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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 19 Dec 2016 11:32:59 +0100

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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/Dec/19/t1482143584f9v7cf48nohac2v.htm/, Retrieved Fri, 17 May 2024 00:51:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301281, Retrieved Fri, 17 May 2024 00:51:40 +0000

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Estimated Impact

103

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-       [(Partial) Autocorrelation Function] [] [2016-12-19 10:32:59] [cefbb908b49c27a772f794ee9c78d9df] [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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301281&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301281&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301281&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.485174	3.4648	0.000542
2	0.762067	5.4422	1e-06
3	0.426507	3.0459	0.001834
4	0.806544	5.7599	0
5	0.323793	2.3123	0.012416
6	0.587904	4.1985	5.4e-05
7	0.279166	1.9936	0.025776
8	0.627421	4.4807	2.1e-05
9	0.185315	1.3234	0.0958
10	0.43567	3.1113	0.001524
11	0.147975	1.0568	0.147802
12	0.466059	3.3283	0.000814
13	0.049489	0.3534	0.362613
14	0.264488	1.8888	0.032304
15	-0.010705	-0.0764	0.469682
16	0.260162	1.8579	0.034478
17	-0.126822	-0.9057	0.184679

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.485174 & 3.4648 & 0.000542 \tabularnewline
2 & 0.762067 & 5.4422 & 1e-06 \tabularnewline
3 & 0.426507 & 3.0459 & 0.001834 \tabularnewline
4 & 0.806544 & 5.7599 & 0 \tabularnewline
5 & 0.323793 & 2.3123 & 0.012416 \tabularnewline
6 & 0.587904 & 4.1985 & 5.4e-05 \tabularnewline
7 & 0.279166 & 1.9936 & 0.025776 \tabularnewline
8 & 0.627421 & 4.4807 & 2.1e-05 \tabularnewline
9 & 0.185315 & 1.3234 & 0.0958 \tabularnewline
10 & 0.43567 & 3.1113 & 0.001524 \tabularnewline
11 & 0.147975 & 1.0568 & 0.147802 \tabularnewline
12 & 0.466059 & 3.3283 & 0.000814 \tabularnewline
13 & 0.049489 & 0.3534 & 0.362613 \tabularnewline
14 & 0.264488 & 1.8888 & 0.032304 \tabularnewline
15 & -0.010705 & -0.0764 & 0.469682 \tabularnewline
16 & 0.260162 & 1.8579 & 0.034478 \tabularnewline
17 & -0.126822 & -0.9057 & 0.184679 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301281&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]0.485174[/C][C]3.4648[/C][C]0.000542[/C][/ROW]
[ROW][C]2[/C][C]0.762067[/C][C]5.4422[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.426507[/C][C]3.0459[/C][C]0.001834[/C][/ROW]
[ROW][C]4[/C][C]0.806544[/C][C]5.7599[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.323793[/C][C]2.3123[/C][C]0.012416[/C][/ROW]
[ROW][C]6[/C][C]0.587904[/C][C]4.1985[/C][C]5.4e-05[/C][/ROW]
[ROW][C]7[/C][C]0.279166[/C][C]1.9936[/C][C]0.025776[/C][/ROW]
[ROW][C]8[/C][C]0.627421[/C][C]4.4807[/C][C]2.1e-05[/C][/ROW]
[ROW][C]9[/C][C]0.185315[/C][C]1.3234[/C][C]0.0958[/C][/ROW]
[ROW][C]10[/C][C]0.43567[/C][C]3.1113[/C][C]0.001524[/C][/ROW]
[ROW][C]11[/C][C]0.147975[/C][C]1.0568[/C][C]0.147802[/C][/ROW]
[ROW][C]12[/C][C]0.466059[/C][C]3.3283[/C][C]0.000814[/C][/ROW]
[ROW][C]13[/C][C]0.049489[/C][C]0.3534[/C][C]0.362613[/C][/ROW]
[ROW][C]14[/C][C]0.264488[/C][C]1.8888[/C][C]0.032304[/C][/ROW]
[ROW][C]15[/C][C]-0.010705[/C][C]-0.0764[/C][C]0.469682[/C][/ROW]
[ROW][C]16[/C][C]0.260162[/C][C]1.8579[/C][C]0.034478[/C][/ROW]
[ROW][C]17[/C][C]-0.126822[/C][C]-0.9057[/C][C]0.184679[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301281&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301281&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	0.485174	3.4648	0.000542
2	0.762067	5.4422	1e-06
3	0.426507	3.0459	0.001834
4	0.806544	5.7599	0
5	0.323793	2.3123	0.012416
6	0.587904	4.1985	5.4e-05
7	0.279166	1.9936	0.025776
8	0.627421	4.4807	2.1e-05
9	0.185315	1.3234	0.0958
10	0.43567	3.1113	0.001524
11	0.147975	1.0568	0.147802
12	0.466059	3.3283	0.000814
13	0.049489	0.3534	0.362613
14	0.264488	1.8888	0.032304
15	-0.010705	-0.0764	0.469682
16	0.260162	1.8579	0.034478
17	-0.126822	-0.9057	0.184679

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.485174	3.4648	0.000542
2	0.688816	4.9191	5e-06
3	-0.056603	-0.4042	0.343867
4	0.553125	3.9501	0.00012
5	-0.477498	-3.41	0.000639
6	-0.108192	-0.7726	0.22165
7	0.100233	0.7158	0.238687
8	0.16046	1.1459	0.12859
9	-0.111412	-0.7956	0.214965
10	-0.133691	-0.9547	0.172106
11	-0.007976	-0.057	0.4774
12	0.069401	0.4956	0.311144
13	-0.073961	-0.5282	0.29983
14	-0.200999	-1.4354	0.078636
15	-0.072748	-0.5195	0.30282
16	-0.035702	-0.255	0.399889
17	-0.017916	-0.1279	0.449347

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.485174 & 3.4648 & 0.000542 \tabularnewline
2 & 0.688816 & 4.9191 & 5e-06 \tabularnewline
3 & -0.056603 & -0.4042 & 0.343867 \tabularnewline
4 & 0.553125 & 3.9501 & 0.00012 \tabularnewline
5 & -0.477498 & -3.41 & 0.000639 \tabularnewline
6 & -0.108192 & -0.7726 & 0.22165 \tabularnewline
7 & 0.100233 & 0.7158 & 0.238687 \tabularnewline
8 & 0.16046 & 1.1459 & 0.12859 \tabularnewline
9 & -0.111412 & -0.7956 & 0.214965 \tabularnewline
10 & -0.133691 & -0.9547 & 0.172106 \tabularnewline
11 & -0.007976 & -0.057 & 0.4774 \tabularnewline
12 & 0.069401 & 0.4956 & 0.311144 \tabularnewline
13 & -0.073961 & -0.5282 & 0.29983 \tabularnewline
14 & -0.200999 & -1.4354 & 0.078636 \tabularnewline
15 & -0.072748 & -0.5195 & 0.30282 \tabularnewline
16 & -0.035702 & -0.255 & 0.399889 \tabularnewline
17 & -0.017916 & -0.1279 & 0.449347 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301281&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]0.485174[/C][C]3.4648[/C][C]0.000542[/C][/ROW]
[ROW][C]2[/C][C]0.688816[/C][C]4.9191[/C][C]5e-06[/C][/ROW]
[ROW][C]3[/C][C]-0.056603[/C][C]-0.4042[/C][C]0.343867[/C][/ROW]
[ROW][C]4[/C][C]0.553125[/C][C]3.9501[/C][C]0.00012[/C][/ROW]
[ROW][C]5[/C][C]-0.477498[/C][C]-3.41[/C][C]0.000639[/C][/ROW]
[ROW][C]6[/C][C]-0.108192[/C][C]-0.7726[/C][C]0.22165[/C][/ROW]
[ROW][C]7[/C][C]0.100233[/C][C]0.7158[/C][C]0.238687[/C][/ROW]
[ROW][C]8[/C][C]0.16046[/C][C]1.1459[/C][C]0.12859[/C][/ROW]
[ROW][C]9[/C][C]-0.111412[/C][C]-0.7956[/C][C]0.214965[/C][/ROW]
[ROW][C]10[/C][C]-0.133691[/C][C]-0.9547[/C][C]0.172106[/C][/ROW]
[ROW][C]11[/C][C]-0.007976[/C][C]-0.057[/C][C]0.4774[/C][/ROW]
[ROW][C]12[/C][C]0.069401[/C][C]0.4956[/C][C]0.311144[/C][/ROW]
[ROW][C]13[/C][C]-0.073961[/C][C]-0.5282[/C][C]0.29983[/C][/ROW]
[ROW][C]14[/C][C]-0.200999[/C][C]-1.4354[/C][C]0.078636[/C][/ROW]
[ROW][C]15[/C][C]-0.072748[/C][C]-0.5195[/C][C]0.30282[/C][/ROW]
[ROW][C]16[/C][C]-0.035702[/C][C]-0.255[/C][C]0.399889[/C][/ROW]
[ROW][C]17[/C][C]-0.017916[/C][C]-0.1279[/C][C]0.449347[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301281&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301281&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	0.485174	3.4648	0.000542
2	0.688816	4.9191	5e-06
3	-0.056603	-0.4042	0.343867
4	0.553125	3.9501	0.00012
5	-0.477498	-3.41	0.000639
6	-0.108192	-0.7726	0.22165
7	0.100233	0.7158	0.238687
8	0.16046	1.1459	0.12859
9	-0.111412	-0.7956	0.214965
10	-0.133691	-0.9547	0.172106
11	-0.007976	-0.057	0.4774
12	0.069401	0.4956	0.311144
13	-0.073961	-0.5282	0.29983
14	-0.200999	-1.4354	0.078636
15	-0.072748	-0.5195	0.30282
16	-0.035702	-0.255	0.399889
17	-0.017916	-0.1279	0.449347

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 = 0.0 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; 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,'ACF(k)',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,'PACF(k)',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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