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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 13 Dec 2016 12:06:28 +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/13/t1481627246a0evy8qu92o6bc8.htm/, Retrieved Sat, 04 May 2024 20:19:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299053, Retrieved Sat, 04 May 2024 20:19:35 +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] [Partial autocorre...] [2016-12-13 11:06:28] [94c1b173d9287822f5e2740a4a602bdd] [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=299053&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=299053&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299053&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	-0.112166	-1.1657	0.12316
2	-0.144669	-1.5034	0.067822
3	-0.016561	-0.1721	0.431838
4	0.031746	0.3299	0.371051
5	0.031784	0.3303	0.370904
6	-0.065372	-0.6794	0.249179
7	-0.065436	-0.68	0.248971
8	-0.088027	-0.9148	0.181167
9	0.026991	0.2805	0.389817
10	0.075436	0.784	0.217391
11	0.164934	1.714	0.044695
12	-0.439095	-4.5632	7e-06
13	0.045886	0.4769	0.317213
14	0.062075	0.6451	0.260113
15	0.016304	0.1694	0.432886
16	-0.0915	-0.9509	0.17189
17	-0.10347	-1.0753	0.14232
18	0.043525	0.4523	0.325972
19	0.102501	1.0652	0.144576
20	0.072043	0.7487	0.227834

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.112166 & -1.1657 & 0.12316 \tabularnewline
2 & -0.144669 & -1.5034 & 0.067822 \tabularnewline
3 & -0.016561 & -0.1721 & 0.431838 \tabularnewline
4 & 0.031746 & 0.3299 & 0.371051 \tabularnewline
5 & 0.031784 & 0.3303 & 0.370904 \tabularnewline
6 & -0.065372 & -0.6794 & 0.249179 \tabularnewline
7 & -0.065436 & -0.68 & 0.248971 \tabularnewline
8 & -0.088027 & -0.9148 & 0.181167 \tabularnewline
9 & 0.026991 & 0.2805 & 0.389817 \tabularnewline
10 & 0.075436 & 0.784 & 0.217391 \tabularnewline
11 & 0.164934 & 1.714 & 0.044695 \tabularnewline
12 & -0.439095 & -4.5632 & 7e-06 \tabularnewline
13 & 0.045886 & 0.4769 & 0.317213 \tabularnewline
14 & 0.062075 & 0.6451 & 0.260113 \tabularnewline
15 & 0.016304 & 0.1694 & 0.432886 \tabularnewline
16 & -0.0915 & -0.9509 & 0.17189 \tabularnewline
17 & -0.10347 & -1.0753 & 0.14232 \tabularnewline
18 & 0.043525 & 0.4523 & 0.325972 \tabularnewline
19 & 0.102501 & 1.0652 & 0.144576 \tabularnewline
20 & 0.072043 & 0.7487 & 0.227834 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299053&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]-0.112166[/C][C]-1.1657[/C][C]0.12316[/C][/ROW]
[ROW][C]2[/C][C]-0.144669[/C][C]-1.5034[/C][C]0.067822[/C][/ROW]
[ROW][C]3[/C][C]-0.016561[/C][C]-0.1721[/C][C]0.431838[/C][/ROW]
[ROW][C]4[/C][C]0.031746[/C][C]0.3299[/C][C]0.371051[/C][/ROW]
[ROW][C]5[/C][C]0.031784[/C][C]0.3303[/C][C]0.370904[/C][/ROW]
[ROW][C]6[/C][C]-0.065372[/C][C]-0.6794[/C][C]0.249179[/C][/ROW]
[ROW][C]7[/C][C]-0.065436[/C][C]-0.68[/C][C]0.248971[/C][/ROW]
[ROW][C]8[/C][C]-0.088027[/C][C]-0.9148[/C][C]0.181167[/C][/ROW]
[ROW][C]9[/C][C]0.026991[/C][C]0.2805[/C][C]0.389817[/C][/ROW]
[ROW][C]10[/C][C]0.075436[/C][C]0.784[/C][C]0.217391[/C][/ROW]
[ROW][C]11[/C][C]0.164934[/C][C]1.714[/C][C]0.044695[/C][/ROW]
[ROW][C]12[/C][C]-0.439095[/C][C]-4.5632[/C][C]7e-06[/C][/ROW]
[ROW][C]13[/C][C]0.045886[/C][C]0.4769[/C][C]0.317213[/C][/ROW]
[ROW][C]14[/C][C]0.062075[/C][C]0.6451[/C][C]0.260113[/C][/ROW]
[ROW][C]15[/C][C]0.016304[/C][C]0.1694[/C][C]0.432886[/C][/ROW]
[ROW][C]16[/C][C]-0.0915[/C][C]-0.9509[/C][C]0.17189[/C][/ROW]
[ROW][C]17[/C][C]-0.10347[/C][C]-1.0753[/C][C]0.14232[/C][/ROW]
[ROW][C]18[/C][C]0.043525[/C][C]0.4523[/C][C]0.325972[/C][/ROW]
[ROW][C]19[/C][C]0.102501[/C][C]1.0652[/C][C]0.144576[/C][/ROW]
[ROW][C]20[/C][C]0.072043[/C][C]0.7487[/C][C]0.227834[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299053&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299053&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	-0.112166	-1.1657	0.12316
2	-0.144669	-1.5034	0.067822
3	-0.016561	-0.1721	0.431838
4	0.031746	0.3299	0.371051
5	0.031784	0.3303	0.370904
6	-0.065372	-0.6794	0.249179
7	-0.065436	-0.68	0.248971
8	-0.088027	-0.9148	0.181167
9	0.026991	0.2805	0.389817
10	0.075436	0.784	0.217391
11	0.164934	1.714	0.044695
12	-0.439095	-4.5632	7e-06
13	0.045886	0.4769	0.317213
14	0.062075	0.6451	0.260113
15	0.016304	0.1694	0.432886
16	-0.0915	-0.9509	0.17189
17	-0.10347	-1.0753	0.14232
18	0.043525	0.4523	0.325972
19	0.102501	1.0652	0.144576
20	0.072043	0.7487	0.227834

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.112166	-1.1657	0.12316
2	-0.159254	-1.655	0.050413
3	-0.055316	-0.5749	0.283291
4	-0.000873	-0.0091	0.496391
5	0.026387	0.2742	0.392221
6	-0.055486	-0.5766	0.282695
7	-0.074377	-0.773	0.22062
8	-0.130104	-1.3521	0.089588
9	-0.03226	-0.3353	0.36904
10	0.040533	0.4212	0.337212
11	0.19364	2.0124	0.023335
12	-0.406083	-4.2201	2.6e-05
13	-0.00592	-0.0615	0.47553
14	-0.089972	-0.935	0.175933
15	-0.006545	-0.068	0.472949
16	-0.126854	-1.3183	0.095095
17	-0.099477	-1.0338	0.151769
18	-0.070308	-0.7307	0.233285
19	0.056861	0.5909	0.277904
20	-0.01906	-0.1981	0.421677

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.112166 & -1.1657 & 0.12316 \tabularnewline
2 & -0.159254 & -1.655 & 0.050413 \tabularnewline
3 & -0.055316 & -0.5749 & 0.283291 \tabularnewline
4 & -0.000873 & -0.0091 & 0.496391 \tabularnewline
5 & 0.026387 & 0.2742 & 0.392221 \tabularnewline
6 & -0.055486 & -0.5766 & 0.282695 \tabularnewline
7 & -0.074377 & -0.773 & 0.22062 \tabularnewline
8 & -0.130104 & -1.3521 & 0.089588 \tabularnewline
9 & -0.03226 & -0.3353 & 0.36904 \tabularnewline
10 & 0.040533 & 0.4212 & 0.337212 \tabularnewline
11 & 0.19364 & 2.0124 & 0.023335 \tabularnewline
12 & -0.406083 & -4.2201 & 2.6e-05 \tabularnewline
13 & -0.00592 & -0.0615 & 0.47553 \tabularnewline
14 & -0.089972 & -0.935 & 0.175933 \tabularnewline
15 & -0.006545 & -0.068 & 0.472949 \tabularnewline
16 & -0.126854 & -1.3183 & 0.095095 \tabularnewline
17 & -0.099477 & -1.0338 & 0.151769 \tabularnewline
18 & -0.070308 & -0.7307 & 0.233285 \tabularnewline
19 & 0.056861 & 0.5909 & 0.277904 \tabularnewline
20 & -0.01906 & -0.1981 & 0.421677 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299053&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]-0.112166[/C][C]-1.1657[/C][C]0.12316[/C][/ROW]
[ROW][C]2[/C][C]-0.159254[/C][C]-1.655[/C][C]0.050413[/C][/ROW]
[ROW][C]3[/C][C]-0.055316[/C][C]-0.5749[/C][C]0.283291[/C][/ROW]
[ROW][C]4[/C][C]-0.000873[/C][C]-0.0091[/C][C]0.496391[/C][/ROW]
[ROW][C]5[/C][C]0.026387[/C][C]0.2742[/C][C]0.392221[/C][/ROW]
[ROW][C]6[/C][C]-0.055486[/C][C]-0.5766[/C][C]0.282695[/C][/ROW]
[ROW][C]7[/C][C]-0.074377[/C][C]-0.773[/C][C]0.22062[/C][/ROW]
[ROW][C]8[/C][C]-0.130104[/C][C]-1.3521[/C][C]0.089588[/C][/ROW]
[ROW][C]9[/C][C]-0.03226[/C][C]-0.3353[/C][C]0.36904[/C][/ROW]
[ROW][C]10[/C][C]0.040533[/C][C]0.4212[/C][C]0.337212[/C][/ROW]
[ROW][C]11[/C][C]0.19364[/C][C]2.0124[/C][C]0.023335[/C][/ROW]
[ROW][C]12[/C][C]-0.406083[/C][C]-4.2201[/C][C]2.6e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.00592[/C][C]-0.0615[/C][C]0.47553[/C][/ROW]
[ROW][C]14[/C][C]-0.089972[/C][C]-0.935[/C][C]0.175933[/C][/ROW]
[ROW][C]15[/C][C]-0.006545[/C][C]-0.068[/C][C]0.472949[/C][/ROW]
[ROW][C]16[/C][C]-0.126854[/C][C]-1.3183[/C][C]0.095095[/C][/ROW]
[ROW][C]17[/C][C]-0.099477[/C][C]-1.0338[/C][C]0.151769[/C][/ROW]
[ROW][C]18[/C][C]-0.070308[/C][C]-0.7307[/C][C]0.233285[/C][/ROW]
[ROW][C]19[/C][C]0.056861[/C][C]0.5909[/C][C]0.277904[/C][/ROW]
[ROW][C]20[/C][C]-0.01906[/C][C]-0.1981[/C][C]0.421677[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299053&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299053&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	-0.112166	-1.1657	0.12316
2	-0.159254	-1.655	0.050413
3	-0.055316	-0.5749	0.283291
4	-0.000873	-0.0091	0.496391
5	0.026387	0.2742	0.392221
6	-0.055486	-0.5766	0.282695
7	-0.074377	-0.773	0.22062
8	-0.130104	-1.3521	0.089588
9	-0.03226	-0.3353	0.36904
10	0.040533	0.4212	0.337212
11	0.19364	2.0124	0.023335
12	-0.406083	-4.2201	2.6e-05
13	-0.00592	-0.0615	0.47553
14	-0.089972	-0.935	0.175933
15	-0.006545	-0.068	0.472949
16	-0.126854	-1.3183	0.095095
17	-0.099477	-1.0338	0.151769
18	-0.070308	-0.7307	0.233285
19	0.056861	0.5909	0.277904
20	-0.01906	-0.1981	0.421677

Figure 1

PNG link

Postscript link

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Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 8 ; par2 = 0 ;

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '2'
par3 <- '0'
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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code