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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 11 Dec 2016 17:45:30 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/11/t1481474894tkb7qauk3lqcs18.htm/, Retrieved Thu, 02 May 2024 06:14:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298829, Retrieved Thu, 02 May 2024 06:14:20 +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] [Autocorrelation f...] [2016-12-11 16:45:30] [10299735033611e1e2dae6371997f8c9] [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=298829&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=298829&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298829&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	-0.155736	-1.5806	0.058523
2	-0.539587	-5.4762	0
3	0.014818	0.1504	0.440378
4	0.513167	5.2081	0
5	0.124116	1.2596	0.105323
6	-0.871881	-8.8486	0
7	0.122374	1.242	0.108537
8	0.502597	5.1008	1e-06
9	-0.032567	-0.3305	0.37084
10	-0.47579	-4.8287	2e-06
11	-0.09589	-0.9732	0.166372
12	0.743366	7.5443	0
13	-0.095341	-0.9676	0.167755
14	-0.483177	-4.9037	2e-06
15	0.053422	0.5422	0.294433
16	0.456667	4.6347	5e-06
17	0.066686	0.6768	0.250029
18	-0.664898	-6.748	0
19	0.094469	0.9588	0.169963
20	0.453816	4.6057	6e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.155736 & -1.5806 & 0.058523 \tabularnewline
2 & -0.539587 & -5.4762 & 0 \tabularnewline
3 & 0.014818 & 0.1504 & 0.440378 \tabularnewline
4 & 0.513167 & 5.2081 & 0 \tabularnewline
5 & 0.124116 & 1.2596 & 0.105323 \tabularnewline
6 & -0.871881 & -8.8486 & 0 \tabularnewline
7 & 0.122374 & 1.242 & 0.108537 \tabularnewline
8 & 0.502597 & 5.1008 & 1e-06 \tabularnewline
9 & -0.032567 & -0.3305 & 0.37084 \tabularnewline
10 & -0.47579 & -4.8287 & 2e-06 \tabularnewline
11 & -0.09589 & -0.9732 & 0.166372 \tabularnewline
12 & 0.743366 & 7.5443 & 0 \tabularnewline
13 & -0.095341 & -0.9676 & 0.167755 \tabularnewline
14 & -0.483177 & -4.9037 & 2e-06 \tabularnewline
15 & 0.053422 & 0.5422 & 0.294433 \tabularnewline
16 & 0.456667 & 4.6347 & 5e-06 \tabularnewline
17 & 0.066686 & 0.6768 & 0.250029 \tabularnewline
18 & -0.664898 & -6.748 & 0 \tabularnewline
19 & 0.094469 & 0.9588 & 0.169963 \tabularnewline
20 & 0.453816 & 4.6057 & 6e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298829&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]-0.155736[/C][C]-1.5806[/C][C]0.058523[/C][/ROW]
[ROW][C]2[/C][C]-0.539587[/C][C]-5.4762[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.014818[/C][C]0.1504[/C][C]0.440378[/C][/ROW]
[ROW][C]4[/C][C]0.513167[/C][C]5.2081[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.124116[/C][C]1.2596[/C][C]0.105323[/C][/ROW]
[ROW][C]6[/C][C]-0.871881[/C][C]-8.8486[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.122374[/C][C]1.242[/C][C]0.108537[/C][/ROW]
[ROW][C]8[/C][C]0.502597[/C][C]5.1008[/C][C]1e-06[/C][/ROW]
[ROW][C]9[/C][C]-0.032567[/C][C]-0.3305[/C][C]0.37084[/C][/ROW]
[ROW][C]10[/C][C]-0.47579[/C][C]-4.8287[/C][C]2e-06[/C][/ROW]
[ROW][C]11[/C][C]-0.09589[/C][C]-0.9732[/C][C]0.166372[/C][/ROW]
[ROW][C]12[/C][C]0.743366[/C][C]7.5443[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.095341[/C][C]-0.9676[/C][C]0.167755[/C][/ROW]
[ROW][C]14[/C][C]-0.483177[/C][C]-4.9037[/C][C]2e-06[/C][/ROW]
[ROW][C]15[/C][C]0.053422[/C][C]0.5422[/C][C]0.294433[/C][/ROW]
[ROW][C]16[/C][C]0.456667[/C][C]4.6347[/C][C]5e-06[/C][/ROW]
[ROW][C]17[/C][C]0.066686[/C][C]0.6768[/C][C]0.250029[/C][/ROW]
[ROW][C]18[/C][C]-0.664898[/C][C]-6.748[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.094469[/C][C]0.9588[/C][C]0.169963[/C][/ROW]
[ROW][C]20[/C][C]0.453816[/C][C]4.6057[/C][C]6e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298829&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298829&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	-0.155736	-1.5806	0.058523
2	-0.539587	-5.4762	0
3	0.014818	0.1504	0.440378
4	0.513167	5.2081	0
5	0.124116	1.2596	0.105323
6	-0.871881	-8.8486	0
7	0.122374	1.242	0.108537
8	0.502597	5.1008	1e-06
9	-0.032567	-0.3305	0.37084
10	-0.47579	-4.8287	2e-06
11	-0.09589	-0.9732	0.166372
12	0.743366	7.5443	0
13	-0.095341	-0.9676	0.167755
14	-0.483177	-4.9037	2e-06
15	0.053422	0.5422	0.294433
16	0.456667	4.6347	5e-06
17	0.066686	0.6768	0.250029
18	-0.664898	-6.748	0
19	0.094469	0.9588	0.169963
20	0.453816	4.6057	6e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.155736	-1.5806	0.058523
2	-0.577856	-5.8646	0
3	-0.319679	-3.2444	0.000794
4	0.198058	2.0101	0.023519
5	0.400762	4.0673	4.7e-05
6	-0.734236	-7.4517	0
7	-0.196878	-1.9981	0.024171
8	-0.258664	-2.6252	0.00499
9	-0.151112	-1.5336	0.064094
10	-0.087995	-0.893	0.186957
11	-0.047047	-0.4775	0.317018
12	-0.114118	-1.1582	0.124735
13	-0.069411	-0.7044	0.241373
14	-0.183292	-1.8602	0.032855
15	-0.09249	-0.9387	0.175048
16	-0.020345	-0.2065	0.418413
17	-0.015445	-0.1568	0.437874
18	-0.137793	-1.3984	0.082491
19	-0.038357	-0.3893	0.348936
20	-0.146583	-1.4877	0.069948

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.155736 & -1.5806 & 0.058523 \tabularnewline
2 & -0.577856 & -5.8646 & 0 \tabularnewline
3 & -0.319679 & -3.2444 & 0.000794 \tabularnewline
4 & 0.198058 & 2.0101 & 0.023519 \tabularnewline
5 & 0.400762 & 4.0673 & 4.7e-05 \tabularnewline
6 & -0.734236 & -7.4517 & 0 \tabularnewline
7 & -0.196878 & -1.9981 & 0.024171 \tabularnewline
8 & -0.258664 & -2.6252 & 0.00499 \tabularnewline
9 & -0.151112 & -1.5336 & 0.064094 \tabularnewline
10 & -0.087995 & -0.893 & 0.186957 \tabularnewline
11 & -0.047047 & -0.4775 & 0.317018 \tabularnewline
12 & -0.114118 & -1.1582 & 0.124735 \tabularnewline
13 & -0.069411 & -0.7044 & 0.241373 \tabularnewline
14 & -0.183292 & -1.8602 & 0.032855 \tabularnewline
15 & -0.09249 & -0.9387 & 0.175048 \tabularnewline
16 & -0.020345 & -0.2065 & 0.418413 \tabularnewline
17 & -0.015445 & -0.1568 & 0.437874 \tabularnewline
18 & -0.137793 & -1.3984 & 0.082491 \tabularnewline
19 & -0.038357 & -0.3893 & 0.348936 \tabularnewline
20 & -0.146583 & -1.4877 & 0.069948 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298829&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]-0.155736[/C][C]-1.5806[/C][C]0.058523[/C][/ROW]
[ROW][C]2[/C][C]-0.577856[/C][C]-5.8646[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.319679[/C][C]-3.2444[/C][C]0.000794[/C][/ROW]
[ROW][C]4[/C][C]0.198058[/C][C]2.0101[/C][C]0.023519[/C][/ROW]
[ROW][C]5[/C][C]0.400762[/C][C]4.0673[/C][C]4.7e-05[/C][/ROW]
[ROW][C]6[/C][C]-0.734236[/C][C]-7.4517[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.196878[/C][C]-1.9981[/C][C]0.024171[/C][/ROW]
[ROW][C]8[/C][C]-0.258664[/C][C]-2.6252[/C][C]0.00499[/C][/ROW]
[ROW][C]9[/C][C]-0.151112[/C][C]-1.5336[/C][C]0.064094[/C][/ROW]
[ROW][C]10[/C][C]-0.087995[/C][C]-0.893[/C][C]0.186957[/C][/ROW]
[ROW][C]11[/C][C]-0.047047[/C][C]-0.4775[/C][C]0.317018[/C][/ROW]
[ROW][C]12[/C][C]-0.114118[/C][C]-1.1582[/C][C]0.124735[/C][/ROW]
[ROW][C]13[/C][C]-0.069411[/C][C]-0.7044[/C][C]0.241373[/C][/ROW]
[ROW][C]14[/C][C]-0.183292[/C][C]-1.8602[/C][C]0.032855[/C][/ROW]
[ROW][C]15[/C][C]-0.09249[/C][C]-0.9387[/C][C]0.175048[/C][/ROW]
[ROW][C]16[/C][C]-0.020345[/C][C]-0.2065[/C][C]0.418413[/C][/ROW]
[ROW][C]17[/C][C]-0.015445[/C][C]-0.1568[/C][C]0.437874[/C][/ROW]
[ROW][C]18[/C][C]-0.137793[/C][C]-1.3984[/C][C]0.082491[/C][/ROW]
[ROW][C]19[/C][C]-0.038357[/C][C]-0.3893[/C][C]0.348936[/C][/ROW]
[ROW][C]20[/C][C]-0.146583[/C][C]-1.4877[/C][C]0.069948[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298829&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298829&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	-0.155736	-1.5806	0.058523
2	-0.577856	-5.8646	0
3	-0.319679	-3.2444	0.000794
4	0.198058	2.0101	0.023519
5	0.400762	4.0673	4.7e-05
6	-0.734236	-7.4517	0
7	-0.196878	-1.9981	0.024171
8	-0.258664	-2.6252	0.00499
9	-0.151112	-1.5336	0.064094
10	-0.087995	-0.893	0.186957
11	-0.047047	-0.4775	0.317018
12	-0.114118	-1.1582	0.124735
13	-0.069411	-0.7044	0.241373
14	-0.183292	-1.8602	0.032855
15	-0.09249	-0.9387	0.175048
16	-0.020345	-0.2065	0.418413
17	-0.015445	-0.1568	0.437874
18	-0.137793	-1.3984	0.082491
19	-0.038357	-0.3893	0.348936
20	-0.146583	-1.4877	0.069948

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 = 1 ; par4 = 2 ; par5 = 6 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 2 ; par5 = 6 ; 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 <- '6'
par4 <- '2'
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