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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 26 Dec 2010 11:25:10 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/26/t1293362582jeyiesbl13fmmvj.htm/, Retrieved Mon, 06 May 2024 20:26:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115527, Retrieved Mon, 06 May 2024 20:26:38 +0000

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127

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

-     [Variance Reduction Matrix] [] [2010-12-15 15:38:06] [234dae34fc2a42f724a2786a39cb083b]
- RMPD  [(Partial) Autocorrelation Function] [] [2010-12-25 14:28:10] [234dae34fc2a42f724a2786a39cb083b]
-   P       [(Partial) Autocorrelation Function] [] [2010-12-26 11:25:10] [cf84dc108eae081aed36d3d050e63ee7] [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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115527&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115527&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115527&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.016658	-0.1154	0.454302
2	0.04549	0.3152	0.377001
3	0.160655	1.113	0.135615
4	0.096789	0.6706	0.252853
5	-0.064955	-0.45	0.327361
6	0.167552	1.1608	0.125725
7	-0.006332	-0.0439	0.482595
8	-0.060671	-0.4203	0.338056
9	0.02596	0.1799	0.429012
10	-0.199874	-1.3848	0.086264
11	0.3259	2.2579	0.014268
12	-0.174711	-1.2104	0.11602
13	-0.17706	-1.2267	0.112958
14	0.04497	0.3116	0.378361
15	0.105395	0.7302	0.234409
16	-0.161643	-1.1199	0.134165
17	0.09191	0.6368	0.26365

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.016658 & -0.1154 & 0.454302 \tabularnewline
2 & 0.04549 & 0.3152 & 0.377001 \tabularnewline
3 & 0.160655 & 1.113 & 0.135615 \tabularnewline
4 & 0.096789 & 0.6706 & 0.252853 \tabularnewline
5 & -0.064955 & -0.45 & 0.327361 \tabularnewline
6 & 0.167552 & 1.1608 & 0.125725 \tabularnewline
7 & -0.006332 & -0.0439 & 0.482595 \tabularnewline
8 & -0.060671 & -0.4203 & 0.338056 \tabularnewline
9 & 0.02596 & 0.1799 & 0.429012 \tabularnewline
10 & -0.199874 & -1.3848 & 0.086264 \tabularnewline
11 & 0.3259 & 2.2579 & 0.014268 \tabularnewline
12 & -0.174711 & -1.2104 & 0.11602 \tabularnewline
13 & -0.17706 & -1.2267 & 0.112958 \tabularnewline
14 & 0.04497 & 0.3116 & 0.378361 \tabularnewline
15 & 0.105395 & 0.7302 & 0.234409 \tabularnewline
16 & -0.161643 & -1.1199 & 0.134165 \tabularnewline
17 & 0.09191 & 0.6368 & 0.26365 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115527&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]-0.016658[/C][C]-0.1154[/C][C]0.454302[/C][/ROW]
[ROW][C]2[/C][C]0.04549[/C][C]0.3152[/C][C]0.377001[/C][/ROW]
[ROW][C]3[/C][C]0.160655[/C][C]1.113[/C][C]0.135615[/C][/ROW]
[ROW][C]4[/C][C]0.096789[/C][C]0.6706[/C][C]0.252853[/C][/ROW]
[ROW][C]5[/C][C]-0.064955[/C][C]-0.45[/C][C]0.327361[/C][/ROW]
[ROW][C]6[/C][C]0.167552[/C][C]1.1608[/C][C]0.125725[/C][/ROW]
[ROW][C]7[/C][C]-0.006332[/C][C]-0.0439[/C][C]0.482595[/C][/ROW]
[ROW][C]8[/C][C]-0.060671[/C][C]-0.4203[/C][C]0.338056[/C][/ROW]
[ROW][C]9[/C][C]0.02596[/C][C]0.1799[/C][C]0.429012[/C][/ROW]
[ROW][C]10[/C][C]-0.199874[/C][C]-1.3848[/C][C]0.086264[/C][/ROW]
[ROW][C]11[/C][C]0.3259[/C][C]2.2579[/C][C]0.014268[/C][/ROW]
[ROW][C]12[/C][C]-0.174711[/C][C]-1.2104[/C][C]0.11602[/C][/ROW]
[ROW][C]13[/C][C]-0.17706[/C][C]-1.2267[/C][C]0.112958[/C][/ROW]
[ROW][C]14[/C][C]0.04497[/C][C]0.3116[/C][C]0.378361[/C][/ROW]
[ROW][C]15[/C][C]0.105395[/C][C]0.7302[/C][C]0.234409[/C][/ROW]
[ROW][C]16[/C][C]-0.161643[/C][C]-1.1199[/C][C]0.134165[/C][/ROW]
[ROW][C]17[/C][C]0.09191[/C][C]0.6368[/C][C]0.26365[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115527&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115527&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	-0.016658	-0.1154	0.454302
2	0.04549	0.3152	0.377001
3	0.160655	1.113	0.135615
4	0.096789	0.6706	0.252853
5	-0.064955	-0.45	0.327361
6	0.167552	1.1608	0.125725
7	-0.006332	-0.0439	0.482595
8	-0.060671	-0.4203	0.338056
9	0.02596	0.1799	0.429012
10	-0.199874	-1.3848	0.086264
11	0.3259	2.2579	0.014268
12	-0.174711	-1.2104	0.11602
13	-0.17706	-1.2267	0.112958
14	0.04497	0.3116	0.378361
15	0.105395	0.7302	0.234409
16	-0.161643	-1.1199	0.134165
17	0.09191	0.6368	0.26365

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.016658	-0.1154	0.454302
2	0.045225	0.3133	0.377693
3	0.162509	1.1259	0.132904
4	0.10404	0.7208	0.237262
5	-0.076725	-0.5316	0.298738
6	0.133167	0.9226	0.180413
7	-0.025104	-0.1739	0.431327
8	-0.066443	-0.4603	0.32368
9	-0.008508	-0.0589	0.476619
10	-0.238734	-1.654	0.052327
11	0.406054	2.8132	0.003544
12	-0.259927	-1.8008	0.039007
13	-0.144988	-1.0045	0.160085
14	0.081047	0.5615	0.288532
15	0.041947	0.2906	0.386297
16	0.080589	0.5583	0.289604
17	-0.113979	-0.7897	0.216803

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.016658 & -0.1154 & 0.454302 \tabularnewline
2 & 0.045225 & 0.3133 & 0.377693 \tabularnewline
3 & 0.162509 & 1.1259 & 0.132904 \tabularnewline
4 & 0.10404 & 0.7208 & 0.237262 \tabularnewline
5 & -0.076725 & -0.5316 & 0.298738 \tabularnewline
6 & 0.133167 & 0.9226 & 0.180413 \tabularnewline
7 & -0.025104 & -0.1739 & 0.431327 \tabularnewline
8 & -0.066443 & -0.4603 & 0.32368 \tabularnewline
9 & -0.008508 & -0.0589 & 0.476619 \tabularnewline
10 & -0.238734 & -1.654 & 0.052327 \tabularnewline
11 & 0.406054 & 2.8132 & 0.003544 \tabularnewline
12 & -0.259927 & -1.8008 & 0.039007 \tabularnewline
13 & -0.144988 & -1.0045 & 0.160085 \tabularnewline
14 & 0.081047 & 0.5615 & 0.288532 \tabularnewline
15 & 0.041947 & 0.2906 & 0.386297 \tabularnewline
16 & 0.080589 & 0.5583 & 0.289604 \tabularnewline
17 & -0.113979 & -0.7897 & 0.216803 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115527&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]-0.016658[/C][C]-0.1154[/C][C]0.454302[/C][/ROW]
[ROW][C]2[/C][C]0.045225[/C][C]0.3133[/C][C]0.377693[/C][/ROW]
[ROW][C]3[/C][C]0.162509[/C][C]1.1259[/C][C]0.132904[/C][/ROW]
[ROW][C]4[/C][C]0.10404[/C][C]0.7208[/C][C]0.237262[/C][/ROW]
[ROW][C]5[/C][C]-0.076725[/C][C]-0.5316[/C][C]0.298738[/C][/ROW]
[ROW][C]6[/C][C]0.133167[/C][C]0.9226[/C][C]0.180413[/C][/ROW]
[ROW][C]7[/C][C]-0.025104[/C][C]-0.1739[/C][C]0.431327[/C][/ROW]
[ROW][C]8[/C][C]-0.066443[/C][C]-0.4603[/C][C]0.32368[/C][/ROW]
[ROW][C]9[/C][C]-0.008508[/C][C]-0.0589[/C][C]0.476619[/C][/ROW]
[ROW][C]10[/C][C]-0.238734[/C][C]-1.654[/C][C]0.052327[/C][/ROW]
[ROW][C]11[/C][C]0.406054[/C][C]2.8132[/C][C]0.003544[/C][/ROW]
[ROW][C]12[/C][C]-0.259927[/C][C]-1.8008[/C][C]0.039007[/C][/ROW]
[ROW][C]13[/C][C]-0.144988[/C][C]-1.0045[/C][C]0.160085[/C][/ROW]
[ROW][C]14[/C][C]0.081047[/C][C]0.5615[/C][C]0.288532[/C][/ROW]
[ROW][C]15[/C][C]0.041947[/C][C]0.2906[/C][C]0.386297[/C][/ROW]
[ROW][C]16[/C][C]0.080589[/C][C]0.5583[/C][C]0.289604[/C][/ROW]
[ROW][C]17[/C][C]-0.113979[/C][C]-0.7897[/C][C]0.216803[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115527&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115527&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	-0.016658	-0.1154	0.454302
2	0.045225	0.3133	0.377693
3	0.162509	1.1259	0.132904
4	0.10404	0.7208	0.237262
5	-0.076725	-0.5316	0.298738
6	0.133167	0.9226	0.180413
7	-0.025104	-0.1739	0.431327
8	-0.066443	-0.4603	0.32368
9	-0.008508	-0.0589	0.476619
10	-0.238734	-1.654	0.052327
11	0.406054	2.8132	0.003544
12	-0.259927	-1.8008	0.039007
13	-0.144988	-1.0045	0.160085
14	0.081047	0.5615	0.288532
15	0.041947	0.2906	0.386297
16	0.080589	0.5583	0.289604
17	-0.113979	-0.7897	0.216803

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 = -0.3 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = -0.3 ; par3 = 1 ; 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')

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Input Parameters & R Code