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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 19 Dec 2016 17:38:43 +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/19/t1482165589csl3tul11ng97nk.htm/, Retrieved Sat, 18 May 2024 03:24:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301415, Retrieved Sat, 18 May 2024 03:24:28 +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] [] [2016-12-19 16:38:43] [361c8dad91b3f1ef2e651cd04783c23b] [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=301415&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=301415&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301415&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	-0.280719	-2.9841	0.001743
2	-0.237142	-2.5209	0.006551
3	0.060746	0.6457	0.259877
4	0.056232	0.5978	0.275601
5	0.071212	0.757	0.225315
6	-0.104601	-1.1119	0.134265
7	-0.042915	-0.4562	0.324565
8	0.056212	0.5975	0.275669
9	0.015312	0.1628	0.435497
10	-0.058523	-0.6221	0.267561
11	0.083651	0.8892	0.187885
12	-0.284939	-3.0289	0.001521
13	0.055958	0.5948	0.276571
14	0.224538	2.3869	0.009326
15	-0.026233	-0.2789	0.390429
16	-0.317173	-3.3716	0.000512
17	0.141773	1.5071	0.067292
18	0.249288	2.65	0.004602
19	-0.131764	-1.4007	0.082026
20	-0.099471	-1.0574	0.146294
21	0.033679	0.358	0.360502

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.280719 & -2.9841 & 0.001743 \tabularnewline
2 & -0.237142 & -2.5209 & 0.006551 \tabularnewline
3 & 0.060746 & 0.6457 & 0.259877 \tabularnewline
4 & 0.056232 & 0.5978 & 0.275601 \tabularnewline
5 & 0.071212 & 0.757 & 0.225315 \tabularnewline
6 & -0.104601 & -1.1119 & 0.134265 \tabularnewline
7 & -0.042915 & -0.4562 & 0.324565 \tabularnewline
8 & 0.056212 & 0.5975 & 0.275669 \tabularnewline
9 & 0.015312 & 0.1628 & 0.435497 \tabularnewline
10 & -0.058523 & -0.6221 & 0.267561 \tabularnewline
11 & 0.083651 & 0.8892 & 0.187885 \tabularnewline
12 & -0.284939 & -3.0289 & 0.001521 \tabularnewline
13 & 0.055958 & 0.5948 & 0.276571 \tabularnewline
14 & 0.224538 & 2.3869 & 0.009326 \tabularnewline
15 & -0.026233 & -0.2789 & 0.390429 \tabularnewline
16 & -0.317173 & -3.3716 & 0.000512 \tabularnewline
17 & 0.141773 & 1.5071 & 0.067292 \tabularnewline
18 & 0.249288 & 2.65 & 0.004602 \tabularnewline
19 & -0.131764 & -1.4007 & 0.082026 \tabularnewline
20 & -0.099471 & -1.0574 & 0.146294 \tabularnewline
21 & 0.033679 & 0.358 & 0.360502 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301415&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]-0.280719[/C][C]-2.9841[/C][C]0.001743[/C][/ROW]
[ROW][C]2[/C][C]-0.237142[/C][C]-2.5209[/C][C]0.006551[/C][/ROW]
[ROW][C]3[/C][C]0.060746[/C][C]0.6457[/C][C]0.259877[/C][/ROW]
[ROW][C]4[/C][C]0.056232[/C][C]0.5978[/C][C]0.275601[/C][/ROW]
[ROW][C]5[/C][C]0.071212[/C][C]0.757[/C][C]0.225315[/C][/ROW]
[ROW][C]6[/C][C]-0.104601[/C][C]-1.1119[/C][C]0.134265[/C][/ROW]
[ROW][C]7[/C][C]-0.042915[/C][C]-0.4562[/C][C]0.324565[/C][/ROW]
[ROW][C]8[/C][C]0.056212[/C][C]0.5975[/C][C]0.275669[/C][/ROW]
[ROW][C]9[/C][C]0.015312[/C][C]0.1628[/C][C]0.435497[/C][/ROW]
[ROW][C]10[/C][C]-0.058523[/C][C]-0.6221[/C][C]0.267561[/C][/ROW]
[ROW][C]11[/C][C]0.083651[/C][C]0.8892[/C][C]0.187885[/C][/ROW]
[ROW][C]12[/C][C]-0.284939[/C][C]-3.0289[/C][C]0.001521[/C][/ROW]
[ROW][C]13[/C][C]0.055958[/C][C]0.5948[/C][C]0.276571[/C][/ROW]
[ROW][C]14[/C][C]0.224538[/C][C]2.3869[/C][C]0.009326[/C][/ROW]
[ROW][C]15[/C][C]-0.026233[/C][C]-0.2789[/C][C]0.390429[/C][/ROW]
[ROW][C]16[/C][C]-0.317173[/C][C]-3.3716[/C][C]0.000512[/C][/ROW]
[ROW][C]17[/C][C]0.141773[/C][C]1.5071[/C][C]0.067292[/C][/ROW]
[ROW][C]18[/C][C]0.249288[/C][C]2.65[/C][C]0.004602[/C][/ROW]
[ROW][C]19[/C][C]-0.131764[/C][C]-1.4007[/C][C]0.082026[/C][/ROW]
[ROW][C]20[/C][C]-0.099471[/C][C]-1.0574[/C][C]0.146294[/C][/ROW]
[ROW][C]21[/C][C]0.033679[/C][C]0.358[/C][C]0.360502[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301415&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301415&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	-0.280719	-2.9841	0.001743
2	-0.237142	-2.5209	0.006551
3	0.060746	0.6457	0.259877
4	0.056232	0.5978	0.275601
5	0.071212	0.757	0.225315
6	-0.104601	-1.1119	0.134265
7	-0.042915	-0.4562	0.324565
8	0.056212	0.5975	0.275669
9	0.015312	0.1628	0.435497
10	-0.058523	-0.6221	0.267561
11	0.083651	0.8892	0.187885
12	-0.284939	-3.0289	0.001521
13	0.055958	0.5948	0.276571
14	0.224538	2.3869	0.009326
15	-0.026233	-0.2789	0.390429
16	-0.317173	-3.3716	0.000512
17	0.141773	1.5071	0.067292
18	0.249288	2.65	0.004602
19	-0.131764	-1.4007	0.082026
20	-0.099471	-1.0574	0.146294
21	0.033679	0.358	0.360502

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.280719	-2.9841	0.001743
2	-0.342972	-3.6458	0.000202
3	-0.153701	-1.6339	0.052535
4	-0.070418	-0.7485	0.227842
5	0.074283	0.7896	0.215697
6	-0.037037	-0.3937	0.347269
7	-0.05481	-0.5826	0.280651
8	-0.029079	-0.3091	0.378902
9	-0.014886	-0.1582	0.437277
10	-0.06139	-0.6526	0.257675
11	0.07846	0.834	0.20301
12	-0.322812	-3.4315	0.00042
13	-0.191064	-2.031	0.022299
14	0.015059	0.1601	0.436553
15	0.085379	0.9076	0.183014
16	-0.299478	-3.1835	0.00094
17	-0.035099	-0.3731	0.354884
18	0.143465	1.5251	0.06502
19	-0.021032	-0.2236	0.411745
20	-0.058476	-0.6216	0.267727
21	0.040795	0.4337	0.332681

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.280719 & -2.9841 & 0.001743 \tabularnewline
2 & -0.342972 & -3.6458 & 0.000202 \tabularnewline
3 & -0.153701 & -1.6339 & 0.052535 \tabularnewline
4 & -0.070418 & -0.7485 & 0.227842 \tabularnewline
5 & 0.074283 & 0.7896 & 0.215697 \tabularnewline
6 & -0.037037 & -0.3937 & 0.347269 \tabularnewline
7 & -0.05481 & -0.5826 & 0.280651 \tabularnewline
8 & -0.029079 & -0.3091 & 0.378902 \tabularnewline
9 & -0.014886 & -0.1582 & 0.437277 \tabularnewline
10 & -0.06139 & -0.6526 & 0.257675 \tabularnewline
11 & 0.07846 & 0.834 & 0.20301 \tabularnewline
12 & -0.322812 & -3.4315 & 0.00042 \tabularnewline
13 & -0.191064 & -2.031 & 0.022299 \tabularnewline
14 & 0.015059 & 0.1601 & 0.436553 \tabularnewline
15 & 0.085379 & 0.9076 & 0.183014 \tabularnewline
16 & -0.299478 & -3.1835 & 0.00094 \tabularnewline
17 & -0.035099 & -0.3731 & 0.354884 \tabularnewline
18 & 0.143465 & 1.5251 & 0.06502 \tabularnewline
19 & -0.021032 & -0.2236 & 0.411745 \tabularnewline
20 & -0.058476 & -0.6216 & 0.267727 \tabularnewline
21 & 0.040795 & 0.4337 & 0.332681 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301415&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]-0.280719[/C][C]-2.9841[/C][C]0.001743[/C][/ROW]
[ROW][C]2[/C][C]-0.342972[/C][C]-3.6458[/C][C]0.000202[/C][/ROW]
[ROW][C]3[/C][C]-0.153701[/C][C]-1.6339[/C][C]0.052535[/C][/ROW]
[ROW][C]4[/C][C]-0.070418[/C][C]-0.7485[/C][C]0.227842[/C][/ROW]
[ROW][C]5[/C][C]0.074283[/C][C]0.7896[/C][C]0.215697[/C][/ROW]
[ROW][C]6[/C][C]-0.037037[/C][C]-0.3937[/C][C]0.347269[/C][/ROW]
[ROW][C]7[/C][C]-0.05481[/C][C]-0.5826[/C][C]0.280651[/C][/ROW]
[ROW][C]8[/C][C]-0.029079[/C][C]-0.3091[/C][C]0.378902[/C][/ROW]
[ROW][C]9[/C][C]-0.014886[/C][C]-0.1582[/C][C]0.437277[/C][/ROW]
[ROW][C]10[/C][C]-0.06139[/C][C]-0.6526[/C][C]0.257675[/C][/ROW]
[ROW][C]11[/C][C]0.07846[/C][C]0.834[/C][C]0.20301[/C][/ROW]
[ROW][C]12[/C][C]-0.322812[/C][C]-3.4315[/C][C]0.00042[/C][/ROW]
[ROW][C]13[/C][C]-0.191064[/C][C]-2.031[/C][C]0.022299[/C][/ROW]
[ROW][C]14[/C][C]0.015059[/C][C]0.1601[/C][C]0.436553[/C][/ROW]
[ROW][C]15[/C][C]0.085379[/C][C]0.9076[/C][C]0.183014[/C][/ROW]
[ROW][C]16[/C][C]-0.299478[/C][C]-3.1835[/C][C]0.00094[/C][/ROW]
[ROW][C]17[/C][C]-0.035099[/C][C]-0.3731[/C][C]0.354884[/C][/ROW]
[ROW][C]18[/C][C]0.143465[/C][C]1.5251[/C][C]0.06502[/C][/ROW]
[ROW][C]19[/C][C]-0.021032[/C][C]-0.2236[/C][C]0.411745[/C][/ROW]
[ROW][C]20[/C][C]-0.058476[/C][C]-0.6216[/C][C]0.267727[/C][/ROW]
[ROW][C]21[/C][C]0.040795[/C][C]0.4337[/C][C]0.332681[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301415&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301415&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	-0.280719	-2.9841	0.001743
2	-0.342972	-3.6458	0.000202
3	-0.153701	-1.6339	0.052535
4	-0.070418	-0.7485	0.227842
5	0.074283	0.7896	0.215697
6	-0.037037	-0.3937	0.347269
7	-0.05481	-0.5826	0.280651
8	-0.029079	-0.3091	0.378902
9	-0.014886	-0.1582	0.437277
10	-0.06139	-0.6526	0.257675
11	0.07846	0.834	0.20301
12	-0.322812	-3.4315	0.00042
13	-0.191064	-2.031	0.022299
14	0.015059	0.1601	0.436553
15	0.085379	0.9076	0.183014
16	-0.299478	-3.1835	0.00094
17	-0.035099	-0.3731	0.354884
18	0.143465	1.5251	0.06502
19	-0.021032	-0.2236	0.411745
20	-0.058476	-0.6216	0.267727
21	0.040795	0.4337	0.332681

Figure 1

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Postscript link

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Figure 2

PNG link

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Figure 3

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Parameters (Session):

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

Parameters (R input):

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