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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 14 Dec 2016 14:20:11 +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/14/t1481721728fwfu7mo044u67j8.htm/, Retrieved Sat, 04 May 2024 05:12:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299405, Retrieved Sat, 04 May 2024 05:12:32 +0000

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-       [(Partial) Autocorrelation Function] [Partial Autocorre...] [2016-12-14 13:20:11] [3b055ff671ad33431c4331443bac114d] [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=299405&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=299405&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299405&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	-0.167798	-0.9343	0.178695
2	0.125689	0.6998	0.244633
3	0.2408	1.3407	0.094877
4	0.134907	0.7511	0.22912
5	0.056051	0.3121	0.378534
6	-0.099589	-0.5545	0.291611
7	0.137469	0.7654	0.224912
8	-0.230385	-1.2827	0.104547
9	0.019591	0.1091	0.456923
10	-0.264302	-1.4716	0.075608
11	0.010772	0.06	0.476279
12	-0.264419	-1.4722	0.075521
13	-0.087045	-0.4846	0.315668
14	-0.076867	-0.428	0.335814
15	-0.122769	-0.6835	0.249669
16	-0.074157	-0.4129	0.341264
17	-0.14556	-0.8104	0.211932

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.167798 & -0.9343 & 0.178695 \tabularnewline
2 & 0.125689 & 0.6998 & 0.244633 \tabularnewline
3 & 0.2408 & 1.3407 & 0.094877 \tabularnewline
4 & 0.134907 & 0.7511 & 0.22912 \tabularnewline
5 & 0.056051 & 0.3121 & 0.378534 \tabularnewline
6 & -0.099589 & -0.5545 & 0.291611 \tabularnewline
7 & 0.137469 & 0.7654 & 0.224912 \tabularnewline
8 & -0.230385 & -1.2827 & 0.104547 \tabularnewline
9 & 0.019591 & 0.1091 & 0.456923 \tabularnewline
10 & -0.264302 & -1.4716 & 0.075608 \tabularnewline
11 & 0.010772 & 0.06 & 0.476279 \tabularnewline
12 & -0.264419 & -1.4722 & 0.075521 \tabularnewline
13 & -0.087045 & -0.4846 & 0.315668 \tabularnewline
14 & -0.076867 & -0.428 & 0.335814 \tabularnewline
15 & -0.122769 & -0.6835 & 0.249669 \tabularnewline
16 & -0.074157 & -0.4129 & 0.341264 \tabularnewline
17 & -0.14556 & -0.8104 & 0.211932 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299405&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]-0.167798[/C][C]-0.9343[/C][C]0.178695[/C][/ROW]
[ROW][C]2[/C][C]0.125689[/C][C]0.6998[/C][C]0.244633[/C][/ROW]
[ROW][C]3[/C][C]0.2408[/C][C]1.3407[/C][C]0.094877[/C][/ROW]
[ROW][C]4[/C][C]0.134907[/C][C]0.7511[/C][C]0.22912[/C][/ROW]
[ROW][C]5[/C][C]0.056051[/C][C]0.3121[/C][C]0.378534[/C][/ROW]
[ROW][C]6[/C][C]-0.099589[/C][C]-0.5545[/C][C]0.291611[/C][/ROW]
[ROW][C]7[/C][C]0.137469[/C][C]0.7654[/C][C]0.224912[/C][/ROW]
[ROW][C]8[/C][C]-0.230385[/C][C]-1.2827[/C][C]0.104547[/C][/ROW]
[ROW][C]9[/C][C]0.019591[/C][C]0.1091[/C][C]0.456923[/C][/ROW]
[ROW][C]10[/C][C]-0.264302[/C][C]-1.4716[/C][C]0.075608[/C][/ROW]
[ROW][C]11[/C][C]0.010772[/C][C]0.06[/C][C]0.476279[/C][/ROW]
[ROW][C]12[/C][C]-0.264419[/C][C]-1.4722[/C][C]0.075521[/C][/ROW]
[ROW][C]13[/C][C]-0.087045[/C][C]-0.4846[/C][C]0.315668[/C][/ROW]
[ROW][C]14[/C][C]-0.076867[/C][C]-0.428[/C][C]0.335814[/C][/ROW]
[ROW][C]15[/C][C]-0.122769[/C][C]-0.6835[/C][C]0.249669[/C][/ROW]
[ROW][C]16[/C][C]-0.074157[/C][C]-0.4129[/C][C]0.341264[/C][/ROW]
[ROW][C]17[/C][C]-0.14556[/C][C]-0.8104[/C][C]0.211932[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299405&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299405&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	-0.167798	-0.9343	0.178695
2	0.125689	0.6998	0.244633
3	0.2408	1.3407	0.094877
4	0.134907	0.7511	0.22912
5	0.056051	0.3121	0.378534
6	-0.099589	-0.5545	0.291611
7	0.137469	0.7654	0.224912
8	-0.230385	-1.2827	0.104547
9	0.019591	0.1091	0.456923
10	-0.264302	-1.4716	0.075608
11	0.010772	0.06	0.476279
12	-0.264419	-1.4722	0.075521
13	-0.087045	-0.4846	0.315668
14	-0.076867	-0.428	0.335814
15	-0.122769	-0.6835	0.249669
16	-0.074157	-0.4129	0.341264
17	-0.14556	-0.8104	0.211932

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.167798	-0.9343	0.178695
2	0.100359	0.5588	0.290165
3	0.287524	1.6009	0.059775
4	0.236122	1.3147	0.099132
5	0.073405	0.4087	0.342783
6	-0.233397	-1.2995	0.101677
7	-0.070911	-0.3948	0.347841
8	-0.294035	-1.6371	0.05586
9	-0.050336	-0.2803	0.39057
10	-0.252365	-1.4051	0.084966
11	0.062055	0.3455	0.366023
12	-0.168601	-0.9387	0.177564
13	0.059606	0.3319	0.371109
14	-0.04159	-0.2316	0.409199
15	0.107251	0.5971	0.277372
16	-0.129388	-0.7204	0.238338
17	-0.077683	-0.4325	0.334179

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.167798 & -0.9343 & 0.178695 \tabularnewline
2 & 0.100359 & 0.5588 & 0.290165 \tabularnewline
3 & 0.287524 & 1.6009 & 0.059775 \tabularnewline
4 & 0.236122 & 1.3147 & 0.099132 \tabularnewline
5 & 0.073405 & 0.4087 & 0.342783 \tabularnewline
6 & -0.233397 & -1.2995 & 0.101677 \tabularnewline
7 & -0.070911 & -0.3948 & 0.347841 \tabularnewline
8 & -0.294035 & -1.6371 & 0.05586 \tabularnewline
9 & -0.050336 & -0.2803 & 0.39057 \tabularnewline
10 & -0.252365 & -1.4051 & 0.084966 \tabularnewline
11 & 0.062055 & 0.3455 & 0.366023 \tabularnewline
12 & -0.168601 & -0.9387 & 0.177564 \tabularnewline
13 & 0.059606 & 0.3319 & 0.371109 \tabularnewline
14 & -0.04159 & -0.2316 & 0.409199 \tabularnewline
15 & 0.107251 & 0.5971 & 0.277372 \tabularnewline
16 & -0.129388 & -0.7204 & 0.238338 \tabularnewline
17 & -0.077683 & -0.4325 & 0.334179 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299405&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]-0.167798[/C][C]-0.9343[/C][C]0.178695[/C][/ROW]
[ROW][C]2[/C][C]0.100359[/C][C]0.5588[/C][C]0.290165[/C][/ROW]
[ROW][C]3[/C][C]0.287524[/C][C]1.6009[/C][C]0.059775[/C][/ROW]
[ROW][C]4[/C][C]0.236122[/C][C]1.3147[/C][C]0.099132[/C][/ROW]
[ROW][C]5[/C][C]0.073405[/C][C]0.4087[/C][C]0.342783[/C][/ROW]
[ROW][C]6[/C][C]-0.233397[/C][C]-1.2995[/C][C]0.101677[/C][/ROW]
[ROW][C]7[/C][C]-0.070911[/C][C]-0.3948[/C][C]0.347841[/C][/ROW]
[ROW][C]8[/C][C]-0.294035[/C][C]-1.6371[/C][C]0.05586[/C][/ROW]
[ROW][C]9[/C][C]-0.050336[/C][C]-0.2803[/C][C]0.39057[/C][/ROW]
[ROW][C]10[/C][C]-0.252365[/C][C]-1.4051[/C][C]0.084966[/C][/ROW]
[ROW][C]11[/C][C]0.062055[/C][C]0.3455[/C][C]0.366023[/C][/ROW]
[ROW][C]12[/C][C]-0.168601[/C][C]-0.9387[/C][C]0.177564[/C][/ROW]
[ROW][C]13[/C][C]0.059606[/C][C]0.3319[/C][C]0.371109[/C][/ROW]
[ROW][C]14[/C][C]-0.04159[/C][C]-0.2316[/C][C]0.409199[/C][/ROW]
[ROW][C]15[/C][C]0.107251[/C][C]0.5971[/C][C]0.277372[/C][/ROW]
[ROW][C]16[/C][C]-0.129388[/C][C]-0.7204[/C][C]0.238338[/C][/ROW]
[ROW][C]17[/C][C]-0.077683[/C][C]-0.4325[/C][C]0.334179[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299405&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299405&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	-0.167798	-0.9343	0.178695
2	0.100359	0.5588	0.290165
3	0.287524	1.6009	0.059775
4	0.236122	1.3147	0.099132
5	0.073405	0.4087	0.342783
6	-0.233397	-1.2995	0.101677
7	-0.070911	-0.3948	0.347841
8	-0.294035	-1.6371	0.05586
9	-0.050336	-0.2803	0.39057
10	-0.252365	-1.4051	0.084966
11	0.062055	0.3455	0.366023
12	-0.168601	-0.9387	0.177564
13	0.059606	0.3319	0.371109
14	-0.04159	-0.2316	0.409199
15	0.107251	0.5971	0.277372
16	-0.129388	-0.7204	0.238338
17	-0.077683	-0.4325	0.334179

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

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Parameters (Session):

par1 = 1 ; par2 = 1 ; par3 = 1 ; par4 = 1 ;

Parameters (R input):

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

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Input Parameters & R Code