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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 03 Apr 2012 16:54:49 -0400

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Apr/03/t1333486585oywou8qmuz72elt.htm/, Retrieved Fri, 03 May 2024 03:37:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=164272, Retrieved Fri, 03 May 2024 03:37:36 +0000

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Estimated Impact

184

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

-       [(Partial) Autocorrelation Function] [Time Series Analy...] [2012-04-03 20:54:49] [1f07dfe249cf12c76d4857e2b59f088a] [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	'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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164272&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164272&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164272&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.936077	7.2508	0
2	0.883514	6.8437	0
3	0.833417	6.4556	0
4	0.782442	6.0608	0
5	0.729414	5.65	0
6	0.677878	5.2508	1e-06
7	0.615718	4.7693	6e-06
8	0.5567	4.3122	3.1e-05
9	0.504689	3.9093	0.000119
10	0.456545	3.5364	0.000395
11	0.398278	3.085	0.001538
12	0.342045	2.6495	0.005145
13	0.292239	2.2637	0.013612
14	0.243072	1.8828	0.032287
15	0.202202	1.5662	0.061275
16	0.157646	1.2211	0.113409
17	0.098929	0.7663	0.223251

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.936077 & 7.2508 & 0 \tabularnewline
2 & 0.883514 & 6.8437 & 0 \tabularnewline
3 & 0.833417 & 6.4556 & 0 \tabularnewline
4 & 0.782442 & 6.0608 & 0 \tabularnewline
5 & 0.729414 & 5.65 & 0 \tabularnewline
6 & 0.677878 & 5.2508 & 1e-06 \tabularnewline
7 & 0.615718 & 4.7693 & 6e-06 \tabularnewline
8 & 0.5567 & 4.3122 & 3.1e-05 \tabularnewline
9 & 0.504689 & 3.9093 & 0.000119 \tabularnewline
10 & 0.456545 & 3.5364 & 0.000395 \tabularnewline
11 & 0.398278 & 3.085 & 0.001538 \tabularnewline
12 & 0.342045 & 2.6495 & 0.005145 \tabularnewline
13 & 0.292239 & 2.2637 & 0.013612 \tabularnewline
14 & 0.243072 & 1.8828 & 0.032287 \tabularnewline
15 & 0.202202 & 1.5662 & 0.061275 \tabularnewline
16 & 0.157646 & 1.2211 & 0.113409 \tabularnewline
17 & 0.098929 & 0.7663 & 0.223251 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164272&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]0.936077[/C][C]7.2508[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.883514[/C][C]6.8437[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.833417[/C][C]6.4556[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.782442[/C][C]6.0608[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.729414[/C][C]5.65[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.677878[/C][C]5.2508[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.615718[/C][C]4.7693[/C][C]6e-06[/C][/ROW]
[ROW][C]8[/C][C]0.5567[/C][C]4.3122[/C][C]3.1e-05[/C][/ROW]
[ROW][C]9[/C][C]0.504689[/C][C]3.9093[/C][C]0.000119[/C][/ROW]
[ROW][C]10[/C][C]0.456545[/C][C]3.5364[/C][C]0.000395[/C][/ROW]
[ROW][C]11[/C][C]0.398278[/C][C]3.085[/C][C]0.001538[/C][/ROW]
[ROW][C]12[/C][C]0.342045[/C][C]2.6495[/C][C]0.005145[/C][/ROW]
[ROW][C]13[/C][C]0.292239[/C][C]2.2637[/C][C]0.013612[/C][/ROW]
[ROW][C]14[/C][C]0.243072[/C][C]1.8828[/C][C]0.032287[/C][/ROW]
[ROW][C]15[/C][C]0.202202[/C][C]1.5662[/C][C]0.061275[/C][/ROW]
[ROW][C]16[/C][C]0.157646[/C][C]1.2211[/C][C]0.113409[/C][/ROW]
[ROW][C]17[/C][C]0.098929[/C][C]0.7663[/C][C]0.223251[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164272&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164272&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	0.936077	7.2508	0
2	0.883514	6.8437	0
3	0.833417	6.4556	0
4	0.782442	6.0608	0
5	0.729414	5.65	0
6	0.677878	5.2508	1e-06
7	0.615718	4.7693	6e-06
8	0.5567	4.3122	3.1e-05
9	0.504689	3.9093	0.000119
10	0.456545	3.5364	0.000395
11	0.398278	3.085	0.001538
12	0.342045	2.6495	0.005145
13	0.292239	2.2637	0.013612
14	0.243072	1.8828	0.032287
15	0.202202	1.5662	0.061275
16	0.157646	1.2211	0.113409
17	0.098929	0.7663	0.223251

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.936077	7.2508	0
2	0.058773	0.4553	0.325286
3	-0.000233	-0.0018	0.499282
4	-0.030411	-0.2356	0.407286
5	-0.045603	-0.3532	0.362575
6	-0.021636	-0.1676	0.433733
7	-0.116134	-0.8996	0.185973
8	-0.027004	-0.2092	0.417512
9	0.01883	0.1459	0.442262
10	0.008239	0.0638	0.474664
11	-0.105191	-0.8148	0.209202
12	-0.038744	-0.3001	0.382567
13	0.015226	0.1179	0.453254
14	-0.026152	-0.2026	0.420076
15	0.026312	0.2038	0.419596
16	-0.059946	-0.4643	0.322042
17	-0.145031	-1.1234	0.13287

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.936077 & 7.2508 & 0 \tabularnewline
2 & 0.058773 & 0.4553 & 0.325286 \tabularnewline
3 & -0.000233 & -0.0018 & 0.499282 \tabularnewline
4 & -0.030411 & -0.2356 & 0.407286 \tabularnewline
5 & -0.045603 & -0.3532 & 0.362575 \tabularnewline
6 & -0.021636 & -0.1676 & 0.433733 \tabularnewline
7 & -0.116134 & -0.8996 & 0.185973 \tabularnewline
8 & -0.027004 & -0.2092 & 0.417512 \tabularnewline
9 & 0.01883 & 0.1459 & 0.442262 \tabularnewline
10 & 0.008239 & 0.0638 & 0.474664 \tabularnewline
11 & -0.105191 & -0.8148 & 0.209202 \tabularnewline
12 & -0.038744 & -0.3001 & 0.382567 \tabularnewline
13 & 0.015226 & 0.1179 & 0.453254 \tabularnewline
14 & -0.026152 & -0.2026 & 0.420076 \tabularnewline
15 & 0.026312 & 0.2038 & 0.419596 \tabularnewline
16 & -0.059946 & -0.4643 & 0.322042 \tabularnewline
17 & -0.145031 & -1.1234 & 0.13287 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164272&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]0.936077[/C][C]7.2508[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.058773[/C][C]0.4553[/C][C]0.325286[/C][/ROW]
[ROW][C]3[/C][C]-0.000233[/C][C]-0.0018[/C][C]0.499282[/C][/ROW]
[ROW][C]4[/C][C]-0.030411[/C][C]-0.2356[/C][C]0.407286[/C][/ROW]
[ROW][C]5[/C][C]-0.045603[/C][C]-0.3532[/C][C]0.362575[/C][/ROW]
[ROW][C]6[/C][C]-0.021636[/C][C]-0.1676[/C][C]0.433733[/C][/ROW]
[ROW][C]7[/C][C]-0.116134[/C][C]-0.8996[/C][C]0.185973[/C][/ROW]
[ROW][C]8[/C][C]-0.027004[/C][C]-0.2092[/C][C]0.417512[/C][/ROW]
[ROW][C]9[/C][C]0.01883[/C][C]0.1459[/C][C]0.442262[/C][/ROW]
[ROW][C]10[/C][C]0.008239[/C][C]0.0638[/C][C]0.474664[/C][/ROW]
[ROW][C]11[/C][C]-0.105191[/C][C]-0.8148[/C][C]0.209202[/C][/ROW]
[ROW][C]12[/C][C]-0.038744[/C][C]-0.3001[/C][C]0.382567[/C][/ROW]
[ROW][C]13[/C][C]0.015226[/C][C]0.1179[/C][C]0.453254[/C][/ROW]
[ROW][C]14[/C][C]-0.026152[/C][C]-0.2026[/C][C]0.420076[/C][/ROW]
[ROW][C]15[/C][C]0.026312[/C][C]0.2038[/C][C]0.419596[/C][/ROW]
[ROW][C]16[/C][C]-0.059946[/C][C]-0.4643[/C][C]0.322042[/C][/ROW]
[ROW][C]17[/C][C]-0.145031[/C][C]-1.1234[/C][C]0.13287[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164272&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164272&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	0.936077	7.2508	0
2	0.058773	0.4553	0.325286
3	-0.000233	-0.0018	0.499282
4	-0.030411	-0.2356	0.407286
5	-0.045603	-0.3532	0.362575
6	-0.021636	-0.1676	0.433733
7	-0.116134	-0.8996	0.185973
8	-0.027004	-0.2092	0.417512
9	0.01883	0.1459	0.442262
10	0.008239	0.0638	0.474664
11	-0.105191	-0.8148	0.209202
12	-0.038744	-0.3001	0.382567
13	0.015226	0.1179	0.453254
14	-0.026152	-0.2026	0.420076
15	0.026312	0.2038	0.419596
16	-0.059946	-0.4643	0.322042
17	-0.145031	-1.1234	0.13287

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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Input Parameters & R Code