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*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 19 Dec 2010 20:59:26 +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/19/t1292792256zblyb81kpl7fcht.htm/, Retrieved Sat, 04 May 2024 20:59:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112740, Retrieved Sat, 04 May 2024 20:59:29 +0000

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User-defined keywords

Estimated Impact

102

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

-       [(Partial) Autocorrelation Function] [paper - autocorre...] [2010-12-19 20:59:26] [5398da98f4f83c6a353e4d3806d4bcaa] [Current]
-   PD    [(Partial) Autocorrelation Function] [Verbetering (P)ACF] [2010-12-28 19:28:48] [c2a9e95daa10045f9fd6252038bcb219] 

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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' @ 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112740&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' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112740&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112740&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' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.477272	4.3743	1.7e-05
2	0.436795	4.0033	6.7e-05
3	0.421454	3.8627	0.00011
4	0.070049	0.642	0.261307
5	0.139963	1.2828	0.101548
6	0.099852	0.9152	0.181363
7	-0.037394	-0.3427	0.366331
8	-0.009012	-0.0826	0.467183
9	0.035732	0.3275	0.372057
10	-0.049771	-0.4562	0.324727
11	0.084141	0.7712	0.221386
12	0.249267	2.2846	0.01243
13	-0.017917	-0.1642	0.434979
14	0.049527	0.4539	0.325528
15	-0.081994	-0.7515	0.22723
16	-0.235064	-2.1544	0.017036
17	-0.131372	-1.204	0.115978
18	-0.216326	-1.9827	0.025337
19	-0.253636	-2.3246	0.011253

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.477272 & 4.3743 & 1.7e-05 \tabularnewline
2 & 0.436795 & 4.0033 & 6.7e-05 \tabularnewline
3 & 0.421454 & 3.8627 & 0.00011 \tabularnewline
4 & 0.070049 & 0.642 & 0.261307 \tabularnewline
5 & 0.139963 & 1.2828 & 0.101548 \tabularnewline
6 & 0.099852 & 0.9152 & 0.181363 \tabularnewline
7 & -0.037394 & -0.3427 & 0.366331 \tabularnewline
8 & -0.009012 & -0.0826 & 0.467183 \tabularnewline
9 & 0.035732 & 0.3275 & 0.372057 \tabularnewline
10 & -0.049771 & -0.4562 & 0.324727 \tabularnewline
11 & 0.084141 & 0.7712 & 0.221386 \tabularnewline
12 & 0.249267 & 2.2846 & 0.01243 \tabularnewline
13 & -0.017917 & -0.1642 & 0.434979 \tabularnewline
14 & 0.049527 & 0.4539 & 0.325528 \tabularnewline
15 & -0.081994 & -0.7515 & 0.22723 \tabularnewline
16 & -0.235064 & -2.1544 & 0.017036 \tabularnewline
17 & -0.131372 & -1.204 & 0.115978 \tabularnewline
18 & -0.216326 & -1.9827 & 0.025337 \tabularnewline
19 & -0.253636 & -2.3246 & 0.011253 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112740&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]0.477272[/C][C]4.3743[/C][C]1.7e-05[/C][/ROW]
[ROW][C]2[/C][C]0.436795[/C][C]4.0033[/C][C]6.7e-05[/C][/ROW]
[ROW][C]3[/C][C]0.421454[/C][C]3.8627[/C][C]0.00011[/C][/ROW]
[ROW][C]4[/C][C]0.070049[/C][C]0.642[/C][C]0.261307[/C][/ROW]
[ROW][C]5[/C][C]0.139963[/C][C]1.2828[/C][C]0.101548[/C][/ROW]
[ROW][C]6[/C][C]0.099852[/C][C]0.9152[/C][C]0.181363[/C][/ROW]
[ROW][C]7[/C][C]-0.037394[/C][C]-0.3427[/C][C]0.366331[/C][/ROW]
[ROW][C]8[/C][C]-0.009012[/C][C]-0.0826[/C][C]0.467183[/C][/ROW]
[ROW][C]9[/C][C]0.035732[/C][C]0.3275[/C][C]0.372057[/C][/ROW]
[ROW][C]10[/C][C]-0.049771[/C][C]-0.4562[/C][C]0.324727[/C][/ROW]
[ROW][C]11[/C][C]0.084141[/C][C]0.7712[/C][C]0.221386[/C][/ROW]
[ROW][C]12[/C][C]0.249267[/C][C]2.2846[/C][C]0.01243[/C][/ROW]
[ROW][C]13[/C][C]-0.017917[/C][C]-0.1642[/C][C]0.434979[/C][/ROW]
[ROW][C]14[/C][C]0.049527[/C][C]0.4539[/C][C]0.325528[/C][/ROW]
[ROW][C]15[/C][C]-0.081994[/C][C]-0.7515[/C][C]0.22723[/C][/ROW]
[ROW][C]16[/C][C]-0.235064[/C][C]-2.1544[/C][C]0.017036[/C][/ROW]
[ROW][C]17[/C][C]-0.131372[/C][C]-1.204[/C][C]0.115978[/C][/ROW]
[ROW][C]18[/C][C]-0.216326[/C][C]-1.9827[/C][C]0.025337[/C][/ROW]
[ROW][C]19[/C][C]-0.253636[/C][C]-2.3246[/C][C]0.011253[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112740&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112740&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	0.477272	4.3743	1.7e-05
2	0.436795	4.0033	6.7e-05
3	0.421454	3.8627	0.00011
4	0.070049	0.642	0.261307
5	0.139963	1.2828	0.101548
6	0.099852	0.9152	0.181363
7	-0.037394	-0.3427	0.366331
8	-0.009012	-0.0826	0.467183
9	0.035732	0.3275	0.372057
10	-0.049771	-0.4562	0.324727
11	0.084141	0.7712	0.221386
12	0.249267	2.2846	0.01243
13	-0.017917	-0.1642	0.434979
14	0.049527	0.4539	0.325528
15	-0.081994	-0.7515	0.22723
16	-0.235064	-2.1544	0.017036
17	-0.131372	-1.204	0.115978
18	-0.216326	-1.9827	0.025337
19	-0.253636	-2.3246	0.011253

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.477272	4.3743	1.7e-05
2	0.270659	2.4806	0.007555
3	0.19595	1.7959	0.038052
4	-0.343312	-3.1465	0.001143
5	0.055982	0.5131	0.30462
6	0.06908	0.6331	0.264186
7	-0.029862	-0.2737	0.392496
8	-0.114273	-1.0473	0.148976
9	0.133444	1.223	0.112368
10	-0.023211	-0.2127	0.416026
11	0.127898	1.1722	0.122214
12	0.261411	2.3959	0.009401
13	-0.322665	-2.9573	0.002015
14	-0.190079	-1.7421	0.042575
15	-0.190542	-1.7463	0.042204
16	0.097739	0.8958	0.186462
17	-0.010747	-0.0985	0.460886
18	-0.024304	-0.2228	0.412134
19	-0.11565	-1.06	0.146103

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.477272 & 4.3743 & 1.7e-05 \tabularnewline
2 & 0.270659 & 2.4806 & 0.007555 \tabularnewline
3 & 0.19595 & 1.7959 & 0.038052 \tabularnewline
4 & -0.343312 & -3.1465 & 0.001143 \tabularnewline
5 & 0.055982 & 0.5131 & 0.30462 \tabularnewline
6 & 0.06908 & 0.6331 & 0.264186 \tabularnewline
7 & -0.029862 & -0.2737 & 0.392496 \tabularnewline
8 & -0.114273 & -1.0473 & 0.148976 \tabularnewline
9 & 0.133444 & 1.223 & 0.112368 \tabularnewline
10 & -0.023211 & -0.2127 & 0.416026 \tabularnewline
11 & 0.127898 & 1.1722 & 0.122214 \tabularnewline
12 & 0.261411 & 2.3959 & 0.009401 \tabularnewline
13 & -0.322665 & -2.9573 & 0.002015 \tabularnewline
14 & -0.190079 & -1.7421 & 0.042575 \tabularnewline
15 & -0.190542 & -1.7463 & 0.042204 \tabularnewline
16 & 0.097739 & 0.8958 & 0.186462 \tabularnewline
17 & -0.010747 & -0.0985 & 0.460886 \tabularnewline
18 & -0.024304 & -0.2228 & 0.412134 \tabularnewline
19 & -0.11565 & -1.06 & 0.146103 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112740&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]0.477272[/C][C]4.3743[/C][C]1.7e-05[/C][/ROW]
[ROW][C]2[/C][C]0.270659[/C][C]2.4806[/C][C]0.007555[/C][/ROW]
[ROW][C]3[/C][C]0.19595[/C][C]1.7959[/C][C]0.038052[/C][/ROW]
[ROW][C]4[/C][C]-0.343312[/C][C]-3.1465[/C][C]0.001143[/C][/ROW]
[ROW][C]5[/C][C]0.055982[/C][C]0.5131[/C][C]0.30462[/C][/ROW]
[ROW][C]6[/C][C]0.06908[/C][C]0.6331[/C][C]0.264186[/C][/ROW]
[ROW][C]7[/C][C]-0.029862[/C][C]-0.2737[/C][C]0.392496[/C][/ROW]
[ROW][C]8[/C][C]-0.114273[/C][C]-1.0473[/C][C]0.148976[/C][/ROW]
[ROW][C]9[/C][C]0.133444[/C][C]1.223[/C][C]0.112368[/C][/ROW]
[ROW][C]10[/C][C]-0.023211[/C][C]-0.2127[/C][C]0.416026[/C][/ROW]
[ROW][C]11[/C][C]0.127898[/C][C]1.1722[/C][C]0.122214[/C][/ROW]
[ROW][C]12[/C][C]0.261411[/C][C]2.3959[/C][C]0.009401[/C][/ROW]
[ROW][C]13[/C][C]-0.322665[/C][C]-2.9573[/C][C]0.002015[/C][/ROW]
[ROW][C]14[/C][C]-0.190079[/C][C]-1.7421[/C][C]0.042575[/C][/ROW]
[ROW][C]15[/C][C]-0.190542[/C][C]-1.7463[/C][C]0.042204[/C][/ROW]
[ROW][C]16[/C][C]0.097739[/C][C]0.8958[/C][C]0.186462[/C][/ROW]
[ROW][C]17[/C][C]-0.010747[/C][C]-0.0985[/C][C]0.460886[/C][/ROW]
[ROW][C]18[/C][C]-0.024304[/C][C]-0.2228[/C][C]0.412134[/C][/ROW]
[ROW][C]19[/C][C]-0.11565[/C][C]-1.06[/C][C]0.146103[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112740&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112740&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	0.477272	4.3743	1.7e-05
2	0.270659	2.4806	0.007555
3	0.19595	1.7959	0.038052
4	-0.343312	-3.1465	0.001143
5	0.055982	0.5131	0.30462
6	0.06908	0.6331	0.264186
7	-0.029862	-0.2737	0.392496
8	-0.114273	-1.0473	0.148976
9	0.133444	1.223	0.112368
10	-0.023211	-0.2127	0.416026
11	0.127898	1.1722	0.122214
12	0.261411	2.3959	0.009401
13	-0.322665	-2.9573	0.002015
14	-0.190079	-1.7421	0.042575
15	-0.190542	-1.7463	0.042204
16	0.097739	0.8958	0.186462
17	-0.010747	-0.0985	0.460886
18	-0.024304	-0.2228	0.412134
19	-0.11565	-1.06	0.146103

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