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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 15 Mar 2016 22:34:54 +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/2016/Mar/15/t14580813077ag5uoibk865e9m.htm/, Retrieved Tue, 30 Apr 2024 15:36:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294132, Retrieved Tue, 30 Apr 2024 15:36:49 +0000

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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] [] [2016-03-15 22:34:54] [b787349f7d799cee4daf21043f8c3664] [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' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294132&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' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294132&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294132&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' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.959845	7.4349	0
2	0.910324	7.0513	0
3	0.866643	6.713	0
4	0.818681	6.3415	0
5	0.773919	5.9948	0
6	0.730246	5.6565	0
7	0.680561	5.2716	1e-06
8	0.629821	4.8786	4e-06
9	0.584218	4.5253	1.5e-05
10	0.542625	4.2032	4.4e-05
11	0.500623	3.8778	0.000132
12	0.457785	3.546	0.000383
13	0.40753	3.1567	0.001248
14	0.355803	2.756	0.003869
15	0.310403	2.4044	0.009652
16	0.259018	2.0063	0.024667
17	0.204595	1.5848	0.059136

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.959845 & 7.4349 & 0 \tabularnewline
2 & 0.910324 & 7.0513 & 0 \tabularnewline
3 & 0.866643 & 6.713 & 0 \tabularnewline
4 & 0.818681 & 6.3415 & 0 \tabularnewline
5 & 0.773919 & 5.9948 & 0 \tabularnewline
6 & 0.730246 & 5.6565 & 0 \tabularnewline
7 & 0.680561 & 5.2716 & 1e-06 \tabularnewline
8 & 0.629821 & 4.8786 & 4e-06 \tabularnewline
9 & 0.584218 & 4.5253 & 1.5e-05 \tabularnewline
10 & 0.542625 & 4.2032 & 4.4e-05 \tabularnewline
11 & 0.500623 & 3.8778 & 0.000132 \tabularnewline
12 & 0.457785 & 3.546 & 0.000383 \tabularnewline
13 & 0.40753 & 3.1567 & 0.001248 \tabularnewline
14 & 0.355803 & 2.756 & 0.003869 \tabularnewline
15 & 0.310403 & 2.4044 & 0.009652 \tabularnewline
16 & 0.259018 & 2.0063 & 0.024667 \tabularnewline
17 & 0.204595 & 1.5848 & 0.059136 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294132&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]0.959845[/C][C]7.4349[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.910324[/C][C]7.0513[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.866643[/C][C]6.713[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.818681[/C][C]6.3415[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.773919[/C][C]5.9948[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.730246[/C][C]5.6565[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.680561[/C][C]5.2716[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]0.629821[/C][C]4.8786[/C][C]4e-06[/C][/ROW]
[ROW][C]9[/C][C]0.584218[/C][C]4.5253[/C][C]1.5e-05[/C][/ROW]
[ROW][C]10[/C][C]0.542625[/C][C]4.2032[/C][C]4.4e-05[/C][/ROW]
[ROW][C]11[/C][C]0.500623[/C][C]3.8778[/C][C]0.000132[/C][/ROW]
[ROW][C]12[/C][C]0.457785[/C][C]3.546[/C][C]0.000383[/C][/ROW]
[ROW][C]13[/C][C]0.40753[/C][C]3.1567[/C][C]0.001248[/C][/ROW]
[ROW][C]14[/C][C]0.355803[/C][C]2.756[/C][C]0.003869[/C][/ROW]
[ROW][C]15[/C][C]0.310403[/C][C]2.4044[/C][C]0.009652[/C][/ROW]
[ROW][C]16[/C][C]0.259018[/C][C]2.0063[/C][C]0.024667[/C][/ROW]
[ROW][C]17[/C][C]0.204595[/C][C]1.5848[/C][C]0.059136[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294132&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294132&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	0.959845	7.4349	0
2	0.910324	7.0513	0
3	0.866643	6.713	0
4	0.818681	6.3415	0
5	0.773919	5.9948	0
6	0.730246	5.6565	0
7	0.680561	5.2716	1e-06
8	0.629821	4.8786	4e-06
9	0.584218	4.5253	1.5e-05
10	0.542625	4.2032	4.4e-05
11	0.500623	3.8778	0.000132
12	0.457785	3.546	0.000383
13	0.40753	3.1567	0.001248
14	0.355803	2.756	0.003869
15	0.310403	2.4044	0.009652
16	0.259018	2.0063	0.024667
17	0.204595	1.5848	0.059136

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.959845	7.4349	0
2	-0.139503	-1.0806	0.142103
3	0.063249	0.4899	0.312987
4	-0.098823	-0.7655	0.223494
5	0.038937	0.3016	0.381998
6	-0.03611	-0.2797	0.390333
7	-0.091297	-0.7072	0.241094
8	-0.030588	-0.2369	0.406758
9	0.027842	0.2157	0.414991
10	0.016538	0.1281	0.449247
11	-0.040702	-0.3153	0.376824
12	-0.038391	-0.2974	0.383604
13	-0.122944	-0.9523	0.172377
14	-0.024065	-0.1864	0.426377
15	0.025166	0.1949	0.423051
16	-0.131774	-1.0207	0.155744
17	-0.051759	-0.4009	0.344951

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.959845 & 7.4349 & 0 \tabularnewline
2 & -0.139503 & -1.0806 & 0.142103 \tabularnewline
3 & 0.063249 & 0.4899 & 0.312987 \tabularnewline
4 & -0.098823 & -0.7655 & 0.223494 \tabularnewline
5 & 0.038937 & 0.3016 & 0.381998 \tabularnewline
6 & -0.03611 & -0.2797 & 0.390333 \tabularnewline
7 & -0.091297 & -0.7072 & 0.241094 \tabularnewline
8 & -0.030588 & -0.2369 & 0.406758 \tabularnewline
9 & 0.027842 & 0.2157 & 0.414991 \tabularnewline
10 & 0.016538 & 0.1281 & 0.449247 \tabularnewline
11 & -0.040702 & -0.3153 & 0.376824 \tabularnewline
12 & -0.038391 & -0.2974 & 0.383604 \tabularnewline
13 & -0.122944 & -0.9523 & 0.172377 \tabularnewline
14 & -0.024065 & -0.1864 & 0.426377 \tabularnewline
15 & 0.025166 & 0.1949 & 0.423051 \tabularnewline
16 & -0.131774 & -1.0207 & 0.155744 \tabularnewline
17 & -0.051759 & -0.4009 & 0.344951 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294132&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]0.959845[/C][C]7.4349[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.139503[/C][C]-1.0806[/C][C]0.142103[/C][/ROW]
[ROW][C]3[/C][C]0.063249[/C][C]0.4899[/C][C]0.312987[/C][/ROW]
[ROW][C]4[/C][C]-0.098823[/C][C]-0.7655[/C][C]0.223494[/C][/ROW]
[ROW][C]5[/C][C]0.038937[/C][C]0.3016[/C][C]0.381998[/C][/ROW]
[ROW][C]6[/C][C]-0.03611[/C][C]-0.2797[/C][C]0.390333[/C][/ROW]
[ROW][C]7[/C][C]-0.091297[/C][C]-0.7072[/C][C]0.241094[/C][/ROW]
[ROW][C]8[/C][C]-0.030588[/C][C]-0.2369[/C][C]0.406758[/C][/ROW]
[ROW][C]9[/C][C]0.027842[/C][C]0.2157[/C][C]0.414991[/C][/ROW]
[ROW][C]10[/C][C]0.016538[/C][C]0.1281[/C][C]0.449247[/C][/ROW]
[ROW][C]11[/C][C]-0.040702[/C][C]-0.3153[/C][C]0.376824[/C][/ROW]
[ROW][C]12[/C][C]-0.038391[/C][C]-0.2974[/C][C]0.383604[/C][/ROW]
[ROW][C]13[/C][C]-0.122944[/C][C]-0.9523[/C][C]0.172377[/C][/ROW]
[ROW][C]14[/C][C]-0.024065[/C][C]-0.1864[/C][C]0.426377[/C][/ROW]
[ROW][C]15[/C][C]0.025166[/C][C]0.1949[/C][C]0.423051[/C][/ROW]
[ROW][C]16[/C][C]-0.131774[/C][C]-1.0207[/C][C]0.155744[/C][/ROW]
[ROW][C]17[/C][C]-0.051759[/C][C]-0.4009[/C][C]0.344951[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294132&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294132&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	0.959845	7.4349	0
2	-0.139503	-1.0806	0.142103
3	0.063249	0.4899	0.312987
4	-0.098823	-0.7655	0.223494
5	0.038937	0.3016	0.381998
6	-0.03611	-0.2797	0.390333
7	-0.091297	-0.7072	0.241094
8	-0.030588	-0.2369	0.406758
9	0.027842	0.2157	0.414991
10	0.016538	0.1281	0.449247
11	-0.040702	-0.3153	0.376824
12	-0.038391	-0.2974	0.383604
13	-0.122944	-0.9523	0.172377
14	-0.024065	-0.1864	0.426377
15	0.025166	0.1949	0.423051
16	-0.131774	-1.0207	0.155744
17	-0.051759	-0.4009	0.344951

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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