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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 13 Mar 2016 11:00:13 +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/2016/Mar/13/t14578668318aovx46j57a0rbg.htm/, Retrieved Wed, 08 May 2024 18:14:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293992, Retrieved Wed, 08 May 2024 18:14:39 +0000

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Estimated Impact

159

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-       [(Partial) Autocorrelation Function] [] [2016-03-13 11:00:13] [3cc5eb308fa11ebf92933824162ee6d9] [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	2 seconds
R Server	'Sir Maurice George Kendall' @ kendall.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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293992&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293992&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293992&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.797198	6.5739	0
2	0.536928	4.4276	1.8e-05
3	0.283066	2.3342	0.011273
4	0.123656	1.0197	0.155744
5	0.045562	0.3757	0.354149
6	0.004247	0.035	0.486083
7	-0.027998	-0.2309	0.40905
8	-0.045839	-0.378	0.353306
9	0.018368	0.1515	0.44003
10	0.062694	0.517	0.303422
11	0.059878	0.4938	0.311531
12	-0.047331	-0.3903	0.348767
13	-0.195352	-1.6109	0.055916
14	-0.261594	-2.1572	0.017265
15	-0.24249	-1.9996	0.024769
16	-0.18314	-1.5102	0.067811
17	-0.064943	-0.5355	0.297015
18	0.028254	0.233	0.408235

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.797198 & 6.5739 & 0 \tabularnewline
2 & 0.536928 & 4.4276 & 1.8e-05 \tabularnewline
3 & 0.283066 & 2.3342 & 0.011273 \tabularnewline
4 & 0.123656 & 1.0197 & 0.155744 \tabularnewline
5 & 0.045562 & 0.3757 & 0.354149 \tabularnewline
6 & 0.004247 & 0.035 & 0.486083 \tabularnewline
7 & -0.027998 & -0.2309 & 0.40905 \tabularnewline
8 & -0.045839 & -0.378 & 0.353306 \tabularnewline
9 & 0.018368 & 0.1515 & 0.44003 \tabularnewline
10 & 0.062694 & 0.517 & 0.303422 \tabularnewline
11 & 0.059878 & 0.4938 & 0.311531 \tabularnewline
12 & -0.047331 & -0.3903 & 0.348767 \tabularnewline
13 & -0.195352 & -1.6109 & 0.055916 \tabularnewline
14 & -0.261594 & -2.1572 & 0.017265 \tabularnewline
15 & -0.24249 & -1.9996 & 0.024769 \tabularnewline
16 & -0.18314 & -1.5102 & 0.067811 \tabularnewline
17 & -0.064943 & -0.5355 & 0.297015 \tabularnewline
18 & 0.028254 & 0.233 & 0.408235 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293992&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]0.797198[/C][C]6.5739[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.536928[/C][C]4.4276[/C][C]1.8e-05[/C][/ROW]
[ROW][C]3[/C][C]0.283066[/C][C]2.3342[/C][C]0.011273[/C][/ROW]
[ROW][C]4[/C][C]0.123656[/C][C]1.0197[/C][C]0.155744[/C][/ROW]
[ROW][C]5[/C][C]0.045562[/C][C]0.3757[/C][C]0.354149[/C][/ROW]
[ROW][C]6[/C][C]0.004247[/C][C]0.035[/C][C]0.486083[/C][/ROW]
[ROW][C]7[/C][C]-0.027998[/C][C]-0.2309[/C][C]0.40905[/C][/ROW]
[ROW][C]8[/C][C]-0.045839[/C][C]-0.378[/C][C]0.353306[/C][/ROW]
[ROW][C]9[/C][C]0.018368[/C][C]0.1515[/C][C]0.44003[/C][/ROW]
[ROW][C]10[/C][C]0.062694[/C][C]0.517[/C][C]0.303422[/C][/ROW]
[ROW][C]11[/C][C]0.059878[/C][C]0.4938[/C][C]0.311531[/C][/ROW]
[ROW][C]12[/C][C]-0.047331[/C][C]-0.3903[/C][C]0.348767[/C][/ROW]
[ROW][C]13[/C][C]-0.195352[/C][C]-1.6109[/C][C]0.055916[/C][/ROW]
[ROW][C]14[/C][C]-0.261594[/C][C]-2.1572[/C][C]0.017265[/C][/ROW]
[ROW][C]15[/C][C]-0.24249[/C][C]-1.9996[/C][C]0.024769[/C][/ROW]
[ROW][C]16[/C][C]-0.18314[/C][C]-1.5102[/C][C]0.067811[/C][/ROW]
[ROW][C]17[/C][C]-0.064943[/C][C]-0.5355[/C][C]0.297015[/C][/ROW]
[ROW][C]18[/C][C]0.028254[/C][C]0.233[/C][C]0.408235[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293992&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293992&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	0.797198	6.5739	0
2	0.536928	4.4276	1.8e-05
3	0.283066	2.3342	0.011273
4	0.123656	1.0197	0.155744
5	0.045562	0.3757	0.354149
6	0.004247	0.035	0.486083
7	-0.027998	-0.2309	0.40905
8	-0.045839	-0.378	0.353306
9	0.018368	0.1515	0.44003
10	0.062694	0.517	0.303422
11	0.059878	0.4938	0.311531
12	-0.047331	-0.3903	0.348767
13	-0.195352	-1.6109	0.055916
14	-0.261594	-2.1572	0.017265
15	-0.24249	-1.9996	0.024769
16	-0.18314	-1.5102	0.067811
17	-0.064943	-0.5355	0.297015
18	0.028254	0.233	0.408235

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.797198	6.5739	0
2	-0.270515	-2.2307	0.014501
3	-0.133535	-1.1012	0.137356
4	0.079144	0.6526	0.258096
5	0.026831	0.2213	0.41278
6	-0.051182	-0.4221	0.337157
7	-0.041941	-0.3459	0.36526
8	0.017182	0.1417	0.443874
9	0.214479	1.7686	0.040719
10	-0.098779	-0.8145	0.209087
11	-0.116625	-0.9617	0.169801
12	-0.210595	-1.7366	0.043492
13	-0.102558	-0.8457	0.20034
14	0.144022	1.1876	0.119555
15	0.026686	0.2201	0.413243
16	-0.074171	-0.6116	0.271411
17	0.230117	1.8976	0.030998
18	-0.00847	-0.0698	0.47226

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.797198 & 6.5739 & 0 \tabularnewline
2 & -0.270515 & -2.2307 & 0.014501 \tabularnewline
3 & -0.133535 & -1.1012 & 0.137356 \tabularnewline
4 & 0.079144 & 0.6526 & 0.258096 \tabularnewline
5 & 0.026831 & 0.2213 & 0.41278 \tabularnewline
6 & -0.051182 & -0.4221 & 0.337157 \tabularnewline
7 & -0.041941 & -0.3459 & 0.36526 \tabularnewline
8 & 0.017182 & 0.1417 & 0.443874 \tabularnewline
9 & 0.214479 & 1.7686 & 0.040719 \tabularnewline
10 & -0.098779 & -0.8145 & 0.209087 \tabularnewline
11 & -0.116625 & -0.9617 & 0.169801 \tabularnewline
12 & -0.210595 & -1.7366 & 0.043492 \tabularnewline
13 & -0.102558 & -0.8457 & 0.20034 \tabularnewline
14 & 0.144022 & 1.1876 & 0.119555 \tabularnewline
15 & 0.026686 & 0.2201 & 0.413243 \tabularnewline
16 & -0.074171 & -0.6116 & 0.271411 \tabularnewline
17 & 0.230117 & 1.8976 & 0.030998 \tabularnewline
18 & -0.00847 & -0.0698 & 0.47226 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293992&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]0.797198[/C][C]6.5739[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.270515[/C][C]-2.2307[/C][C]0.014501[/C][/ROW]
[ROW][C]3[/C][C]-0.133535[/C][C]-1.1012[/C][C]0.137356[/C][/ROW]
[ROW][C]4[/C][C]0.079144[/C][C]0.6526[/C][C]0.258096[/C][/ROW]
[ROW][C]5[/C][C]0.026831[/C][C]0.2213[/C][C]0.41278[/C][/ROW]
[ROW][C]6[/C][C]-0.051182[/C][C]-0.4221[/C][C]0.337157[/C][/ROW]
[ROW][C]7[/C][C]-0.041941[/C][C]-0.3459[/C][C]0.36526[/C][/ROW]
[ROW][C]8[/C][C]0.017182[/C][C]0.1417[/C][C]0.443874[/C][/ROW]
[ROW][C]9[/C][C]0.214479[/C][C]1.7686[/C][C]0.040719[/C][/ROW]
[ROW][C]10[/C][C]-0.098779[/C][C]-0.8145[/C][C]0.209087[/C][/ROW]
[ROW][C]11[/C][C]-0.116625[/C][C]-0.9617[/C][C]0.169801[/C][/ROW]
[ROW][C]12[/C][C]-0.210595[/C][C]-1.7366[/C][C]0.043492[/C][/ROW]
[ROW][C]13[/C][C]-0.102558[/C][C]-0.8457[/C][C]0.20034[/C][/ROW]
[ROW][C]14[/C][C]0.144022[/C][C]1.1876[/C][C]0.119555[/C][/ROW]
[ROW][C]15[/C][C]0.026686[/C][C]0.2201[/C][C]0.413243[/C][/ROW]
[ROW][C]16[/C][C]-0.074171[/C][C]-0.6116[/C][C]0.271411[/C][/ROW]
[ROW][C]17[/C][C]0.230117[/C][C]1.8976[/C][C]0.030998[/C][/ROW]
[ROW][C]18[/C][C]-0.00847[/C][C]-0.0698[/C][C]0.47226[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293992&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293992&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	0.797198	6.5739	0
2	-0.270515	-2.2307	0.014501
3	-0.133535	-1.1012	0.137356
4	0.079144	0.6526	0.258096
5	0.026831	0.2213	0.41278
6	-0.051182	-0.4221	0.337157
7	-0.041941	-0.3459	0.36526
8	0.017182	0.1417	0.443874
9	0.214479	1.7686	0.040719
10	-0.098779	-0.8145	0.209087
11	-0.116625	-0.9617	0.169801
12	-0.210595	-1.7366	0.043492
13	-0.102558	-0.8457	0.20034
14	0.144022	1.1876	0.119555
15	0.026686	0.2201	0.413243
16	-0.074171	-0.6116	0.271411
17	0.230117	1.8976	0.030998
18	-0.00847	-0.0698	0.47226

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)
x <- na.omit(x)
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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code