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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 14 Dec 2014 09:50:33 +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/2014/Dec/14/t1418550644gp7t3onjwzvicor.htm/, Retrieved Thu, 16 May 2024 19:11:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267369, Retrieved Thu, 16 May 2024 19:11:34 +0000

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No (this computation is public)

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Estimated Impact

117

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

-       [(Partial) Autocorrelation Function] [] [2014-12-14 09:50:33] [c7f962214140f976f2c4b1bb2571d9df] [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	'George Udny Yule' @ yule.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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267369&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267369&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267369&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	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.372742	3.1628	0.001144
2	0.073043	0.6198	0.268677
3	-0.086427	-0.7334	0.232862
4	-0.143798	-1.2202	0.113191
5	-0.216292	-1.8353	0.035296
6	-0.083677	-0.71	0.23999
7	0.051996	0.4412	0.330196
8	-0.013857	-0.1176	0.453364
9	0.033735	0.2862	0.387755
10	-0.163275	-1.3854	0.085098
11	-0.378024	-3.2076	0.000999
12	-0.487604	-4.1375	4.7e-05
13	-0.048894	-0.4149	0.339733
14	0.221202	1.877	0.032288
15	0.254503	2.1595	0.01707
16	0.313416	2.6594	0.004821
17	0.283218	2.4032	0.009415
18	0.111656	0.9474	0.173293
19	-0.020939	-0.1777	0.429738

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.372742 & 3.1628 & 0.001144 \tabularnewline
2 & 0.073043 & 0.6198 & 0.268677 \tabularnewline
3 & -0.086427 & -0.7334 & 0.232862 \tabularnewline
4 & -0.143798 & -1.2202 & 0.113191 \tabularnewline
5 & -0.216292 & -1.8353 & 0.035296 \tabularnewline
6 & -0.083677 & -0.71 & 0.23999 \tabularnewline
7 & 0.051996 & 0.4412 & 0.330196 \tabularnewline
8 & -0.013857 & -0.1176 & 0.453364 \tabularnewline
9 & 0.033735 & 0.2862 & 0.387755 \tabularnewline
10 & -0.163275 & -1.3854 & 0.085098 \tabularnewline
11 & -0.378024 & -3.2076 & 0.000999 \tabularnewline
12 & -0.487604 & -4.1375 & 4.7e-05 \tabularnewline
13 & -0.048894 & -0.4149 & 0.339733 \tabularnewline
14 & 0.221202 & 1.877 & 0.032288 \tabularnewline
15 & 0.254503 & 2.1595 & 0.01707 \tabularnewline
16 & 0.313416 & 2.6594 & 0.004821 \tabularnewline
17 & 0.283218 & 2.4032 & 0.009415 \tabularnewline
18 & 0.111656 & 0.9474 & 0.173293 \tabularnewline
19 & -0.020939 & -0.1777 & 0.429738 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267369&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]0.372742[/C][C]3.1628[/C][C]0.001144[/C][/ROW]
[ROW][C]2[/C][C]0.073043[/C][C]0.6198[/C][C]0.268677[/C][/ROW]
[ROW][C]3[/C][C]-0.086427[/C][C]-0.7334[/C][C]0.232862[/C][/ROW]
[ROW][C]4[/C][C]-0.143798[/C][C]-1.2202[/C][C]0.113191[/C][/ROW]
[ROW][C]5[/C][C]-0.216292[/C][C]-1.8353[/C][C]0.035296[/C][/ROW]
[ROW][C]6[/C][C]-0.083677[/C][C]-0.71[/C][C]0.23999[/C][/ROW]
[ROW][C]7[/C][C]0.051996[/C][C]0.4412[/C][C]0.330196[/C][/ROW]
[ROW][C]8[/C][C]-0.013857[/C][C]-0.1176[/C][C]0.453364[/C][/ROW]
[ROW][C]9[/C][C]0.033735[/C][C]0.2862[/C][C]0.387755[/C][/ROW]
[ROW][C]10[/C][C]-0.163275[/C][C]-1.3854[/C][C]0.085098[/C][/ROW]
[ROW][C]11[/C][C]-0.378024[/C][C]-3.2076[/C][C]0.000999[/C][/ROW]
[ROW][C]12[/C][C]-0.487604[/C][C]-4.1375[/C][C]4.7e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.048894[/C][C]-0.4149[/C][C]0.339733[/C][/ROW]
[ROW][C]14[/C][C]0.221202[/C][C]1.877[/C][C]0.032288[/C][/ROW]
[ROW][C]15[/C][C]0.254503[/C][C]2.1595[/C][C]0.01707[/C][/ROW]
[ROW][C]16[/C][C]0.313416[/C][C]2.6594[/C][C]0.004821[/C][/ROW]
[ROW][C]17[/C][C]0.283218[/C][C]2.4032[/C][C]0.009415[/C][/ROW]
[ROW][C]18[/C][C]0.111656[/C][C]0.9474[/C][C]0.173293[/C][/ROW]
[ROW][C]19[/C][C]-0.020939[/C][C]-0.1777[/C][C]0.429738[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267369&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267369&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	0.372742	3.1628	0.001144
2	0.073043	0.6198	0.268677
3	-0.086427	-0.7334	0.232862
4	-0.143798	-1.2202	0.113191
5	-0.216292	-1.8353	0.035296
6	-0.083677	-0.71	0.23999
7	0.051996	0.4412	0.330196
8	-0.013857	-0.1176	0.453364
9	0.033735	0.2862	0.387755
10	-0.163275	-1.3854	0.085098
11	-0.378024	-3.2076	0.000999
12	-0.487604	-4.1375	4.7e-05
13	-0.048894	-0.4149	0.339733
14	0.221202	1.877	0.032288
15	0.254503	2.1595	0.01707
16	0.313416	2.6594	0.004821
17	0.283218	2.4032	0.009415
18	0.111656	0.9474	0.173293
19	-0.020939	-0.1777	0.429738

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.372742	3.1628	0.001144
2	-0.076526	-0.6493	0.25909
3	-0.101881	-0.8645	0.195096
4	-0.081703	-0.6933	0.245185
5	-0.152937	-1.2977	0.099264
6	0.051084	0.4335	0.332987
7	0.066961	0.5682	0.28584
8	-0.116901	-0.9919	0.162276
9	0.051424	0.4363	0.331946
10	-0.257554	-2.1854	0.016056
11	-0.318421	-2.7019	0.004296
12	-0.333171	-2.827	0.003039
13	0.216376	1.836	0.035242
14	0.225374	1.9124	0.029904
15	0.021677	0.1839	0.42729
16	0.07063	0.5993	0.275421
17	0.074532	0.6324	0.264557
18	0.029953	0.2542	0.400048
19	0.07856	0.6666	0.253578

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.372742 & 3.1628 & 0.001144 \tabularnewline
2 & -0.076526 & -0.6493 & 0.25909 \tabularnewline
3 & -0.101881 & -0.8645 & 0.195096 \tabularnewline
4 & -0.081703 & -0.6933 & 0.245185 \tabularnewline
5 & -0.152937 & -1.2977 & 0.099264 \tabularnewline
6 & 0.051084 & 0.4335 & 0.332987 \tabularnewline
7 & 0.066961 & 0.5682 & 0.28584 \tabularnewline
8 & -0.116901 & -0.9919 & 0.162276 \tabularnewline
9 & 0.051424 & 0.4363 & 0.331946 \tabularnewline
10 & -0.257554 & -2.1854 & 0.016056 \tabularnewline
11 & -0.318421 & -2.7019 & 0.004296 \tabularnewline
12 & -0.333171 & -2.827 & 0.003039 \tabularnewline
13 & 0.216376 & 1.836 & 0.035242 \tabularnewline
14 & 0.225374 & 1.9124 & 0.029904 \tabularnewline
15 & 0.021677 & 0.1839 & 0.42729 \tabularnewline
16 & 0.07063 & 0.5993 & 0.275421 \tabularnewline
17 & 0.074532 & 0.6324 & 0.264557 \tabularnewline
18 & 0.029953 & 0.2542 & 0.400048 \tabularnewline
19 & 0.07856 & 0.6666 & 0.253578 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267369&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]0.372742[/C][C]3.1628[/C][C]0.001144[/C][/ROW]
[ROW][C]2[/C][C]-0.076526[/C][C]-0.6493[/C][C]0.25909[/C][/ROW]
[ROW][C]3[/C][C]-0.101881[/C][C]-0.8645[/C][C]0.195096[/C][/ROW]
[ROW][C]4[/C][C]-0.081703[/C][C]-0.6933[/C][C]0.245185[/C][/ROW]
[ROW][C]5[/C][C]-0.152937[/C][C]-1.2977[/C][C]0.099264[/C][/ROW]
[ROW][C]6[/C][C]0.051084[/C][C]0.4335[/C][C]0.332987[/C][/ROW]
[ROW][C]7[/C][C]0.066961[/C][C]0.5682[/C][C]0.28584[/C][/ROW]
[ROW][C]8[/C][C]-0.116901[/C][C]-0.9919[/C][C]0.162276[/C][/ROW]
[ROW][C]9[/C][C]0.051424[/C][C]0.4363[/C][C]0.331946[/C][/ROW]
[ROW][C]10[/C][C]-0.257554[/C][C]-2.1854[/C][C]0.016056[/C][/ROW]
[ROW][C]11[/C][C]-0.318421[/C][C]-2.7019[/C][C]0.004296[/C][/ROW]
[ROW][C]12[/C][C]-0.333171[/C][C]-2.827[/C][C]0.003039[/C][/ROW]
[ROW][C]13[/C][C]0.216376[/C][C]1.836[/C][C]0.035242[/C][/ROW]
[ROW][C]14[/C][C]0.225374[/C][C]1.9124[/C][C]0.029904[/C][/ROW]
[ROW][C]15[/C][C]0.021677[/C][C]0.1839[/C][C]0.42729[/C][/ROW]
[ROW][C]16[/C][C]0.07063[/C][C]0.5993[/C][C]0.275421[/C][/ROW]
[ROW][C]17[/C][C]0.074532[/C][C]0.6324[/C][C]0.264557[/C][/ROW]
[ROW][C]18[/C][C]0.029953[/C][C]0.2542[/C][C]0.400048[/C][/ROW]
[ROW][C]19[/C][C]0.07856[/C][C]0.6666[/C][C]0.253578[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267369&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267369&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	0.372742	3.1628	0.001144
2	-0.076526	-0.6493	0.25909
3	-0.101881	-0.8645	0.195096
4	-0.081703	-0.6933	0.245185
5	-0.152937	-1.2977	0.099264
6	0.051084	0.4335	0.332987
7	0.066961	0.5682	0.28584
8	-0.116901	-0.9919	0.162276
9	0.051424	0.4363	0.331946
10	-0.257554	-2.1854	0.016056
11	-0.318421	-2.7019	0.004296
12	-0.333171	-2.827	0.003039
13	0.216376	1.836	0.035242
14	0.225374	1.9124	0.029904
15	0.021677	0.1839	0.42729
16	0.07063	0.5993	0.275421
17	0.074532	0.6324	0.264557
18	0.029953	0.2542	0.400048
19	0.07856	0.6666	0.253578

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