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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 13 Dec 2016 11:26:16 +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/t1481624878x8ol3sedk1r52d2.htm/, Retrieved Sat, 04 May 2024 20:30:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299031, Retrieved Sat, 04 May 2024 20:30:25 +0000

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Estimated Impact

108

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [Autocorrelatie N2013] [2016-12-13 10:26:16] [7b02c9ca65294818d9c418453f92ae83] [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=299031&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=299031&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299031&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	0.225199	2.5278	0.006356
2	0.304963	3.4232	0.000418
3	0.260949	2.9291	0.002018
4	0.2144	2.4066	0.008776
5	0.18789	2.1091	0.018459
6	0.290866	3.265	0.000705
7	0.170791	1.9171	0.028743
8	0.121655	1.3656	0.087253
9	0.195484	2.1943	0.015024
10	0.188974	2.1212	0.017931
11	0.136586	1.5332	0.06387
12	0.081029	0.9095	0.1824
13	0.196136	2.2016	0.014757
14	0.178154	1.9998	0.023838
15	0.127925	1.436	0.076746
16	0.0586	0.6578	0.255938
17	0.171314	1.923	0.028368
18	-0.00468	-0.0525	0.479093
19	0.088426	0.9926	0.161409
20	0.125595	1.4098	0.080532
21	0.028611	0.3212	0.374309

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.225199 & 2.5278 & 0.006356 \tabularnewline
2 & 0.304963 & 3.4232 & 0.000418 \tabularnewline
3 & 0.260949 & 2.9291 & 0.002018 \tabularnewline
4 & 0.2144 & 2.4066 & 0.008776 \tabularnewline
5 & 0.18789 & 2.1091 & 0.018459 \tabularnewline
6 & 0.290866 & 3.265 & 0.000705 \tabularnewline
7 & 0.170791 & 1.9171 & 0.028743 \tabularnewline
8 & 0.121655 & 1.3656 & 0.087253 \tabularnewline
9 & 0.195484 & 2.1943 & 0.015024 \tabularnewline
10 & 0.188974 & 2.1212 & 0.017931 \tabularnewline
11 & 0.136586 & 1.5332 & 0.06387 \tabularnewline
12 & 0.081029 & 0.9095 & 0.1824 \tabularnewline
13 & 0.196136 & 2.2016 & 0.014757 \tabularnewline
14 & 0.178154 & 1.9998 & 0.023838 \tabularnewline
15 & 0.127925 & 1.436 & 0.076746 \tabularnewline
16 & 0.0586 & 0.6578 & 0.255938 \tabularnewline
17 & 0.171314 & 1.923 & 0.028368 \tabularnewline
18 & -0.00468 & -0.0525 & 0.479093 \tabularnewline
19 & 0.088426 & 0.9926 & 0.161409 \tabularnewline
20 & 0.125595 & 1.4098 & 0.080532 \tabularnewline
21 & 0.028611 & 0.3212 & 0.374309 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299031&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]0.225199[/C][C]2.5278[/C][C]0.006356[/C][/ROW]
[ROW][C]2[/C][C]0.304963[/C][C]3.4232[/C][C]0.000418[/C][/ROW]
[ROW][C]3[/C][C]0.260949[/C][C]2.9291[/C][C]0.002018[/C][/ROW]
[ROW][C]4[/C][C]0.2144[/C][C]2.4066[/C][C]0.008776[/C][/ROW]
[ROW][C]5[/C][C]0.18789[/C][C]2.1091[/C][C]0.018459[/C][/ROW]
[ROW][C]6[/C][C]0.290866[/C][C]3.265[/C][C]0.000705[/C][/ROW]
[ROW][C]7[/C][C]0.170791[/C][C]1.9171[/C][C]0.028743[/C][/ROW]
[ROW][C]8[/C][C]0.121655[/C][C]1.3656[/C][C]0.087253[/C][/ROW]
[ROW][C]9[/C][C]0.195484[/C][C]2.1943[/C][C]0.015024[/C][/ROW]
[ROW][C]10[/C][C]0.188974[/C][C]2.1212[/C][C]0.017931[/C][/ROW]
[ROW][C]11[/C][C]0.136586[/C][C]1.5332[/C][C]0.06387[/C][/ROW]
[ROW][C]12[/C][C]0.081029[/C][C]0.9095[/C][C]0.1824[/C][/ROW]
[ROW][C]13[/C][C]0.196136[/C][C]2.2016[/C][C]0.014757[/C][/ROW]
[ROW][C]14[/C][C]0.178154[/C][C]1.9998[/C][C]0.023838[/C][/ROW]
[ROW][C]15[/C][C]0.127925[/C][C]1.436[/C][C]0.076746[/C][/ROW]
[ROW][C]16[/C][C]0.0586[/C][C]0.6578[/C][C]0.255938[/C][/ROW]
[ROW][C]17[/C][C]0.171314[/C][C]1.923[/C][C]0.028368[/C][/ROW]
[ROW][C]18[/C][C]-0.00468[/C][C]-0.0525[/C][C]0.479093[/C][/ROW]
[ROW][C]19[/C][C]0.088426[/C][C]0.9926[/C][C]0.161409[/C][/ROW]
[ROW][C]20[/C][C]0.125595[/C][C]1.4098[/C][C]0.080532[/C][/ROW]
[ROW][C]21[/C][C]0.028611[/C][C]0.3212[/C][C]0.374309[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299031&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299031&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	0.225199	2.5278	0.006356
2	0.304963	3.4232	0.000418
3	0.260949	2.9291	0.002018
4	0.2144	2.4066	0.008776
5	0.18789	2.1091	0.018459
6	0.290866	3.265	0.000705
7	0.170791	1.9171	0.028743
8	0.121655	1.3656	0.087253
9	0.195484	2.1943	0.015024
10	0.188974	2.1212	0.017931
11	0.136586	1.5332	0.06387
12	0.081029	0.9095	0.1824
13	0.196136	2.2016	0.014757
14	0.178154	1.9998	0.023838
15	0.127925	1.436	0.076746
16	0.0586	0.6578	0.255938
17	0.171314	1.923	0.028368
18	-0.00468	-0.0525	0.479093
19	0.088426	0.9926	0.161409
20	0.125595	1.4098	0.080532
21	0.028611	0.3212	0.374309

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.225199	2.5278	0.006356
2	0.267831	3.0064	0.001596
3	0.170623	1.9152	0.028865
4	0.083895	0.9417	0.174068
5	0.047353	0.5315	0.297993
6	0.179945	2.0199	0.022758
7	0.024725	0.2775	0.390913
8	-0.058339	-0.6549	0.256877
9	0.065693	0.7374	0.231125
10	0.088621	0.9948	0.160877
11	0.004168	0.0468	0.481379
12	-0.095317	-1.0699	0.143348
13	0.107328	1.2048	0.115279
14	0.126127	1.4158	0.079654
15	-0.024077	-0.2703	0.393701
16	-0.138132	-1.5505	0.061761
17	0.106165	1.1917	0.117809
18	-0.063788	-0.716	0.237652
19	-0.053559	-0.6012	0.274395
20	0.037352	0.4193	0.337865
21	0.000534	0.006	0.497612

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.225199 & 2.5278 & 0.006356 \tabularnewline
2 & 0.267831 & 3.0064 & 0.001596 \tabularnewline
3 & 0.170623 & 1.9152 & 0.028865 \tabularnewline
4 & 0.083895 & 0.9417 & 0.174068 \tabularnewline
5 & 0.047353 & 0.5315 & 0.297993 \tabularnewline
6 & 0.179945 & 2.0199 & 0.022758 \tabularnewline
7 & 0.024725 & 0.2775 & 0.390913 \tabularnewline
8 & -0.058339 & -0.6549 & 0.256877 \tabularnewline
9 & 0.065693 & 0.7374 & 0.231125 \tabularnewline
10 & 0.088621 & 0.9948 & 0.160877 \tabularnewline
11 & 0.004168 & 0.0468 & 0.481379 \tabularnewline
12 & -0.095317 & -1.0699 & 0.143348 \tabularnewline
13 & 0.107328 & 1.2048 & 0.115279 \tabularnewline
14 & 0.126127 & 1.4158 & 0.079654 \tabularnewline
15 & -0.024077 & -0.2703 & 0.393701 \tabularnewline
16 & -0.138132 & -1.5505 & 0.061761 \tabularnewline
17 & 0.106165 & 1.1917 & 0.117809 \tabularnewline
18 & -0.063788 & -0.716 & 0.237652 \tabularnewline
19 & -0.053559 & -0.6012 & 0.274395 \tabularnewline
20 & 0.037352 & 0.4193 & 0.337865 \tabularnewline
21 & 0.000534 & 0.006 & 0.497612 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299031&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]0.225199[/C][C]2.5278[/C][C]0.006356[/C][/ROW]
[ROW][C]2[/C][C]0.267831[/C][C]3.0064[/C][C]0.001596[/C][/ROW]
[ROW][C]3[/C][C]0.170623[/C][C]1.9152[/C][C]0.028865[/C][/ROW]
[ROW][C]4[/C][C]0.083895[/C][C]0.9417[/C][C]0.174068[/C][/ROW]
[ROW][C]5[/C][C]0.047353[/C][C]0.5315[/C][C]0.297993[/C][/ROW]
[ROW][C]6[/C][C]0.179945[/C][C]2.0199[/C][C]0.022758[/C][/ROW]
[ROW][C]7[/C][C]0.024725[/C][C]0.2775[/C][C]0.390913[/C][/ROW]
[ROW][C]8[/C][C]-0.058339[/C][C]-0.6549[/C][C]0.256877[/C][/ROW]
[ROW][C]9[/C][C]0.065693[/C][C]0.7374[/C][C]0.231125[/C][/ROW]
[ROW][C]10[/C][C]0.088621[/C][C]0.9948[/C][C]0.160877[/C][/ROW]
[ROW][C]11[/C][C]0.004168[/C][C]0.0468[/C][C]0.481379[/C][/ROW]
[ROW][C]12[/C][C]-0.095317[/C][C]-1.0699[/C][C]0.143348[/C][/ROW]
[ROW][C]13[/C][C]0.107328[/C][C]1.2048[/C][C]0.115279[/C][/ROW]
[ROW][C]14[/C][C]0.126127[/C][C]1.4158[/C][C]0.079654[/C][/ROW]
[ROW][C]15[/C][C]-0.024077[/C][C]-0.2703[/C][C]0.393701[/C][/ROW]
[ROW][C]16[/C][C]-0.138132[/C][C]-1.5505[/C][C]0.061761[/C][/ROW]
[ROW][C]17[/C][C]0.106165[/C][C]1.1917[/C][C]0.117809[/C][/ROW]
[ROW][C]18[/C][C]-0.063788[/C][C]-0.716[/C][C]0.237652[/C][/ROW]
[ROW][C]19[/C][C]-0.053559[/C][C]-0.6012[/C][C]0.274395[/C][/ROW]
[ROW][C]20[/C][C]0.037352[/C][C]0.4193[/C][C]0.337865[/C][/ROW]
[ROW][C]21[/C][C]0.000534[/C][C]0.006[/C][C]0.497612[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299031&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299031&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	0.225199	2.5278	0.006356
2	0.267831	3.0064	0.001596
3	0.170623	1.9152	0.028865
4	0.083895	0.9417	0.174068
5	0.047353	0.5315	0.297993
6	0.179945	2.0199	0.022758
7	0.024725	0.2775	0.390913
8	-0.058339	-0.6549	0.256877
9	0.065693	0.7374	0.231125
10	0.088621	0.9948	0.160877
11	0.004168	0.0468	0.481379
12	-0.095317	-1.0699	0.143348
13	0.107328	1.2048	0.115279
14	0.126127	1.4158	0.079654
15	-0.024077	-0.2703	0.393701
16	-0.138132	-1.5505	0.061761
17	0.106165	1.1917	0.117809
18	-0.063788	-0.716	0.237652
19	-0.053559	-0.6012	0.274395
20	0.037352	0.4193	0.337865
21	0.000534	0.006	0.497612

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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