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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 16 Nov 2011 16:15:07 -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/Nov/16/t1321478143tebotljqjx33o2w.htm/, Retrieved Thu, 25 Apr 2024 06:53:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=144222, Retrieved Thu, 25 Apr 2024 06:53:10 +0000

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User-defined keywords

KDGP2W12

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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] [] [2011-11-16 21:15:07] [25bd055699d3ffa05f522cc79bb2ff75] [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	'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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=144222&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=144222&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=144222&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' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.876135	8.0299	0
2	0.684311	6.2718	0
3	0.556976	5.1048	1e-06
4	0.51798	4.7474	4e-06
5	0.539328	4.943	2e-06
6	0.535635	4.9092	2e-06
7	0.47219	4.3277	2.1e-05
8	0.381879	3.5	0.000374
9	0.34179	3.1326	0.001193
10	0.37537	3.4403	0.000454
11	0.467806	4.2875	2.4e-05
12	0.498172	4.5658	8e-06
13	0.337243	3.0909	0.001354
14	0.135902	1.2456	0.108194
15	0.001488	0.0136	0.494574
16	-0.049241	-0.4513	0.326467
17	-0.048758	-0.4469	0.328058
18	-0.071441	-0.6548	0.257203
19	-0.140621	-1.2888	0.100501

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.876135 & 8.0299 & 0 \tabularnewline
2 & 0.684311 & 6.2718 & 0 \tabularnewline
3 & 0.556976 & 5.1048 & 1e-06 \tabularnewline
4 & 0.51798 & 4.7474 & 4e-06 \tabularnewline
5 & 0.539328 & 4.943 & 2e-06 \tabularnewline
6 & 0.535635 & 4.9092 & 2e-06 \tabularnewline
7 & 0.47219 & 4.3277 & 2.1e-05 \tabularnewline
8 & 0.381879 & 3.5 & 0.000374 \tabularnewline
9 & 0.34179 & 3.1326 & 0.001193 \tabularnewline
10 & 0.37537 & 3.4403 & 0.000454 \tabularnewline
11 & 0.467806 & 4.2875 & 2.4e-05 \tabularnewline
12 & 0.498172 & 4.5658 & 8e-06 \tabularnewline
13 & 0.337243 & 3.0909 & 0.001354 \tabularnewline
14 & 0.135902 & 1.2456 & 0.108194 \tabularnewline
15 & 0.001488 & 0.0136 & 0.494574 \tabularnewline
16 & -0.049241 & -0.4513 & 0.326467 \tabularnewline
17 & -0.048758 & -0.4469 & 0.328058 \tabularnewline
18 & -0.071441 & -0.6548 & 0.257203 \tabularnewline
19 & -0.140621 & -1.2888 & 0.100501 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=144222&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]0.876135[/C][C]8.0299[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.684311[/C][C]6.2718[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.556976[/C][C]5.1048[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]0.51798[/C][C]4.7474[/C][C]4e-06[/C][/ROW]
[ROW][C]5[/C][C]0.539328[/C][C]4.943[/C][C]2e-06[/C][/ROW]
[ROW][C]6[/C][C]0.535635[/C][C]4.9092[/C][C]2e-06[/C][/ROW]
[ROW][C]7[/C][C]0.47219[/C][C]4.3277[/C][C]2.1e-05[/C][/ROW]
[ROW][C]8[/C][C]0.381879[/C][C]3.5[/C][C]0.000374[/C][/ROW]
[ROW][C]9[/C][C]0.34179[/C][C]3.1326[/C][C]0.001193[/C][/ROW]
[ROW][C]10[/C][C]0.37537[/C][C]3.4403[/C][C]0.000454[/C][/ROW]
[ROW][C]11[/C][C]0.467806[/C][C]4.2875[/C][C]2.4e-05[/C][/ROW]
[ROW][C]12[/C][C]0.498172[/C][C]4.5658[/C][C]8e-06[/C][/ROW]
[ROW][C]13[/C][C]0.337243[/C][C]3.0909[/C][C]0.001354[/C][/ROW]
[ROW][C]14[/C][C]0.135902[/C][C]1.2456[/C][C]0.108194[/C][/ROW]
[ROW][C]15[/C][C]0.001488[/C][C]0.0136[/C][C]0.494574[/C][/ROW]
[ROW][C]16[/C][C]-0.049241[/C][C]-0.4513[/C][C]0.326467[/C][/ROW]
[ROW][C]17[/C][C]-0.048758[/C][C]-0.4469[/C][C]0.328058[/C][/ROW]
[ROW][C]18[/C][C]-0.071441[/C][C]-0.6548[/C][C]0.257203[/C][/ROW]
[ROW][C]19[/C][C]-0.140621[/C][C]-1.2888[/C][C]0.100501[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=144222&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=144222&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	0.876135	8.0299	0
2	0.684311	6.2718	0
3	0.556976	5.1048	1e-06
4	0.51798	4.7474	4e-06
5	0.539328	4.943	2e-06
6	0.535635	4.9092	2e-06
7	0.47219	4.3277	2.1e-05
8	0.381879	3.5	0.000374
9	0.34179	3.1326	0.001193
10	0.37537	3.4403	0.000454
11	0.467806	4.2875	2.4e-05
12	0.498172	4.5658	8e-06
13	0.337243	3.0909	0.001354
14	0.135902	1.2456	0.108194
15	0.001488	0.0136	0.494574
16	-0.049241	-0.4513	0.326467
17	-0.048758	-0.4469	0.328058
18	-0.071441	-0.6548	0.257203
19	-0.140621	-1.2888	0.100501

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.876135	8.0299	0
2	-0.358454	-3.2853	0.000744
3	0.279321	2.56	0.006128
4	0.146599	1.3436	0.091348
5	0.166622	1.5271	0.065244
6	-0.11599	-1.0631	0.145399
7	-0.054266	-0.4974	0.310119
8	-0.0225	-0.2062	0.41856
9	0.185364	1.6989	0.046521
10	0.108392	0.9934	0.161677
11	0.251501	2.305	0.011815
12	-0.272157	-2.4944	0.007289
13	-0.66319	-6.0782	0
14	0.195235	1.7894	0.03858
15	-0.109531	-1.0039	0.159163
16	-0.137296	-1.2583	0.105878
17	-0.113223	-1.0377	0.151192
18	-0.00665	-0.061	0.475772
19	0.031355	0.2874	0.387268

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.876135 & 8.0299 & 0 \tabularnewline
2 & -0.358454 & -3.2853 & 0.000744 \tabularnewline
3 & 0.279321 & 2.56 & 0.006128 \tabularnewline
4 & 0.146599 & 1.3436 & 0.091348 \tabularnewline
5 & 0.166622 & 1.5271 & 0.065244 \tabularnewline
6 & -0.11599 & -1.0631 & 0.145399 \tabularnewline
7 & -0.054266 & -0.4974 & 0.310119 \tabularnewline
8 & -0.0225 & -0.2062 & 0.41856 \tabularnewline
9 & 0.185364 & 1.6989 & 0.046521 \tabularnewline
10 & 0.108392 & 0.9934 & 0.161677 \tabularnewline
11 & 0.251501 & 2.305 & 0.011815 \tabularnewline
12 & -0.272157 & -2.4944 & 0.007289 \tabularnewline
13 & -0.66319 & -6.0782 & 0 \tabularnewline
14 & 0.195235 & 1.7894 & 0.03858 \tabularnewline
15 & -0.109531 & -1.0039 & 0.159163 \tabularnewline
16 & -0.137296 & -1.2583 & 0.105878 \tabularnewline
17 & -0.113223 & -1.0377 & 0.151192 \tabularnewline
18 & -0.00665 & -0.061 & 0.475772 \tabularnewline
19 & 0.031355 & 0.2874 & 0.387268 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=144222&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]0.876135[/C][C]8.0299[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.358454[/C][C]-3.2853[/C][C]0.000744[/C][/ROW]
[ROW][C]3[/C][C]0.279321[/C][C]2.56[/C][C]0.006128[/C][/ROW]
[ROW][C]4[/C][C]0.146599[/C][C]1.3436[/C][C]0.091348[/C][/ROW]
[ROW][C]5[/C][C]0.166622[/C][C]1.5271[/C][C]0.065244[/C][/ROW]
[ROW][C]6[/C][C]-0.11599[/C][C]-1.0631[/C][C]0.145399[/C][/ROW]
[ROW][C]7[/C][C]-0.054266[/C][C]-0.4974[/C][C]0.310119[/C][/ROW]
[ROW][C]8[/C][C]-0.0225[/C][C]-0.2062[/C][C]0.41856[/C][/ROW]
[ROW][C]9[/C][C]0.185364[/C][C]1.6989[/C][C]0.046521[/C][/ROW]
[ROW][C]10[/C][C]0.108392[/C][C]0.9934[/C][C]0.161677[/C][/ROW]
[ROW][C]11[/C][C]0.251501[/C][C]2.305[/C][C]0.011815[/C][/ROW]
[ROW][C]12[/C][C]-0.272157[/C][C]-2.4944[/C][C]0.007289[/C][/ROW]
[ROW][C]13[/C][C]-0.66319[/C][C]-6.0782[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.195235[/C][C]1.7894[/C][C]0.03858[/C][/ROW]
[ROW][C]15[/C][C]-0.109531[/C][C]-1.0039[/C][C]0.159163[/C][/ROW]
[ROW][C]16[/C][C]-0.137296[/C][C]-1.2583[/C][C]0.105878[/C][/ROW]
[ROW][C]17[/C][C]-0.113223[/C][C]-1.0377[/C][C]0.151192[/C][/ROW]
[ROW][C]18[/C][C]-0.00665[/C][C]-0.061[/C][C]0.475772[/C][/ROW]
[ROW][C]19[/C][C]0.031355[/C][C]0.2874[/C][C]0.387268[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=144222&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=144222&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	0.876135	8.0299	0
2	-0.358454	-3.2853	0.000744
3	0.279321	2.56	0.006128
4	0.146599	1.3436	0.091348
5	0.166622	1.5271	0.065244
6	-0.11599	-1.0631	0.145399
7	-0.054266	-0.4974	0.310119
8	-0.0225	-0.2062	0.41856
9	0.185364	1.6989	0.046521
10	0.108392	0.9934	0.161677
11	0.251501	2.305	0.011815
12	-0.272157	-2.4944	0.007289
13	-0.66319	-6.0782	0
14	0.195235	1.7894	0.03858
15	-0.109531	-1.0039	0.159163
16	-0.137296	-1.2583	0.105878
17	-0.113223	-1.0377	0.151192
18	-0.00665	-0.061	0.475772
19	0.031355	0.2874	0.387268

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code