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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 21 Dec 2016 14:55:00 +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/21/t1482328783w9wcbzmqi563nk2.htm/, Retrieved Tue, 07 May 2024 03:17:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302302, Retrieved Tue, 07 May 2024 03:17:49 +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] [(Partial) autocor...] [2016-12-21 13:55:00] [d4ebbcc95b180bc93fc42d05f31a3dde] [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=302302&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=302302&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302302&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	-0.450127	-5.0326	1e-06
2	0.12257	1.3704	0.086514
3	-0.104289	-1.166	0.12292
4	-0.066563	-0.7442	0.229078
5	0.11773	1.3163	0.095248
6	-0.150448	-1.6821	0.047526
7	0.183353	2.0499	0.02123
8	-0.150306	-1.6805	0.047681
9	0.010217	0.1142	0.45462
10	0.095727	1.0703	0.143283
11	-0.08303	-0.9283	0.177519
12	0.149142	1.6675	0.048963
13	-0.251678	-2.8138	0.002844
14	0.18025	2.0153	0.023012
15	-0.10885	-1.217	0.112952
16	-9.5e-05	-0.0011	0.499578
17	0.091129	1.0189	0.155119
18	-0.145369	-1.6253	0.053312
19	0.108755	1.2159	0.113153
20	-0.032348	-0.3617	0.359106
21	-0.060845	-0.6803	0.248798

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.450127 & -5.0326 & 1e-06 \tabularnewline
2 & 0.12257 & 1.3704 & 0.086514 \tabularnewline
3 & -0.104289 & -1.166 & 0.12292 \tabularnewline
4 & -0.066563 & -0.7442 & 0.229078 \tabularnewline
5 & 0.11773 & 1.3163 & 0.095248 \tabularnewline
6 & -0.150448 & -1.6821 & 0.047526 \tabularnewline
7 & 0.183353 & 2.0499 & 0.02123 \tabularnewline
8 & -0.150306 & -1.6805 & 0.047681 \tabularnewline
9 & 0.010217 & 0.1142 & 0.45462 \tabularnewline
10 & 0.095727 & 1.0703 & 0.143283 \tabularnewline
11 & -0.08303 & -0.9283 & 0.177519 \tabularnewline
12 & 0.149142 & 1.6675 & 0.048963 \tabularnewline
13 & -0.251678 & -2.8138 & 0.002844 \tabularnewline
14 & 0.18025 & 2.0153 & 0.023012 \tabularnewline
15 & -0.10885 & -1.217 & 0.112952 \tabularnewline
16 & -9.5e-05 & -0.0011 & 0.499578 \tabularnewline
17 & 0.091129 & 1.0189 & 0.155119 \tabularnewline
18 & -0.145369 & -1.6253 & 0.053312 \tabularnewline
19 & 0.108755 & 1.2159 & 0.113153 \tabularnewline
20 & -0.032348 & -0.3617 & 0.359106 \tabularnewline
21 & -0.060845 & -0.6803 & 0.248798 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302302&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]-0.450127[/C][C]-5.0326[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.12257[/C][C]1.3704[/C][C]0.086514[/C][/ROW]
[ROW][C]3[/C][C]-0.104289[/C][C]-1.166[/C][C]0.12292[/C][/ROW]
[ROW][C]4[/C][C]-0.066563[/C][C]-0.7442[/C][C]0.229078[/C][/ROW]
[ROW][C]5[/C][C]0.11773[/C][C]1.3163[/C][C]0.095248[/C][/ROW]
[ROW][C]6[/C][C]-0.150448[/C][C]-1.6821[/C][C]0.047526[/C][/ROW]
[ROW][C]7[/C][C]0.183353[/C][C]2.0499[/C][C]0.02123[/C][/ROW]
[ROW][C]8[/C][C]-0.150306[/C][C]-1.6805[/C][C]0.047681[/C][/ROW]
[ROW][C]9[/C][C]0.010217[/C][C]0.1142[/C][C]0.45462[/C][/ROW]
[ROW][C]10[/C][C]0.095727[/C][C]1.0703[/C][C]0.143283[/C][/ROW]
[ROW][C]11[/C][C]-0.08303[/C][C]-0.9283[/C][C]0.177519[/C][/ROW]
[ROW][C]12[/C][C]0.149142[/C][C]1.6675[/C][C]0.048963[/C][/ROW]
[ROW][C]13[/C][C]-0.251678[/C][C]-2.8138[/C][C]0.002844[/C][/ROW]
[ROW][C]14[/C][C]0.18025[/C][C]2.0153[/C][C]0.023012[/C][/ROW]
[ROW][C]15[/C][C]-0.10885[/C][C]-1.217[/C][C]0.112952[/C][/ROW]
[ROW][C]16[/C][C]-9.5e-05[/C][C]-0.0011[/C][C]0.499578[/C][/ROW]
[ROW][C]17[/C][C]0.091129[/C][C]1.0189[/C][C]0.155119[/C][/ROW]
[ROW][C]18[/C][C]-0.145369[/C][C]-1.6253[/C][C]0.053312[/C][/ROW]
[ROW][C]19[/C][C]0.108755[/C][C]1.2159[/C][C]0.113153[/C][/ROW]
[ROW][C]20[/C][C]-0.032348[/C][C]-0.3617[/C][C]0.359106[/C][/ROW]
[ROW][C]21[/C][C]-0.060845[/C][C]-0.6803[/C][C]0.248798[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302302&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302302&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	-0.450127	-5.0326	1e-06
2	0.12257	1.3704	0.086514
3	-0.104289	-1.166	0.12292
4	-0.066563	-0.7442	0.229078
5	0.11773	1.3163	0.095248
6	-0.150448	-1.6821	0.047526
7	0.183353	2.0499	0.02123
8	-0.150306	-1.6805	0.047681
9	0.010217	0.1142	0.45462
10	0.095727	1.0703	0.143283
11	-0.08303	-0.9283	0.177519
12	0.149142	1.6675	0.048963
13	-0.251678	-2.8138	0.002844
14	0.18025	2.0153	0.023012
15	-0.10885	-1.217	0.112952
16	-9.5e-05	-0.0011	0.499578
17	0.091129	1.0189	0.155119
18	-0.145369	-1.6253	0.053312
19	0.108755	1.2159	0.113153
20	-0.032348	-0.3617	0.359106
21	-0.060845	-0.6803	0.248798

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.450127	-5.0326	1e-06
2	-0.100384	-1.1223	0.131938
3	-0.112452	-1.2573	0.105503
4	-0.193595	-2.1645	0.016165
5	0.00239	0.0267	0.489363
6	-0.130539	-1.4595	0.073472
7	0.053981	0.6035	0.273625
8	-0.057088	-0.6383	0.262234
9	-0.112779	-1.2609	0.104845
10	0.062485	0.6986	0.243048
11	0.002152	0.0241	0.490424
12	0.095825	1.0714	0.143037
13	-0.146915	-1.6426	0.051494
14	0.002381	0.0266	0.489402
15	-0.029886	-0.3341	0.369417
16	-0.083706	-0.9359	0.175574
17	0.003403	0.038	0.484855
18	-0.08495	-0.9498	0.172031
19	-0.061279	-0.6851	0.24727
20	0.053289	0.5958	0.276195
21	-0.146777	-1.641	0.051654

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.450127 & -5.0326 & 1e-06 \tabularnewline
2 & -0.100384 & -1.1223 & 0.131938 \tabularnewline
3 & -0.112452 & -1.2573 & 0.105503 \tabularnewline
4 & -0.193595 & -2.1645 & 0.016165 \tabularnewline
5 & 0.00239 & 0.0267 & 0.489363 \tabularnewline
6 & -0.130539 & -1.4595 & 0.073472 \tabularnewline
7 & 0.053981 & 0.6035 & 0.273625 \tabularnewline
8 & -0.057088 & -0.6383 & 0.262234 \tabularnewline
9 & -0.112779 & -1.2609 & 0.104845 \tabularnewline
10 & 0.062485 & 0.6986 & 0.243048 \tabularnewline
11 & 0.002152 & 0.0241 & 0.490424 \tabularnewline
12 & 0.095825 & 1.0714 & 0.143037 \tabularnewline
13 & -0.146915 & -1.6426 & 0.051494 \tabularnewline
14 & 0.002381 & 0.0266 & 0.489402 \tabularnewline
15 & -0.029886 & -0.3341 & 0.369417 \tabularnewline
16 & -0.083706 & -0.9359 & 0.175574 \tabularnewline
17 & 0.003403 & 0.038 & 0.484855 \tabularnewline
18 & -0.08495 & -0.9498 & 0.172031 \tabularnewline
19 & -0.061279 & -0.6851 & 0.24727 \tabularnewline
20 & 0.053289 & 0.5958 & 0.276195 \tabularnewline
21 & -0.146777 & -1.641 & 0.051654 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302302&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]-0.450127[/C][C]-5.0326[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.100384[/C][C]-1.1223[/C][C]0.131938[/C][/ROW]
[ROW][C]3[/C][C]-0.112452[/C][C]-1.2573[/C][C]0.105503[/C][/ROW]
[ROW][C]4[/C][C]-0.193595[/C][C]-2.1645[/C][C]0.016165[/C][/ROW]
[ROW][C]5[/C][C]0.00239[/C][C]0.0267[/C][C]0.489363[/C][/ROW]
[ROW][C]6[/C][C]-0.130539[/C][C]-1.4595[/C][C]0.073472[/C][/ROW]
[ROW][C]7[/C][C]0.053981[/C][C]0.6035[/C][C]0.273625[/C][/ROW]
[ROW][C]8[/C][C]-0.057088[/C][C]-0.6383[/C][C]0.262234[/C][/ROW]
[ROW][C]9[/C][C]-0.112779[/C][C]-1.2609[/C][C]0.104845[/C][/ROW]
[ROW][C]10[/C][C]0.062485[/C][C]0.6986[/C][C]0.243048[/C][/ROW]
[ROW][C]11[/C][C]0.002152[/C][C]0.0241[/C][C]0.490424[/C][/ROW]
[ROW][C]12[/C][C]0.095825[/C][C]1.0714[/C][C]0.143037[/C][/ROW]
[ROW][C]13[/C][C]-0.146915[/C][C]-1.6426[/C][C]0.051494[/C][/ROW]
[ROW][C]14[/C][C]0.002381[/C][C]0.0266[/C][C]0.489402[/C][/ROW]
[ROW][C]15[/C][C]-0.029886[/C][C]-0.3341[/C][C]0.369417[/C][/ROW]
[ROW][C]16[/C][C]-0.083706[/C][C]-0.9359[/C][C]0.175574[/C][/ROW]
[ROW][C]17[/C][C]0.003403[/C][C]0.038[/C][C]0.484855[/C][/ROW]
[ROW][C]18[/C][C]-0.08495[/C][C]-0.9498[/C][C]0.172031[/C][/ROW]
[ROW][C]19[/C][C]-0.061279[/C][C]-0.6851[/C][C]0.24727[/C][/ROW]
[ROW][C]20[/C][C]0.053289[/C][C]0.5958[/C][C]0.276195[/C][/ROW]
[ROW][C]21[/C][C]-0.146777[/C][C]-1.641[/C][C]0.051654[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302302&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302302&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	-0.450127	-5.0326	1e-06
2	-0.100384	-1.1223	0.131938
3	-0.112452	-1.2573	0.105503
4	-0.193595	-2.1645	0.016165
5	0.00239	0.0267	0.489363
6	-0.130539	-1.4595	0.073472
7	0.053981	0.6035	0.273625
8	-0.057088	-0.6383	0.262234
9	-0.112779	-1.2609	0.104845
10	0.062485	0.6986	0.243048
11	0.002152	0.0241	0.490424
12	0.095825	1.0714	0.143037
13	-0.146915	-1.6426	0.051494
14	0.002381	0.0266	0.489402
15	-0.029886	-0.3341	0.369417
16	-0.083706	-0.9359	0.175574
17	0.003403	0.038	0.484855
18	-0.08495	-0.9498	0.172031
19	-0.061279	-0.6851	0.24727
20	0.053289	0.5958	0.276195
21	-0.146777	-1.641	0.051654

Figure 1

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Figure 2

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Figure 3

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Parameters (Session):

par1 = 1 ;

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 <- '1'
par4 <- '0'
par3 <- '1'
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code