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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 30 Nov 2016 14:33:18 +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/Nov/30/t1480513504ntfb0vnmo4jar26.htm/, Retrieved Sun, 19 May 2024 01:28:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297417, Retrieved Sun, 19 May 2024 01:28:43 +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] [] [2016-11-30 13:33:18] [d06ec19b175650a2a09ee5879d174acf] [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=297417&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=297417&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297417&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	0.420915	4.5138	8e-06
2	0.444929	4.7713	3e-06
3	0.419106	4.4944	8e-06
4	0.364332	3.907	7.9e-05
5	0.284602	3.052	0.001412
6	0.349266	3.7455	0.000141
7	0.320448	3.4364	0.000411
8	0.342625	3.6742	0.000182
9	0.296342	3.1779	0.000953
10	0.318634	3.417	0.000438
11	0.30355	3.2552	0.000744
12	0.264084	2.832	0.002732
13	0.278524	2.9868	0.001723
14	0.287682	3.085	0.001275
15	0.251079	2.6925	0.004076
16	0.191119	2.0495	0.021343
17	0.253429	2.7177	0.003795
18	0.238574	2.5584	0.005907
19	0.215933	2.3156	0.011176
20	0.239373	2.567	0.005771

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.420915 & 4.5138 & 8e-06 \tabularnewline
2 & 0.444929 & 4.7713 & 3e-06 \tabularnewline
3 & 0.419106 & 4.4944 & 8e-06 \tabularnewline
4 & 0.364332 & 3.907 & 7.9e-05 \tabularnewline
5 & 0.284602 & 3.052 & 0.001412 \tabularnewline
6 & 0.349266 & 3.7455 & 0.000141 \tabularnewline
7 & 0.320448 & 3.4364 & 0.000411 \tabularnewline
8 & 0.342625 & 3.6742 & 0.000182 \tabularnewline
9 & 0.296342 & 3.1779 & 0.000953 \tabularnewline
10 & 0.318634 & 3.417 & 0.000438 \tabularnewline
11 & 0.30355 & 3.2552 & 0.000744 \tabularnewline
12 & 0.264084 & 2.832 & 0.002732 \tabularnewline
13 & 0.278524 & 2.9868 & 0.001723 \tabularnewline
14 & 0.287682 & 3.085 & 0.001275 \tabularnewline
15 & 0.251079 & 2.6925 & 0.004076 \tabularnewline
16 & 0.191119 & 2.0495 & 0.021343 \tabularnewline
17 & 0.253429 & 2.7177 & 0.003795 \tabularnewline
18 & 0.238574 & 2.5584 & 0.005907 \tabularnewline
19 & 0.215933 & 2.3156 & 0.011176 \tabularnewline
20 & 0.239373 & 2.567 & 0.005771 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297417&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]0.420915[/C][C]4.5138[/C][C]8e-06[/C][/ROW]
[ROW][C]2[/C][C]0.444929[/C][C]4.7713[/C][C]3e-06[/C][/ROW]
[ROW][C]3[/C][C]0.419106[/C][C]4.4944[/C][C]8e-06[/C][/ROW]
[ROW][C]4[/C][C]0.364332[/C][C]3.907[/C][C]7.9e-05[/C][/ROW]
[ROW][C]5[/C][C]0.284602[/C][C]3.052[/C][C]0.001412[/C][/ROW]
[ROW][C]6[/C][C]0.349266[/C][C]3.7455[/C][C]0.000141[/C][/ROW]
[ROW][C]7[/C][C]0.320448[/C][C]3.4364[/C][C]0.000411[/C][/ROW]
[ROW][C]8[/C][C]0.342625[/C][C]3.6742[/C][C]0.000182[/C][/ROW]
[ROW][C]9[/C][C]0.296342[/C][C]3.1779[/C][C]0.000953[/C][/ROW]
[ROW][C]10[/C][C]0.318634[/C][C]3.417[/C][C]0.000438[/C][/ROW]
[ROW][C]11[/C][C]0.30355[/C][C]3.2552[/C][C]0.000744[/C][/ROW]
[ROW][C]12[/C][C]0.264084[/C][C]2.832[/C][C]0.002732[/C][/ROW]
[ROW][C]13[/C][C]0.278524[/C][C]2.9868[/C][C]0.001723[/C][/ROW]
[ROW][C]14[/C][C]0.287682[/C][C]3.085[/C][C]0.001275[/C][/ROW]
[ROW][C]15[/C][C]0.251079[/C][C]2.6925[/C][C]0.004076[/C][/ROW]
[ROW][C]16[/C][C]0.191119[/C][C]2.0495[/C][C]0.021343[/C][/ROW]
[ROW][C]17[/C][C]0.253429[/C][C]2.7177[/C][C]0.003795[/C][/ROW]
[ROW][C]18[/C][C]0.238574[/C][C]2.5584[/C][C]0.005907[/C][/ROW]
[ROW][C]19[/C][C]0.215933[/C][C]2.3156[/C][C]0.011176[/C][/ROW]
[ROW][C]20[/C][C]0.239373[/C][C]2.567[/C][C]0.005771[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297417&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297417&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	0.420915	4.5138	8e-06
2	0.444929	4.7713	3e-06
3	0.419106	4.4944	8e-06
4	0.364332	3.907	7.9e-05
5	0.284602	3.052	0.001412
6	0.349266	3.7455	0.000141
7	0.320448	3.4364	0.000411
8	0.342625	3.6742	0.000182
9	0.296342	3.1779	0.000953
10	0.318634	3.417	0.000438
11	0.30355	3.2552	0.000744
12	0.264084	2.832	0.002732
13	0.278524	2.9868	0.001723
14	0.287682	3.085	0.001275
15	0.251079	2.6925	0.004076
16	0.191119	2.0495	0.021343
17	0.253429	2.7177	0.003795
18	0.238574	2.5584	0.005907
19	0.215933	2.3156	0.011176
20	0.239373	2.567	0.005771

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.420915	4.5138	8e-06
2	0.325413	3.4897	0.000343
3	0.211771	2.271	0.012504
4	0.095405	1.0231	0.154202
5	-0.017531	-0.188	0.425605
6	0.123807	1.3277	0.093456
7	0.088435	0.9484	0.172469
8	0.111106	1.1915	0.11796
9	0.013746	0.1474	0.441534
10	0.047806	0.5127	0.304587
11	0.048961	0.5251	0.30028
12	-0.009003	-0.0965	0.461628
13	0.037685	0.4041	0.343435
14	0.046721	0.501	0.308656
15	0.004108	0.0441	0.482469
16	-0.086881	-0.9317	0.176723
17	0.046598	0.4997	0.309116
18	0.048875	0.5241	0.300601
19	0.009623	0.1032	0.458993
20	0.030519	0.3273	0.372025

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.420915 & 4.5138 & 8e-06 \tabularnewline
2 & 0.325413 & 3.4897 & 0.000343 \tabularnewline
3 & 0.211771 & 2.271 & 0.012504 \tabularnewline
4 & 0.095405 & 1.0231 & 0.154202 \tabularnewline
5 & -0.017531 & -0.188 & 0.425605 \tabularnewline
6 & 0.123807 & 1.3277 & 0.093456 \tabularnewline
7 & 0.088435 & 0.9484 & 0.172469 \tabularnewline
8 & 0.111106 & 1.1915 & 0.11796 \tabularnewline
9 & 0.013746 & 0.1474 & 0.441534 \tabularnewline
10 & 0.047806 & 0.5127 & 0.304587 \tabularnewline
11 & 0.048961 & 0.5251 & 0.30028 \tabularnewline
12 & -0.009003 & -0.0965 & 0.461628 \tabularnewline
13 & 0.037685 & 0.4041 & 0.343435 \tabularnewline
14 & 0.046721 & 0.501 & 0.308656 \tabularnewline
15 & 0.004108 & 0.0441 & 0.482469 \tabularnewline
16 & -0.086881 & -0.9317 & 0.176723 \tabularnewline
17 & 0.046598 & 0.4997 & 0.309116 \tabularnewline
18 & 0.048875 & 0.5241 & 0.300601 \tabularnewline
19 & 0.009623 & 0.1032 & 0.458993 \tabularnewline
20 & 0.030519 & 0.3273 & 0.372025 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297417&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]0.420915[/C][C]4.5138[/C][C]8e-06[/C][/ROW]
[ROW][C]2[/C][C]0.325413[/C][C]3.4897[/C][C]0.000343[/C][/ROW]
[ROW][C]3[/C][C]0.211771[/C][C]2.271[/C][C]0.012504[/C][/ROW]
[ROW][C]4[/C][C]0.095405[/C][C]1.0231[/C][C]0.154202[/C][/ROW]
[ROW][C]5[/C][C]-0.017531[/C][C]-0.188[/C][C]0.425605[/C][/ROW]
[ROW][C]6[/C][C]0.123807[/C][C]1.3277[/C][C]0.093456[/C][/ROW]
[ROW][C]7[/C][C]0.088435[/C][C]0.9484[/C][C]0.172469[/C][/ROW]
[ROW][C]8[/C][C]0.111106[/C][C]1.1915[/C][C]0.11796[/C][/ROW]
[ROW][C]9[/C][C]0.013746[/C][C]0.1474[/C][C]0.441534[/C][/ROW]
[ROW][C]10[/C][C]0.047806[/C][C]0.5127[/C][C]0.304587[/C][/ROW]
[ROW][C]11[/C][C]0.048961[/C][C]0.5251[/C][C]0.30028[/C][/ROW]
[ROW][C]12[/C][C]-0.009003[/C][C]-0.0965[/C][C]0.461628[/C][/ROW]
[ROW][C]13[/C][C]0.037685[/C][C]0.4041[/C][C]0.343435[/C][/ROW]
[ROW][C]14[/C][C]0.046721[/C][C]0.501[/C][C]0.308656[/C][/ROW]
[ROW][C]15[/C][C]0.004108[/C][C]0.0441[/C][C]0.482469[/C][/ROW]
[ROW][C]16[/C][C]-0.086881[/C][C]-0.9317[/C][C]0.176723[/C][/ROW]
[ROW][C]17[/C][C]0.046598[/C][C]0.4997[/C][C]0.309116[/C][/ROW]
[ROW][C]18[/C][C]0.048875[/C][C]0.5241[/C][C]0.300601[/C][/ROW]
[ROW][C]19[/C][C]0.009623[/C][C]0.1032[/C][C]0.458993[/C][/ROW]
[ROW][C]20[/C][C]0.030519[/C][C]0.3273[/C][C]0.372025[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297417&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297417&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	0.420915	4.5138	8e-06
2	0.325413	3.4897	0.000343
3	0.211771	2.271	0.012504
4	0.095405	1.0231	0.154202
5	-0.017531	-0.188	0.425605
6	0.123807	1.3277	0.093456
7	0.088435	0.9484	0.172469
8	0.111106	1.1915	0.11796
9	0.013746	0.1474	0.441534
10	0.047806	0.5127	0.304587
11	0.048961	0.5251	0.30028
12	-0.009003	-0.0965	0.461628
13	0.037685	0.4041	0.343435
14	0.046721	0.501	0.308656
15	0.004108	0.0441	0.482469
16	-0.086881	-0.9317	0.176723
17	0.046598	0.4997	0.309116
18	0.048875	0.5241	0.300601
19	0.009623	0.1032	0.458993
20	0.030519	0.3273	0.372025

Figure 1

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Figure 2

PNG link

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Figure 3

PNG link

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Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code