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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 28 Nov 2009 02:54:59 -0700

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/2009/Nov/28/t1259402202nk0ggp4slb3dh8w.htm/, Retrieved Fri, 03 May 2024 05:56:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61396, Retrieved Fri, 03 May 2024 05:56:17 +0000

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No (this computation is public)

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Estimated Impact

135

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

-       [(Partial) Autocorrelation Function] [Autocorrelatie fu...] [2009-11-28 09:54:59] [762da55b2e2304daaed24a7cc507d14d] [Current]
-   P     [(Partial) Autocorrelation Function] [verbetering 2] [2009-11-30 18:27:52] [42ad1186d39724f834063794eac7cea3] 

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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=61396&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=61396&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61396&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	0.88878	6.8845	0
2	0.747528	5.7903	0
3	0.652794	5.0565	2e-06
4	0.611459	4.7363	7e-06
5	0.604875	4.6853	8e-06
6	0.584777	4.5297	1.4e-05
7	0.523773	4.0571	7.3e-05
8	0.452005	3.5012	0.00044
9	0.431338	3.3411	0.00072
10	0.463198	3.5879	0.000336
11	0.530712	4.1109	6.1e-05
12	0.521067	4.0362	7.8e-05
13	0.371258	2.8758	0.002786
14	0.215202	1.6669	0.050369
15	0.110584	0.8566	0.197542
16	0.051493	0.3989	0.345706
17	0.024757	0.1918	0.424288

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.88878 & 6.8845 & 0 \tabularnewline
2 & 0.747528 & 5.7903 & 0 \tabularnewline
3 & 0.652794 & 5.0565 & 2e-06 \tabularnewline
4 & 0.611459 & 4.7363 & 7e-06 \tabularnewline
5 & 0.604875 & 4.6853 & 8e-06 \tabularnewline
6 & 0.584777 & 4.5297 & 1.4e-05 \tabularnewline
7 & 0.523773 & 4.0571 & 7.3e-05 \tabularnewline
8 & 0.452005 & 3.5012 & 0.00044 \tabularnewline
9 & 0.431338 & 3.3411 & 0.00072 \tabularnewline
10 & 0.463198 & 3.5879 & 0.000336 \tabularnewline
11 & 0.530712 & 4.1109 & 6.1e-05 \tabularnewline
12 & 0.521067 & 4.0362 & 7.8e-05 \tabularnewline
13 & 0.371258 & 2.8758 & 0.002786 \tabularnewline
14 & 0.215202 & 1.6669 & 0.050369 \tabularnewline
15 & 0.110584 & 0.8566 & 0.197542 \tabularnewline
16 & 0.051493 & 0.3989 & 0.345706 \tabularnewline
17 & 0.024757 & 0.1918 & 0.424288 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61396&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]0.88878[/C][C]6.8845[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.747528[/C][C]5.7903[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.652794[/C][C]5.0565[/C][C]2e-06[/C][/ROW]
[ROW][C]4[/C][C]0.611459[/C][C]4.7363[/C][C]7e-06[/C][/ROW]
[ROW][C]5[/C][C]0.604875[/C][C]4.6853[/C][C]8e-06[/C][/ROW]
[ROW][C]6[/C][C]0.584777[/C][C]4.5297[/C][C]1.4e-05[/C][/ROW]
[ROW][C]7[/C][C]0.523773[/C][C]4.0571[/C][C]7.3e-05[/C][/ROW]
[ROW][C]8[/C][C]0.452005[/C][C]3.5012[/C][C]0.00044[/C][/ROW]
[ROW][C]9[/C][C]0.431338[/C][C]3.3411[/C][C]0.00072[/C][/ROW]
[ROW][C]10[/C][C]0.463198[/C][C]3.5879[/C][C]0.000336[/C][/ROW]
[ROW][C]11[/C][C]0.530712[/C][C]4.1109[/C][C]6.1e-05[/C][/ROW]
[ROW][C]12[/C][C]0.521067[/C][C]4.0362[/C][C]7.8e-05[/C][/ROW]
[ROW][C]13[/C][C]0.371258[/C][C]2.8758[/C][C]0.002786[/C][/ROW]
[ROW][C]14[/C][C]0.215202[/C][C]1.6669[/C][C]0.050369[/C][/ROW]
[ROW][C]15[/C][C]0.110584[/C][C]0.8566[/C][C]0.197542[/C][/ROW]
[ROW][C]16[/C][C]0.051493[/C][C]0.3989[/C][C]0.345706[/C][/ROW]
[ROW][C]17[/C][C]0.024757[/C][C]0.1918[/C][C]0.424288[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61396&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61396&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	0.88878	6.8845	0
2	0.747528	5.7903	0
3	0.652794	5.0565	2e-06
4	0.611459	4.7363	7e-06
5	0.604875	4.6853	8e-06
6	0.584777	4.5297	1.4e-05
7	0.523773	4.0571	7.3e-05
8	0.452005	3.5012	0.00044
9	0.431338	3.3411	0.00072
10	0.463198	3.5879	0.000336
11	0.530712	4.1109	6.1e-05
12	0.521067	4.0362	7.8e-05
13	0.371258	2.8758	0.002786
14	0.215202	1.6669	0.050369
15	0.110584	0.8566	0.197542
16	0.051493	0.3989	0.345706
17	0.024757	0.1918	0.424288

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.88878	6.8845	0
2	-0.201845	-1.5635	0.061599
3	0.167227	1.2953	0.100083
4	0.1425	1.1038	0.137043
5	0.126946	0.9833	0.164699
6	-0.036287	-0.2811	0.389808
7	-0.110394	-0.8551	0.197947
8	-0.00806	-0.0624	0.475212
9	0.188949	1.4636	0.074262
10	0.145155	1.1244	0.132668
11	0.206704	1.6011	0.057301
12	-0.285578	-2.2121	0.01539
13	-0.568851	-4.4063	2.2e-05
14	-0.097299	-0.7537	0.226996
15	-0.057952	-0.4489	0.327562
16	-0.101301	-0.7847	0.217866
17	0.016947	0.1313	0.448001

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.88878 & 6.8845 & 0 \tabularnewline
2 & -0.201845 & -1.5635 & 0.061599 \tabularnewline
3 & 0.167227 & 1.2953 & 0.100083 \tabularnewline
4 & 0.1425 & 1.1038 & 0.137043 \tabularnewline
5 & 0.126946 & 0.9833 & 0.164699 \tabularnewline
6 & -0.036287 & -0.2811 & 0.389808 \tabularnewline
7 & -0.110394 & -0.8551 & 0.197947 \tabularnewline
8 & -0.00806 & -0.0624 & 0.475212 \tabularnewline
9 & 0.188949 & 1.4636 & 0.074262 \tabularnewline
10 & 0.145155 & 1.1244 & 0.132668 \tabularnewline
11 & 0.206704 & 1.6011 & 0.057301 \tabularnewline
12 & -0.285578 & -2.2121 & 0.01539 \tabularnewline
13 & -0.568851 & -4.4063 & 2.2e-05 \tabularnewline
14 & -0.097299 & -0.7537 & 0.226996 \tabularnewline
15 & -0.057952 & -0.4489 & 0.327562 \tabularnewline
16 & -0.101301 & -0.7847 & 0.217866 \tabularnewline
17 & 0.016947 & 0.1313 & 0.448001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61396&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]0.88878[/C][C]6.8845[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.201845[/C][C]-1.5635[/C][C]0.061599[/C][/ROW]
[ROW][C]3[/C][C]0.167227[/C][C]1.2953[/C][C]0.100083[/C][/ROW]
[ROW][C]4[/C][C]0.1425[/C][C]1.1038[/C][C]0.137043[/C][/ROW]
[ROW][C]5[/C][C]0.126946[/C][C]0.9833[/C][C]0.164699[/C][/ROW]
[ROW][C]6[/C][C]-0.036287[/C][C]-0.2811[/C][C]0.389808[/C][/ROW]
[ROW][C]7[/C][C]-0.110394[/C][C]-0.8551[/C][C]0.197947[/C][/ROW]
[ROW][C]8[/C][C]-0.00806[/C][C]-0.0624[/C][C]0.475212[/C][/ROW]
[ROW][C]9[/C][C]0.188949[/C][C]1.4636[/C][C]0.074262[/C][/ROW]
[ROW][C]10[/C][C]0.145155[/C][C]1.1244[/C][C]0.132668[/C][/ROW]
[ROW][C]11[/C][C]0.206704[/C][C]1.6011[/C][C]0.057301[/C][/ROW]
[ROW][C]12[/C][C]-0.285578[/C][C]-2.2121[/C][C]0.01539[/C][/ROW]
[ROW][C]13[/C][C]-0.568851[/C][C]-4.4063[/C][C]2.2e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.097299[/C][C]-0.7537[/C][C]0.226996[/C][/ROW]
[ROW][C]15[/C][C]-0.057952[/C][C]-0.4489[/C][C]0.327562[/C][/ROW]
[ROW][C]16[/C][C]-0.101301[/C][C]-0.7847[/C][C]0.217866[/C][/ROW]
[ROW][C]17[/C][C]0.016947[/C][C]0.1313[/C][C]0.448001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61396&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61396&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	0.88878	6.8845	0
2	-0.201845	-1.5635	0.061599
3	0.167227	1.2953	0.100083
4	0.1425	1.1038	0.137043
5	0.126946	0.9833	0.164699
6	-0.036287	-0.2811	0.389808
7	-0.110394	-0.8551	0.197947
8	-0.00806	-0.0624	0.475212
9	0.188949	1.4636	0.074262
10	0.145155	1.1244	0.132668
11	0.206704	1.6011	0.057301
12	-0.285578	-2.2121	0.01539
13	-0.568851	-4.4063	2.2e-05
14	-0.097299	-0.7537	0.226996
15	-0.057952	-0.4489	0.327562
16	-0.101301	-0.7847	0.217866
17	0.016947	0.1313	0.448001

Figure 1

PNG link

Postscript link

PDF link

Figure 2

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 ;

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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code