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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 20 Dec 2016 13:23:18 +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/20/t1482236641289oyzmtv4fzdhj.htm/, Retrieved Sat, 27 Apr 2024 13:57:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301628, Retrieved Sat, 27 Apr 2024 13:57:05 +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...] [2016-12-20 12:23:18] [86c9a777e8dbb7ef3face68c75fc8376] [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=301628&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=301628&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301628&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	-0.483597	-5.1179	1e-06
2	-0.219617	-2.3242	0.010959
3	0.324168	3.4307	0.000422
4	-0.142067	-1.5035	0.067763
5	0.018685	0.1977	0.421801
6	0.055485	0.5872	0.279128
7	-0.042544	-0.4502	0.326704
8	-0.14811	-1.5675	0.059915
9	0.346248	3.6643	0.00019
10	-0.197766	-2.093	0.019305
11	-0.271477	-2.873	0.002432
12	0.562814	5.9563	0
13	-0.33258	-3.5197	0.000313
14	-0.08879	-0.9397	0.174706
15	0.21835	2.3108	0.011337
16	-0.106073	-1.1226	0.13201
17	0.0374	0.3958	0.3465
18	-0.048978	-0.5183	0.302625
19	0.053264	0.5637	0.287046
20	-0.11587	-1.2263	0.111338

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.483597 & -5.1179 & 1e-06 \tabularnewline
2 & -0.219617 & -2.3242 & 0.010959 \tabularnewline
3 & 0.324168 & 3.4307 & 0.000422 \tabularnewline
4 & -0.142067 & -1.5035 & 0.067763 \tabularnewline
5 & 0.018685 & 0.1977 & 0.421801 \tabularnewline
6 & 0.055485 & 0.5872 & 0.279128 \tabularnewline
7 & -0.042544 & -0.4502 & 0.326704 \tabularnewline
8 & -0.14811 & -1.5675 & 0.059915 \tabularnewline
9 & 0.346248 & 3.6643 & 0.00019 \tabularnewline
10 & -0.197766 & -2.093 & 0.019305 \tabularnewline
11 & -0.271477 & -2.873 & 0.002432 \tabularnewline
12 & 0.562814 & 5.9563 & 0 \tabularnewline
13 & -0.33258 & -3.5197 & 0.000313 \tabularnewline
14 & -0.08879 & -0.9397 & 0.174706 \tabularnewline
15 & 0.21835 & 2.3108 & 0.011337 \tabularnewline
16 & -0.106073 & -1.1226 & 0.13201 \tabularnewline
17 & 0.0374 & 0.3958 & 0.3465 \tabularnewline
18 & -0.048978 & -0.5183 & 0.302625 \tabularnewline
19 & 0.053264 & 0.5637 & 0.287046 \tabularnewline
20 & -0.11587 & -1.2263 & 0.111338 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301628&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]-0.483597[/C][C]-5.1179[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.219617[/C][C]-2.3242[/C][C]0.010959[/C][/ROW]
[ROW][C]3[/C][C]0.324168[/C][C]3.4307[/C][C]0.000422[/C][/ROW]
[ROW][C]4[/C][C]-0.142067[/C][C]-1.5035[/C][C]0.067763[/C][/ROW]
[ROW][C]5[/C][C]0.018685[/C][C]0.1977[/C][C]0.421801[/C][/ROW]
[ROW][C]6[/C][C]0.055485[/C][C]0.5872[/C][C]0.279128[/C][/ROW]
[ROW][C]7[/C][C]-0.042544[/C][C]-0.4502[/C][C]0.326704[/C][/ROW]
[ROW][C]8[/C][C]-0.14811[/C][C]-1.5675[/C][C]0.059915[/C][/ROW]
[ROW][C]9[/C][C]0.346248[/C][C]3.6643[/C][C]0.00019[/C][/ROW]
[ROW][C]10[/C][C]-0.197766[/C][C]-2.093[/C][C]0.019305[/C][/ROW]
[ROW][C]11[/C][C]-0.271477[/C][C]-2.873[/C][C]0.002432[/C][/ROW]
[ROW][C]12[/C][C]0.562814[/C][C]5.9563[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.33258[/C][C]-3.5197[/C][C]0.000313[/C][/ROW]
[ROW][C]14[/C][C]-0.08879[/C][C]-0.9397[/C][C]0.174706[/C][/ROW]
[ROW][C]15[/C][C]0.21835[/C][C]2.3108[/C][C]0.011337[/C][/ROW]
[ROW][C]16[/C][C]-0.106073[/C][C]-1.1226[/C][C]0.13201[/C][/ROW]
[ROW][C]17[/C][C]0.0374[/C][C]0.3958[/C][C]0.3465[/C][/ROW]
[ROW][C]18[/C][C]-0.048978[/C][C]-0.5183[/C][C]0.302625[/C][/ROW]
[ROW][C]19[/C][C]0.053264[/C][C]0.5637[/C][C]0.287046[/C][/ROW]
[ROW][C]20[/C][C]-0.11587[/C][C]-1.2263[/C][C]0.111338[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301628&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301628&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	-0.483597	-5.1179	1e-06
2	-0.219617	-2.3242	0.010959
3	0.324168	3.4307	0.000422
4	-0.142067	-1.5035	0.067763
5	0.018685	0.1977	0.421801
6	0.055485	0.5872	0.279128
7	-0.042544	-0.4502	0.326704
8	-0.14811	-1.5675	0.059915
9	0.346248	3.6643	0.00019
10	-0.197766	-2.093	0.019305
11	-0.271477	-2.873	0.002432
12	0.562814	5.9563	0
13	-0.33258	-3.5197	0.000313
14	-0.08879	-0.9397	0.174706
15	0.21835	2.3108	0.011337
16	-0.106073	-1.1226	0.13201
17	0.0374	0.3958	0.3465
18	-0.048978	-0.5183	0.302625
19	0.053264	0.5637	0.287046
20	-0.11587	-1.2263	0.111338

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.483597	-5.1179	1e-06
2	-0.591911	-6.2642	0
3	-0.263506	-2.7887	0.00311
4	-0.310746	-3.2886	0.000673
5	-0.138866	-1.4696	0.072235
6	-0.059235	-0.6269	0.266006
7	0.067627	0.7157	0.237834
8	-0.265179	-2.8064	0.002955
9	0.187218	1.9813	0.025003
10	0.112841	1.1942	0.117463
11	-0.260878	-2.7609	0.003369
12	0.220209	2.3305	0.010786
13	0.057416	0.6076	0.272329
14	0.037482	0.3967	0.346181
15	-0.042979	-0.4549	0.325049
16	-0.007395	-0.0783	0.468879
17	0.109793	1.1619	0.123864
18	-0.144859	-1.533	0.064042
19	-0.004669	-0.0494	0.480338
20	-0.037332	-0.3951	0.346766

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.483597 & -5.1179 & 1e-06 \tabularnewline
2 & -0.591911 & -6.2642 & 0 \tabularnewline
3 & -0.263506 & -2.7887 & 0.00311 \tabularnewline
4 & -0.310746 & -3.2886 & 0.000673 \tabularnewline
5 & -0.138866 & -1.4696 & 0.072235 \tabularnewline
6 & -0.059235 & -0.6269 & 0.266006 \tabularnewline
7 & 0.067627 & 0.7157 & 0.237834 \tabularnewline
8 & -0.265179 & -2.8064 & 0.002955 \tabularnewline
9 & 0.187218 & 1.9813 & 0.025003 \tabularnewline
10 & 0.112841 & 1.1942 & 0.117463 \tabularnewline
11 & -0.260878 & -2.7609 & 0.003369 \tabularnewline
12 & 0.220209 & 2.3305 & 0.010786 \tabularnewline
13 & 0.057416 & 0.6076 & 0.272329 \tabularnewline
14 & 0.037482 & 0.3967 & 0.346181 \tabularnewline
15 & -0.042979 & -0.4549 & 0.325049 \tabularnewline
16 & -0.007395 & -0.0783 & 0.468879 \tabularnewline
17 & 0.109793 & 1.1619 & 0.123864 \tabularnewline
18 & -0.144859 & -1.533 & 0.064042 \tabularnewline
19 & -0.004669 & -0.0494 & 0.480338 \tabularnewline
20 & -0.037332 & -0.3951 & 0.346766 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301628&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]-0.483597[/C][C]-5.1179[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.591911[/C][C]-6.2642[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.263506[/C][C]-2.7887[/C][C]0.00311[/C][/ROW]
[ROW][C]4[/C][C]-0.310746[/C][C]-3.2886[/C][C]0.000673[/C][/ROW]
[ROW][C]5[/C][C]-0.138866[/C][C]-1.4696[/C][C]0.072235[/C][/ROW]
[ROW][C]6[/C][C]-0.059235[/C][C]-0.6269[/C][C]0.266006[/C][/ROW]
[ROW][C]7[/C][C]0.067627[/C][C]0.7157[/C][C]0.237834[/C][/ROW]
[ROW][C]8[/C][C]-0.265179[/C][C]-2.8064[/C][C]0.002955[/C][/ROW]
[ROW][C]9[/C][C]0.187218[/C][C]1.9813[/C][C]0.025003[/C][/ROW]
[ROW][C]10[/C][C]0.112841[/C][C]1.1942[/C][C]0.117463[/C][/ROW]
[ROW][C]11[/C][C]-0.260878[/C][C]-2.7609[/C][C]0.003369[/C][/ROW]
[ROW][C]12[/C][C]0.220209[/C][C]2.3305[/C][C]0.010786[/C][/ROW]
[ROW][C]13[/C][C]0.057416[/C][C]0.6076[/C][C]0.272329[/C][/ROW]
[ROW][C]14[/C][C]0.037482[/C][C]0.3967[/C][C]0.346181[/C][/ROW]
[ROW][C]15[/C][C]-0.042979[/C][C]-0.4549[/C][C]0.325049[/C][/ROW]
[ROW][C]16[/C][C]-0.007395[/C][C]-0.0783[/C][C]0.468879[/C][/ROW]
[ROW][C]17[/C][C]0.109793[/C][C]1.1619[/C][C]0.123864[/C][/ROW]
[ROW][C]18[/C][C]-0.144859[/C][C]-1.533[/C][C]0.064042[/C][/ROW]
[ROW][C]19[/C][C]-0.004669[/C][C]-0.0494[/C][C]0.480338[/C][/ROW]
[ROW][C]20[/C][C]-0.037332[/C][C]-0.3951[/C][C]0.346766[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301628&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301628&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	-0.483597	-5.1179	1e-06
2	-0.591911	-6.2642	0
3	-0.263506	-2.7887	0.00311
4	-0.310746	-3.2886	0.000673
5	-0.138866	-1.4696	0.072235
6	-0.059235	-0.6269	0.266006
7	0.067627	0.7157	0.237834
8	-0.265179	-2.8064	0.002955
9	0.187218	1.9813	0.025003
10	0.112841	1.1942	0.117463
11	-0.260878	-2.7609	0.003369
12	0.220209	2.3305	0.010786
13	0.057416	0.6076	0.272329
14	0.037482	0.3967	0.346181
15	-0.042979	-0.4549	0.325049
16	-0.007395	-0.0783	0.468879
17	0.109793	1.1619	0.123864
18	-0.144859	-1.533	0.064042
19	-0.004669	-0.0494	0.480338
20	-0.037332	-0.3951	0.346766

Figure 1

PNG link

Postscript link

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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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; 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