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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 18 Dec 2016 16:16:42 +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/18/t1482074230xs7hist79art7i3.htm/, Retrieved Fri, 01 Nov 2024 03:28:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301132, Retrieved Fri, 01 Nov 2024 03:28:22 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-18 15:16:42] [94ac3c9a028ddd47e8862e80eac9f626] [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=301132&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=301132&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301132&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	-0.160564	-1.0529	0.149137
2	-0.01848	-0.1212	0.452055
3	-0.072435	-0.475	0.3186
4	-0.058157	-0.3814	0.352406
5	-0.14146	-0.9276	0.179393
6	-0.079622	-0.5221	0.302135
7	0.243675	1.5979	0.058696
8	-0.249891	-1.6386	0.054292
9	0.145367	0.9532	0.172899
10	0.053276	0.3494	0.364265
11	0.210817	1.3824	0.086991
12	-0.202951	-1.3308	0.095128
13	0.167777	1.1002	0.138686
14	-0.118187	-0.775	0.221289
15	-0.041844	-0.2744	0.39255
16	-0.019113	-0.1253	0.450422

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.160564 & -1.0529 & 0.149137 \tabularnewline
2 & -0.01848 & -0.1212 & 0.452055 \tabularnewline
3 & -0.072435 & -0.475 & 0.3186 \tabularnewline
4 & -0.058157 & -0.3814 & 0.352406 \tabularnewline
5 & -0.14146 & -0.9276 & 0.179393 \tabularnewline
6 & -0.079622 & -0.5221 & 0.302135 \tabularnewline
7 & 0.243675 & 1.5979 & 0.058696 \tabularnewline
8 & -0.249891 & -1.6386 & 0.054292 \tabularnewline
9 & 0.145367 & 0.9532 & 0.172899 \tabularnewline
10 & 0.053276 & 0.3494 & 0.364265 \tabularnewline
11 & 0.210817 & 1.3824 & 0.086991 \tabularnewline
12 & -0.202951 & -1.3308 & 0.095128 \tabularnewline
13 & 0.167777 & 1.1002 & 0.138686 \tabularnewline
14 & -0.118187 & -0.775 & 0.221289 \tabularnewline
15 & -0.041844 & -0.2744 & 0.39255 \tabularnewline
16 & -0.019113 & -0.1253 & 0.450422 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301132&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]-0.160564[/C][C]-1.0529[/C][C]0.149137[/C][/ROW]
[ROW][C]2[/C][C]-0.01848[/C][C]-0.1212[/C][C]0.452055[/C][/ROW]
[ROW][C]3[/C][C]-0.072435[/C][C]-0.475[/C][C]0.3186[/C][/ROW]
[ROW][C]4[/C][C]-0.058157[/C][C]-0.3814[/C][C]0.352406[/C][/ROW]
[ROW][C]5[/C][C]-0.14146[/C][C]-0.9276[/C][C]0.179393[/C][/ROW]
[ROW][C]6[/C][C]-0.079622[/C][C]-0.5221[/C][C]0.302135[/C][/ROW]
[ROW][C]7[/C][C]0.243675[/C][C]1.5979[/C][C]0.058696[/C][/ROW]
[ROW][C]8[/C][C]-0.249891[/C][C]-1.6386[/C][C]0.054292[/C][/ROW]
[ROW][C]9[/C][C]0.145367[/C][C]0.9532[/C][C]0.172899[/C][/ROW]
[ROW][C]10[/C][C]0.053276[/C][C]0.3494[/C][C]0.364265[/C][/ROW]
[ROW][C]11[/C][C]0.210817[/C][C]1.3824[/C][C]0.086991[/C][/ROW]
[ROW][C]12[/C][C]-0.202951[/C][C]-1.3308[/C][C]0.095128[/C][/ROW]
[ROW][C]13[/C][C]0.167777[/C][C]1.1002[/C][C]0.138686[/C][/ROW]
[ROW][C]14[/C][C]-0.118187[/C][C]-0.775[/C][C]0.221289[/C][/ROW]
[ROW][C]15[/C][C]-0.041844[/C][C]-0.2744[/C][C]0.39255[/C][/ROW]
[ROW][C]16[/C][C]-0.019113[/C][C]-0.1253[/C][C]0.450422[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301132&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301132&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	-0.160564	-1.0529	0.149137
2	-0.01848	-0.1212	0.452055
3	-0.072435	-0.475	0.3186
4	-0.058157	-0.3814	0.352406
5	-0.14146	-0.9276	0.179393
6	-0.079622	-0.5221	0.302135
7	0.243675	1.5979	0.058696
8	-0.249891	-1.6386	0.054292
9	0.145367	0.9532	0.172899
10	0.053276	0.3494	0.364265
11	0.210817	1.3824	0.086991
12	-0.202951	-1.3308	0.095128
13	0.167777	1.1002	0.138686
14	-0.118187	-0.775	0.221289
15	-0.041844	-0.2744	0.39255
16	-0.019113	-0.1253	0.450422

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.160564	-1.0529	0.149137
2	-0.045432	-0.2979	0.3836
3	-0.085199	-0.5587	0.289636
4	-0.088463	-0.5801	0.28244
5	-0.180299	-1.1823	0.121791
6	-0.163388	-1.0714	0.144982
7	0.181608	1.1909	0.120116
8	-0.247769	-1.6247	0.055764
9	0.04768	0.3127	0.378025
10	0.06033	0.3956	0.347174
11	0.233549	1.5315	0.066487
12	-0.123663	-0.8109	0.210941
13	0.198345	1.3006	0.100155
14	-0.135022	-0.8854	0.190434
15	0.170765	1.1198	0.134512
16	-0.126613	-0.8303	0.20549

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.160564 & -1.0529 & 0.149137 \tabularnewline
2 & -0.045432 & -0.2979 & 0.3836 \tabularnewline
3 & -0.085199 & -0.5587 & 0.289636 \tabularnewline
4 & -0.088463 & -0.5801 & 0.28244 \tabularnewline
5 & -0.180299 & -1.1823 & 0.121791 \tabularnewline
6 & -0.163388 & -1.0714 & 0.144982 \tabularnewline
7 & 0.181608 & 1.1909 & 0.120116 \tabularnewline
8 & -0.247769 & -1.6247 & 0.055764 \tabularnewline
9 & 0.04768 & 0.3127 & 0.378025 \tabularnewline
10 & 0.06033 & 0.3956 & 0.347174 \tabularnewline
11 & 0.233549 & 1.5315 & 0.066487 \tabularnewline
12 & -0.123663 & -0.8109 & 0.210941 \tabularnewline
13 & 0.198345 & 1.3006 & 0.100155 \tabularnewline
14 & -0.135022 & -0.8854 & 0.190434 \tabularnewline
15 & 0.170765 & 1.1198 & 0.134512 \tabularnewline
16 & -0.126613 & -0.8303 & 0.20549 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301132&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]-0.160564[/C][C]-1.0529[/C][C]0.149137[/C][/ROW]
[ROW][C]2[/C][C]-0.045432[/C][C]-0.2979[/C][C]0.3836[/C][/ROW]
[ROW][C]3[/C][C]-0.085199[/C][C]-0.5587[/C][C]0.289636[/C][/ROW]
[ROW][C]4[/C][C]-0.088463[/C][C]-0.5801[/C][C]0.28244[/C][/ROW]
[ROW][C]5[/C][C]-0.180299[/C][C]-1.1823[/C][C]0.121791[/C][/ROW]
[ROW][C]6[/C][C]-0.163388[/C][C]-1.0714[/C][C]0.144982[/C][/ROW]
[ROW][C]7[/C][C]0.181608[/C][C]1.1909[/C][C]0.120116[/C][/ROW]
[ROW][C]8[/C][C]-0.247769[/C][C]-1.6247[/C][C]0.055764[/C][/ROW]
[ROW][C]9[/C][C]0.04768[/C][C]0.3127[/C][C]0.378025[/C][/ROW]
[ROW][C]10[/C][C]0.06033[/C][C]0.3956[/C][C]0.347174[/C][/ROW]
[ROW][C]11[/C][C]0.233549[/C][C]1.5315[/C][C]0.066487[/C][/ROW]
[ROW][C]12[/C][C]-0.123663[/C][C]-0.8109[/C][C]0.210941[/C][/ROW]
[ROW][C]13[/C][C]0.198345[/C][C]1.3006[/C][C]0.100155[/C][/ROW]
[ROW][C]14[/C][C]-0.135022[/C][C]-0.8854[/C][C]0.190434[/C][/ROW]
[ROW][C]15[/C][C]0.170765[/C][C]1.1198[/C][C]0.134512[/C][/ROW]
[ROW][C]16[/C][C]-0.126613[/C][C]-0.8303[/C][C]0.20549[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301132&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301132&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	-0.160564	-1.0529	0.149137
2	-0.045432	-0.2979	0.3836
3	-0.085199	-0.5587	0.289636
4	-0.088463	-0.5801	0.28244
5	-0.180299	-1.1823	0.121791
6	-0.163388	-1.0714	0.144982
7	0.181608	1.1909	0.120116
8	-0.247769	-1.6247	0.055764
9	0.04768	0.3127	0.378025
10	0.06033	0.3956	0.347174
11	0.233549	1.5315	0.066487
12	-0.123663	-0.8109	0.210941
13	0.198345	1.3006	0.100155
14	-0.135022	-0.8854	0.190434
15	0.170765	1.1198	0.134512
16	-0.126613	-0.8303	0.20549

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 = 1 ; par2 = 1 ; par3 = 0 ; par4 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; 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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Input Parameters & R Code