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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 19 Dec 2016 15:20:38 +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/19/t1482157272kotn5qbxmrtl1fy.htm/, Retrieved Fri, 17 May 2024 16:49:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301366, Retrieved Fri, 17 May 2024 16:49:54 +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] [auto 1 0] [2016-12-19 14:20:38] [06fd994a2f2098873ec640c3e39346e5] [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=301366&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=301366&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301366&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	-0.307512	-3.4381	0.000398
2	0.162268	1.8142	0.036022
3	0.155889	1.7429	0.041906
4	-0.382321	-4.2745	1.9e-05
5	0.097538	1.0905	0.138794
6	-0.371164	-4.1497	3.1e-05
7	0.041235	0.461	0.322791
8	-0.338943	-3.7895	0.000117
9	0.144957	1.6207	0.053804
10	0.107166	1.1982	0.116562
11	-0.107487	-1.2017	0.115868
12	0.66784	7.4667	0
13	-0.294132	-3.2885	0.000654
14	0.285989	3.1975	0.000878
15	0.079222	0.8857	0.188731
16	-0.332141	-3.7134	0.000153
17	0.137094	1.5328	0.063932
18	-0.383251	-4.2849	1.8e-05
19	0.00061	0.0068	0.497285
20	-0.209465	-2.3419	0.010384
21	0.03683	0.4118	0.340604

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.307512 & -3.4381 & 0.000398 \tabularnewline
2 & 0.162268 & 1.8142 & 0.036022 \tabularnewline
3 & 0.155889 & 1.7429 & 0.041906 \tabularnewline
4 & -0.382321 & -4.2745 & 1.9e-05 \tabularnewline
5 & 0.097538 & 1.0905 & 0.138794 \tabularnewline
6 & -0.371164 & -4.1497 & 3.1e-05 \tabularnewline
7 & 0.041235 & 0.461 & 0.322791 \tabularnewline
8 & -0.338943 & -3.7895 & 0.000117 \tabularnewline
9 & 0.144957 & 1.6207 & 0.053804 \tabularnewline
10 & 0.107166 & 1.1982 & 0.116562 \tabularnewline
11 & -0.107487 & -1.2017 & 0.115868 \tabularnewline
12 & 0.66784 & 7.4667 & 0 \tabularnewline
13 & -0.294132 & -3.2885 & 0.000654 \tabularnewline
14 & 0.285989 & 3.1975 & 0.000878 \tabularnewline
15 & 0.079222 & 0.8857 & 0.188731 \tabularnewline
16 & -0.332141 & -3.7134 & 0.000153 \tabularnewline
17 & 0.137094 & 1.5328 & 0.063932 \tabularnewline
18 & -0.383251 & -4.2849 & 1.8e-05 \tabularnewline
19 & 0.00061 & 0.0068 & 0.497285 \tabularnewline
20 & -0.209465 & -2.3419 & 0.010384 \tabularnewline
21 & 0.03683 & 0.4118 & 0.340604 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301366&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]-0.307512[/C][C]-3.4381[/C][C]0.000398[/C][/ROW]
[ROW][C]2[/C][C]0.162268[/C][C]1.8142[/C][C]0.036022[/C][/ROW]
[ROW][C]3[/C][C]0.155889[/C][C]1.7429[/C][C]0.041906[/C][/ROW]
[ROW][C]4[/C][C]-0.382321[/C][C]-4.2745[/C][C]1.9e-05[/C][/ROW]
[ROW][C]5[/C][C]0.097538[/C][C]1.0905[/C][C]0.138794[/C][/ROW]
[ROW][C]6[/C][C]-0.371164[/C][C]-4.1497[/C][C]3.1e-05[/C][/ROW]
[ROW][C]7[/C][C]0.041235[/C][C]0.461[/C][C]0.322791[/C][/ROW]
[ROW][C]8[/C][C]-0.338943[/C][C]-3.7895[/C][C]0.000117[/C][/ROW]
[ROW][C]9[/C][C]0.144957[/C][C]1.6207[/C][C]0.053804[/C][/ROW]
[ROW][C]10[/C][C]0.107166[/C][C]1.1982[/C][C]0.116562[/C][/ROW]
[ROW][C]11[/C][C]-0.107487[/C][C]-1.2017[/C][C]0.115868[/C][/ROW]
[ROW][C]12[/C][C]0.66784[/C][C]7.4667[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.294132[/C][C]-3.2885[/C][C]0.000654[/C][/ROW]
[ROW][C]14[/C][C]0.285989[/C][C]3.1975[/C][C]0.000878[/C][/ROW]
[ROW][C]15[/C][C]0.079222[/C][C]0.8857[/C][C]0.188731[/C][/ROW]
[ROW][C]16[/C][C]-0.332141[/C][C]-3.7134[/C][C]0.000153[/C][/ROW]
[ROW][C]17[/C][C]0.137094[/C][C]1.5328[/C][C]0.063932[/C][/ROW]
[ROW][C]18[/C][C]-0.383251[/C][C]-4.2849[/C][C]1.8e-05[/C][/ROW]
[ROW][C]19[/C][C]0.00061[/C][C]0.0068[/C][C]0.497285[/C][/ROW]
[ROW][C]20[/C][C]-0.209465[/C][C]-2.3419[/C][C]0.010384[/C][/ROW]
[ROW][C]21[/C][C]0.03683[/C][C]0.4118[/C][C]0.340604[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301366&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301366&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	-0.307512	-3.4381	0.000398
2	0.162268	1.8142	0.036022
3	0.155889	1.7429	0.041906
4	-0.382321	-4.2745	1.9e-05
5	0.097538	1.0905	0.138794
6	-0.371164	-4.1497	3.1e-05
7	0.041235	0.461	0.322791
8	-0.338943	-3.7895	0.000117
9	0.144957	1.6207	0.053804
10	0.107166	1.1982	0.116562
11	-0.107487	-1.2017	0.115868
12	0.66784	7.4667	0
13	-0.294132	-3.2885	0.000654
14	0.285989	3.1975	0.000878
15	0.079222	0.8857	0.188731
16	-0.332141	-3.7134	0.000153
17	0.137094	1.5328	0.063932
18	-0.383251	-4.2849	1.8e-05
19	0.00061	0.0068	0.497285
20	-0.209465	-2.3419	0.010384
21	0.03683	0.4118	0.340604

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.307512	-3.4381	0.000398
2	0.074775	0.836	0.202373
3	0.249953	2.7946	0.003008
4	-0.333914	-3.7333	0.000143
5	-0.1915	-2.141	0.017106
6	-0.394564	-4.4114	1.1e-05
7	-0.044985	-0.5029	0.307945
8	-0.543388	-6.0753	0
9	-0.10054	-1.1241	0.131569
10	-0.169503	-1.8951	0.030194
11	-0.164604	-1.8403	0.034046
12	0.330143	3.6911	0.000166
13	-0.053573	-0.599	0.275141
14	0.042208	0.4719	0.318911
15	0.063313	0.7079	0.240175
16	-0.040863	-0.4569	0.324282
17	0.001166	0.013	0.49481
18	-0.044602	-0.4987	0.309446
19	-0.054267	-0.6067	0.272568
20	0.035629	0.3983	0.345528
21	-0.146062	-1.633	0.052491

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.307512 & -3.4381 & 0.000398 \tabularnewline
2 & 0.074775 & 0.836 & 0.202373 \tabularnewline
3 & 0.249953 & 2.7946 & 0.003008 \tabularnewline
4 & -0.333914 & -3.7333 & 0.000143 \tabularnewline
5 & -0.1915 & -2.141 & 0.017106 \tabularnewline
6 & -0.394564 & -4.4114 & 1.1e-05 \tabularnewline
7 & -0.044985 & -0.5029 & 0.307945 \tabularnewline
8 & -0.543388 & -6.0753 & 0 \tabularnewline
9 & -0.10054 & -1.1241 & 0.131569 \tabularnewline
10 & -0.169503 & -1.8951 & 0.030194 \tabularnewline
11 & -0.164604 & -1.8403 & 0.034046 \tabularnewline
12 & 0.330143 & 3.6911 & 0.000166 \tabularnewline
13 & -0.053573 & -0.599 & 0.275141 \tabularnewline
14 & 0.042208 & 0.4719 & 0.318911 \tabularnewline
15 & 0.063313 & 0.7079 & 0.240175 \tabularnewline
16 & -0.040863 & -0.4569 & 0.324282 \tabularnewline
17 & 0.001166 & 0.013 & 0.49481 \tabularnewline
18 & -0.044602 & -0.4987 & 0.309446 \tabularnewline
19 & -0.054267 & -0.6067 & 0.272568 \tabularnewline
20 & 0.035629 & 0.3983 & 0.345528 \tabularnewline
21 & -0.146062 & -1.633 & 0.052491 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301366&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]-0.307512[/C][C]-3.4381[/C][C]0.000398[/C][/ROW]
[ROW][C]2[/C][C]0.074775[/C][C]0.836[/C][C]0.202373[/C][/ROW]
[ROW][C]3[/C][C]0.249953[/C][C]2.7946[/C][C]0.003008[/C][/ROW]
[ROW][C]4[/C][C]-0.333914[/C][C]-3.7333[/C][C]0.000143[/C][/ROW]
[ROW][C]5[/C][C]-0.1915[/C][C]-2.141[/C][C]0.017106[/C][/ROW]
[ROW][C]6[/C][C]-0.394564[/C][C]-4.4114[/C][C]1.1e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.044985[/C][C]-0.5029[/C][C]0.307945[/C][/ROW]
[ROW][C]8[/C][C]-0.543388[/C][C]-6.0753[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]-0.10054[/C][C]-1.1241[/C][C]0.131569[/C][/ROW]
[ROW][C]10[/C][C]-0.169503[/C][C]-1.8951[/C][C]0.030194[/C][/ROW]
[ROW][C]11[/C][C]-0.164604[/C][C]-1.8403[/C][C]0.034046[/C][/ROW]
[ROW][C]12[/C][C]0.330143[/C][C]3.6911[/C][C]0.000166[/C][/ROW]
[ROW][C]13[/C][C]-0.053573[/C][C]-0.599[/C][C]0.275141[/C][/ROW]
[ROW][C]14[/C][C]0.042208[/C][C]0.4719[/C][C]0.318911[/C][/ROW]
[ROW][C]15[/C][C]0.063313[/C][C]0.7079[/C][C]0.240175[/C][/ROW]
[ROW][C]16[/C][C]-0.040863[/C][C]-0.4569[/C][C]0.324282[/C][/ROW]
[ROW][C]17[/C][C]0.001166[/C][C]0.013[/C][C]0.49481[/C][/ROW]
[ROW][C]18[/C][C]-0.044602[/C][C]-0.4987[/C][C]0.309446[/C][/ROW]
[ROW][C]19[/C][C]-0.054267[/C][C]-0.6067[/C][C]0.272568[/C][/ROW]
[ROW][C]20[/C][C]0.035629[/C][C]0.3983[/C][C]0.345528[/C][/ROW]
[ROW][C]21[/C][C]-0.146062[/C][C]-1.633[/C][C]0.052491[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301366&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301366&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	-0.307512	-3.4381	0.000398
2	0.074775	0.836	0.202373
3	0.249953	2.7946	0.003008
4	-0.333914	-3.7333	0.000143
5	-0.1915	-2.141	0.017106
6	-0.394564	-4.4114	1.1e-05
7	-0.044985	-0.5029	0.307945
8	-0.543388	-6.0753	0
9	-0.10054	-1.1241	0.131569
10	-0.169503	-1.8951	0.030194
11	-0.164604	-1.8403	0.034046
12	0.330143	3.6911	0.000166
13	-0.053573	-0.599	0.275141
14	0.042208	0.4719	0.318911
15	0.063313	0.7079	0.240175
16	-0.040863	-0.4569	0.324282
17	0.001166	0.013	0.49481
18	-0.044602	-0.4987	0.309446
19	-0.054267	-0.6067	0.272568
20	0.035629	0.3983	0.345528
21	-0.146062	-1.633	0.052491

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

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Parameters (Session):

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