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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Dec 2016 10:08:51 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/23/t1482484149zic5c7eoh8rpvam.htm/, Retrieved Fri, 01 Nov 2024 03:44:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302792, Retrieved Fri, 01 Nov 2024 03:44:09 +0000

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Estimated Impact

103

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-       [(Partial) Autocorrelation Function] [Partial correlati...] [2016-12-23 09:08:51] [bb262dce3bb40077245e847c94886178] [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=302792&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=302792&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302792&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	-0.481383	-5.382	0
2	0.096042	1.0738	0.142495
3	0.04027	0.4502	0.32666
4	-0.200658	-2.2434	0.013315
5	0.372777	4.1678	2.8e-05
6	-0.621627	-6.95	0
7	0.334057	3.7349	0.000142
8	-0.175017	-1.9568	0.026303
9	0.078591	0.8787	0.190633
10	-0.01874	-0.2095	0.417193
11	-0.297501	-3.3262	0.000578
12	0.782196	8.7452	0
13	-0.433765	-4.8496	2e-06
14	0.193617	2.1647	0.016155
15	-0.06697	-0.7487	0.227708
16	-0.143714	-1.6068	0.055313
17	0.357212	3.9937	5.5e-05
18	-0.591564	-6.6139	0
19	0.313792	3.5083	0.000314
20	-0.116296	-1.3002	0.097957
21	-0.003457	-0.0386	0.484617

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.481383 & -5.382 & 0 \tabularnewline
2 & 0.096042 & 1.0738 & 0.142495 \tabularnewline
3 & 0.04027 & 0.4502 & 0.32666 \tabularnewline
4 & -0.200658 & -2.2434 & 0.013315 \tabularnewline
5 & 0.372777 & 4.1678 & 2.8e-05 \tabularnewline
6 & -0.621627 & -6.95 & 0 \tabularnewline
7 & 0.334057 & 3.7349 & 0.000142 \tabularnewline
8 & -0.175017 & -1.9568 & 0.026303 \tabularnewline
9 & 0.078591 & 0.8787 & 0.190633 \tabularnewline
10 & -0.01874 & -0.2095 & 0.417193 \tabularnewline
11 & -0.297501 & -3.3262 & 0.000578 \tabularnewline
12 & 0.782196 & 8.7452 & 0 \tabularnewline
13 & -0.433765 & -4.8496 & 2e-06 \tabularnewline
14 & 0.193617 & 2.1647 & 0.016155 \tabularnewline
15 & -0.06697 & -0.7487 & 0.227708 \tabularnewline
16 & -0.143714 & -1.6068 & 0.055313 \tabularnewline
17 & 0.357212 & 3.9937 & 5.5e-05 \tabularnewline
18 & -0.591564 & -6.6139 & 0 \tabularnewline
19 & 0.313792 & 3.5083 & 0.000314 \tabularnewline
20 & -0.116296 & -1.3002 & 0.097957 \tabularnewline
21 & -0.003457 & -0.0386 & 0.484617 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302792&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]-0.481383[/C][C]-5.382[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.096042[/C][C]1.0738[/C][C]0.142495[/C][/ROW]
[ROW][C]3[/C][C]0.04027[/C][C]0.4502[/C][C]0.32666[/C][/ROW]
[ROW][C]4[/C][C]-0.200658[/C][C]-2.2434[/C][C]0.013315[/C][/ROW]
[ROW][C]5[/C][C]0.372777[/C][C]4.1678[/C][C]2.8e-05[/C][/ROW]
[ROW][C]6[/C][C]-0.621627[/C][C]-6.95[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.334057[/C][C]3.7349[/C][C]0.000142[/C][/ROW]
[ROW][C]8[/C][C]-0.175017[/C][C]-1.9568[/C][C]0.026303[/C][/ROW]
[ROW][C]9[/C][C]0.078591[/C][C]0.8787[/C][C]0.190633[/C][/ROW]
[ROW][C]10[/C][C]-0.01874[/C][C]-0.2095[/C][C]0.417193[/C][/ROW]
[ROW][C]11[/C][C]-0.297501[/C][C]-3.3262[/C][C]0.000578[/C][/ROW]
[ROW][C]12[/C][C]0.782196[/C][C]8.7452[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.433765[/C][C]-4.8496[/C][C]2e-06[/C][/ROW]
[ROW][C]14[/C][C]0.193617[/C][C]2.1647[/C][C]0.016155[/C][/ROW]
[ROW][C]15[/C][C]-0.06697[/C][C]-0.7487[/C][C]0.227708[/C][/ROW]
[ROW][C]16[/C][C]-0.143714[/C][C]-1.6068[/C][C]0.055313[/C][/ROW]
[ROW][C]17[/C][C]0.357212[/C][C]3.9937[/C][C]5.5e-05[/C][/ROW]
[ROW][C]18[/C][C]-0.591564[/C][C]-6.6139[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.313792[/C][C]3.5083[/C][C]0.000314[/C][/ROW]
[ROW][C]20[/C][C]-0.116296[/C][C]-1.3002[/C][C]0.097957[/C][/ROW]
[ROW][C]21[/C][C]-0.003457[/C][C]-0.0386[/C][C]0.484617[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302792&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302792&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	-0.481383	-5.382	0
2	0.096042	1.0738	0.142495
3	0.04027	0.4502	0.32666
4	-0.200658	-2.2434	0.013315
5	0.372777	4.1678	2.8e-05
6	-0.621627	-6.95	0
7	0.334057	3.7349	0.000142
8	-0.175017	-1.9568	0.026303
9	0.078591	0.8787	0.190633
10	-0.01874	-0.2095	0.417193
11	-0.297501	-3.3262	0.000578
12	0.782196	8.7452	0
13	-0.433765	-4.8496	2e-06
14	0.193617	2.1647	0.016155
15	-0.06697	-0.7487	0.227708
16	-0.143714	-1.6068	0.055313
17	0.357212	3.9937	5.5e-05
18	-0.591564	-6.6139	0
19	0.313792	3.5083	0.000314
20	-0.116296	-1.3002	0.097957
21	-0.003457	-0.0386	0.484617

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.481383	-5.382	0
2	-0.176615	-1.9746	0.025258
3	0.012964	0.1449	0.442496
4	-0.208878	-2.3353	0.01056
5	0.249944	2.7945	0.003009
6	-0.507373	-5.6726	0
7	-0.156294	-1.7474	0.04151
8	-0.348035	-3.8912	8.1e-05
9	0.024317	0.2719	0.393083
10	-0.475849	-5.3202	0
11	-0.531925	-5.9471	0
12	0.305511	3.4157	0.000429
13	0.211313	2.3626	0.009847
14	0.126456	1.4138	0.07995
15	0.047383	0.5298	0.29861
16	-0.122382	-1.3683	0.086841
17	-0.029921	-0.3345	0.36927
18	-0.002423	-0.0271	0.489217
19	0.013702	0.1532	0.439245
20	0.195769	2.1888	0.015236
21	-0.10494	-1.1733	0.12146

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.481383 & -5.382 & 0 \tabularnewline
2 & -0.176615 & -1.9746 & 0.025258 \tabularnewline
3 & 0.012964 & 0.1449 & 0.442496 \tabularnewline
4 & -0.208878 & -2.3353 & 0.01056 \tabularnewline
5 & 0.249944 & 2.7945 & 0.003009 \tabularnewline
6 & -0.507373 & -5.6726 & 0 \tabularnewline
7 & -0.156294 & -1.7474 & 0.04151 \tabularnewline
8 & -0.348035 & -3.8912 & 8.1e-05 \tabularnewline
9 & 0.024317 & 0.2719 & 0.393083 \tabularnewline
10 & -0.475849 & -5.3202 & 0 \tabularnewline
11 & -0.531925 & -5.9471 & 0 \tabularnewline
12 & 0.305511 & 3.4157 & 0.000429 \tabularnewline
13 & 0.211313 & 2.3626 & 0.009847 \tabularnewline
14 & 0.126456 & 1.4138 & 0.07995 \tabularnewline
15 & 0.047383 & 0.5298 & 0.29861 \tabularnewline
16 & -0.122382 & -1.3683 & 0.086841 \tabularnewline
17 & -0.029921 & -0.3345 & 0.36927 \tabularnewline
18 & -0.002423 & -0.0271 & 0.489217 \tabularnewline
19 & 0.013702 & 0.1532 & 0.439245 \tabularnewline
20 & 0.195769 & 2.1888 & 0.015236 \tabularnewline
21 & -0.10494 & -1.1733 & 0.12146 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302792&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]-0.481383[/C][C]-5.382[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.176615[/C][C]-1.9746[/C][C]0.025258[/C][/ROW]
[ROW][C]3[/C][C]0.012964[/C][C]0.1449[/C][C]0.442496[/C][/ROW]
[ROW][C]4[/C][C]-0.208878[/C][C]-2.3353[/C][C]0.01056[/C][/ROW]
[ROW][C]5[/C][C]0.249944[/C][C]2.7945[/C][C]0.003009[/C][/ROW]
[ROW][C]6[/C][C]-0.507373[/C][C]-5.6726[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.156294[/C][C]-1.7474[/C][C]0.04151[/C][/ROW]
[ROW][C]8[/C][C]-0.348035[/C][C]-3.8912[/C][C]8.1e-05[/C][/ROW]
[ROW][C]9[/C][C]0.024317[/C][C]0.2719[/C][C]0.393083[/C][/ROW]
[ROW][C]10[/C][C]-0.475849[/C][C]-5.3202[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]-0.531925[/C][C]-5.9471[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.305511[/C][C]3.4157[/C][C]0.000429[/C][/ROW]
[ROW][C]13[/C][C]0.211313[/C][C]2.3626[/C][C]0.009847[/C][/ROW]
[ROW][C]14[/C][C]0.126456[/C][C]1.4138[/C][C]0.07995[/C][/ROW]
[ROW][C]15[/C][C]0.047383[/C][C]0.5298[/C][C]0.29861[/C][/ROW]
[ROW][C]16[/C][C]-0.122382[/C][C]-1.3683[/C][C]0.086841[/C][/ROW]
[ROW][C]17[/C][C]-0.029921[/C][C]-0.3345[/C][C]0.36927[/C][/ROW]
[ROW][C]18[/C][C]-0.002423[/C][C]-0.0271[/C][C]0.489217[/C][/ROW]
[ROW][C]19[/C][C]0.013702[/C][C]0.1532[/C][C]0.439245[/C][/ROW]
[ROW][C]20[/C][C]0.195769[/C][C]2.1888[/C][C]0.015236[/C][/ROW]
[ROW][C]21[/C][C]-0.10494[/C][C]-1.1733[/C][C]0.12146[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302792&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302792&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	-0.481383	-5.382	0
2	-0.176615	-1.9746	0.025258
3	0.012964	0.1449	0.442496
4	-0.208878	-2.3353	0.01056
5	0.249944	2.7945	0.003009
6	-0.507373	-5.6726	0
7	-0.156294	-1.7474	0.04151
8	-0.348035	-3.8912	8.1e-05
9	0.024317	0.2719	0.393083
10	-0.475849	-5.3202	0
11	-0.531925	-5.9471	0
12	0.305511	3.4157	0.000429
13	0.211313	2.3626	0.009847
14	0.126456	1.4138	0.07995
15	0.047383	0.5298	0.29861
16	-0.122382	-1.3683	0.086841
17	-0.029921	-0.3345	0.36927
18	-0.002423	-0.0271	0.489217
19	0.013702	0.1532	0.439245
20	0.195769	2.1888	0.015236
21	-0.10494	-1.1733	0.12146

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

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):

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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code