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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 14 Dec 2016 18:33:44 +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/14/t1481736859gaiv6uf8j9dyenj.htm/, Retrieved Fri, 03 May 2024 15:50:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299656, Retrieved Fri, 03 May 2024 15:50:46 +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] [] [2016-12-14 17:33:44] [59384cc4294cbecf8e09b453c4247580] [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=299656&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=299656&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299656&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	-0.233554	-1.584	0.060018
2	0.11376	0.7716	0.222161
3	0.028637	0.1942	0.423429
4	0.024176	0.164	0.435237
5	0.189503	1.2853	0.102566
6	-0.507615	-3.4428	0.000618
7	0.21823	1.4801	0.072831
8	-0.224326	-1.5215	0.067496
9	0.014145	0.0959	0.461994
10	-0.047405	-0.3215	0.374638
11	-0.06914	-0.4689	0.320667
12	-0.014539	-0.0986	0.460938
13	-0.143662	-0.9744	0.167486
14	0.200966	1.363	0.089756
15	-0.161851	-1.0977	0.139018
16	-0.102899	-0.6979	0.244378
17	-0.002151	-0.0146	0.494212

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.233554 & -1.584 & 0.060018 \tabularnewline
2 & 0.11376 & 0.7716 & 0.222161 \tabularnewline
3 & 0.028637 & 0.1942 & 0.423429 \tabularnewline
4 & 0.024176 & 0.164 & 0.435237 \tabularnewline
5 & 0.189503 & 1.2853 & 0.102566 \tabularnewline
6 & -0.507615 & -3.4428 & 0.000618 \tabularnewline
7 & 0.21823 & 1.4801 & 0.072831 \tabularnewline
8 & -0.224326 & -1.5215 & 0.067496 \tabularnewline
9 & 0.014145 & 0.0959 & 0.461994 \tabularnewline
10 & -0.047405 & -0.3215 & 0.374638 \tabularnewline
11 & -0.06914 & -0.4689 & 0.320667 \tabularnewline
12 & -0.014539 & -0.0986 & 0.460938 \tabularnewline
13 & -0.143662 & -0.9744 & 0.167486 \tabularnewline
14 & 0.200966 & 1.363 & 0.089756 \tabularnewline
15 & -0.161851 & -1.0977 & 0.139018 \tabularnewline
16 & -0.102899 & -0.6979 & 0.244378 \tabularnewline
17 & -0.002151 & -0.0146 & 0.494212 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299656&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]-0.233554[/C][C]-1.584[/C][C]0.060018[/C][/ROW]
[ROW][C]2[/C][C]0.11376[/C][C]0.7716[/C][C]0.222161[/C][/ROW]
[ROW][C]3[/C][C]0.028637[/C][C]0.1942[/C][C]0.423429[/C][/ROW]
[ROW][C]4[/C][C]0.024176[/C][C]0.164[/C][C]0.435237[/C][/ROW]
[ROW][C]5[/C][C]0.189503[/C][C]1.2853[/C][C]0.102566[/C][/ROW]
[ROW][C]6[/C][C]-0.507615[/C][C]-3.4428[/C][C]0.000618[/C][/ROW]
[ROW][C]7[/C][C]0.21823[/C][C]1.4801[/C][C]0.072831[/C][/ROW]
[ROW][C]8[/C][C]-0.224326[/C][C]-1.5215[/C][C]0.067496[/C][/ROW]
[ROW][C]9[/C][C]0.014145[/C][C]0.0959[/C][C]0.461994[/C][/ROW]
[ROW][C]10[/C][C]-0.047405[/C][C]-0.3215[/C][C]0.374638[/C][/ROW]
[ROW][C]11[/C][C]-0.06914[/C][C]-0.4689[/C][C]0.320667[/C][/ROW]
[ROW][C]12[/C][C]-0.014539[/C][C]-0.0986[/C][C]0.460938[/C][/ROW]
[ROW][C]13[/C][C]-0.143662[/C][C]-0.9744[/C][C]0.167486[/C][/ROW]
[ROW][C]14[/C][C]0.200966[/C][C]1.363[/C][C]0.089756[/C][/ROW]
[ROW][C]15[/C][C]-0.161851[/C][C]-1.0977[/C][C]0.139018[/C][/ROW]
[ROW][C]16[/C][C]-0.102899[/C][C]-0.6979[/C][C]0.244378[/C][/ROW]
[ROW][C]17[/C][C]-0.002151[/C][C]-0.0146[/C][C]0.494212[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299656&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299656&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	-0.233554	-1.584	0.060018
2	0.11376	0.7716	0.222161
3	0.028637	0.1942	0.423429
4	0.024176	0.164	0.435237
5	0.189503	1.2853	0.102566
6	-0.507615	-3.4428	0.000618
7	0.21823	1.4801	0.072831
8	-0.224326	-1.5215	0.067496
9	0.014145	0.0959	0.461994
10	-0.047405	-0.3215	0.374638
11	-0.06914	-0.4689	0.320667
12	-0.014539	-0.0986	0.460938
13	-0.143662	-0.9744	0.167486
14	0.200966	1.363	0.089756
15	-0.161851	-1.0977	0.139018
16	-0.102899	-0.6979	0.244378
17	-0.002151	-0.0146	0.494212

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.233554	-1.584	0.060018
2	0.062629	0.4248	0.336493
3	0.072386	0.4909	0.3129
4	0.041154	0.2791	0.390701
5	0.206532	1.4008	0.083997
6	-0.478217	-3.2434	0.001101
7	0.002885	0.0196	0.492236
8	-0.163561	-1.1093	0.136528
9	-0.021654	-0.1469	0.44194
10	0.015788	0.1071	0.457596
11	0.105003	0.7122	0.239979
12	-0.352112	-2.3881	0.010548
13	-0.037478	-0.2542	0.400242
14	0.026968	0.1829	0.427839
15	-0.113107	-0.7671	0.223463
16	-0.26448	-1.7938	0.039711
17	0.030336	0.2057	0.418948

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.233554 & -1.584 & 0.060018 \tabularnewline
2 & 0.062629 & 0.4248 & 0.336493 \tabularnewline
3 & 0.072386 & 0.4909 & 0.3129 \tabularnewline
4 & 0.041154 & 0.2791 & 0.390701 \tabularnewline
5 & 0.206532 & 1.4008 & 0.083997 \tabularnewline
6 & -0.478217 & -3.2434 & 0.001101 \tabularnewline
7 & 0.002885 & 0.0196 & 0.492236 \tabularnewline
8 & -0.163561 & -1.1093 & 0.136528 \tabularnewline
9 & -0.021654 & -0.1469 & 0.44194 \tabularnewline
10 & 0.015788 & 0.1071 & 0.457596 \tabularnewline
11 & 0.105003 & 0.7122 & 0.239979 \tabularnewline
12 & -0.352112 & -2.3881 & 0.010548 \tabularnewline
13 & -0.037478 & -0.2542 & 0.400242 \tabularnewline
14 & 0.026968 & 0.1829 & 0.427839 \tabularnewline
15 & -0.113107 & -0.7671 & 0.223463 \tabularnewline
16 & -0.26448 & -1.7938 & 0.039711 \tabularnewline
17 & 0.030336 & 0.2057 & 0.418948 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299656&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]-0.233554[/C][C]-1.584[/C][C]0.060018[/C][/ROW]
[ROW][C]2[/C][C]0.062629[/C][C]0.4248[/C][C]0.336493[/C][/ROW]
[ROW][C]3[/C][C]0.072386[/C][C]0.4909[/C][C]0.3129[/C][/ROW]
[ROW][C]4[/C][C]0.041154[/C][C]0.2791[/C][C]0.390701[/C][/ROW]
[ROW][C]5[/C][C]0.206532[/C][C]1.4008[/C][C]0.083997[/C][/ROW]
[ROW][C]6[/C][C]-0.478217[/C][C]-3.2434[/C][C]0.001101[/C][/ROW]
[ROW][C]7[/C][C]0.002885[/C][C]0.0196[/C][C]0.492236[/C][/ROW]
[ROW][C]8[/C][C]-0.163561[/C][C]-1.1093[/C][C]0.136528[/C][/ROW]
[ROW][C]9[/C][C]-0.021654[/C][C]-0.1469[/C][C]0.44194[/C][/ROW]
[ROW][C]10[/C][C]0.015788[/C][C]0.1071[/C][C]0.457596[/C][/ROW]
[ROW][C]11[/C][C]0.105003[/C][C]0.7122[/C][C]0.239979[/C][/ROW]
[ROW][C]12[/C][C]-0.352112[/C][C]-2.3881[/C][C]0.010548[/C][/ROW]
[ROW][C]13[/C][C]-0.037478[/C][C]-0.2542[/C][C]0.400242[/C][/ROW]
[ROW][C]14[/C][C]0.026968[/C][C]0.1829[/C][C]0.427839[/C][/ROW]
[ROW][C]15[/C][C]-0.113107[/C][C]-0.7671[/C][C]0.223463[/C][/ROW]
[ROW][C]16[/C][C]-0.26448[/C][C]-1.7938[/C][C]0.039711[/C][/ROW]
[ROW][C]17[/C][C]0.030336[/C][C]0.2057[/C][C]0.418948[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299656&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299656&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	-0.233554	-1.584	0.060018
2	0.062629	0.4248	0.336493
3	0.072386	0.4909	0.3129
4	0.041154	0.2791	0.390701
5	0.206532	1.4008	0.083997
6	-0.478217	-3.2434	0.001101
7	0.002885	0.0196	0.492236
8	-0.163561	-1.1093	0.136528
9	-0.021654	-0.1469	0.44194
10	0.015788	0.1071	0.457596
11	0.105003	0.7122	0.239979
12	-0.352112	-2.3881	0.010548
13	-0.037478	-0.2542	0.400242
14	0.026968	0.1829	0.427839
15	-0.113107	-0.7671	0.223463
16	-0.26448	-1.7938	0.039711
17	0.030336	0.2057	0.418948

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 0 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 6 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 6 ; 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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Dataset

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Input Parameters & R Code