0.391675 \tabularnewline
5 & 0.13259 & 1.5233 & 0.065033 \tabularnewline
6 & 0.203883 & 2.3424 & 0.010327 \tabularnewline
7 & -0.137829 & -1.5835 & 0.057847 \tabularnewline
8 & -0.004043 & -0.0465 & 0.48151 \tabularnewline
9 & 0.171046 & 1.9652 & 0.025747 \tabularnewline
10 & -0.029369 & -0.3374 & 0.368168 \tabularnewline
11 & -0.014902 & -0.1712 & 0.43216 \tabularnewline
12 & -0.485753 & -5.5809 & 0 \tabularnewline
13 & -0.091507 & -1.0513 & 0.147513 \tabularnewline
14 & -0.090548 & -1.0403 & 0.150048 \tabularnewline
15 & 0.078027 & 0.8965 & 0.18582 \tabularnewline
16 & -0.081218 & -0.9331 & 0.176229 \tabularnewline
17 & 0.166988 & 1.9185 & 0.028601 \tabularnewline
18 & 0.054202 & 0.6227 & 0.267266 \tabularnewline
19 & -0.22553 & -2.5911 & 0.005321 \tabularnewline
20 & 0.061957 & 0.7118 & 0.238913 \tabularnewline
21 & 0.064073 & 0.7361 & 0.231476 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117023&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]-0.098457[/C][C]-1.1312[/C][C]0.130015[/C][/ROW]
[ROW][C]2[/C][C]0.058203[/C][C]0.6687[/C][C]0.252427[/C][/ROW]
[ROW][C]3[/C][C]0.206331[/C][C]2.3706[/C][C]0.009604[/C][/ROW]
[ROW][C]4[/C][C]0.023981[/C][C]0.2755[/C][C]0.391675[/C][/ROW]
[ROW][C]5[/C][C]0.13259[/C][C]1.5233[/C][C]0.065033[/C][/ROW]
[ROW][C]6[/C][C]0.203883[/C][C]2.3424[/C][C]0.010327[/C][/ROW]
[ROW][C]7[/C][C]-0.137829[/C][C]-1.5835[/C][C]0.057847[/C][/ROW]
[ROW][C]8[/C][C]-0.004043[/C][C]-0.0465[/C][C]0.48151[/C][/ROW]
[ROW][C]9[/C][C]0.171046[/C][C]1.9652[/C][C]0.025747[/C][/ROW]
[ROW][C]10[/C][C]-0.029369[/C][C]-0.3374[/C][C]0.368168[/C][/ROW]
[ROW][C]11[/C][C]-0.014902[/C][C]-0.1712[/C][C]0.43216[/C][/ROW]
[ROW][C]12[/C][C]-0.485753[/C][C]-5.5809[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.091507[/C][C]-1.0513[/C][C]0.147513[/C][/ROW]
[ROW][C]14[/C][C]-0.090548[/C][C]-1.0403[/C][C]0.150048[/C][/ROW]
[ROW][C]15[/C][C]0.078027[/C][C]0.8965[/C][C]0.18582[/C][/ROW]
[ROW][C]16[/C][C]-0.081218[/C][C]-0.9331[/C][C]0.176229[/C][/ROW]
[ROW][C]17[/C][C]0.166988[/C][C]1.9185[/C][C]0.028601[/C][/ROW]
[ROW][C]18[/C][C]0.054202[/C][C]0.6227[/C][C]0.267266[/C][/ROW]
[ROW][C]19[/C][C]-0.22553[/C][C]-2.5911[/C][C]0.005321[/C][/ROW]
[ROW][C]20[/C][C]0.061957[/C][C]0.7118[/C][C]0.238913[/C][/ROW]
[ROW][C]21[/C][C]0.064073[/C][C]0.7361[/C][C]0.231476[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117023&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117023&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	-0.098457	-1.1312	0.130015
2	0.058203	0.6687	0.252427
3	0.206331	2.3706	0.009604
4	0.023981	0.2755	0.391675
5	0.13259	1.5233	0.065033
6	0.203883	2.3424	0.010327
7	-0.137829	-1.5835	0.057847
8	-0.004043	-0.0465	0.48151
9	0.171046	1.9652	0.025747
10	-0.029369	-0.3374	0.368168
11	-0.014902	-0.1712	0.43216
12	-0.485753	-5.5809	0
13	-0.091507	-1.0513	0.147513
14	-0.090548	-1.0403	0.150048
15	0.078027	0.8965	0.18582
16	-0.081218	-0.9331	0.176229
17	0.166988	1.9185	0.028601
18	0.054202	0.6227	0.267266
19	-0.22553	-2.5911	0.005321
20	0.061957	0.7118	0.238913
21	0.064073	0.7361	0.231476

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 = -0.2 ; par3 = 0 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = -0.2 ; par3 = 0 ; par4 = 2 ; 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