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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 15 Aug 2017 14:40:46 +0200

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Aug/15/t1502800892nuronmojk6vri75.htm/, Retrieved Mon, 20 May 2024 00:33:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307278, Retrieved Mon, 20 May 2024 00:33:03 +0000

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-       [(Partial) Autocorrelation Function] [] [2017-08-15 12:40:46] [eec775fda337aa2da775a098928b5865] [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=307278&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=307278&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307278&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	-0.34099	-3.5272	0.00031
2	0.161171	1.6672	0.049203
3	-0.187224	-1.9367	0.027712
4	-0.339596	-3.5128	0.000325
5	0.370955	3.8372	0.000105
6	-0.34395	-3.5578	0.000279
7	0.418111	4.325	1.7e-05
8	-0.287596	-2.9749	0.001811
9	-0.184079	-1.9041	0.02979
10	0.134419	1.3904	0.083641
11	-0.313093	-3.2387	8e-04
12	0.789552	8.1672	0
13	-0.255181	-2.6396	0.00477
14	0.190657	1.9722	0.025585
15	-0.164844	-1.7052	0.045533
16	-0.350569	-3.6263	0.000221
17	0.337735	3.4936	0.000347
18	-0.308274	-3.1888	0.000937
19	0.376507	3.8946	8.6e-05
20	-0.224228	-2.3194	0.011135

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.34099 & -3.5272 & 0.00031 \tabularnewline
2 & 0.161171 & 1.6672 & 0.049203 \tabularnewline
3 & -0.187224 & -1.9367 & 0.027712 \tabularnewline
4 & -0.339596 & -3.5128 & 0.000325 \tabularnewline
5 & 0.370955 & 3.8372 & 0.000105 \tabularnewline
6 & -0.34395 & -3.5578 & 0.000279 \tabularnewline
7 & 0.418111 & 4.325 & 1.7e-05 \tabularnewline
8 & -0.287596 & -2.9749 & 0.001811 \tabularnewline
9 & -0.184079 & -1.9041 & 0.02979 \tabularnewline
10 & 0.134419 & 1.3904 & 0.083641 \tabularnewline
11 & -0.313093 & -3.2387 & 8e-04 \tabularnewline
12 & 0.789552 & 8.1672 & 0 \tabularnewline
13 & -0.255181 & -2.6396 & 0.00477 \tabularnewline
14 & 0.190657 & 1.9722 & 0.025585 \tabularnewline
15 & -0.164844 & -1.7052 & 0.045533 \tabularnewline
16 & -0.350569 & -3.6263 & 0.000221 \tabularnewline
17 & 0.337735 & 3.4936 & 0.000347 \tabularnewline
18 & -0.308274 & -3.1888 & 0.000937 \tabularnewline
19 & 0.376507 & 3.8946 & 8.6e-05 \tabularnewline
20 & -0.224228 & -2.3194 & 0.011135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307278&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]-0.34099[/C][C]-3.5272[/C][C]0.00031[/C][/ROW]
[ROW][C]2[/C][C]0.161171[/C][C]1.6672[/C][C]0.049203[/C][/ROW]
[ROW][C]3[/C][C]-0.187224[/C][C]-1.9367[/C][C]0.027712[/C][/ROW]
[ROW][C]4[/C][C]-0.339596[/C][C]-3.5128[/C][C]0.000325[/C][/ROW]
[ROW][C]5[/C][C]0.370955[/C][C]3.8372[/C][C]0.000105[/C][/ROW]
[ROW][C]6[/C][C]-0.34395[/C][C]-3.5578[/C][C]0.000279[/C][/ROW]
[ROW][C]7[/C][C]0.418111[/C][C]4.325[/C][C]1.7e-05[/C][/ROW]
[ROW][C]8[/C][C]-0.287596[/C][C]-2.9749[/C][C]0.001811[/C][/ROW]
[ROW][C]9[/C][C]-0.184079[/C][C]-1.9041[/C][C]0.02979[/C][/ROW]
[ROW][C]10[/C][C]0.134419[/C][C]1.3904[/C][C]0.083641[/C][/ROW]
[ROW][C]11[/C][C]-0.313093[/C][C]-3.2387[/C][C]8e-04[/C][/ROW]
[ROW][C]12[/C][C]0.789552[/C][C]8.1672[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.255181[/C][C]-2.6396[/C][C]0.00477[/C][/ROW]
[ROW][C]14[/C][C]0.190657[/C][C]1.9722[/C][C]0.025585[/C][/ROW]
[ROW][C]15[/C][C]-0.164844[/C][C]-1.7052[/C][C]0.045533[/C][/ROW]
[ROW][C]16[/C][C]-0.350569[/C][C]-3.6263[/C][C]0.000221[/C][/ROW]
[ROW][C]17[/C][C]0.337735[/C][C]3.4936[/C][C]0.000347[/C][/ROW]
[ROW][C]18[/C][C]-0.308274[/C][C]-3.1888[/C][C]0.000937[/C][/ROW]
[ROW][C]19[/C][C]0.376507[/C][C]3.8946[/C][C]8.6e-05[/C][/ROW]
[ROW][C]20[/C][C]-0.224228[/C][C]-2.3194[/C][C]0.011135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307278&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307278&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	-0.34099	-3.5272	0.00031
2	0.161171	1.6672	0.049203
3	-0.187224	-1.9367	0.027712
4	-0.339596	-3.5128	0.000325
5	0.370955	3.8372	0.000105
6	-0.34395	-3.5578	0.000279
7	0.418111	4.325	1.7e-05
8	-0.287596	-2.9749	0.001811
9	-0.184079	-1.9041	0.02979
10	0.134419	1.3904	0.083641
11	-0.313093	-3.2387	8e-04
12	0.789552	8.1672	0
13	-0.255181	-2.6396	0.00477
14	0.190657	1.9722	0.025585
15	-0.164844	-1.7052	0.045533
16	-0.350569	-3.6263	0.000221
17	0.337735	3.4936	0.000347
18	-0.308274	-3.1888	0.000937
19	0.376507	3.8946	8.6e-05
20	-0.224228	-2.3194	0.011135

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.34099	-3.5272	0.00031
2	0.050804	0.5255	0.300154
3	-0.13357	-1.3817	0.084977
4	-0.514821	-5.3253	0
5	0.179815	1.86	0.032814
6	-0.220958	-2.2856	0.012124
7	0.076756	0.794	0.214484
8	-0.234549	-2.4262	0.008465
9	-0.434093	-4.4903	9e-06
10	-0.217	-2.2447	0.013423
11	-0.396937	-4.1059	3.9e-05
12	0.445036	4.6035	6e-06
13	0.108652	1.1239	0.131784
14	0.043625	0.4513	0.326357
15	-0.004306	-0.0445	0.48228
16	-0.015357	-0.1589	0.43704
17	0.049771	0.5148	0.303866
18	0.089724	0.9281	0.17772
19	-0.104654	-1.0825	0.140722
20	-0.051051	-0.5281	0.299269

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.34099 & -3.5272 & 0.00031 \tabularnewline
2 & 0.050804 & 0.5255 & 0.300154 \tabularnewline
3 & -0.13357 & -1.3817 & 0.084977 \tabularnewline
4 & -0.514821 & -5.3253 & 0 \tabularnewline
5 & 0.179815 & 1.86 & 0.032814 \tabularnewline
6 & -0.220958 & -2.2856 & 0.012124 \tabularnewline
7 & 0.076756 & 0.794 & 0.214484 \tabularnewline
8 & -0.234549 & -2.4262 & 0.008465 \tabularnewline
9 & -0.434093 & -4.4903 & 9e-06 \tabularnewline
10 & -0.217 & -2.2447 & 0.013423 \tabularnewline
11 & -0.396937 & -4.1059 & 3.9e-05 \tabularnewline
12 & 0.445036 & 4.6035 & 6e-06 \tabularnewline
13 & 0.108652 & 1.1239 & 0.131784 \tabularnewline
14 & 0.043625 & 0.4513 & 0.326357 \tabularnewline
15 & -0.004306 & -0.0445 & 0.48228 \tabularnewline
16 & -0.015357 & -0.1589 & 0.43704 \tabularnewline
17 & 0.049771 & 0.5148 & 0.303866 \tabularnewline
18 & 0.089724 & 0.9281 & 0.17772 \tabularnewline
19 & -0.104654 & -1.0825 & 0.140722 \tabularnewline
20 & -0.051051 & -0.5281 & 0.299269 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307278&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]-0.34099[/C][C]-3.5272[/C][C]0.00031[/C][/ROW]
[ROW][C]2[/C][C]0.050804[/C][C]0.5255[/C][C]0.300154[/C][/ROW]
[ROW][C]3[/C][C]-0.13357[/C][C]-1.3817[/C][C]0.084977[/C][/ROW]
[ROW][C]4[/C][C]-0.514821[/C][C]-5.3253[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.179815[/C][C]1.86[/C][C]0.032814[/C][/ROW]
[ROW][C]6[/C][C]-0.220958[/C][C]-2.2856[/C][C]0.012124[/C][/ROW]
[ROW][C]7[/C][C]0.076756[/C][C]0.794[/C][C]0.214484[/C][/ROW]
[ROW][C]8[/C][C]-0.234549[/C][C]-2.4262[/C][C]0.008465[/C][/ROW]
[ROW][C]9[/C][C]-0.434093[/C][C]-4.4903[/C][C]9e-06[/C][/ROW]
[ROW][C]10[/C][C]-0.217[/C][C]-2.2447[/C][C]0.013423[/C][/ROW]
[ROW][C]11[/C][C]-0.396937[/C][C]-4.1059[/C][C]3.9e-05[/C][/ROW]
[ROW][C]12[/C][C]0.445036[/C][C]4.6035[/C][C]6e-06[/C][/ROW]
[ROW][C]13[/C][C]0.108652[/C][C]1.1239[/C][C]0.131784[/C][/ROW]
[ROW][C]14[/C][C]0.043625[/C][C]0.4513[/C][C]0.326357[/C][/ROW]
[ROW][C]15[/C][C]-0.004306[/C][C]-0.0445[/C][C]0.48228[/C][/ROW]
[ROW][C]16[/C][C]-0.015357[/C][C]-0.1589[/C][C]0.43704[/C][/ROW]
[ROW][C]17[/C][C]0.049771[/C][C]0.5148[/C][C]0.303866[/C][/ROW]
[ROW][C]18[/C][C]0.089724[/C][C]0.9281[/C][C]0.17772[/C][/ROW]
[ROW][C]19[/C][C]-0.104654[/C][C]-1.0825[/C][C]0.140722[/C][/ROW]
[ROW][C]20[/C][C]-0.051051[/C][C]-0.5281[/C][C]0.299269[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307278&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307278&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	-0.34099	-3.5272	0.00031
2	0.050804	0.5255	0.300154
3	-0.13357	-1.3817	0.084977
4	-0.514821	-5.3253	0
5	0.179815	1.86	0.032814
6	-0.220958	-2.2856	0.012124
7	0.076756	0.794	0.214484
8	-0.234549	-2.4262	0.008465
9	-0.434093	-4.4903	9e-06
10	-0.217	-2.2447	0.013423
11	-0.396937	-4.1059	3.9e-05
12	0.445036	4.6035	6e-06
13	0.108652	1.1239	0.131784
14	0.043625	0.4513	0.326357
15	-0.004306	-0.0445	0.48228
16	-0.015357	-0.1589	0.43704
17	0.049771	0.5148	0.303866
18	0.089724	0.9281	0.17772
19	-0.104654	-1.0825	0.140722
20	-0.051051	-0.5281	0.299269

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

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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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code