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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 20:55:11 +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/16/t1481918189ibjzib5jt90vsq8.htm/, Retrieved Thu, 02 May 2024 21:25:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300515, Retrieved Thu, 02 May 2024 21:25:37 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-16 19:55:11] [404ac5ee4f7301873f6a96ef36861981] [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	2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300515&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300515&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300515&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	2 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.126566	-0.8005	0.214083
2	-0.192704	-1.2188	0.115036
3	0.089372	0.5652	0.287535
4	-0.058772	-0.3717	0.356036
5	0.125373	0.7929	0.216249
6	-0.012966	-0.082	0.467526
7	-0.029667	-0.1876	0.426058
8	-0.015312	-0.0968	0.461667
9	-0.000962	-0.0061	0.497587
10	-0.071868	-0.4545	0.325952
11	-0.00513	-0.0324	0.487138
12	0.086055	0.5443	0.294642
13	-0.002163	-0.0137	0.494575
14	0.044518	0.2816	0.389867
15	-0.107	-0.6767	0.251236
16	-0.146898	-0.9291	0.179214

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.126566 & -0.8005 & 0.214083 \tabularnewline
2 & -0.192704 & -1.2188 & 0.115036 \tabularnewline
3 & 0.089372 & 0.5652 & 0.287535 \tabularnewline
4 & -0.058772 & -0.3717 & 0.356036 \tabularnewline
5 & 0.125373 & 0.7929 & 0.216249 \tabularnewline
6 & -0.012966 & -0.082 & 0.467526 \tabularnewline
7 & -0.029667 & -0.1876 & 0.426058 \tabularnewline
8 & -0.015312 & -0.0968 & 0.461667 \tabularnewline
9 & -0.000962 & -0.0061 & 0.497587 \tabularnewline
10 & -0.071868 & -0.4545 & 0.325952 \tabularnewline
11 & -0.00513 & -0.0324 & 0.487138 \tabularnewline
12 & 0.086055 & 0.5443 & 0.294642 \tabularnewline
13 & -0.002163 & -0.0137 & 0.494575 \tabularnewline
14 & 0.044518 & 0.2816 & 0.389867 \tabularnewline
15 & -0.107 & -0.6767 & 0.251236 \tabularnewline
16 & -0.146898 & -0.9291 & 0.179214 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300515&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]-0.126566[/C][C]-0.8005[/C][C]0.214083[/C][/ROW]
[ROW][C]2[/C][C]-0.192704[/C][C]-1.2188[/C][C]0.115036[/C][/ROW]
[ROW][C]3[/C][C]0.089372[/C][C]0.5652[/C][C]0.287535[/C][/ROW]
[ROW][C]4[/C][C]-0.058772[/C][C]-0.3717[/C][C]0.356036[/C][/ROW]
[ROW][C]5[/C][C]0.125373[/C][C]0.7929[/C][C]0.216249[/C][/ROW]
[ROW][C]6[/C][C]-0.012966[/C][C]-0.082[/C][C]0.467526[/C][/ROW]
[ROW][C]7[/C][C]-0.029667[/C][C]-0.1876[/C][C]0.426058[/C][/ROW]
[ROW][C]8[/C][C]-0.015312[/C][C]-0.0968[/C][C]0.461667[/C][/ROW]
[ROW][C]9[/C][C]-0.000962[/C][C]-0.0061[/C][C]0.497587[/C][/ROW]
[ROW][C]10[/C][C]-0.071868[/C][C]-0.4545[/C][C]0.325952[/C][/ROW]
[ROW][C]11[/C][C]-0.00513[/C][C]-0.0324[/C][C]0.487138[/C][/ROW]
[ROW][C]12[/C][C]0.086055[/C][C]0.5443[/C][C]0.294642[/C][/ROW]
[ROW][C]13[/C][C]-0.002163[/C][C]-0.0137[/C][C]0.494575[/C][/ROW]
[ROW][C]14[/C][C]0.044518[/C][C]0.2816[/C][C]0.389867[/C][/ROW]
[ROW][C]15[/C][C]-0.107[/C][C]-0.6767[/C][C]0.251236[/C][/ROW]
[ROW][C]16[/C][C]-0.146898[/C][C]-0.9291[/C][C]0.179214[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300515&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300515&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	-0.126566	-0.8005	0.214083
2	-0.192704	-1.2188	0.115036
3	0.089372	0.5652	0.287535
4	-0.058772	-0.3717	0.356036
5	0.125373	0.7929	0.216249
6	-0.012966	-0.082	0.467526
7	-0.029667	-0.1876	0.426058
8	-0.015312	-0.0968	0.461667
9	-0.000962	-0.0061	0.497587
10	-0.071868	-0.4545	0.325952
11	-0.00513	-0.0324	0.487138
12	0.086055	0.5443	0.294642
13	-0.002163	-0.0137	0.494575
14	0.044518	0.2816	0.389867
15	-0.107	-0.6767	0.251236
16	-0.146898	-0.9291	0.179214

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.126566	-0.8005	0.214083
2	-0.21212	-1.3416	0.093652
3	0.035076	0.2218	0.412783
4	-0.086438	-0.5467	0.293817
5	0.14002	0.8856	0.190573
6	-0.010779	-0.0682	0.472994
7	0.035048	0.2217	0.412852
8	-0.047507	-0.3005	0.38269
9	0.011174	0.0707	0.472007
10	-0.115207	-0.7286	0.235235
11	-0.018435	-0.1166	0.453882
12	0.042932	0.2715	0.39369
13	0.039067	0.2471	0.403054
14	0.076256	0.4823	0.316116
15	-0.081296	-0.5142	0.304984
16	-0.160546	-1.0154	0.158013

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.126566 & -0.8005 & 0.214083 \tabularnewline
2 & -0.21212 & -1.3416 & 0.093652 \tabularnewline
3 & 0.035076 & 0.2218 & 0.412783 \tabularnewline
4 & -0.086438 & -0.5467 & 0.293817 \tabularnewline
5 & 0.14002 & 0.8856 & 0.190573 \tabularnewline
6 & -0.010779 & -0.0682 & 0.472994 \tabularnewline
7 & 0.035048 & 0.2217 & 0.412852 \tabularnewline
8 & -0.047507 & -0.3005 & 0.38269 \tabularnewline
9 & 0.011174 & 0.0707 & 0.472007 \tabularnewline
10 & -0.115207 & -0.7286 & 0.235235 \tabularnewline
11 & -0.018435 & -0.1166 & 0.453882 \tabularnewline
12 & 0.042932 & 0.2715 & 0.39369 \tabularnewline
13 & 0.039067 & 0.2471 & 0.403054 \tabularnewline
14 & 0.076256 & 0.4823 & 0.316116 \tabularnewline
15 & -0.081296 & -0.5142 & 0.304984 \tabularnewline
16 & -0.160546 & -1.0154 & 0.158013 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300515&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]-0.126566[/C][C]-0.8005[/C][C]0.214083[/C][/ROW]
[ROW][C]2[/C][C]-0.21212[/C][C]-1.3416[/C][C]0.093652[/C][/ROW]
[ROW][C]3[/C][C]0.035076[/C][C]0.2218[/C][C]0.412783[/C][/ROW]
[ROW][C]4[/C][C]-0.086438[/C][C]-0.5467[/C][C]0.293817[/C][/ROW]
[ROW][C]5[/C][C]0.14002[/C][C]0.8856[/C][C]0.190573[/C][/ROW]
[ROW][C]6[/C][C]-0.010779[/C][C]-0.0682[/C][C]0.472994[/C][/ROW]
[ROW][C]7[/C][C]0.035048[/C][C]0.2217[/C][C]0.412852[/C][/ROW]
[ROW][C]8[/C][C]-0.047507[/C][C]-0.3005[/C][C]0.38269[/C][/ROW]
[ROW][C]9[/C][C]0.011174[/C][C]0.0707[/C][C]0.472007[/C][/ROW]
[ROW][C]10[/C][C]-0.115207[/C][C]-0.7286[/C][C]0.235235[/C][/ROW]
[ROW][C]11[/C][C]-0.018435[/C][C]-0.1166[/C][C]0.453882[/C][/ROW]
[ROW][C]12[/C][C]0.042932[/C][C]0.2715[/C][C]0.39369[/C][/ROW]
[ROW][C]13[/C][C]0.039067[/C][C]0.2471[/C][C]0.403054[/C][/ROW]
[ROW][C]14[/C][C]0.076256[/C][C]0.4823[/C][C]0.316116[/C][/ROW]
[ROW][C]15[/C][C]-0.081296[/C][C]-0.5142[/C][C]0.304984[/C][/ROW]
[ROW][C]16[/C][C]-0.160546[/C][C]-1.0154[/C][C]0.158013[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300515&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300515&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	-0.126566	-0.8005	0.214083
2	-0.21212	-1.3416	0.093652
3	0.035076	0.2218	0.412783
4	-0.086438	-0.5467	0.293817
5	0.14002	0.8856	0.190573
6	-0.010779	-0.0682	0.472994
7	0.035048	0.2217	0.412852
8	-0.047507	-0.3005	0.38269
9	0.011174	0.0707	0.472007
10	-0.115207	-0.7286	0.235235
11	-0.018435	-0.1166	0.453882
12	0.042932	0.2715	0.39369
13	0.039067	0.2471	0.403054
14	0.076256	0.4823	0.316116
15	-0.081296	-0.5142	0.304984
16	-0.160546	-1.0154	0.158013

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 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1'
par1 <- 'Default'
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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