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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 14 Dec 2016 16:29:13 +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/t1481729382skgdqle4rwub8at.htm/, Retrieved Sat, 04 May 2024 04:24:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299565, Retrieved Sat, 04 May 2024 04:24:35 +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] [] [2016-12-14 15:29:13] [85f5800284aab30c091766186b093bb4] [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=299565&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=299565&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299565&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	-0.24365	-1.4415	0.079172
2	-0.228935	-1.3544	0.092144
3	-0.194993	-1.1536	0.128242
4	0.439513	2.6002	0.006778
5	-0.144995	-0.8578	0.198419
6	-0.115273	-0.682	0.249874
7	0.016841	0.0996	0.460603
8	0.265246	1.5692	0.062798
9	-0.269758	-1.5959	0.05975
10	0.048841	0.2889	0.387164
11	-0.052311	-0.3095	0.379397
12	0.279575	1.654	0.053536
13	-0.296525	-1.7543	0.044069
14	0.034513	0.2042	0.419697
15	-0.120952	-0.7156	0.239505

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.24365 & -1.4415 & 0.079172 \tabularnewline
2 & -0.228935 & -1.3544 & 0.092144 \tabularnewline
3 & -0.194993 & -1.1536 & 0.128242 \tabularnewline
4 & 0.439513 & 2.6002 & 0.006778 \tabularnewline
5 & -0.144995 & -0.8578 & 0.198419 \tabularnewline
6 & -0.115273 & -0.682 & 0.249874 \tabularnewline
7 & 0.016841 & 0.0996 & 0.460603 \tabularnewline
8 & 0.265246 & 1.5692 & 0.062798 \tabularnewline
9 & -0.269758 & -1.5959 & 0.05975 \tabularnewline
10 & 0.048841 & 0.2889 & 0.387164 \tabularnewline
11 & -0.052311 & -0.3095 & 0.379397 \tabularnewline
12 & 0.279575 & 1.654 & 0.053536 \tabularnewline
13 & -0.296525 & -1.7543 & 0.044069 \tabularnewline
14 & 0.034513 & 0.2042 & 0.419697 \tabularnewline
15 & -0.120952 & -0.7156 & 0.239505 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299565&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]-0.24365[/C][C]-1.4415[/C][C]0.079172[/C][/ROW]
[ROW][C]2[/C][C]-0.228935[/C][C]-1.3544[/C][C]0.092144[/C][/ROW]
[ROW][C]3[/C][C]-0.194993[/C][C]-1.1536[/C][C]0.128242[/C][/ROW]
[ROW][C]4[/C][C]0.439513[/C][C]2.6002[/C][C]0.006778[/C][/ROW]
[ROW][C]5[/C][C]-0.144995[/C][C]-0.8578[/C][C]0.198419[/C][/ROW]
[ROW][C]6[/C][C]-0.115273[/C][C]-0.682[/C][C]0.249874[/C][/ROW]
[ROW][C]7[/C][C]0.016841[/C][C]0.0996[/C][C]0.460603[/C][/ROW]
[ROW][C]8[/C][C]0.265246[/C][C]1.5692[/C][C]0.062798[/C][/ROW]
[ROW][C]9[/C][C]-0.269758[/C][C]-1.5959[/C][C]0.05975[/C][/ROW]
[ROW][C]10[/C][C]0.048841[/C][C]0.2889[/C][C]0.387164[/C][/ROW]
[ROW][C]11[/C][C]-0.052311[/C][C]-0.3095[/C][C]0.379397[/C][/ROW]
[ROW][C]12[/C][C]0.279575[/C][C]1.654[/C][C]0.053536[/C][/ROW]
[ROW][C]13[/C][C]-0.296525[/C][C]-1.7543[/C][C]0.044069[/C][/ROW]
[ROW][C]14[/C][C]0.034513[/C][C]0.2042[/C][C]0.419697[/C][/ROW]
[ROW][C]15[/C][C]-0.120952[/C][C]-0.7156[/C][C]0.239505[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299565&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299565&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	-0.24365	-1.4415	0.079172
2	-0.228935	-1.3544	0.092144
3	-0.194993	-1.1536	0.128242
4	0.439513	2.6002	0.006778
5	-0.144995	-0.8578	0.198419
6	-0.115273	-0.682	0.249874
7	0.016841	0.0996	0.460603
8	0.265246	1.5692	0.062798
9	-0.269758	-1.5959	0.05975
10	0.048841	0.2889	0.387164
11	-0.052311	-0.3095	0.379397
12	0.279575	1.654	0.053536
13	-0.296525	-1.7543	0.044069
14	0.034513	0.2042	0.419697
15	-0.120952	-0.7156	0.239505

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.24365	-1.4415	0.079172
2	-0.306496	-1.8133	0.039188
3	-0.401923	-2.3778	0.011505
4	0.218352	1.2918	0.102448
5	-0.106495	-0.63	0.266382
6	-0.075586	-0.4472	0.328754
7	0.102538	0.6066	0.274007
8	0.134518	0.7958	0.215752
9	-0.161503	-0.9555	0.172948
10	0.139066	0.8227	0.208117
11	-0.115696	-0.6845	0.249094
12	0.130379	0.7713	0.222843
13	-0.078078	-0.4619	0.3235
14	-0.070005	-0.4142	0.340644
15	-0.212332	-1.2562	0.108687

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.24365 & -1.4415 & 0.079172 \tabularnewline
2 & -0.306496 & -1.8133 & 0.039188 \tabularnewline
3 & -0.401923 & -2.3778 & 0.011505 \tabularnewline
4 & 0.218352 & 1.2918 & 0.102448 \tabularnewline
5 & -0.106495 & -0.63 & 0.266382 \tabularnewline
6 & -0.075586 & -0.4472 & 0.328754 \tabularnewline
7 & 0.102538 & 0.6066 & 0.274007 \tabularnewline
8 & 0.134518 & 0.7958 & 0.215752 \tabularnewline
9 & -0.161503 & -0.9555 & 0.172948 \tabularnewline
10 & 0.139066 & 0.8227 & 0.208117 \tabularnewline
11 & -0.115696 & -0.6845 & 0.249094 \tabularnewline
12 & 0.130379 & 0.7713 & 0.222843 \tabularnewline
13 & -0.078078 & -0.4619 & 0.3235 \tabularnewline
14 & -0.070005 & -0.4142 & 0.340644 \tabularnewline
15 & -0.212332 & -1.2562 & 0.108687 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299565&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]-0.24365[/C][C]-1.4415[/C][C]0.079172[/C][/ROW]
[ROW][C]2[/C][C]-0.306496[/C][C]-1.8133[/C][C]0.039188[/C][/ROW]
[ROW][C]3[/C][C]-0.401923[/C][C]-2.3778[/C][C]0.011505[/C][/ROW]
[ROW][C]4[/C][C]0.218352[/C][C]1.2918[/C][C]0.102448[/C][/ROW]
[ROW][C]5[/C][C]-0.106495[/C][C]-0.63[/C][C]0.266382[/C][/ROW]
[ROW][C]6[/C][C]-0.075586[/C][C]-0.4472[/C][C]0.328754[/C][/ROW]
[ROW][C]7[/C][C]0.102538[/C][C]0.6066[/C][C]0.274007[/C][/ROW]
[ROW][C]8[/C][C]0.134518[/C][C]0.7958[/C][C]0.215752[/C][/ROW]
[ROW][C]9[/C][C]-0.161503[/C][C]-0.9555[/C][C]0.172948[/C][/ROW]
[ROW][C]10[/C][C]0.139066[/C][C]0.8227[/C][C]0.208117[/C][/ROW]
[ROW][C]11[/C][C]-0.115696[/C][C]-0.6845[/C][C]0.249094[/C][/ROW]
[ROW][C]12[/C][C]0.130379[/C][C]0.7713[/C][C]0.222843[/C][/ROW]
[ROW][C]13[/C][C]-0.078078[/C][C]-0.4619[/C][C]0.3235[/C][/ROW]
[ROW][C]14[/C][C]-0.070005[/C][C]-0.4142[/C][C]0.340644[/C][/ROW]
[ROW][C]15[/C][C]-0.212332[/C][C]-1.2562[/C][C]0.108687[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299565&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299565&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	-0.24365	-1.4415	0.079172
2	-0.306496	-1.8133	0.039188
3	-0.401923	-2.3778	0.011505
4	0.218352	1.2918	0.102448
5	-0.106495	-0.63	0.266382
6	-0.075586	-0.4472	0.328754
7	0.102538	0.6066	0.274007
8	0.134518	0.7958	0.215752
9	-0.161503	-0.9555	0.172948
10	0.139066	0.8227	0.208117
11	-0.115696	-0.6845	0.249094
12	0.130379	0.7713	0.222843
13	-0.078078	-0.4619	0.3235
14	-0.070005	-0.4142	0.340644
15	-0.212332	-1.2562	0.108687

Figure 1

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Figure 2

PNG link

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Figure 3

PNG link

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PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 4 ; 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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Input Parameters & R Code