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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

Thu, 17 Dec 2009 06:43:25 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/17/t1261057463wyxr44alw8k6nwe.htm/, Retrieved Tue, 30 Apr 2024 01:42:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68882, Retrieved Tue, 30 Apr 2024 01:42:30 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

lambda: 2 d: 1 D:1

Estimated Impact

104

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

-     [Notched Boxplots] [3/11/2009] [2009-11-02 21:10:41] [b98453cac15ba1066b407e146608df68]
- RMPD  [Multiple Regression] [Paper:Bryan Beute...] [2009-12-04 12:54:13] [408e92805dcb18620260f240a7fb9d53]
- RMPD    [(Partial) Autocorrelation Function] [] [2009-12-04 14:39:07] [408e92805dcb18620260f240a7fb9d53]
-           [(Partial) Autocorrelation Function] [Paper:Bryan Beute...] [2009-12-04 14:44:24] [408e92805dcb18620260f240a7fb9d53]
-   PD          [(Partial) Autocorrelation Function] [CVM Paper: ACF (W...] [2009-12-17 13:43:25] [a5ada8bd39e806b5b90f09589c89554a] [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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68882&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68882&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68882&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.09998	-0.768	0.222787
2	-0.273524	-2.101	0.019962
3	-0.144834	-1.1125	0.135219
4	-0.23424	-1.7992	0.038548
5	0.091747	0.7047	0.241879
6	0.218156	1.6757	0.049546
7	0.163917	1.2591	0.106482
8	-0.142512	-1.0947	0.139057
9	-0.119435	-0.9174	0.181335
10	-0.192306	-1.4771	0.07248
11	-0.09362	-0.7191	0.237456
12	0.631291	4.849	5e-06
13	-0.152395	-1.1706	0.123239
14	-0.154712	-1.1884	0.119725
15	0.025558	0.1963	0.422518
16	-0.097015	-0.7452	0.229559
17	0.05814	0.4466	0.328407

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.09998 & -0.768 & 0.222787 \tabularnewline
2 & -0.273524 & -2.101 & 0.019962 \tabularnewline
3 & -0.144834 & -1.1125 & 0.135219 \tabularnewline
4 & -0.23424 & -1.7992 & 0.038548 \tabularnewline
5 & 0.091747 & 0.7047 & 0.241879 \tabularnewline
6 & 0.218156 & 1.6757 & 0.049546 \tabularnewline
7 & 0.163917 & 1.2591 & 0.106482 \tabularnewline
8 & -0.142512 & -1.0947 & 0.139057 \tabularnewline
9 & -0.119435 & -0.9174 & 0.181335 \tabularnewline
10 & -0.192306 & -1.4771 & 0.07248 \tabularnewline
11 & -0.09362 & -0.7191 & 0.237456 \tabularnewline
12 & 0.631291 & 4.849 & 5e-06 \tabularnewline
13 & -0.152395 & -1.1706 & 0.123239 \tabularnewline
14 & -0.154712 & -1.1884 & 0.119725 \tabularnewline
15 & 0.025558 & 0.1963 & 0.422518 \tabularnewline
16 & -0.097015 & -0.7452 & 0.229559 \tabularnewline
17 & 0.05814 & 0.4466 & 0.328407 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68882&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]-0.09998[/C][C]-0.768[/C][C]0.222787[/C][/ROW]
[ROW][C]2[/C][C]-0.273524[/C][C]-2.101[/C][C]0.019962[/C][/ROW]
[ROW][C]3[/C][C]-0.144834[/C][C]-1.1125[/C][C]0.135219[/C][/ROW]
[ROW][C]4[/C][C]-0.23424[/C][C]-1.7992[/C][C]0.038548[/C][/ROW]
[ROW][C]5[/C][C]0.091747[/C][C]0.7047[/C][C]0.241879[/C][/ROW]
[ROW][C]6[/C][C]0.218156[/C][C]1.6757[/C][C]0.049546[/C][/ROW]
[ROW][C]7[/C][C]0.163917[/C][C]1.2591[/C][C]0.106482[/C][/ROW]
[ROW][C]8[/C][C]-0.142512[/C][C]-1.0947[/C][C]0.139057[/C][/ROW]
[ROW][C]9[/C][C]-0.119435[/C][C]-0.9174[/C][C]0.181335[/C][/ROW]
[ROW][C]10[/C][C]-0.192306[/C][C]-1.4771[/C][C]0.07248[/C][/ROW]
[ROW][C]11[/C][C]-0.09362[/C][C]-0.7191[/C][C]0.237456[/C][/ROW]
[ROW][C]12[/C][C]0.631291[/C][C]4.849[/C][C]5e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.152395[/C][C]-1.1706[/C][C]0.123239[/C][/ROW]
[ROW][C]14[/C][C]-0.154712[/C][C]-1.1884[/C][C]0.119725[/C][/ROW]
[ROW][C]15[/C][C]0.025558[/C][C]0.1963[/C][C]0.422518[/C][/ROW]
[ROW][C]16[/C][C]-0.097015[/C][C]-0.7452[/C][C]0.229559[/C][/ROW]
[ROW][C]17[/C][C]0.05814[/C][C]0.4466[/C][C]0.328407[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68882&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68882&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	-0.09998	-0.768	0.222787
2	-0.273524	-2.101	0.019962
3	-0.144834	-1.1125	0.135219
4	-0.23424	-1.7992	0.038548
5	0.091747	0.7047	0.241879
6	0.218156	1.6757	0.049546
7	0.163917	1.2591	0.106482
8	-0.142512	-1.0947	0.139057
9	-0.119435	-0.9174	0.181335
10	-0.192306	-1.4771	0.07248
11	-0.09362	-0.7191	0.237456
12	0.631291	4.849	5e-06
13	-0.152395	-1.1706	0.123239
14	-0.154712	-1.1884	0.119725
15	0.025558	0.1963	0.422518
16	-0.097015	-0.7452	0.229559
17	0.05814	0.4466	0.328407

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.09998	-0.768	0.222787
2	-0.286383	-2.1997	0.015877
3	-0.229581	-1.7634	0.041502
4	-0.431814	-3.3168	0.000781
5	-0.24478	-1.8802	0.032511
6	-0.140983	-1.0829	0.141627
7	0.031013	0.2382	0.40627
8	-0.163058	-1.2525	0.10767
9	-0.081556	-0.6264	0.26672
10	-0.313548	-2.4084	0.009583
11	-0.467286	-3.5893	0.000338
12	0.294858	2.2648	0.013605
13	-0.380915	-2.9259	0.002435
14	-0.215129	-1.6524	0.051879
15	-0.150871	-1.1589	0.125591
16	0.055355	0.4252	0.336122
17	0.031306	0.2405	0.4054

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.09998 & -0.768 & 0.222787 \tabularnewline
2 & -0.286383 & -2.1997 & 0.015877 \tabularnewline
3 & -0.229581 & -1.7634 & 0.041502 \tabularnewline
4 & -0.431814 & -3.3168 & 0.000781 \tabularnewline
5 & -0.24478 & -1.8802 & 0.032511 \tabularnewline
6 & -0.140983 & -1.0829 & 0.141627 \tabularnewline
7 & 0.031013 & 0.2382 & 0.40627 \tabularnewline
8 & -0.163058 & -1.2525 & 0.10767 \tabularnewline
9 & -0.081556 & -0.6264 & 0.26672 \tabularnewline
10 & -0.313548 & -2.4084 & 0.009583 \tabularnewline
11 & -0.467286 & -3.5893 & 0.000338 \tabularnewline
12 & 0.294858 & 2.2648 & 0.013605 \tabularnewline
13 & -0.380915 & -2.9259 & 0.002435 \tabularnewline
14 & -0.215129 & -1.6524 & 0.051879 \tabularnewline
15 & -0.150871 & -1.1589 & 0.125591 \tabularnewline
16 & 0.055355 & 0.4252 & 0.336122 \tabularnewline
17 & 0.031306 & 0.2405 & 0.4054 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68882&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]-0.09998[/C][C]-0.768[/C][C]0.222787[/C][/ROW]
[ROW][C]2[/C][C]-0.286383[/C][C]-2.1997[/C][C]0.015877[/C][/ROW]
[ROW][C]3[/C][C]-0.229581[/C][C]-1.7634[/C][C]0.041502[/C][/ROW]
[ROW][C]4[/C][C]-0.431814[/C][C]-3.3168[/C][C]0.000781[/C][/ROW]
[ROW][C]5[/C][C]-0.24478[/C][C]-1.8802[/C][C]0.032511[/C][/ROW]
[ROW][C]6[/C][C]-0.140983[/C][C]-1.0829[/C][C]0.141627[/C][/ROW]
[ROW][C]7[/C][C]0.031013[/C][C]0.2382[/C][C]0.40627[/C][/ROW]
[ROW][C]8[/C][C]-0.163058[/C][C]-1.2525[/C][C]0.10767[/C][/ROW]
[ROW][C]9[/C][C]-0.081556[/C][C]-0.6264[/C][C]0.26672[/C][/ROW]
[ROW][C]10[/C][C]-0.313548[/C][C]-2.4084[/C][C]0.009583[/C][/ROW]
[ROW][C]11[/C][C]-0.467286[/C][C]-3.5893[/C][C]0.000338[/C][/ROW]
[ROW][C]12[/C][C]0.294858[/C][C]2.2648[/C][C]0.013605[/C][/ROW]
[ROW][C]13[/C][C]-0.380915[/C][C]-2.9259[/C][C]0.002435[/C][/ROW]
[ROW][C]14[/C][C]-0.215129[/C][C]-1.6524[/C][C]0.051879[/C][/ROW]
[ROW][C]15[/C][C]-0.150871[/C][C]-1.1589[/C][C]0.125591[/C][/ROW]
[ROW][C]16[/C][C]0.055355[/C][C]0.4252[/C][C]0.336122[/C][/ROW]
[ROW][C]17[/C][C]0.031306[/C][C]0.2405[/C][C]0.4054[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68882&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68882&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	-0.09998	-0.768	0.222787
2	-0.286383	-2.1997	0.015877
3	-0.229581	-1.7634	0.041502
4	-0.431814	-3.3168	0.000781
5	-0.24478	-1.8802	0.032511
6	-0.140983	-1.0829	0.141627
7	0.031013	0.2382	0.40627
8	-0.163058	-1.2525	0.10767
9	-0.081556	-0.6264	0.26672
10	-0.313548	-2.4084	0.009583
11	-0.467286	-3.5893	0.000338
12	0.294858	2.2648	0.013605
13	-0.380915	-2.9259	0.002435
14	-0.215129	-1.6524	0.051879
15	-0.150871	-1.1589	0.125591
16	0.055355	0.4252	0.336122
17	0.031306	0.2405	0.4054

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 2.0 ; par3 = 1 ; par4 = 1 ; par5 = 1 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 2.0 ; par3 = 1 ; par4 = 1 ; par5 = 1 ; par6 = White Noise ; par7 = 0.95 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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