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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 17 Mar 2014 12:44:56 -0400

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/2014/Mar/17/t13950747215tfbq8e8ywyje0i.htm/, Retrieved Tue, 14 May 2024 23:49:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234313, Retrieved Tue, 14 May 2024 23:49:38 +0000

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

-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2014-03-17 16:44:56] [1195732e18620915cb775ad7ef5494bd] [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	4 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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234313&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]4 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=234313&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234313&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	4 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.936616	8.5842	0
2	0.871155	7.9843	0
3	0.812874	7.4501	0
4	0.749208	6.8666	0
5	0.696277	6.3815	0
6	0.627927	5.755	0
7	0.548389	5.0261	1e-06
8	0.469094	4.2993	2.3e-05
9	0.382018	3.5013	0.000372
10	0.319861	2.9316	0.002172
11	0.263791	2.4177	0.008891
12	0.20047	1.8373	0.034848
13	0.141278	1.2948	0.099463
14	0.076856	0.7044	0.241568
15	0.028313	0.2595	0.397947
16	0.013489	0.1236	0.450951
17	-0.010134	-0.0929	0.46311
18	-0.021343	-0.1956	0.422693
19	-0.036769	-0.337	0.368482

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.936616 & 8.5842 & 0 \tabularnewline
2 & 0.871155 & 7.9843 & 0 \tabularnewline
3 & 0.812874 & 7.4501 & 0 \tabularnewline
4 & 0.749208 & 6.8666 & 0 \tabularnewline
5 & 0.696277 & 6.3815 & 0 \tabularnewline
6 & 0.627927 & 5.755 & 0 \tabularnewline
7 & 0.548389 & 5.0261 & 1e-06 \tabularnewline
8 & 0.469094 & 4.2993 & 2.3e-05 \tabularnewline
9 & 0.382018 & 3.5013 & 0.000372 \tabularnewline
10 & 0.319861 & 2.9316 & 0.002172 \tabularnewline
11 & 0.263791 & 2.4177 & 0.008891 \tabularnewline
12 & 0.20047 & 1.8373 & 0.034848 \tabularnewline
13 & 0.141278 & 1.2948 & 0.099463 \tabularnewline
14 & 0.076856 & 0.7044 & 0.241568 \tabularnewline
15 & 0.028313 & 0.2595 & 0.397947 \tabularnewline
16 & 0.013489 & 0.1236 & 0.450951 \tabularnewline
17 & -0.010134 & -0.0929 & 0.46311 \tabularnewline
18 & -0.021343 & -0.1956 & 0.422693 \tabularnewline
19 & -0.036769 & -0.337 & 0.368482 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234313&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]0.936616[/C][C]8.5842[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.871155[/C][C]7.9843[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.812874[/C][C]7.4501[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.749208[/C][C]6.8666[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.696277[/C][C]6.3815[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.627927[/C][C]5.755[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.548389[/C][C]5.0261[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]0.469094[/C][C]4.2993[/C][C]2.3e-05[/C][/ROW]
[ROW][C]9[/C][C]0.382018[/C][C]3.5013[/C][C]0.000372[/C][/ROW]
[ROW][C]10[/C][C]0.319861[/C][C]2.9316[/C][C]0.002172[/C][/ROW]
[ROW][C]11[/C][C]0.263791[/C][C]2.4177[/C][C]0.008891[/C][/ROW]
[ROW][C]12[/C][C]0.20047[/C][C]1.8373[/C][C]0.034848[/C][/ROW]
[ROW][C]13[/C][C]0.141278[/C][C]1.2948[/C][C]0.099463[/C][/ROW]
[ROW][C]14[/C][C]0.076856[/C][C]0.7044[/C][C]0.241568[/C][/ROW]
[ROW][C]15[/C][C]0.028313[/C][C]0.2595[/C][C]0.397947[/C][/ROW]
[ROW][C]16[/C][C]0.013489[/C][C]0.1236[/C][C]0.450951[/C][/ROW]
[ROW][C]17[/C][C]-0.010134[/C][C]-0.0929[/C][C]0.46311[/C][/ROW]
[ROW][C]18[/C][C]-0.021343[/C][C]-0.1956[/C][C]0.422693[/C][/ROW]
[ROW][C]19[/C][C]-0.036769[/C][C]-0.337[/C][C]0.368482[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234313&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234313&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	0.936616	8.5842	0
2	0.871155	7.9843	0
3	0.812874	7.4501	0
4	0.749208	6.8666	0
5	0.696277	6.3815	0
6	0.627927	5.755	0
7	0.548389	5.0261	1e-06
8	0.469094	4.2993	2.3e-05
9	0.382018	3.5013	0.000372
10	0.319861	2.9316	0.002172
11	0.263791	2.4177	0.008891
12	0.20047	1.8373	0.034848
13	0.141278	1.2948	0.099463
14	0.076856	0.7044	0.241568
15	0.028313	0.2595	0.397947
16	0.013489	0.1236	0.450951
17	-0.010134	-0.0929	0.46311
18	-0.021343	-0.1956	0.422693
19	-0.036769	-0.337	0.368482

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.936616	8.5842	0
2	-0.049648	-0.455	0.325131
3	0.023914	0.2192	0.413521
4	-0.07823	-0.717	0.237684
5	0.056771	0.5203	0.302106
6	-0.167824	-1.5381	0.063887
7	-0.116291	-1.0658	0.144779
8	-0.071037	-0.6511	0.258391
9	-0.113085	-1.0364	0.151485
10	0.136951	1.2552	0.106448
11	-0.011503	-0.1054	0.458143
12	-0.058511	-0.5363	0.296597
13	-0.028755	-0.2635	0.396389
14	-0.0618	-0.5664	0.286313
15	0.063372	0.5808	0.281462
16	0.19194	1.7592	0.041096
17	-0.094551	-0.8666	0.194322
18	0.074409	0.682	0.248566
19	-0.057853	-0.5302	0.298674

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.936616 & 8.5842 & 0 \tabularnewline
2 & -0.049648 & -0.455 & 0.325131 \tabularnewline
3 & 0.023914 & 0.2192 & 0.413521 \tabularnewline
4 & -0.07823 & -0.717 & 0.237684 \tabularnewline
5 & 0.056771 & 0.5203 & 0.302106 \tabularnewline
6 & -0.167824 & -1.5381 & 0.063887 \tabularnewline
7 & -0.116291 & -1.0658 & 0.144779 \tabularnewline
8 & -0.071037 & -0.6511 & 0.258391 \tabularnewline
9 & -0.113085 & -1.0364 & 0.151485 \tabularnewline
10 & 0.136951 & 1.2552 & 0.106448 \tabularnewline
11 & -0.011503 & -0.1054 & 0.458143 \tabularnewline
12 & -0.058511 & -0.5363 & 0.296597 \tabularnewline
13 & -0.028755 & -0.2635 & 0.396389 \tabularnewline
14 & -0.0618 & -0.5664 & 0.286313 \tabularnewline
15 & 0.063372 & 0.5808 & 0.281462 \tabularnewline
16 & 0.19194 & 1.7592 & 0.041096 \tabularnewline
17 & -0.094551 & -0.8666 & 0.194322 \tabularnewline
18 & 0.074409 & 0.682 & 0.248566 \tabularnewline
19 & -0.057853 & -0.5302 & 0.298674 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234313&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]0.936616[/C][C]8.5842[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.049648[/C][C]-0.455[/C][C]0.325131[/C][/ROW]
[ROW][C]3[/C][C]0.023914[/C][C]0.2192[/C][C]0.413521[/C][/ROW]
[ROW][C]4[/C][C]-0.07823[/C][C]-0.717[/C][C]0.237684[/C][/ROW]
[ROW][C]5[/C][C]0.056771[/C][C]0.5203[/C][C]0.302106[/C][/ROW]
[ROW][C]6[/C][C]-0.167824[/C][C]-1.5381[/C][C]0.063887[/C][/ROW]
[ROW][C]7[/C][C]-0.116291[/C][C]-1.0658[/C][C]0.144779[/C][/ROW]
[ROW][C]8[/C][C]-0.071037[/C][C]-0.6511[/C][C]0.258391[/C][/ROW]
[ROW][C]9[/C][C]-0.113085[/C][C]-1.0364[/C][C]0.151485[/C][/ROW]
[ROW][C]10[/C][C]0.136951[/C][C]1.2552[/C][C]0.106448[/C][/ROW]
[ROW][C]11[/C][C]-0.011503[/C][C]-0.1054[/C][C]0.458143[/C][/ROW]
[ROW][C]12[/C][C]-0.058511[/C][C]-0.5363[/C][C]0.296597[/C][/ROW]
[ROW][C]13[/C][C]-0.028755[/C][C]-0.2635[/C][C]0.396389[/C][/ROW]
[ROW][C]14[/C][C]-0.0618[/C][C]-0.5664[/C][C]0.286313[/C][/ROW]
[ROW][C]15[/C][C]0.063372[/C][C]0.5808[/C][C]0.281462[/C][/ROW]
[ROW][C]16[/C][C]0.19194[/C][C]1.7592[/C][C]0.041096[/C][/ROW]
[ROW][C]17[/C][C]-0.094551[/C][C]-0.8666[/C][C]0.194322[/C][/ROW]
[ROW][C]18[/C][C]0.074409[/C][C]0.682[/C][C]0.248566[/C][/ROW]
[ROW][C]19[/C][C]-0.057853[/C][C]-0.5302[/C][C]0.298674[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234313&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234313&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	0.936616	8.5842	0
2	-0.049648	-0.455	0.325131
3	0.023914	0.2192	0.413521
4	-0.07823	-0.717	0.237684
5	0.056771	0.5203	0.302106
6	-0.167824	-1.5381	0.063887
7	-0.116291	-1.0658	0.144779
8	-0.071037	-0.6511	0.258391
9	-0.113085	-1.0364	0.151485
10	0.136951	1.2552	0.106448
11	-0.011503	-0.1054	0.458143
12	-0.058511	-0.5363	0.296597
13	-0.028755	-0.2635	0.396389
14	-0.0618	-0.5664	0.286313
15	0.063372	0.5808	0.281462
16	0.19194	1.7592	0.041096
17	-0.094551	-0.8666	0.194322
18	0.074409	0.682	0.248566
19	-0.057853	-0.5302	0.298674

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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code