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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 15 Dec 2016 10:24:34 +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/t1481797681dp3k3bis5r0a9cm.htm/, Retrieved Fri, 03 May 2024 09:04:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299827, Retrieved Fri, 03 May 2024 09:04:49 +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] [N1993 Autocorrela...] [2016-12-15 09:24:34] [1eb03b74c4069f30e782d39ada1a3213] [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=299827&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=299827&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299827&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	-0.102174	-1.0861	0.139867
2	-0.150246	-1.5971	0.056514
3	0.066122	0.7029	0.241787
4	-0.090714	-0.9643	0.168475
5	0.070702	0.7516	0.226934
6	0.101988	1.0841	0.140305
7	0.045378	0.4824	0.315235
8	0.055128	0.586	0.279517
9	-0.045486	-0.4835	0.314831
10	0.015736	0.1673	0.433725
11	0.14774	1.5705	0.059548
12	-0.433983	-4.6133	5e-06
13	0.051408	0.5465	0.292908
14	0.149635	1.5906	0.057242
15	-0.105212	-1.1184	0.132881
16	0.053451	0.5682	0.285515
17	0.006289	0.0669	0.473407
18	-0.127611	-1.3565	0.088818
19	-0.124852	-1.3272	0.09356
20	0.030596	0.3252	0.372802
21	0.084622	0.8995	0.185139

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.102174 & -1.0861 & 0.139867 \tabularnewline
2 & -0.150246 & -1.5971 & 0.056514 \tabularnewline
3 & 0.066122 & 0.7029 & 0.241787 \tabularnewline
4 & -0.090714 & -0.9643 & 0.168475 \tabularnewline
5 & 0.070702 & 0.7516 & 0.226934 \tabularnewline
6 & 0.101988 & 1.0841 & 0.140305 \tabularnewline
7 & 0.045378 & 0.4824 & 0.315235 \tabularnewline
8 & 0.055128 & 0.586 & 0.279517 \tabularnewline
9 & -0.045486 & -0.4835 & 0.314831 \tabularnewline
10 & 0.015736 & 0.1673 & 0.433725 \tabularnewline
11 & 0.14774 & 1.5705 & 0.059548 \tabularnewline
12 & -0.433983 & -4.6133 & 5e-06 \tabularnewline
13 & 0.051408 & 0.5465 & 0.292908 \tabularnewline
14 & 0.149635 & 1.5906 & 0.057242 \tabularnewline
15 & -0.105212 & -1.1184 & 0.132881 \tabularnewline
16 & 0.053451 & 0.5682 & 0.285515 \tabularnewline
17 & 0.006289 & 0.0669 & 0.473407 \tabularnewline
18 & -0.127611 & -1.3565 & 0.088818 \tabularnewline
19 & -0.124852 & -1.3272 & 0.09356 \tabularnewline
20 & 0.030596 & 0.3252 & 0.372802 \tabularnewline
21 & 0.084622 & 0.8995 & 0.185139 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299827&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]-0.102174[/C][C]-1.0861[/C][C]0.139867[/C][/ROW]
[ROW][C]2[/C][C]-0.150246[/C][C]-1.5971[/C][C]0.056514[/C][/ROW]
[ROW][C]3[/C][C]0.066122[/C][C]0.7029[/C][C]0.241787[/C][/ROW]
[ROW][C]4[/C][C]-0.090714[/C][C]-0.9643[/C][C]0.168475[/C][/ROW]
[ROW][C]5[/C][C]0.070702[/C][C]0.7516[/C][C]0.226934[/C][/ROW]
[ROW][C]6[/C][C]0.101988[/C][C]1.0841[/C][C]0.140305[/C][/ROW]
[ROW][C]7[/C][C]0.045378[/C][C]0.4824[/C][C]0.315235[/C][/ROW]
[ROW][C]8[/C][C]0.055128[/C][C]0.586[/C][C]0.279517[/C][/ROW]
[ROW][C]9[/C][C]-0.045486[/C][C]-0.4835[/C][C]0.314831[/C][/ROW]
[ROW][C]10[/C][C]0.015736[/C][C]0.1673[/C][C]0.433725[/C][/ROW]
[ROW][C]11[/C][C]0.14774[/C][C]1.5705[/C][C]0.059548[/C][/ROW]
[ROW][C]12[/C][C]-0.433983[/C][C]-4.6133[/C][C]5e-06[/C][/ROW]
[ROW][C]13[/C][C]0.051408[/C][C]0.5465[/C][C]0.292908[/C][/ROW]
[ROW][C]14[/C][C]0.149635[/C][C]1.5906[/C][C]0.057242[/C][/ROW]
[ROW][C]15[/C][C]-0.105212[/C][C]-1.1184[/C][C]0.132881[/C][/ROW]
[ROW][C]16[/C][C]0.053451[/C][C]0.5682[/C][C]0.285515[/C][/ROW]
[ROW][C]17[/C][C]0.006289[/C][C]0.0669[/C][C]0.473407[/C][/ROW]
[ROW][C]18[/C][C]-0.127611[/C][C]-1.3565[/C][C]0.088818[/C][/ROW]
[ROW][C]19[/C][C]-0.124852[/C][C]-1.3272[/C][C]0.09356[/C][/ROW]
[ROW][C]20[/C][C]0.030596[/C][C]0.3252[/C][C]0.372802[/C][/ROW]
[ROW][C]21[/C][C]0.084622[/C][C]0.8995[/C][C]0.185139[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299827&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299827&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	-0.102174	-1.0861	0.139867
2	-0.150246	-1.5971	0.056514
3	0.066122	0.7029	0.241787
4	-0.090714	-0.9643	0.168475
5	0.070702	0.7516	0.226934
6	0.101988	1.0841	0.140305
7	0.045378	0.4824	0.315235
8	0.055128	0.586	0.279517
9	-0.045486	-0.4835	0.314831
10	0.015736	0.1673	0.433725
11	0.14774	1.5705	0.059548
12	-0.433983	-4.6133	5e-06
13	0.051408	0.5465	0.292908
14	0.149635	1.5906	0.057242
15	-0.105212	-1.1184	0.132881
16	0.053451	0.5682	0.285515
17	0.006289	0.0669	0.473407
18	-0.127611	-1.3565	0.088818
19	-0.124852	-1.3272	0.09356
20	0.030596	0.3252	0.372802
21	0.084622	0.8995	0.185139

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.102174	-1.0861	0.139867
2	-0.162381	-1.7261	0.043529
3	0.032888	0.3496	0.363643
4	-0.107712	-1.145	0.127316
5	0.067744	0.7201	0.236467
6	0.087542	0.9306	0.177026
7	0.103347	1.0986	0.137141
8	0.093489	0.9938	0.161221
9	-0.000147	-0.0016	0.499377
10	0.040655	0.4322	0.333219
11	0.146578	1.5581	0.060998
12	-0.441629	-4.6946	4e-06
13	-0.024181	-0.257	0.398806
14	-0.019616	-0.2085	0.417599
15	-0.058326	-0.62	0.268247
16	-0.03196	-0.3397	0.367341
17	0.049537	0.5266	0.299757
18	-0.034493	-0.3667	0.357276
19	-0.119386	-1.2691	0.103508
20	0.04042	0.4297	0.334128
21	0.074724	0.7943	0.214334

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.102174 & -1.0861 & 0.139867 \tabularnewline
2 & -0.162381 & -1.7261 & 0.043529 \tabularnewline
3 & 0.032888 & 0.3496 & 0.363643 \tabularnewline
4 & -0.107712 & -1.145 & 0.127316 \tabularnewline
5 & 0.067744 & 0.7201 & 0.236467 \tabularnewline
6 & 0.087542 & 0.9306 & 0.177026 \tabularnewline
7 & 0.103347 & 1.0986 & 0.137141 \tabularnewline
8 & 0.093489 & 0.9938 & 0.161221 \tabularnewline
9 & -0.000147 & -0.0016 & 0.499377 \tabularnewline
10 & 0.040655 & 0.4322 & 0.333219 \tabularnewline
11 & 0.146578 & 1.5581 & 0.060998 \tabularnewline
12 & -0.441629 & -4.6946 & 4e-06 \tabularnewline
13 & -0.024181 & -0.257 & 0.398806 \tabularnewline
14 & -0.019616 & -0.2085 & 0.417599 \tabularnewline
15 & -0.058326 & -0.62 & 0.268247 \tabularnewline
16 & -0.03196 & -0.3397 & 0.367341 \tabularnewline
17 & 0.049537 & 0.5266 & 0.299757 \tabularnewline
18 & -0.034493 & -0.3667 & 0.357276 \tabularnewline
19 & -0.119386 & -1.2691 & 0.103508 \tabularnewline
20 & 0.04042 & 0.4297 & 0.334128 \tabularnewline
21 & 0.074724 & 0.7943 & 0.214334 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299827&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]-0.102174[/C][C]-1.0861[/C][C]0.139867[/C][/ROW]
[ROW][C]2[/C][C]-0.162381[/C][C]-1.7261[/C][C]0.043529[/C][/ROW]
[ROW][C]3[/C][C]0.032888[/C][C]0.3496[/C][C]0.363643[/C][/ROW]
[ROW][C]4[/C][C]-0.107712[/C][C]-1.145[/C][C]0.127316[/C][/ROW]
[ROW][C]5[/C][C]0.067744[/C][C]0.7201[/C][C]0.236467[/C][/ROW]
[ROW][C]6[/C][C]0.087542[/C][C]0.9306[/C][C]0.177026[/C][/ROW]
[ROW][C]7[/C][C]0.103347[/C][C]1.0986[/C][C]0.137141[/C][/ROW]
[ROW][C]8[/C][C]0.093489[/C][C]0.9938[/C][C]0.161221[/C][/ROW]
[ROW][C]9[/C][C]-0.000147[/C][C]-0.0016[/C][C]0.499377[/C][/ROW]
[ROW][C]10[/C][C]0.040655[/C][C]0.4322[/C][C]0.333219[/C][/ROW]
[ROW][C]11[/C][C]0.146578[/C][C]1.5581[/C][C]0.060998[/C][/ROW]
[ROW][C]12[/C][C]-0.441629[/C][C]-4.6946[/C][C]4e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.024181[/C][C]-0.257[/C][C]0.398806[/C][/ROW]
[ROW][C]14[/C][C]-0.019616[/C][C]-0.2085[/C][C]0.417599[/C][/ROW]
[ROW][C]15[/C][C]-0.058326[/C][C]-0.62[/C][C]0.268247[/C][/ROW]
[ROW][C]16[/C][C]-0.03196[/C][C]-0.3397[/C][C]0.367341[/C][/ROW]
[ROW][C]17[/C][C]0.049537[/C][C]0.5266[/C][C]0.299757[/C][/ROW]
[ROW][C]18[/C][C]-0.034493[/C][C]-0.3667[/C][C]0.357276[/C][/ROW]
[ROW][C]19[/C][C]-0.119386[/C][C]-1.2691[/C][C]0.103508[/C][/ROW]
[ROW][C]20[/C][C]0.04042[/C][C]0.4297[/C][C]0.334128[/C][/ROW]
[ROW][C]21[/C][C]0.074724[/C][C]0.7943[/C][C]0.214334[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299827&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299827&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	-0.102174	-1.0861	0.139867
2	-0.162381	-1.7261	0.043529
3	0.032888	0.3496	0.363643
4	-0.107712	-1.145	0.127316
5	0.067744	0.7201	0.236467
6	0.087542	0.9306	0.177026
7	0.103347	1.0986	0.137141
8	0.093489	0.9938	0.161221
9	-0.000147	-0.0016	0.499377
10	0.040655	0.4322	0.333219
11	0.146578	1.5581	0.060998
12	-0.441629	-4.6946	4e-06
13	-0.024181	-0.257	0.398806
14	-0.019616	-0.2085	0.417599
15	-0.058326	-0.62	0.268247
16	-0.03196	-0.3397	0.367341
17	0.049537	0.5266	0.299757
18	-0.034493	-0.3667	0.357276
19	-0.119386	-1.2691	0.103508
20	0.04042	0.4297	0.334128
21	0.074724	0.7943	0.214334

Figure 1

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Figure 2

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Figure 3

PNG link

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Parameters (Session):

par1 = Default ; par2 = 1.8 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1.8 ; 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