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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 06 Sep 2017 13:56:53 +0200

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/2017/Sep/06/t15046990365xrm8t6h7494xwq.htm/, Retrieved Thu, 16 May 2024 01:31:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307647, Retrieved Thu, 16 May 2024 01:31:05 +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] [vvv] [2017-09-06 11:56:53] [5a51f23852103e2c2ec1d52ada9b446b] [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=307647&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=307647&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307647&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	-0.674479	-7.3267	0
2	0.030821	0.3348	0.369184
3	0.434011	4.7146	3e-06
4	-0.469393	-5.0989	1e-06
5	0.119587	1.299	0.098231
6	0.309201	3.3588	0.000527
7	-0.491374	-5.3377	0
8	0.322699	3.5054	0.000323
9	0.049072	0.5331	0.297498
10	-0.343411	-3.7304	0.000148
11	0.373151	4.0535	4.5e-05
12	-0.159815	-1.736	0.042584
13	-0.1074	-1.1667	0.12285
14	0.202432	2.199	0.014915
15	-0.084972	-0.923	0.178937
16	-0.102119	-1.1093	0.134778
17	0.207341	2.2523	0.013076
18	-0.146802	-1.5947	0.05673
19	-0.02355	-0.2558	0.399267
20	0.130235	1.4147	0.079893
21	-0.057092	-0.6202	0.268167

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.674479 & -7.3267 & 0 \tabularnewline
2 & 0.030821 & 0.3348 & 0.369184 \tabularnewline
3 & 0.434011 & 4.7146 & 3e-06 \tabularnewline
4 & -0.469393 & -5.0989 & 1e-06 \tabularnewline
5 & 0.119587 & 1.299 & 0.098231 \tabularnewline
6 & 0.309201 & 3.3588 & 0.000527 \tabularnewline
7 & -0.491374 & -5.3377 & 0 \tabularnewline
8 & 0.322699 & 3.5054 & 0.000323 \tabularnewline
9 & 0.049072 & 0.5331 & 0.297498 \tabularnewline
10 & -0.343411 & -3.7304 & 0.000148 \tabularnewline
11 & 0.373151 & 4.0535 & 4.5e-05 \tabularnewline
12 & -0.159815 & -1.736 & 0.042584 \tabularnewline
13 & -0.1074 & -1.1667 & 0.12285 \tabularnewline
14 & 0.202432 & 2.199 & 0.014915 \tabularnewline
15 & -0.084972 & -0.923 & 0.178937 \tabularnewline
16 & -0.102119 & -1.1093 & 0.134778 \tabularnewline
17 & 0.207341 & 2.2523 & 0.013076 \tabularnewline
18 & -0.146802 & -1.5947 & 0.05673 \tabularnewline
19 & -0.02355 & -0.2558 & 0.399267 \tabularnewline
20 & 0.130235 & 1.4147 & 0.079893 \tabularnewline
21 & -0.057092 & -0.6202 & 0.268167 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307647&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]-0.674479[/C][C]-7.3267[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.030821[/C][C]0.3348[/C][C]0.369184[/C][/ROW]
[ROW][C]3[/C][C]0.434011[/C][C]4.7146[/C][C]3e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.469393[/C][C]-5.0989[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]0.119587[/C][C]1.299[/C][C]0.098231[/C][/ROW]
[ROW][C]6[/C][C]0.309201[/C][C]3.3588[/C][C]0.000527[/C][/ROW]
[ROW][C]7[/C][C]-0.491374[/C][C]-5.3377[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.322699[/C][C]3.5054[/C][C]0.000323[/C][/ROW]
[ROW][C]9[/C][C]0.049072[/C][C]0.5331[/C][C]0.297498[/C][/ROW]
[ROW][C]10[/C][C]-0.343411[/C][C]-3.7304[/C][C]0.000148[/C][/ROW]
[ROW][C]11[/C][C]0.373151[/C][C]4.0535[/C][C]4.5e-05[/C][/ROW]
[ROW][C]12[/C][C]-0.159815[/C][C]-1.736[/C][C]0.042584[/C][/ROW]
[ROW][C]13[/C][C]-0.1074[/C][C]-1.1667[/C][C]0.12285[/C][/ROW]
[ROW][C]14[/C][C]0.202432[/C][C]2.199[/C][C]0.014915[/C][/ROW]
[ROW][C]15[/C][C]-0.084972[/C][C]-0.923[/C][C]0.178937[/C][/ROW]
[ROW][C]16[/C][C]-0.102119[/C][C]-1.1093[/C][C]0.134778[/C][/ROW]
[ROW][C]17[/C][C]0.207341[/C][C]2.2523[/C][C]0.013076[/C][/ROW]
[ROW][C]18[/C][C]-0.146802[/C][C]-1.5947[/C][C]0.05673[/C][/ROW]
[ROW][C]19[/C][C]-0.02355[/C][C]-0.2558[/C][C]0.399267[/C][/ROW]
[ROW][C]20[/C][C]0.130235[/C][C]1.4147[/C][C]0.079893[/C][/ROW]
[ROW][C]21[/C][C]-0.057092[/C][C]-0.6202[/C][C]0.268167[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307647&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307647&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	-0.674479	-7.3267	0
2	0.030821	0.3348	0.369184
3	0.434011	4.7146	3e-06
4	-0.469393	-5.0989	1e-06
5	0.119587	1.299	0.098231
6	0.309201	3.3588	0.000527
7	-0.491374	-5.3377	0
8	0.322699	3.5054	0.000323
9	0.049072	0.5331	0.297498
10	-0.343411	-3.7304	0.000148
11	0.373151	4.0535	4.5e-05
12	-0.159815	-1.736	0.042584
13	-0.1074	-1.1667	0.12285
14	0.202432	2.199	0.014915
15	-0.084972	-0.923	0.178937
16	-0.102119	-1.1093	0.134778
17	0.207341	2.2523	0.013076
18	-0.146802	-1.5947	0.05673
19	-0.02355	-0.2558	0.399267
20	0.130235	1.4147	0.079893
21	-0.057092	-0.6202	0.268167

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.674479	-7.3267	0
2	-0.778054	-8.4518	0
3	-0.250147	-2.7173	0.003787
4	0.000383	0.0042	0.498343
5	-0.29256	-3.178	0.000947
6	-0.020866	-0.2267	0.410541
7	-0.040989	-0.4453	0.328476
8	-0.057492	-0.6245	0.266746
9	0.056117	0.6096	0.271655
10	0.001606	0.0174	0.493056
11	0.074523	0.8095	0.209919
12	-0.005374	-0.0584	0.476773
13	0.083366	0.9056	0.1835
14	-0.160401	-1.7424	0.042022
15	-0.06906	-0.7502	0.22732
16	0.009402	0.1021	0.459411
17	0.004373	0.0475	0.481096
18	0.091774	0.9969	0.160421
19	0.012253	0.1331	0.447169
20	-0.1158	-1.2579	0.105453
21	0.157019	1.7057	0.045351

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.674479 & -7.3267 & 0 \tabularnewline
2 & -0.778054 & -8.4518 & 0 \tabularnewline
3 & -0.250147 & -2.7173 & 0.003787 \tabularnewline
4 & 0.000383 & 0.0042 & 0.498343 \tabularnewline
5 & -0.29256 & -3.178 & 0.000947 \tabularnewline
6 & -0.020866 & -0.2267 & 0.410541 \tabularnewline
7 & -0.040989 & -0.4453 & 0.328476 \tabularnewline
8 & -0.057492 & -0.6245 & 0.266746 \tabularnewline
9 & 0.056117 & 0.6096 & 0.271655 \tabularnewline
10 & 0.001606 & 0.0174 & 0.493056 \tabularnewline
11 & 0.074523 & 0.8095 & 0.209919 \tabularnewline
12 & -0.005374 & -0.0584 & 0.476773 \tabularnewline
13 & 0.083366 & 0.9056 & 0.1835 \tabularnewline
14 & -0.160401 & -1.7424 & 0.042022 \tabularnewline
15 & -0.06906 & -0.7502 & 0.22732 \tabularnewline
16 & 0.009402 & 0.1021 & 0.459411 \tabularnewline
17 & 0.004373 & 0.0475 & 0.481096 \tabularnewline
18 & 0.091774 & 0.9969 & 0.160421 \tabularnewline
19 & 0.012253 & 0.1331 & 0.447169 \tabularnewline
20 & -0.1158 & -1.2579 & 0.105453 \tabularnewline
21 & 0.157019 & 1.7057 & 0.045351 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307647&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]-0.674479[/C][C]-7.3267[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.778054[/C][C]-8.4518[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.250147[/C][C]-2.7173[/C][C]0.003787[/C][/ROW]
[ROW][C]4[/C][C]0.000383[/C][C]0.0042[/C][C]0.498343[/C][/ROW]
[ROW][C]5[/C][C]-0.29256[/C][C]-3.178[/C][C]0.000947[/C][/ROW]
[ROW][C]6[/C][C]-0.020866[/C][C]-0.2267[/C][C]0.410541[/C][/ROW]
[ROW][C]7[/C][C]-0.040989[/C][C]-0.4453[/C][C]0.328476[/C][/ROW]
[ROW][C]8[/C][C]-0.057492[/C][C]-0.6245[/C][C]0.266746[/C][/ROW]
[ROW][C]9[/C][C]0.056117[/C][C]0.6096[/C][C]0.271655[/C][/ROW]
[ROW][C]10[/C][C]0.001606[/C][C]0.0174[/C][C]0.493056[/C][/ROW]
[ROW][C]11[/C][C]0.074523[/C][C]0.8095[/C][C]0.209919[/C][/ROW]
[ROW][C]12[/C][C]-0.005374[/C][C]-0.0584[/C][C]0.476773[/C][/ROW]
[ROW][C]13[/C][C]0.083366[/C][C]0.9056[/C][C]0.1835[/C][/ROW]
[ROW][C]14[/C][C]-0.160401[/C][C]-1.7424[/C][C]0.042022[/C][/ROW]
[ROW][C]15[/C][C]-0.06906[/C][C]-0.7502[/C][C]0.22732[/C][/ROW]
[ROW][C]16[/C][C]0.009402[/C][C]0.1021[/C][C]0.459411[/C][/ROW]
[ROW][C]17[/C][C]0.004373[/C][C]0.0475[/C][C]0.481096[/C][/ROW]
[ROW][C]18[/C][C]0.091774[/C][C]0.9969[/C][C]0.160421[/C][/ROW]
[ROW][C]19[/C][C]0.012253[/C][C]0.1331[/C][C]0.447169[/C][/ROW]
[ROW][C]20[/C][C]-0.1158[/C][C]-1.2579[/C][C]0.105453[/C][/ROW]
[ROW][C]21[/C][C]0.157019[/C][C]1.7057[/C][C]0.045351[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307647&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307647&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	-0.674479	-7.3267	0
2	-0.778054	-8.4518	0
3	-0.250147	-2.7173	0.003787
4	0.000383	0.0042	0.498343
5	-0.29256	-3.178	0.000947
6	-0.020866	-0.2267	0.410541
7	-0.040989	-0.4453	0.328476
8	-0.057492	-0.6245	0.266746
9	0.056117	0.6096	0.271655
10	0.001606	0.0174	0.493056
11	0.074523	0.8095	0.209919
12	-0.005374	-0.0584	0.476773
13	0.083366	0.9056	0.1835
14	-0.160401	-1.7424	0.042022
15	-0.06906	-0.7502	0.22732
16	0.009402	0.1021	0.459411
17	0.004373	0.0475	0.481096
18	0.091774	0.9969	0.160421
19	0.012253	0.1331	0.447169
20	-0.1158	-1.2579	0.105453
21	0.157019	1.7057	0.045351

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 = 2 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 1 ; 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 <- '12'
par4 <- '0'
par3 <- '2'
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