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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Dec 2016 15:59:27 +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/23/t1482505247chyiqq5cofmart3.htm/, Retrieved Tue, 07 May 2024 11:07:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302974, Retrieved Tue, 07 May 2024 11:07:36 +0000

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-       [(Partial) Autocorrelation Function] [autocorrelatie N2...] [2016-12-23 14:59:27] [6f830dc7e8de22be3233942ffbe3aaba] [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=302974&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=302974&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302974&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	0.97099	9.8545	0
2	0.943974	9.5803	0
3	0.918178	9.3185	0
4	0.892553	9.0584	0
5	0.865815	8.7871	0
6	0.836835	8.4929	0
7	0.808904	8.2095	0
8	0.781083	7.9271	0
9	0.75357	7.6479	0
10	0.724551	7.3534	0
11	0.6994	7.0981	0
12	0.671937	6.8194	0
13	0.645216	6.5482	0
14	0.619025	6.2824	0
15	0.592401	6.0122	0
16	0.566486	5.7492	0
17	0.539082	5.4711	0
18	0.510516	5.1812	1e-06
19	0.482033	4.8921	2e-06
20	0.455272	4.6205	6e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.97099 & 9.8545 & 0 \tabularnewline
2 & 0.943974 & 9.5803 & 0 \tabularnewline
3 & 0.918178 & 9.3185 & 0 \tabularnewline
4 & 0.892553 & 9.0584 & 0 \tabularnewline
5 & 0.865815 & 8.7871 & 0 \tabularnewline
6 & 0.836835 & 8.4929 & 0 \tabularnewline
7 & 0.808904 & 8.2095 & 0 \tabularnewline
8 & 0.781083 & 7.9271 & 0 \tabularnewline
9 & 0.75357 & 7.6479 & 0 \tabularnewline
10 & 0.724551 & 7.3534 & 0 \tabularnewline
11 & 0.6994 & 7.0981 & 0 \tabularnewline
12 & 0.671937 & 6.8194 & 0 \tabularnewline
13 & 0.645216 & 6.5482 & 0 \tabularnewline
14 & 0.619025 & 6.2824 & 0 \tabularnewline
15 & 0.592401 & 6.0122 & 0 \tabularnewline
16 & 0.566486 & 5.7492 & 0 \tabularnewline
17 & 0.539082 & 5.4711 & 0 \tabularnewline
18 & 0.510516 & 5.1812 & 1e-06 \tabularnewline
19 & 0.482033 & 4.8921 & 2e-06 \tabularnewline
20 & 0.455272 & 4.6205 & 6e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302974&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]0.97099[/C][C]9.8545[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.943974[/C][C]9.5803[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.918178[/C][C]9.3185[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.892553[/C][C]9.0584[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.865815[/C][C]8.7871[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.836835[/C][C]8.4929[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.808904[/C][C]8.2095[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.781083[/C][C]7.9271[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.75357[/C][C]7.6479[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.724551[/C][C]7.3534[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.6994[/C][C]7.0981[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.671937[/C][C]6.8194[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.645216[/C][C]6.5482[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.619025[/C][C]6.2824[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.592401[/C][C]6.0122[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.566486[/C][C]5.7492[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.539082[/C][C]5.4711[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.510516[/C][C]5.1812[/C][C]1e-06[/C][/ROW]
[ROW][C]19[/C][C]0.482033[/C][C]4.8921[/C][C]2e-06[/C][/ROW]
[ROW][C]20[/C][C]0.455272[/C][C]4.6205[/C][C]6e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302974&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302974&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	0.97099	9.8545	0
2	0.943974	9.5803	0
3	0.918178	9.3185	0
4	0.892553	9.0584	0
5	0.865815	8.7871	0
6	0.836835	8.4929	0
7	0.808904	8.2095	0
8	0.781083	7.9271	0
9	0.75357	7.6479	0
10	0.724551	7.3534	0
11	0.6994	7.0981	0
12	0.671937	6.8194	0
13	0.645216	6.5482	0
14	0.619025	6.2824	0
15	0.592401	6.0122	0
16	0.566486	5.7492	0
17	0.539082	5.4711	0
18	0.510516	5.1812	1e-06
19	0.482033	4.8921	2e-06
20	0.455272	4.6205	6e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.97099	9.8545	0
2	0.020166	0.2047	0.419121
3	0.00861	0.0874	0.46527
4	-0.009	-0.0913	0.463699
5	-0.032282	-0.3276	0.37193
6	-0.054762	-0.5558	0.289784
7	-0.000916	-0.0093	0.496301
8	-0.014215	-0.1443	0.442788
9	-0.009312	-0.0945	0.462446
10	-0.040094	-0.4069	0.342459
11	0.050646	0.514	0.304175
12	-0.053466	-0.5426	0.29428
13	-0.003107	-0.0315	0.487452
14	-0.006938	-0.0704	0.471999
15	-0.023153	-0.235	0.407346
16	-0.008864	-0.09	0.464246
17	-0.037818	-0.3838	0.350956
18	-0.04213	-0.4276	0.334928
19	-0.018673	-0.1895	0.425031
20	0.007073	0.0718	0.471455

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.97099 & 9.8545 & 0 \tabularnewline
2 & 0.020166 & 0.2047 & 0.419121 \tabularnewline
3 & 0.00861 & 0.0874 & 0.46527 \tabularnewline
4 & -0.009 & -0.0913 & 0.463699 \tabularnewline
5 & -0.032282 & -0.3276 & 0.37193 \tabularnewline
6 & -0.054762 & -0.5558 & 0.289784 \tabularnewline
7 & -0.000916 & -0.0093 & 0.496301 \tabularnewline
8 & -0.014215 & -0.1443 & 0.442788 \tabularnewline
9 & -0.009312 & -0.0945 & 0.462446 \tabularnewline
10 & -0.040094 & -0.4069 & 0.342459 \tabularnewline
11 & 0.050646 & 0.514 & 0.304175 \tabularnewline
12 & -0.053466 & -0.5426 & 0.29428 \tabularnewline
13 & -0.003107 & -0.0315 & 0.487452 \tabularnewline
14 & -0.006938 & -0.0704 & 0.471999 \tabularnewline
15 & -0.023153 & -0.235 & 0.407346 \tabularnewline
16 & -0.008864 & -0.09 & 0.464246 \tabularnewline
17 & -0.037818 & -0.3838 & 0.350956 \tabularnewline
18 & -0.04213 & -0.4276 & 0.334928 \tabularnewline
19 & -0.018673 & -0.1895 & 0.425031 \tabularnewline
20 & 0.007073 & 0.0718 & 0.471455 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302974&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]0.97099[/C][C]9.8545[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.020166[/C][C]0.2047[/C][C]0.419121[/C][/ROW]
[ROW][C]3[/C][C]0.00861[/C][C]0.0874[/C][C]0.46527[/C][/ROW]
[ROW][C]4[/C][C]-0.009[/C][C]-0.0913[/C][C]0.463699[/C][/ROW]
[ROW][C]5[/C][C]-0.032282[/C][C]-0.3276[/C][C]0.37193[/C][/ROW]
[ROW][C]6[/C][C]-0.054762[/C][C]-0.5558[/C][C]0.289784[/C][/ROW]
[ROW][C]7[/C][C]-0.000916[/C][C]-0.0093[/C][C]0.496301[/C][/ROW]
[ROW][C]8[/C][C]-0.014215[/C][C]-0.1443[/C][C]0.442788[/C][/ROW]
[ROW][C]9[/C][C]-0.009312[/C][C]-0.0945[/C][C]0.462446[/C][/ROW]
[ROW][C]10[/C][C]-0.040094[/C][C]-0.4069[/C][C]0.342459[/C][/ROW]
[ROW][C]11[/C][C]0.050646[/C][C]0.514[/C][C]0.304175[/C][/ROW]
[ROW][C]12[/C][C]-0.053466[/C][C]-0.5426[/C][C]0.29428[/C][/ROW]
[ROW][C]13[/C][C]-0.003107[/C][C]-0.0315[/C][C]0.487452[/C][/ROW]
[ROW][C]14[/C][C]-0.006938[/C][C]-0.0704[/C][C]0.471999[/C][/ROW]
[ROW][C]15[/C][C]-0.023153[/C][C]-0.235[/C][C]0.407346[/C][/ROW]
[ROW][C]16[/C][C]-0.008864[/C][C]-0.09[/C][C]0.464246[/C][/ROW]
[ROW][C]17[/C][C]-0.037818[/C][C]-0.3838[/C][C]0.350956[/C][/ROW]
[ROW][C]18[/C][C]-0.04213[/C][C]-0.4276[/C][C]0.334928[/C][/ROW]
[ROW][C]19[/C][C]-0.018673[/C][C]-0.1895[/C][C]0.425031[/C][/ROW]
[ROW][C]20[/C][C]0.007073[/C][C]0.0718[/C][C]0.471455[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302974&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302974&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	0.97099	9.8545	0
2	0.020166	0.2047	0.419121
3	0.00861	0.0874	0.46527
4	-0.009	-0.0913	0.463699
5	-0.032282	-0.3276	0.37193
6	-0.054762	-0.5558	0.289784
7	-0.000916	-0.0093	0.496301
8	-0.014215	-0.1443	0.442788
9	-0.009312	-0.0945	0.462446
10	-0.040094	-0.4069	0.342459
11	0.050646	0.514	0.304175
12	-0.053466	-0.5426	0.29428
13	-0.003107	-0.0315	0.487452
14	-0.006938	-0.0704	0.471999
15	-0.023153	-0.235	0.407346
16	-0.008864	-0.09	0.464246
17	-0.037818	-0.3838	0.350956
18	-0.04213	-0.4276	0.334928
19	-0.018673	-0.1895	0.425031
20	0.007073	0.0718	0.471455

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

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Parameters (Session):

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

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)
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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code