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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 22 Nov 2016 12:20:14 +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/Nov/22/t1479813706pnmez417fae9qp5.htm/, Retrieved Sun, 05 May 2024 13:15:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296899, Retrieved Sun, 05 May 2024 13:15:53 +0000

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Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [Partial auto corr...] [2016-11-22 11:20:14] [67fe698233d7575d27222b521501ef35] [Current]
- RMPD    [Spectral Analysis] [spectral analysis] [2016-11-29 15:27:16] [fdf9a0df6d9fd79bb352d27c92a6cf36] 
-    D      [Spectral Analysis] [spec an d1] [2016-11-29 15:59:02] [fdf9a0df6d9fd79bb352d27c92a6cf36] 
-    D      [Spectral Analysis] [spec anal D en d ...] [2016-11-29 16:02:07] [fdf9a0df6d9fd79bb352d27c92a6cf36] 
-   PD    [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2016-11-29 15:32:36] [fdf9a0df6d9fd79bb352d27c92a6cf36] 

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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=296899&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=296899&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296899&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	0.022792	0.1612	0.436306
2	0.065637	0.4641	0.322287
3	-0.087464	-0.6185	0.269538
4	0.176388	1.2473	0.109058
5	-0.042965	-0.3038	0.381267
6	-0.037438	-0.2647	0.396154
7	-0.127318	-0.9003	0.186146
8	-0.22576	-1.5964	0.058354
9	-0.090662	-0.6411	0.262201
10	-0.172019	-1.2164	0.11478
11	-0.020491	-0.1449	0.44269
12	-0.12561	-0.8882	0.189345
13	-0.066823	-0.4725	0.319308
14	-0.051201	-0.362	0.359422
15	0.082423	0.5828	0.281316
16	0.130458	0.9225	0.180355

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.022792 & 0.1612 & 0.436306 \tabularnewline
2 & 0.065637 & 0.4641 & 0.322287 \tabularnewline
3 & -0.087464 & -0.6185 & 0.269538 \tabularnewline
4 & 0.176388 & 1.2473 & 0.109058 \tabularnewline
5 & -0.042965 & -0.3038 & 0.381267 \tabularnewline
6 & -0.037438 & -0.2647 & 0.396154 \tabularnewline
7 & -0.127318 & -0.9003 & 0.186146 \tabularnewline
8 & -0.22576 & -1.5964 & 0.058354 \tabularnewline
9 & -0.090662 & -0.6411 & 0.262201 \tabularnewline
10 & -0.172019 & -1.2164 & 0.11478 \tabularnewline
11 & -0.020491 & -0.1449 & 0.44269 \tabularnewline
12 & -0.12561 & -0.8882 & 0.189345 \tabularnewline
13 & -0.066823 & -0.4725 & 0.319308 \tabularnewline
14 & -0.051201 & -0.362 & 0.359422 \tabularnewline
15 & 0.082423 & 0.5828 & 0.281316 \tabularnewline
16 & 0.130458 & 0.9225 & 0.180355 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296899&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]0.022792[/C][C]0.1612[/C][C]0.436306[/C][/ROW]
[ROW][C]2[/C][C]0.065637[/C][C]0.4641[/C][C]0.322287[/C][/ROW]
[ROW][C]3[/C][C]-0.087464[/C][C]-0.6185[/C][C]0.269538[/C][/ROW]
[ROW][C]4[/C][C]0.176388[/C][C]1.2473[/C][C]0.109058[/C][/ROW]
[ROW][C]5[/C][C]-0.042965[/C][C]-0.3038[/C][C]0.381267[/C][/ROW]
[ROW][C]6[/C][C]-0.037438[/C][C]-0.2647[/C][C]0.396154[/C][/ROW]
[ROW][C]7[/C][C]-0.127318[/C][C]-0.9003[/C][C]0.186146[/C][/ROW]
[ROW][C]8[/C][C]-0.22576[/C][C]-1.5964[/C][C]0.058354[/C][/ROW]
[ROW][C]9[/C][C]-0.090662[/C][C]-0.6411[/C][C]0.262201[/C][/ROW]
[ROW][C]10[/C][C]-0.172019[/C][C]-1.2164[/C][C]0.11478[/C][/ROW]
[ROW][C]11[/C][C]-0.020491[/C][C]-0.1449[/C][C]0.44269[/C][/ROW]
[ROW][C]12[/C][C]-0.12561[/C][C]-0.8882[/C][C]0.189345[/C][/ROW]
[ROW][C]13[/C][C]-0.066823[/C][C]-0.4725[/C][C]0.319308[/C][/ROW]
[ROW][C]14[/C][C]-0.051201[/C][C]-0.362[/C][C]0.359422[/C][/ROW]
[ROW][C]15[/C][C]0.082423[/C][C]0.5828[/C][C]0.281316[/C][/ROW]
[ROW][C]16[/C][C]0.130458[/C][C]0.9225[/C][C]0.180355[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296899&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296899&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	0.022792	0.1612	0.436306
2	0.065637	0.4641	0.322287
3	-0.087464	-0.6185	0.269538
4	0.176388	1.2473	0.109058
5	-0.042965	-0.3038	0.381267
6	-0.037438	-0.2647	0.396154
7	-0.127318	-0.9003	0.186146
8	-0.22576	-1.5964	0.058354
9	-0.090662	-0.6411	0.262201
10	-0.172019	-1.2164	0.11478
11	-0.020491	-0.1449	0.44269
12	-0.12561	-0.8882	0.189345
13	-0.066823	-0.4725	0.319308
14	-0.051201	-0.362	0.359422
15	0.082423	0.5828	0.281316
16	0.130458	0.9225	0.180355

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.022792	0.1612	0.436306
2	0.065151	0.4607	0.32351
3	-0.09078	-0.6419	0.261931
4	0.178752	1.264	0.106051
5	-0.045637	-0.3227	0.374132
6	-0.066215	-0.4682	0.320833
7	-0.08944	-0.6324	0.264992
8	-0.265139	-1.8748	0.033333
9	-0.065621	-0.464	0.322327
10	-0.169641	-1.1995	0.117985
11	-0.025367	-0.1794	0.429186
12	-0.05938	-0.4199	0.338186
13	-0.119124	-0.8423	0.201806
14	-0.033321	-0.2356	0.407348
15	-0.009054	-0.064	0.474605
16	0.069131	0.4888	0.31355

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.022792 & 0.1612 & 0.436306 \tabularnewline
2 & 0.065151 & 0.4607 & 0.32351 \tabularnewline
3 & -0.09078 & -0.6419 & 0.261931 \tabularnewline
4 & 0.178752 & 1.264 & 0.106051 \tabularnewline
5 & -0.045637 & -0.3227 & 0.374132 \tabularnewline
6 & -0.066215 & -0.4682 & 0.320833 \tabularnewline
7 & -0.08944 & -0.6324 & 0.264992 \tabularnewline
8 & -0.265139 & -1.8748 & 0.033333 \tabularnewline
9 & -0.065621 & -0.464 & 0.322327 \tabularnewline
10 & -0.169641 & -1.1995 & 0.117985 \tabularnewline
11 & -0.025367 & -0.1794 & 0.429186 \tabularnewline
12 & -0.05938 & -0.4199 & 0.338186 \tabularnewline
13 & -0.119124 & -0.8423 & 0.201806 \tabularnewline
14 & -0.033321 & -0.2356 & 0.407348 \tabularnewline
15 & -0.009054 & -0.064 & 0.474605 \tabularnewline
16 & 0.069131 & 0.4888 & 0.31355 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296899&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]0.022792[/C][C]0.1612[/C][C]0.436306[/C][/ROW]
[ROW][C]2[/C][C]0.065151[/C][C]0.4607[/C][C]0.32351[/C][/ROW]
[ROW][C]3[/C][C]-0.09078[/C][C]-0.6419[/C][C]0.261931[/C][/ROW]
[ROW][C]4[/C][C]0.178752[/C][C]1.264[/C][C]0.106051[/C][/ROW]
[ROW][C]5[/C][C]-0.045637[/C][C]-0.3227[/C][C]0.374132[/C][/ROW]
[ROW][C]6[/C][C]-0.066215[/C][C]-0.4682[/C][C]0.320833[/C][/ROW]
[ROW][C]7[/C][C]-0.08944[/C][C]-0.6324[/C][C]0.264992[/C][/ROW]
[ROW][C]8[/C][C]-0.265139[/C][C]-1.8748[/C][C]0.033333[/C][/ROW]
[ROW][C]9[/C][C]-0.065621[/C][C]-0.464[/C][C]0.322327[/C][/ROW]
[ROW][C]10[/C][C]-0.169641[/C][C]-1.1995[/C][C]0.117985[/C][/ROW]
[ROW][C]11[/C][C]-0.025367[/C][C]-0.1794[/C][C]0.429186[/C][/ROW]
[ROW][C]12[/C][C]-0.05938[/C][C]-0.4199[/C][C]0.338186[/C][/ROW]
[ROW][C]13[/C][C]-0.119124[/C][C]-0.8423[/C][C]0.201806[/C][/ROW]
[ROW][C]14[/C][C]-0.033321[/C][C]-0.2356[/C][C]0.407348[/C][/ROW]
[ROW][C]15[/C][C]-0.009054[/C][C]-0.064[/C][C]0.474605[/C][/ROW]
[ROW][C]16[/C][C]0.069131[/C][C]0.4888[/C][C]0.31355[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296899&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296899&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	0.022792	0.1612	0.436306
2	0.065151	0.4607	0.32351
3	-0.09078	-0.6419	0.261931
4	0.178752	1.264	0.106051
5	-0.045637	-0.3227	0.374132
6	-0.066215	-0.4682	0.320833
7	-0.08944	-0.6324	0.264992
8	-0.265139	-1.8748	0.033333
9	-0.065621	-0.464	0.322327
10	-0.169641	-1.1995	0.117985
11	-0.025367	-0.1794	0.429186
12	-0.05938	-0.4199	0.338186
13	-0.119124	-0.8423	0.201806
14	-0.033321	-0.2356	0.407348
15	-0.009054	-0.064	0.474605
16	0.069131	0.4888	0.31355

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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')

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Figures (Output of Computation)

Input Parameters & R Code