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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 13 Dec 2016 16:21:54 +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/t1481642679v8ze4yygayvb1hv.htm/, Retrieved Fri, 17 May 2024 15:40:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299151, Retrieved Fri, 17 May 2024 15:40:55 +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 15:21:54] [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=299151&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=299151&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299151&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	0.298877	2.9284	0.002128
2	0.097582	0.9561	0.17071
3	-0.07028	-0.6886	0.246367
4	-0.112043	-1.0978	0.137521
5	-0.157806	-1.5462	0.062676
6	-0.121894	-1.1943	0.117649
7	-0.098858	-0.9686	0.167588
8	0.115201	1.1287	0.130911
9	-0.036456	-0.3572	0.360867
10	-0.053489	-0.5241	0.300715
11	-0.184994	-1.8126	0.036513
12	-0.448646	-4.3958	1.4e-05
13	-0.038171	-0.374	0.354614
14	0.003757	0.0368	0.485356
15	0.112636	1.1036	0.136261
16	0.158008	1.5482	0.062438
17	0.20768	2.0348	0.022312
18	0.173852	1.7034	0.045864
19	0.059871	0.5866	0.27942
20	-0.209767	-2.0553	0.021284

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.298877 & 2.9284 & 0.002128 \tabularnewline
2 & 0.097582 & 0.9561 & 0.17071 \tabularnewline
3 & -0.07028 & -0.6886 & 0.246367 \tabularnewline
4 & -0.112043 & -1.0978 & 0.137521 \tabularnewline
5 & -0.157806 & -1.5462 & 0.062676 \tabularnewline
6 & -0.121894 & -1.1943 & 0.117649 \tabularnewline
7 & -0.098858 & -0.9686 & 0.167588 \tabularnewline
8 & 0.115201 & 1.1287 & 0.130911 \tabularnewline
9 & -0.036456 & -0.3572 & 0.360867 \tabularnewline
10 & -0.053489 & -0.5241 & 0.300715 \tabularnewline
11 & -0.184994 & -1.8126 & 0.036513 \tabularnewline
12 & -0.448646 & -4.3958 & 1.4e-05 \tabularnewline
13 & -0.038171 & -0.374 & 0.354614 \tabularnewline
14 & 0.003757 & 0.0368 & 0.485356 \tabularnewline
15 & 0.112636 & 1.1036 & 0.136261 \tabularnewline
16 & 0.158008 & 1.5482 & 0.062438 \tabularnewline
17 & 0.20768 & 2.0348 & 0.022312 \tabularnewline
18 & 0.173852 & 1.7034 & 0.045864 \tabularnewline
19 & 0.059871 & 0.5866 & 0.27942 \tabularnewline
20 & -0.209767 & -2.0553 & 0.021284 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299151&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]0.298877[/C][C]2.9284[/C][C]0.002128[/C][/ROW]
[ROW][C]2[/C][C]0.097582[/C][C]0.9561[/C][C]0.17071[/C][/ROW]
[ROW][C]3[/C][C]-0.07028[/C][C]-0.6886[/C][C]0.246367[/C][/ROW]
[ROW][C]4[/C][C]-0.112043[/C][C]-1.0978[/C][C]0.137521[/C][/ROW]
[ROW][C]5[/C][C]-0.157806[/C][C]-1.5462[/C][C]0.062676[/C][/ROW]
[ROW][C]6[/C][C]-0.121894[/C][C]-1.1943[/C][C]0.117649[/C][/ROW]
[ROW][C]7[/C][C]-0.098858[/C][C]-0.9686[/C][C]0.167588[/C][/ROW]
[ROW][C]8[/C][C]0.115201[/C][C]1.1287[/C][C]0.130911[/C][/ROW]
[ROW][C]9[/C][C]-0.036456[/C][C]-0.3572[/C][C]0.360867[/C][/ROW]
[ROW][C]10[/C][C]-0.053489[/C][C]-0.5241[/C][C]0.300715[/C][/ROW]
[ROW][C]11[/C][C]-0.184994[/C][C]-1.8126[/C][C]0.036513[/C][/ROW]
[ROW][C]12[/C][C]-0.448646[/C][C]-4.3958[/C][C]1.4e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.038171[/C][C]-0.374[/C][C]0.354614[/C][/ROW]
[ROW][C]14[/C][C]0.003757[/C][C]0.0368[/C][C]0.485356[/C][/ROW]
[ROW][C]15[/C][C]0.112636[/C][C]1.1036[/C][C]0.136261[/C][/ROW]
[ROW][C]16[/C][C]0.158008[/C][C]1.5482[/C][C]0.062438[/C][/ROW]
[ROW][C]17[/C][C]0.20768[/C][C]2.0348[/C][C]0.022312[/C][/ROW]
[ROW][C]18[/C][C]0.173852[/C][C]1.7034[/C][C]0.045864[/C][/ROW]
[ROW][C]19[/C][C]0.059871[/C][C]0.5866[/C][C]0.27942[/C][/ROW]
[ROW][C]20[/C][C]-0.209767[/C][C]-2.0553[/C][C]0.021284[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299151&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299151&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	0.298877	2.9284	0.002128
2	0.097582	0.9561	0.17071
3	-0.07028	-0.6886	0.246367
4	-0.112043	-1.0978	0.137521
5	-0.157806	-1.5462	0.062676
6	-0.121894	-1.1943	0.117649
7	-0.098858	-0.9686	0.167588
8	0.115201	1.1287	0.130911
9	-0.036456	-0.3572	0.360867
10	-0.053489	-0.5241	0.300715
11	-0.184994	-1.8126	0.036513
12	-0.448646	-4.3958	1.4e-05
13	-0.038171	-0.374	0.354614
14	0.003757	0.0368	0.485356
15	0.112636	1.1036	0.136261
16	0.158008	1.5482	0.062438
17	0.20768	2.0348	0.022312
18	0.173852	1.7034	0.045864
19	0.059871	0.5866	0.27942
20	-0.209767	-2.0553	0.021284

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.298877	2.9284	0.002128
2	0.009064	0.0888	0.464708
3	-0.111893	-1.0963	0.137839
4	-0.068764	-0.6737	0.251045
5	-0.103609	-1.0152	0.156292
6	-0.050482	-0.4946	0.311001
7	-0.055226	-0.5411	0.294845
8	0.159247	1.5603	0.06099
9	-0.151262	-1.4821	0.0708
10	-0.068937	-0.6754	0.250508
11	-0.173364	-1.6986	0.046315
12	-0.443101	-4.3415	1.8e-05
13	0.280956	2.7528	0.003533
14	-0.069623	-0.6822	0.248389
15	0.044541	0.4364	0.331759
16	0.025725	0.2521	0.400768
17	0.029868	0.2926	0.385211
18	0.057459	0.563	0.287379
19	-0.080587	-0.7896	0.215858
20	-0.072191	-0.7073	0.24054

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.298877 & 2.9284 & 0.002128 \tabularnewline
2 & 0.009064 & 0.0888 & 0.464708 \tabularnewline
3 & -0.111893 & -1.0963 & 0.137839 \tabularnewline
4 & -0.068764 & -0.6737 & 0.251045 \tabularnewline
5 & -0.103609 & -1.0152 & 0.156292 \tabularnewline
6 & -0.050482 & -0.4946 & 0.311001 \tabularnewline
7 & -0.055226 & -0.5411 & 0.294845 \tabularnewline
8 & 0.159247 & 1.5603 & 0.06099 \tabularnewline
9 & -0.151262 & -1.4821 & 0.0708 \tabularnewline
10 & -0.068937 & -0.6754 & 0.250508 \tabularnewline
11 & -0.173364 & -1.6986 & 0.046315 \tabularnewline
12 & -0.443101 & -4.3415 & 1.8e-05 \tabularnewline
13 & 0.280956 & 2.7528 & 0.003533 \tabularnewline
14 & -0.069623 & -0.6822 & 0.248389 \tabularnewline
15 & 0.044541 & 0.4364 & 0.331759 \tabularnewline
16 & 0.025725 & 0.2521 & 0.400768 \tabularnewline
17 & 0.029868 & 0.2926 & 0.385211 \tabularnewline
18 & 0.057459 & 0.563 & 0.287379 \tabularnewline
19 & -0.080587 & -0.7896 & 0.215858 \tabularnewline
20 & -0.072191 & -0.7073 & 0.24054 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299151&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]0.298877[/C][C]2.9284[/C][C]0.002128[/C][/ROW]
[ROW][C]2[/C][C]0.009064[/C][C]0.0888[/C][C]0.464708[/C][/ROW]
[ROW][C]3[/C][C]-0.111893[/C][C]-1.0963[/C][C]0.137839[/C][/ROW]
[ROW][C]4[/C][C]-0.068764[/C][C]-0.6737[/C][C]0.251045[/C][/ROW]
[ROW][C]5[/C][C]-0.103609[/C][C]-1.0152[/C][C]0.156292[/C][/ROW]
[ROW][C]6[/C][C]-0.050482[/C][C]-0.4946[/C][C]0.311001[/C][/ROW]
[ROW][C]7[/C][C]-0.055226[/C][C]-0.5411[/C][C]0.294845[/C][/ROW]
[ROW][C]8[/C][C]0.159247[/C][C]1.5603[/C][C]0.06099[/C][/ROW]
[ROW][C]9[/C][C]-0.151262[/C][C]-1.4821[/C][C]0.0708[/C][/ROW]
[ROW][C]10[/C][C]-0.068937[/C][C]-0.6754[/C][C]0.250508[/C][/ROW]
[ROW][C]11[/C][C]-0.173364[/C][C]-1.6986[/C][C]0.046315[/C][/ROW]
[ROW][C]12[/C][C]-0.443101[/C][C]-4.3415[/C][C]1.8e-05[/C][/ROW]
[ROW][C]13[/C][C]0.280956[/C][C]2.7528[/C][C]0.003533[/C][/ROW]
[ROW][C]14[/C][C]-0.069623[/C][C]-0.6822[/C][C]0.248389[/C][/ROW]
[ROW][C]15[/C][C]0.044541[/C][C]0.4364[/C][C]0.331759[/C][/ROW]
[ROW][C]16[/C][C]0.025725[/C][C]0.2521[/C][C]0.400768[/C][/ROW]
[ROW][C]17[/C][C]0.029868[/C][C]0.2926[/C][C]0.385211[/C][/ROW]
[ROW][C]18[/C][C]0.057459[/C][C]0.563[/C][C]0.287379[/C][/ROW]
[ROW][C]19[/C][C]-0.080587[/C][C]-0.7896[/C][C]0.215858[/C][/ROW]
[ROW][C]20[/C][C]-0.072191[/C][C]-0.7073[/C][C]0.24054[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299151&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299151&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	0.298877	2.9284	0.002128
2	0.009064	0.0888	0.464708
3	-0.111893	-1.0963	0.137839
4	-0.068764	-0.6737	0.251045
5	-0.103609	-1.0152	0.156292
6	-0.050482	-0.4946	0.311001
7	-0.055226	-0.5411	0.294845
8	0.159247	1.5603	0.06099
9	-0.151262	-1.4821	0.0708
10	-0.068937	-0.6754	0.250508
11	-0.173364	-1.6986	0.046315
12	-0.443101	-4.3415	1.8e-05
13	0.280956	2.7528	0.003533
14	-0.069623	-0.6822	0.248389
15	0.044541	0.4364	0.331759
16	0.025725	0.2521	0.400768
17	0.029868	0.2926	0.385211
18	0.057459	0.563	0.287379
19	-0.080587	-0.7896	0.215858
20	-0.072191	-0.7073	0.24054

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 8 ; par2 = 0 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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 <- '0'
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