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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 12 Dec 2016 19:03:39 +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/12/t1481566014t4xsrkzs01hqj2x.htm/, Retrieved Sat, 04 May 2024 03:58:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298951, Retrieved Sat, 04 May 2024 03:58:44 +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] [(Partial) Autocor...] [2016-12-12 18:03:39] [59384cc4294cbecf8e09b453c4247580] [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=298951&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=298951&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298951&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	-0.193277	-1.3937	0.084662
2	0.001078	0.0078	0.496914
3	0.111372	0.8031	0.212781
4	-0.099185	-0.7152	0.238832
5	0.113668	0.8197	0.208072
6	-0.099892	-0.7203	0.237274
7	0.005082	0.0366	0.485452
8	-0.270796	-1.9527	0.028122
9	0.043735	0.3154	0.376868
10	-0.034876	-0.2515	0.401211
11	-0.079604	-0.574	0.284211
12	0.096696	0.6973	0.244365
13	-0.230308	-1.6608	0.051389
14	0.054182	0.3907	0.348803
15	0.018482	0.1333	0.447246
16	-0.058886	-0.4246	0.336429
17	0.039841	0.2873	0.387512

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.193277 & -1.3937 & 0.084662 \tabularnewline
2 & 0.001078 & 0.0078 & 0.496914 \tabularnewline
3 & 0.111372 & 0.8031 & 0.212781 \tabularnewline
4 & -0.099185 & -0.7152 & 0.238832 \tabularnewline
5 & 0.113668 & 0.8197 & 0.208072 \tabularnewline
6 & -0.099892 & -0.7203 & 0.237274 \tabularnewline
7 & 0.005082 & 0.0366 & 0.485452 \tabularnewline
8 & -0.270796 & -1.9527 & 0.028122 \tabularnewline
9 & 0.043735 & 0.3154 & 0.376868 \tabularnewline
10 & -0.034876 & -0.2515 & 0.401211 \tabularnewline
11 & -0.079604 & -0.574 & 0.284211 \tabularnewline
12 & 0.096696 & 0.6973 & 0.244365 \tabularnewline
13 & -0.230308 & -1.6608 & 0.051389 \tabularnewline
14 & 0.054182 & 0.3907 & 0.348803 \tabularnewline
15 & 0.018482 & 0.1333 & 0.447246 \tabularnewline
16 & -0.058886 & -0.4246 & 0.336429 \tabularnewline
17 & 0.039841 & 0.2873 & 0.387512 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298951&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]-0.193277[/C][C]-1.3937[/C][C]0.084662[/C][/ROW]
[ROW][C]2[/C][C]0.001078[/C][C]0.0078[/C][C]0.496914[/C][/ROW]
[ROW][C]3[/C][C]0.111372[/C][C]0.8031[/C][C]0.212781[/C][/ROW]
[ROW][C]4[/C][C]-0.099185[/C][C]-0.7152[/C][C]0.238832[/C][/ROW]
[ROW][C]5[/C][C]0.113668[/C][C]0.8197[/C][C]0.208072[/C][/ROW]
[ROW][C]6[/C][C]-0.099892[/C][C]-0.7203[/C][C]0.237274[/C][/ROW]
[ROW][C]7[/C][C]0.005082[/C][C]0.0366[/C][C]0.485452[/C][/ROW]
[ROW][C]8[/C][C]-0.270796[/C][C]-1.9527[/C][C]0.028122[/C][/ROW]
[ROW][C]9[/C][C]0.043735[/C][C]0.3154[/C][C]0.376868[/C][/ROW]
[ROW][C]10[/C][C]-0.034876[/C][C]-0.2515[/C][C]0.401211[/C][/ROW]
[ROW][C]11[/C][C]-0.079604[/C][C]-0.574[/C][C]0.284211[/C][/ROW]
[ROW][C]12[/C][C]0.096696[/C][C]0.6973[/C][C]0.244365[/C][/ROW]
[ROW][C]13[/C][C]-0.230308[/C][C]-1.6608[/C][C]0.051389[/C][/ROW]
[ROW][C]14[/C][C]0.054182[/C][C]0.3907[/C][C]0.348803[/C][/ROW]
[ROW][C]15[/C][C]0.018482[/C][C]0.1333[/C][C]0.447246[/C][/ROW]
[ROW][C]16[/C][C]-0.058886[/C][C]-0.4246[/C][C]0.336429[/C][/ROW]
[ROW][C]17[/C][C]0.039841[/C][C]0.2873[/C][C]0.387512[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298951&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298951&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	-0.193277	-1.3937	0.084662
2	0.001078	0.0078	0.496914
3	0.111372	0.8031	0.212781
4	-0.099185	-0.7152	0.238832
5	0.113668	0.8197	0.208072
6	-0.099892	-0.7203	0.237274
7	0.005082	0.0366	0.485452
8	-0.270796	-1.9527	0.028122
9	0.043735	0.3154	0.376868
10	-0.034876	-0.2515	0.401211
11	-0.079604	-0.574	0.284211
12	0.096696	0.6973	0.244365
13	-0.230308	-1.6608	0.051389
14	0.054182	0.3907	0.348803
15	0.018482	0.1333	0.447246
16	-0.058886	-0.4246	0.336429
17	0.039841	0.2873	0.387512

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.193277	-1.3937	0.084662
2	-0.037686	-0.2718	0.393443
3	0.108507	0.7825	0.218749
4	-0.059281	-0.4275	0.335397
5	0.089937	0.6485	0.259744
6	-0.079834	-0.5757	0.283653
7	-0.010085	-0.0727	0.471152
8	-0.32074	-2.3129	0.012359
9	-0.031948	-0.2304	0.409351
10	-0.079736	-0.575	0.28389
11	-0.014517	-0.1047	0.458515
12	0.028735	0.2072	0.418329
13	-0.167949	-1.2111	0.115667
14	-0.079203	-0.5711	0.285182
15	-0.039883	-0.2876	0.387399
16	-0.117569	-0.8478	0.200218
17	-0.052503	-0.3786	0.353262

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.193277 & -1.3937 & 0.084662 \tabularnewline
2 & -0.037686 & -0.2718 & 0.393443 \tabularnewline
3 & 0.108507 & 0.7825 & 0.218749 \tabularnewline
4 & -0.059281 & -0.4275 & 0.335397 \tabularnewline
5 & 0.089937 & 0.6485 & 0.259744 \tabularnewline
6 & -0.079834 & -0.5757 & 0.283653 \tabularnewline
7 & -0.010085 & -0.0727 & 0.471152 \tabularnewline
8 & -0.32074 & -2.3129 & 0.012359 \tabularnewline
9 & -0.031948 & -0.2304 & 0.409351 \tabularnewline
10 & -0.079736 & -0.575 & 0.28389 \tabularnewline
11 & -0.014517 & -0.1047 & 0.458515 \tabularnewline
12 & 0.028735 & 0.2072 & 0.418329 \tabularnewline
13 & -0.167949 & -1.2111 & 0.115667 \tabularnewline
14 & -0.079203 & -0.5711 & 0.285182 \tabularnewline
15 & -0.039883 & -0.2876 & 0.387399 \tabularnewline
16 & -0.117569 & -0.8478 & 0.200218 \tabularnewline
17 & -0.052503 & -0.3786 & 0.353262 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298951&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]-0.193277[/C][C]-1.3937[/C][C]0.084662[/C][/ROW]
[ROW][C]2[/C][C]-0.037686[/C][C]-0.2718[/C][C]0.393443[/C][/ROW]
[ROW][C]3[/C][C]0.108507[/C][C]0.7825[/C][C]0.218749[/C][/ROW]
[ROW][C]4[/C][C]-0.059281[/C][C]-0.4275[/C][C]0.335397[/C][/ROW]
[ROW][C]5[/C][C]0.089937[/C][C]0.6485[/C][C]0.259744[/C][/ROW]
[ROW][C]6[/C][C]-0.079834[/C][C]-0.5757[/C][C]0.283653[/C][/ROW]
[ROW][C]7[/C][C]-0.010085[/C][C]-0.0727[/C][C]0.471152[/C][/ROW]
[ROW][C]8[/C][C]-0.32074[/C][C]-2.3129[/C][C]0.012359[/C][/ROW]
[ROW][C]9[/C][C]-0.031948[/C][C]-0.2304[/C][C]0.409351[/C][/ROW]
[ROW][C]10[/C][C]-0.079736[/C][C]-0.575[/C][C]0.28389[/C][/ROW]
[ROW][C]11[/C][C]-0.014517[/C][C]-0.1047[/C][C]0.458515[/C][/ROW]
[ROW][C]12[/C][C]0.028735[/C][C]0.2072[/C][C]0.418329[/C][/ROW]
[ROW][C]13[/C][C]-0.167949[/C][C]-1.2111[/C][C]0.115667[/C][/ROW]
[ROW][C]14[/C][C]-0.079203[/C][C]-0.5711[/C][C]0.285182[/C][/ROW]
[ROW][C]15[/C][C]-0.039883[/C][C]-0.2876[/C][C]0.387399[/C][/ROW]
[ROW][C]16[/C][C]-0.117569[/C][C]-0.8478[/C][C]0.200218[/C][/ROW]
[ROW][C]17[/C][C]-0.052503[/C][C]-0.3786[/C][C]0.353262[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298951&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298951&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	-0.193277	-1.3937	0.084662
2	-0.037686	-0.2718	0.393443
3	0.108507	0.7825	0.218749
4	-0.059281	-0.4275	0.335397
5	0.089937	0.6485	0.259744
6	-0.079834	-0.5757	0.283653
7	-0.010085	-0.0727	0.471152
8	-0.32074	-2.3129	0.012359
9	-0.031948	-0.2304	0.409351
10	-0.079736	-0.575	0.28389
11	-0.014517	-0.1047	0.458515
12	0.028735	0.2072	0.418329
13	-0.167949	-1.2111	0.115667
14	-0.079203	-0.5711	0.285182
15	-0.039883	-0.2876	0.387399
16	-0.117569	-0.8478	0.200218
17	-0.052503	-0.3786	0.353262

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 = 0 ; par5 = 6 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 6 ; 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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Dataset

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Input Parameters & R Code