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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 07 Nov 2015 11:17:00 +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/2015/Nov/07/t1446895048gq8o9260795u3b1.htm/, Retrieved Mon, 13 May 2024 22:11:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283226, Retrieved Mon, 13 May 2024 22:11:58 +0000

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141

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-       [(Partial) Autocorrelation Function] [Task 24 - Chapter 4] [2015-11-07 11:17:00] [39661ea0cc1af7d66f31b3ef3719ea7a] [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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283226&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283226&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283226&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.000634	0.0054	0.497845
2	0.015662	0.1338	0.446959
3	-0.114636	-0.9795	0.165295
4	-0.017088	-0.146	0.442163
5	-0.065235	-0.5574	0.28949
6	-0.104394	-0.8919	0.187678
7	0.006008	0.0513	0.4796
8	0.044536	0.3805	0.352333
9	0.102822	0.8785	0.191275
10	0.013912	0.1189	0.452856
11	0.08024	0.6856	0.247577
12	-0.10634	-0.9086	0.183283
13	-0.039552	-0.3379	0.368191
14	-0.142631	-1.2186	0.113452
15	-0.214035	-1.8287	0.035763
16	-0.060937	-0.5206	0.302094
17	0.126774	1.0832	0.141151
18	0.018126	0.1549	0.438676

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.000634 & 0.0054 & 0.497845 \tabularnewline
2 & 0.015662 & 0.1338 & 0.446959 \tabularnewline
3 & -0.114636 & -0.9795 & 0.165295 \tabularnewline
4 & -0.017088 & -0.146 & 0.442163 \tabularnewline
5 & -0.065235 & -0.5574 & 0.28949 \tabularnewline
6 & -0.104394 & -0.8919 & 0.187678 \tabularnewline
7 & 0.006008 & 0.0513 & 0.4796 \tabularnewline
8 & 0.044536 & 0.3805 & 0.352333 \tabularnewline
9 & 0.102822 & 0.8785 & 0.191275 \tabularnewline
10 & 0.013912 & 0.1189 & 0.452856 \tabularnewline
11 & 0.08024 & 0.6856 & 0.247577 \tabularnewline
12 & -0.10634 & -0.9086 & 0.183283 \tabularnewline
13 & -0.039552 & -0.3379 & 0.368191 \tabularnewline
14 & -0.142631 & -1.2186 & 0.113452 \tabularnewline
15 & -0.214035 & -1.8287 & 0.035763 \tabularnewline
16 & -0.060937 & -0.5206 & 0.302094 \tabularnewline
17 & 0.126774 & 1.0832 & 0.141151 \tabularnewline
18 & 0.018126 & 0.1549 & 0.438676 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283226&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]0.000634[/C][C]0.0054[/C][C]0.497845[/C][/ROW]
[ROW][C]2[/C][C]0.015662[/C][C]0.1338[/C][C]0.446959[/C][/ROW]
[ROW][C]3[/C][C]-0.114636[/C][C]-0.9795[/C][C]0.165295[/C][/ROW]
[ROW][C]4[/C][C]-0.017088[/C][C]-0.146[/C][C]0.442163[/C][/ROW]
[ROW][C]5[/C][C]-0.065235[/C][C]-0.5574[/C][C]0.28949[/C][/ROW]
[ROW][C]6[/C][C]-0.104394[/C][C]-0.8919[/C][C]0.187678[/C][/ROW]
[ROW][C]7[/C][C]0.006008[/C][C]0.0513[/C][C]0.4796[/C][/ROW]
[ROW][C]8[/C][C]0.044536[/C][C]0.3805[/C][C]0.352333[/C][/ROW]
[ROW][C]9[/C][C]0.102822[/C][C]0.8785[/C][C]0.191275[/C][/ROW]
[ROW][C]10[/C][C]0.013912[/C][C]0.1189[/C][C]0.452856[/C][/ROW]
[ROW][C]11[/C][C]0.08024[/C][C]0.6856[/C][C]0.247577[/C][/ROW]
[ROW][C]12[/C][C]-0.10634[/C][C]-0.9086[/C][C]0.183283[/C][/ROW]
[ROW][C]13[/C][C]-0.039552[/C][C]-0.3379[/C][C]0.368191[/C][/ROW]
[ROW][C]14[/C][C]-0.142631[/C][C]-1.2186[/C][C]0.113452[/C][/ROW]
[ROW][C]15[/C][C]-0.214035[/C][C]-1.8287[/C][C]0.035763[/C][/ROW]
[ROW][C]16[/C][C]-0.060937[/C][C]-0.5206[/C][C]0.302094[/C][/ROW]
[ROW][C]17[/C][C]0.126774[/C][C]1.0832[/C][C]0.141151[/C][/ROW]
[ROW][C]18[/C][C]0.018126[/C][C]0.1549[/C][C]0.438676[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283226&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283226&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	0.000634	0.0054	0.497845
2	0.015662	0.1338	0.446959
3	-0.114636	-0.9795	0.165295
4	-0.017088	-0.146	0.442163
5	-0.065235	-0.5574	0.28949
6	-0.104394	-0.8919	0.187678
7	0.006008	0.0513	0.4796
8	0.044536	0.3805	0.352333
9	0.102822	0.8785	0.191275
10	0.013912	0.1189	0.452856
11	0.08024	0.6856	0.247577
12	-0.10634	-0.9086	0.183283
13	-0.039552	-0.3379	0.368191
14	-0.142631	-1.2186	0.113452
15	-0.214035	-1.8287	0.035763
16	-0.060937	-0.5206	0.302094
17	0.126774	1.0832	0.141151
18	0.018126	0.1549	0.438676

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.000634	0.0054	0.497845
2	0.015661	0.1338	0.44696
3	-0.114684	-0.9799	0.165195
4	-0.017215	-0.1471	0.441737
5	-0.062441	-0.5335	0.297655
6	-0.11909	-1.0175	0.156136
7	0.002728	0.0233	0.490735
8	0.032463	0.2774	0.391142
9	0.076804	0.6562	0.256875
10	0.008466	0.0723	0.471267
11	0.077054	0.6583	0.256193
12	-0.098356	-0.8404	0.201726
13	-0.033536	-0.2865	0.387643
14	-0.110504	-0.9441	0.174105
15	-0.232561	-1.987	0.025338
16	-0.080921	-0.6914	0.245758
17	0.101711	0.869	0.193843
18	-0.066502	-0.5682	0.285825

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.000634 & 0.0054 & 0.497845 \tabularnewline
2 & 0.015661 & 0.1338 & 0.44696 \tabularnewline
3 & -0.114684 & -0.9799 & 0.165195 \tabularnewline
4 & -0.017215 & -0.1471 & 0.441737 \tabularnewline
5 & -0.062441 & -0.5335 & 0.297655 \tabularnewline
6 & -0.11909 & -1.0175 & 0.156136 \tabularnewline
7 & 0.002728 & 0.0233 & 0.490735 \tabularnewline
8 & 0.032463 & 0.2774 & 0.391142 \tabularnewline
9 & 0.076804 & 0.6562 & 0.256875 \tabularnewline
10 & 0.008466 & 0.0723 & 0.471267 \tabularnewline
11 & 0.077054 & 0.6583 & 0.256193 \tabularnewline
12 & -0.098356 & -0.8404 & 0.201726 \tabularnewline
13 & -0.033536 & -0.2865 & 0.387643 \tabularnewline
14 & -0.110504 & -0.9441 & 0.174105 \tabularnewline
15 & -0.232561 & -1.987 & 0.025338 \tabularnewline
16 & -0.080921 & -0.6914 & 0.245758 \tabularnewline
17 & 0.101711 & 0.869 & 0.193843 \tabularnewline
18 & -0.066502 & -0.5682 & 0.285825 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283226&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]0.000634[/C][C]0.0054[/C][C]0.497845[/C][/ROW]
[ROW][C]2[/C][C]0.015661[/C][C]0.1338[/C][C]0.44696[/C][/ROW]
[ROW][C]3[/C][C]-0.114684[/C][C]-0.9799[/C][C]0.165195[/C][/ROW]
[ROW][C]4[/C][C]-0.017215[/C][C]-0.1471[/C][C]0.441737[/C][/ROW]
[ROW][C]5[/C][C]-0.062441[/C][C]-0.5335[/C][C]0.297655[/C][/ROW]
[ROW][C]6[/C][C]-0.11909[/C][C]-1.0175[/C][C]0.156136[/C][/ROW]
[ROW][C]7[/C][C]0.002728[/C][C]0.0233[/C][C]0.490735[/C][/ROW]
[ROW][C]8[/C][C]0.032463[/C][C]0.2774[/C][C]0.391142[/C][/ROW]
[ROW][C]9[/C][C]0.076804[/C][C]0.6562[/C][C]0.256875[/C][/ROW]
[ROW][C]10[/C][C]0.008466[/C][C]0.0723[/C][C]0.471267[/C][/ROW]
[ROW][C]11[/C][C]0.077054[/C][C]0.6583[/C][C]0.256193[/C][/ROW]
[ROW][C]12[/C][C]-0.098356[/C][C]-0.8404[/C][C]0.201726[/C][/ROW]
[ROW][C]13[/C][C]-0.033536[/C][C]-0.2865[/C][C]0.387643[/C][/ROW]
[ROW][C]14[/C][C]-0.110504[/C][C]-0.9441[/C][C]0.174105[/C][/ROW]
[ROW][C]15[/C][C]-0.232561[/C][C]-1.987[/C][C]0.025338[/C][/ROW]
[ROW][C]16[/C][C]-0.080921[/C][C]-0.6914[/C][C]0.245758[/C][/ROW]
[ROW][C]17[/C][C]0.101711[/C][C]0.869[/C][C]0.193843[/C][/ROW]
[ROW][C]18[/C][C]-0.066502[/C][C]-0.5682[/C][C]0.285825[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283226&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283226&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	0.000634	0.0054	0.497845
2	0.015661	0.1338	0.44696
3	-0.114684	-0.9799	0.165195
4	-0.017215	-0.1471	0.441737
5	-0.062441	-0.5335	0.297655
6	-0.11909	-1.0175	0.156136
7	0.002728	0.0233	0.490735
8	0.032463	0.2774	0.391142
9	0.076804	0.6562	0.256875
10	0.008466	0.0723	0.471267
11	0.077054	0.6583	0.256193
12	-0.098356	-0.8404	0.201726
13	-0.033536	-0.2865	0.387643
14	-0.110504	-0.9441	0.174105
15	-0.232561	-1.987	0.025338
16	-0.080921	-0.6914	0.245758
17	0.101711	0.869	0.193843
18	-0.066502	-0.5682	0.285825

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):

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code