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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 15 Dec 2016 11:41:50 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/15/t14817985983h4mbwkbrdh1tdh.htm/, Retrieved Fri, 03 May 2024 09:55:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299844, Retrieved Fri, 03 May 2024 09:55:04 +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] [F1 Autocorrelatio...] [2016-12-15 10:41:50] [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	2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299844&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299844&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299844&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	2 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.273714	-2.7508	0.003523
2	-0.019639	-0.1974	0.421969
3	0.036694	0.3688	0.356537
4	-0.04131	-0.4152	0.339454
5	-0.166363	-1.6719	0.048817
6	0.093935	0.944	0.173703
7	-0.034962	-0.3514	0.363022
8	0.071825	0.7218	0.236033
9	-0.07299	-0.7335	0.232466
10	0.094359	0.9483	0.172621
11	-0.115048	-1.1562	0.12516
12	0.055419	0.557	0.289395
13	0.052781	0.5304	0.298485
14	-0.120508	-1.2111	0.114344
15	-0.02617	-0.263	0.39654
16	0.168167	1.6901	0.047051
17	-0.214653	-2.1572	0.01668
18	0.090036	0.9049	0.183848
19	-0.024998	-0.2512	0.401076
20	0.084482	0.849	0.198936

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.273714 & -2.7508 & 0.003523 \tabularnewline
2 & -0.019639 & -0.1974 & 0.421969 \tabularnewline
3 & 0.036694 & 0.3688 & 0.356537 \tabularnewline
4 & -0.04131 & -0.4152 & 0.339454 \tabularnewline
5 & -0.166363 & -1.6719 & 0.048817 \tabularnewline
6 & 0.093935 & 0.944 & 0.173703 \tabularnewline
7 & -0.034962 & -0.3514 & 0.363022 \tabularnewline
8 & 0.071825 & 0.7218 & 0.236033 \tabularnewline
9 & -0.07299 & -0.7335 & 0.232466 \tabularnewline
10 & 0.094359 & 0.9483 & 0.172621 \tabularnewline
11 & -0.115048 & -1.1562 & 0.12516 \tabularnewline
12 & 0.055419 & 0.557 & 0.289395 \tabularnewline
13 & 0.052781 & 0.5304 & 0.298485 \tabularnewline
14 & -0.120508 & -1.2111 & 0.114344 \tabularnewline
15 & -0.02617 & -0.263 & 0.39654 \tabularnewline
16 & 0.168167 & 1.6901 & 0.047051 \tabularnewline
17 & -0.214653 & -2.1572 & 0.01668 \tabularnewline
18 & 0.090036 & 0.9049 & 0.183848 \tabularnewline
19 & -0.024998 & -0.2512 & 0.401076 \tabularnewline
20 & 0.084482 & 0.849 & 0.198936 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299844&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]-0.273714[/C][C]-2.7508[/C][C]0.003523[/C][/ROW]
[ROW][C]2[/C][C]-0.019639[/C][C]-0.1974[/C][C]0.421969[/C][/ROW]
[ROW][C]3[/C][C]0.036694[/C][C]0.3688[/C][C]0.356537[/C][/ROW]
[ROW][C]4[/C][C]-0.04131[/C][C]-0.4152[/C][C]0.339454[/C][/ROW]
[ROW][C]5[/C][C]-0.166363[/C][C]-1.6719[/C][C]0.048817[/C][/ROW]
[ROW][C]6[/C][C]0.093935[/C][C]0.944[/C][C]0.173703[/C][/ROW]
[ROW][C]7[/C][C]-0.034962[/C][C]-0.3514[/C][C]0.363022[/C][/ROW]
[ROW][C]8[/C][C]0.071825[/C][C]0.7218[/C][C]0.236033[/C][/ROW]
[ROW][C]9[/C][C]-0.07299[/C][C]-0.7335[/C][C]0.232466[/C][/ROW]
[ROW][C]10[/C][C]0.094359[/C][C]0.9483[/C][C]0.172621[/C][/ROW]
[ROW][C]11[/C][C]-0.115048[/C][C]-1.1562[/C][C]0.12516[/C][/ROW]
[ROW][C]12[/C][C]0.055419[/C][C]0.557[/C][C]0.289395[/C][/ROW]
[ROW][C]13[/C][C]0.052781[/C][C]0.5304[/C][C]0.298485[/C][/ROW]
[ROW][C]14[/C][C]-0.120508[/C][C]-1.2111[/C][C]0.114344[/C][/ROW]
[ROW][C]15[/C][C]-0.02617[/C][C]-0.263[/C][C]0.39654[/C][/ROW]
[ROW][C]16[/C][C]0.168167[/C][C]1.6901[/C][C]0.047051[/C][/ROW]
[ROW][C]17[/C][C]-0.214653[/C][C]-2.1572[/C][C]0.01668[/C][/ROW]
[ROW][C]18[/C][C]0.090036[/C][C]0.9049[/C][C]0.183848[/C][/ROW]
[ROW][C]19[/C][C]-0.024998[/C][C]-0.2512[/C][C]0.401076[/C][/ROW]
[ROW][C]20[/C][C]0.084482[/C][C]0.849[/C][C]0.198936[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299844&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299844&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	-0.273714	-2.7508	0.003523
2	-0.019639	-0.1974	0.421969
3	0.036694	0.3688	0.356537
4	-0.04131	-0.4152	0.339454
5	-0.166363	-1.6719	0.048817
6	0.093935	0.944	0.173703
7	-0.034962	-0.3514	0.363022
8	0.071825	0.7218	0.236033
9	-0.07299	-0.7335	0.232466
10	0.094359	0.9483	0.172621
11	-0.115048	-1.1562	0.12516
12	0.055419	0.557	0.289395
13	0.052781	0.5304	0.298485
14	-0.120508	-1.2111	0.114344
15	-0.02617	-0.263	0.39654
16	0.168167	1.6901	0.047051
17	-0.214653	-2.1572	0.01668
18	0.090036	0.9049	0.183848
19	-0.024998	-0.2512	0.401076
20	0.084482	0.849	0.198936

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.273714	-2.7508	0.003523
2	-0.102216	-1.0273	0.153377
3	0.003049	0.0306	0.487809
4	-0.034308	-0.3448	0.365484
5	-0.201785	-2.0279	0.022601
6	-0.020275	-0.2038	0.419477
7	-0.03523	-0.3541	0.362016
8	0.068282	0.6862	0.247072
9	-0.066057	-0.6639	0.254143
10	0.041705	0.4191	0.338007
11	-0.084933	-0.8536	0.197682
12	0.013689	0.1376	0.445428
13	0.084465	0.8489	0.198983
14	-0.108456	-1.09	0.13916
15	-0.079324	-0.7972	0.213602
16	0.103104	1.0362	0.151297
17	-0.122921	-1.2353	0.109786
18	0.003517	0.0353	0.485937
19	-0.064532	-0.6485	0.259055
20	0.081057	0.8146	0.208604

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.273714 & -2.7508 & 0.003523 \tabularnewline
2 & -0.102216 & -1.0273 & 0.153377 \tabularnewline
3 & 0.003049 & 0.0306 & 0.487809 \tabularnewline
4 & -0.034308 & -0.3448 & 0.365484 \tabularnewline
5 & -0.201785 & -2.0279 & 0.022601 \tabularnewline
6 & -0.020275 & -0.2038 & 0.419477 \tabularnewline
7 & -0.03523 & -0.3541 & 0.362016 \tabularnewline
8 & 0.068282 & 0.6862 & 0.247072 \tabularnewline
9 & -0.066057 & -0.6639 & 0.254143 \tabularnewline
10 & 0.041705 & 0.4191 & 0.338007 \tabularnewline
11 & -0.084933 & -0.8536 & 0.197682 \tabularnewline
12 & 0.013689 & 0.1376 & 0.445428 \tabularnewline
13 & 0.084465 & 0.8489 & 0.198983 \tabularnewline
14 & -0.108456 & -1.09 & 0.13916 \tabularnewline
15 & -0.079324 & -0.7972 & 0.213602 \tabularnewline
16 & 0.103104 & 1.0362 & 0.151297 \tabularnewline
17 & -0.122921 & -1.2353 & 0.109786 \tabularnewline
18 & 0.003517 & 0.0353 & 0.485937 \tabularnewline
19 & -0.064532 & -0.6485 & 0.259055 \tabularnewline
20 & 0.081057 & 0.8146 & 0.208604 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299844&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]-0.273714[/C][C]-2.7508[/C][C]0.003523[/C][/ROW]
[ROW][C]2[/C][C]-0.102216[/C][C]-1.0273[/C][C]0.153377[/C][/ROW]
[ROW][C]3[/C][C]0.003049[/C][C]0.0306[/C][C]0.487809[/C][/ROW]
[ROW][C]4[/C][C]-0.034308[/C][C]-0.3448[/C][C]0.365484[/C][/ROW]
[ROW][C]5[/C][C]-0.201785[/C][C]-2.0279[/C][C]0.022601[/C][/ROW]
[ROW][C]6[/C][C]-0.020275[/C][C]-0.2038[/C][C]0.419477[/C][/ROW]
[ROW][C]7[/C][C]-0.03523[/C][C]-0.3541[/C][C]0.362016[/C][/ROW]
[ROW][C]8[/C][C]0.068282[/C][C]0.6862[/C][C]0.247072[/C][/ROW]
[ROW][C]9[/C][C]-0.066057[/C][C]-0.6639[/C][C]0.254143[/C][/ROW]
[ROW][C]10[/C][C]0.041705[/C][C]0.4191[/C][C]0.338007[/C][/ROW]
[ROW][C]11[/C][C]-0.084933[/C][C]-0.8536[/C][C]0.197682[/C][/ROW]
[ROW][C]12[/C][C]0.013689[/C][C]0.1376[/C][C]0.445428[/C][/ROW]
[ROW][C]13[/C][C]0.084465[/C][C]0.8489[/C][C]0.198983[/C][/ROW]
[ROW][C]14[/C][C]-0.108456[/C][C]-1.09[/C][C]0.13916[/C][/ROW]
[ROW][C]15[/C][C]-0.079324[/C][C]-0.7972[/C][C]0.213602[/C][/ROW]
[ROW][C]16[/C][C]0.103104[/C][C]1.0362[/C][C]0.151297[/C][/ROW]
[ROW][C]17[/C][C]-0.122921[/C][C]-1.2353[/C][C]0.109786[/C][/ROW]
[ROW][C]18[/C][C]0.003517[/C][C]0.0353[/C][C]0.485937[/C][/ROW]
[ROW][C]19[/C][C]-0.064532[/C][C]-0.6485[/C][C]0.259055[/C][/ROW]
[ROW][C]20[/C][C]0.081057[/C][C]0.8146[/C][C]0.208604[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299844&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299844&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	-0.273714	-2.7508	0.003523
2	-0.102216	-1.0273	0.153377
3	0.003049	0.0306	0.487809
4	-0.034308	-0.3448	0.365484
5	-0.201785	-2.0279	0.022601
6	-0.020275	-0.2038	0.419477
7	-0.03523	-0.3541	0.362016
8	0.068282	0.6862	0.247072
9	-0.066057	-0.6639	0.254143
10	0.041705	0.4191	0.338007
11	-0.084933	-0.8536	0.197682
12	0.013689	0.1376	0.445428
13	0.084465	0.8489	0.198983
14	-0.108456	-1.09	0.13916
15	-0.079324	-0.7972	0.213602
16	0.103104	1.0362	0.151297
17	-0.122921	-1.2353	0.109786
18	0.003517	0.0353	0.485937
19	-0.064532	-0.6485	0.259055
20	0.081057	0.8146	0.208604

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code