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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Dec 2011 13:58:24 -0500

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/2011/Dec/23/t1324666727a9kd1rjl0sx2gln.htm/, Retrieved Mon, 29 Apr 2024 22:06:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160651, Retrieved Mon, 29 Apr 2024 22:06:58 +0000

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

-     [Spectral Analysis] [] [2011-12-23 18:50:40] [2ba7ee2cbaa966a49160c7cfb7436069]
- RMP     [(Partial) Autocorrelation Function] [] [2011-12-23 18:58:24] [393d554610c677f923bed472882d0fdb] [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	'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160651&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160651&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160651&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	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.376082	3.6463	0.000218
2	0.092833	0.9	0.185197
3	-0.078421	-0.7603	0.224484
4	-0.116698	-1.1314	0.130376
5	-0.011804	-0.1144	0.454563
6	-0.082145	-0.7964	0.213896
7	-0.112661	-1.0923	0.138748
8	-0.032004	-0.3103	0.378515
9	-0.052945	-0.5133	0.304467
10	-0.101733	-0.9863	0.163248
11	-0.27851	-2.7003	0.004109
12	-0.414605	-4.0197	5.9e-05
13	-0.014647	-0.142	0.443687
14	0.015533	0.1506	0.440307
15	0.10687	1.0361	0.151397
16	0.054928	0.5325	0.297803
17	0.00425	0.0412	0.483609
18	0.097446	0.9448	0.173597
19	0.090355	0.876	0.191626
20	0.034822	0.3376	0.368203

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.376082 & 3.6463 & 0.000218 \tabularnewline
2 & 0.092833 & 0.9 & 0.185197 \tabularnewline
3 & -0.078421 & -0.7603 & 0.224484 \tabularnewline
4 & -0.116698 & -1.1314 & 0.130376 \tabularnewline
5 & -0.011804 & -0.1144 & 0.454563 \tabularnewline
6 & -0.082145 & -0.7964 & 0.213896 \tabularnewline
7 & -0.112661 & -1.0923 & 0.138748 \tabularnewline
8 & -0.032004 & -0.3103 & 0.378515 \tabularnewline
9 & -0.052945 & -0.5133 & 0.304467 \tabularnewline
10 & -0.101733 & -0.9863 & 0.163248 \tabularnewline
11 & -0.27851 & -2.7003 & 0.004109 \tabularnewline
12 & -0.414605 & -4.0197 & 5.9e-05 \tabularnewline
13 & -0.014647 & -0.142 & 0.443687 \tabularnewline
14 & 0.015533 & 0.1506 & 0.440307 \tabularnewline
15 & 0.10687 & 1.0361 & 0.151397 \tabularnewline
16 & 0.054928 & 0.5325 & 0.297803 \tabularnewline
17 & 0.00425 & 0.0412 & 0.483609 \tabularnewline
18 & 0.097446 & 0.9448 & 0.173597 \tabularnewline
19 & 0.090355 & 0.876 & 0.191626 \tabularnewline
20 & 0.034822 & 0.3376 & 0.368203 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160651&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]0.376082[/C][C]3.6463[/C][C]0.000218[/C][/ROW]
[ROW][C]2[/C][C]0.092833[/C][C]0.9[/C][C]0.185197[/C][/ROW]
[ROW][C]3[/C][C]-0.078421[/C][C]-0.7603[/C][C]0.224484[/C][/ROW]
[ROW][C]4[/C][C]-0.116698[/C][C]-1.1314[/C][C]0.130376[/C][/ROW]
[ROW][C]5[/C][C]-0.011804[/C][C]-0.1144[/C][C]0.454563[/C][/ROW]
[ROW][C]6[/C][C]-0.082145[/C][C]-0.7964[/C][C]0.213896[/C][/ROW]
[ROW][C]7[/C][C]-0.112661[/C][C]-1.0923[/C][C]0.138748[/C][/ROW]
[ROW][C]8[/C][C]-0.032004[/C][C]-0.3103[/C][C]0.378515[/C][/ROW]
[ROW][C]9[/C][C]-0.052945[/C][C]-0.5133[/C][C]0.304467[/C][/ROW]
[ROW][C]10[/C][C]-0.101733[/C][C]-0.9863[/C][C]0.163248[/C][/ROW]
[ROW][C]11[/C][C]-0.27851[/C][C]-2.7003[/C][C]0.004109[/C][/ROW]
[ROW][C]12[/C][C]-0.414605[/C][C]-4.0197[/C][C]5.9e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.014647[/C][C]-0.142[/C][C]0.443687[/C][/ROW]
[ROW][C]14[/C][C]0.015533[/C][C]0.1506[/C][C]0.440307[/C][/ROW]
[ROW][C]15[/C][C]0.10687[/C][C]1.0361[/C][C]0.151397[/C][/ROW]
[ROW][C]16[/C][C]0.054928[/C][C]0.5325[/C][C]0.297803[/C][/ROW]
[ROW][C]17[/C][C]0.00425[/C][C]0.0412[/C][C]0.483609[/C][/ROW]
[ROW][C]18[/C][C]0.097446[/C][C]0.9448[/C][C]0.173597[/C][/ROW]
[ROW][C]19[/C][C]0.090355[/C][C]0.876[/C][C]0.191626[/C][/ROW]
[ROW][C]20[/C][C]0.034822[/C][C]0.3376[/C][C]0.368203[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160651&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160651&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	0.376082	3.6463	0.000218
2	0.092833	0.9	0.185197
3	-0.078421	-0.7603	0.224484
4	-0.116698	-1.1314	0.130376
5	-0.011804	-0.1144	0.454563
6	-0.082145	-0.7964	0.213896
7	-0.112661	-1.0923	0.138748
8	-0.032004	-0.3103	0.378515
9	-0.052945	-0.5133	0.304467
10	-0.101733	-0.9863	0.163248
11	-0.27851	-2.7003	0.004109
12	-0.414605	-4.0197	5.9e-05
13	-0.014647	-0.142	0.443687
14	0.015533	0.1506	0.440307
15	0.10687	1.0361	0.151397
16	0.054928	0.5325	0.297803
17	0.00425	0.0412	0.483609
18	0.097446	0.9448	0.173597
19	0.090355	0.876	0.191626
20	0.034822	0.3376	0.368203

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.376082	3.6463	0.000218
2	-0.056612	-0.5489	0.292197
3	-0.10986	-1.0651	0.144772
4	-0.051455	-0.4989	0.309515
5	0.070912	0.6875	0.246725
6	-0.124808	-1.2101	0.114646
7	-0.075339	-0.7304	0.233469
8	0.056121	0.5441	0.293827
9	-0.068281	-0.662	0.254794
10	-0.123536	-1.1977	0.117018
11	-0.251352	-2.4369	0.008347
12	-0.292682	-2.8377	0.002784
13	0.262898	2.5489	0.006213
14	-0.142153	-1.3782	0.085703
15	-0.005899	-0.0572	0.477256
16	-0.045747	-0.4435	0.3292
17	-0.002449	-0.0237	0.490554
18	-0.001358	-0.0132	0.494761
19	-0.000223	-0.0022	0.499139
20	-0.019587	-0.1899	0.424897

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.376082 & 3.6463 & 0.000218 \tabularnewline
2 & -0.056612 & -0.5489 & 0.292197 \tabularnewline
3 & -0.10986 & -1.0651 & 0.144772 \tabularnewline
4 & -0.051455 & -0.4989 & 0.309515 \tabularnewline
5 & 0.070912 & 0.6875 & 0.246725 \tabularnewline
6 & -0.124808 & -1.2101 & 0.114646 \tabularnewline
7 & -0.075339 & -0.7304 & 0.233469 \tabularnewline
8 & 0.056121 & 0.5441 & 0.293827 \tabularnewline
9 & -0.068281 & -0.662 & 0.254794 \tabularnewline
10 & -0.123536 & -1.1977 & 0.117018 \tabularnewline
11 & -0.251352 & -2.4369 & 0.008347 \tabularnewline
12 & -0.292682 & -2.8377 & 0.002784 \tabularnewline
13 & 0.262898 & 2.5489 & 0.006213 \tabularnewline
14 & -0.142153 & -1.3782 & 0.085703 \tabularnewline
15 & -0.005899 & -0.0572 & 0.477256 \tabularnewline
16 & -0.045747 & -0.4435 & 0.3292 \tabularnewline
17 & -0.002449 & -0.0237 & 0.490554 \tabularnewline
18 & -0.001358 & -0.0132 & 0.494761 \tabularnewline
19 & -0.000223 & -0.0022 & 0.499139 \tabularnewline
20 & -0.019587 & -0.1899 & 0.424897 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160651&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]0.376082[/C][C]3.6463[/C][C]0.000218[/C][/ROW]
[ROW][C]2[/C][C]-0.056612[/C][C]-0.5489[/C][C]0.292197[/C][/ROW]
[ROW][C]3[/C][C]-0.10986[/C][C]-1.0651[/C][C]0.144772[/C][/ROW]
[ROW][C]4[/C][C]-0.051455[/C][C]-0.4989[/C][C]0.309515[/C][/ROW]
[ROW][C]5[/C][C]0.070912[/C][C]0.6875[/C][C]0.246725[/C][/ROW]
[ROW][C]6[/C][C]-0.124808[/C][C]-1.2101[/C][C]0.114646[/C][/ROW]
[ROW][C]7[/C][C]-0.075339[/C][C]-0.7304[/C][C]0.233469[/C][/ROW]
[ROW][C]8[/C][C]0.056121[/C][C]0.5441[/C][C]0.293827[/C][/ROW]
[ROW][C]9[/C][C]-0.068281[/C][C]-0.662[/C][C]0.254794[/C][/ROW]
[ROW][C]10[/C][C]-0.123536[/C][C]-1.1977[/C][C]0.117018[/C][/ROW]
[ROW][C]11[/C][C]-0.251352[/C][C]-2.4369[/C][C]0.008347[/C][/ROW]
[ROW][C]12[/C][C]-0.292682[/C][C]-2.8377[/C][C]0.002784[/C][/ROW]
[ROW][C]13[/C][C]0.262898[/C][C]2.5489[/C][C]0.006213[/C][/ROW]
[ROW][C]14[/C][C]-0.142153[/C][C]-1.3782[/C][C]0.085703[/C][/ROW]
[ROW][C]15[/C][C]-0.005899[/C][C]-0.0572[/C][C]0.477256[/C][/ROW]
[ROW][C]16[/C][C]-0.045747[/C][C]-0.4435[/C][C]0.3292[/C][/ROW]
[ROW][C]17[/C][C]-0.002449[/C][C]-0.0237[/C][C]0.490554[/C][/ROW]
[ROW][C]18[/C][C]-0.001358[/C][C]-0.0132[/C][C]0.494761[/C][/ROW]
[ROW][C]19[/C][C]-0.000223[/C][C]-0.0022[/C][C]0.499139[/C][/ROW]
[ROW][C]20[/C][C]-0.019587[/C][C]-0.1899[/C][C]0.424897[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160651&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160651&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	0.376082	3.6463	0.000218
2	-0.056612	-0.5489	0.292197
3	-0.10986	-1.0651	0.144772
4	-0.051455	-0.4989	0.309515
5	0.070912	0.6875	0.246725
6	-0.124808	-1.2101	0.114646
7	-0.075339	-0.7304	0.233469
8	0.056121	0.5441	0.293827
9	-0.068281	-0.662	0.254794
10	-0.123536	-1.1977	0.117018
11	-0.251352	-2.4369	0.008347
12	-0.292682	-2.8377	0.002784
13	0.262898	2.5489	0.006213
14	-0.142153	-1.3782	0.085703
15	-0.005899	-0.0572	0.477256
16	-0.045747	-0.4435	0.3292
17	-0.002449	-0.0237	0.490554
18	-0.001358	-0.0132	0.494761
19	-0.000223	-0.0022	0.499139
20	-0.019587	-0.1899	0.424897

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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