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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 04 Dec 2016 17:04:21 +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/04/t1480867579pjxykd9ys2txfrd.htm/, Retrieved Fri, 01 Nov 2024 03:39:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297679, Retrieved Fri, 01 Nov 2024 03:39:34 +0000

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Estimated Impact

140

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-       [(Partial) Autocorrelation Function] [] [2016-12-04 16:04:21] [6deb082de88ded72ec069288c69f9f98] [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=297679&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=297679&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297679&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	-0.457523	-4.7547	3e-06
2	-0.086388	-0.8978	0.185653
3	0.051944	0.5398	0.295216
4	0.024019	0.2496	0.401679
5	0.00495	0.0514	0.479535
6	0.018112	0.1882	0.425526
7	-0.069405	-0.7213	0.236148
8	0.139674	1.4515	0.074765
9	-0.1573	-1.6347	0.05251
10	0.046684	0.4852	0.314274
11	0.239885	2.493	0.007093
12	-0.409269	-4.2533	2.2e-05
13	0.151062	1.5699	0.059684
14	0.068525	0.7121	0.238958
15	-0.005545	-0.0576	0.477076
16	-0.043687	-0.454	0.325365
17	0.000272	0.0028	0.498876
18	-0.015331	-0.1593	0.436854
19	0.066409	0.6901	0.245793
20	-0.179404	-1.8644	0.032489

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.457523 & -4.7547 & 3e-06 \tabularnewline
2 & -0.086388 & -0.8978 & 0.185653 \tabularnewline
3 & 0.051944 & 0.5398 & 0.295216 \tabularnewline
4 & 0.024019 & 0.2496 & 0.401679 \tabularnewline
5 & 0.00495 & 0.0514 & 0.479535 \tabularnewline
6 & 0.018112 & 0.1882 & 0.425526 \tabularnewline
7 & -0.069405 & -0.7213 & 0.236148 \tabularnewline
8 & 0.139674 & 1.4515 & 0.074765 \tabularnewline
9 & -0.1573 & -1.6347 & 0.05251 \tabularnewline
10 & 0.046684 & 0.4852 & 0.314274 \tabularnewline
11 & 0.239885 & 2.493 & 0.007093 \tabularnewline
12 & -0.409269 & -4.2533 & 2.2e-05 \tabularnewline
13 & 0.151062 & 1.5699 & 0.059684 \tabularnewline
14 & 0.068525 & 0.7121 & 0.238958 \tabularnewline
15 & -0.005545 & -0.0576 & 0.477076 \tabularnewline
16 & -0.043687 & -0.454 & 0.325365 \tabularnewline
17 & 0.000272 & 0.0028 & 0.498876 \tabularnewline
18 & -0.015331 & -0.1593 & 0.436854 \tabularnewline
19 & 0.066409 & 0.6901 & 0.245793 \tabularnewline
20 & -0.179404 & -1.8644 & 0.032489 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297679&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]-0.457523[/C][C]-4.7547[/C][C]3e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.086388[/C][C]-0.8978[/C][C]0.185653[/C][/ROW]
[ROW][C]3[/C][C]0.051944[/C][C]0.5398[/C][C]0.295216[/C][/ROW]
[ROW][C]4[/C][C]0.024019[/C][C]0.2496[/C][C]0.401679[/C][/ROW]
[ROW][C]5[/C][C]0.00495[/C][C]0.0514[/C][C]0.479535[/C][/ROW]
[ROW][C]6[/C][C]0.018112[/C][C]0.1882[/C][C]0.425526[/C][/ROW]
[ROW][C]7[/C][C]-0.069405[/C][C]-0.7213[/C][C]0.236148[/C][/ROW]
[ROW][C]8[/C][C]0.139674[/C][C]1.4515[/C][C]0.074765[/C][/ROW]
[ROW][C]9[/C][C]-0.1573[/C][C]-1.6347[/C][C]0.05251[/C][/ROW]
[ROW][C]10[/C][C]0.046684[/C][C]0.4852[/C][C]0.314274[/C][/ROW]
[ROW][C]11[/C][C]0.239885[/C][C]2.493[/C][C]0.007093[/C][/ROW]
[ROW][C]12[/C][C]-0.409269[/C][C]-4.2533[/C][C]2.2e-05[/C][/ROW]
[ROW][C]13[/C][C]0.151062[/C][C]1.5699[/C][C]0.059684[/C][/ROW]
[ROW][C]14[/C][C]0.068525[/C][C]0.7121[/C][C]0.238958[/C][/ROW]
[ROW][C]15[/C][C]-0.005545[/C][C]-0.0576[/C][C]0.477076[/C][/ROW]
[ROW][C]16[/C][C]-0.043687[/C][C]-0.454[/C][C]0.325365[/C][/ROW]
[ROW][C]17[/C][C]0.000272[/C][C]0.0028[/C][C]0.498876[/C][/ROW]
[ROW][C]18[/C][C]-0.015331[/C][C]-0.1593[/C][C]0.436854[/C][/ROW]
[ROW][C]19[/C][C]0.066409[/C][C]0.6901[/C][C]0.245793[/C][/ROW]
[ROW][C]20[/C][C]-0.179404[/C][C]-1.8644[/C][C]0.032489[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297679&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297679&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	-0.457523	-4.7547	3e-06
2	-0.086388	-0.8978	0.185653
3	0.051944	0.5398	0.295216
4	0.024019	0.2496	0.401679
5	0.00495	0.0514	0.479535
6	0.018112	0.1882	0.425526
7	-0.069405	-0.7213	0.236148
8	0.139674	1.4515	0.074765
9	-0.1573	-1.6347	0.05251
10	0.046684	0.4852	0.314274
11	0.239885	2.493	0.007093
12	-0.409269	-4.2533	2.2e-05
13	0.151062	1.5699	0.059684
14	0.068525	0.7121	0.238958
15	-0.005545	-0.0576	0.477076
16	-0.043687	-0.454	0.325365
17	0.000272	0.0028	0.498876
18	-0.015331	-0.1593	0.436854
19	0.066409	0.6901	0.245793
20	-0.179404	-1.8644	0.032489

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.457523	-4.7547	3e-06
2	-0.374005	-3.8868	8.8e-05
3	-0.255087	-2.6509	0.004617
4	-0.159229	-1.6548	0.050438
5	-0.079641	-0.8277	0.204846
6	0.006325	0.0657	0.473857
7	-0.055952	-0.5815	0.281066
8	0.134267	1.3953	0.082887
9	-0.036476	-0.3791	0.35269
10	-0.029228	-0.3037	0.380954
11	0.32487	3.3762	0.000511
12	-0.167875	-1.7446	0.041949
13	-0.116538	-1.2111	0.114251
14	-0.088084	-0.9154	0.181012
15	-0.031913	-0.3316	0.370398
16	-0.047457	-0.4932	0.31144
17	-0.010236	-0.1064	0.457741
18	-0.019459	-0.2022	0.420063
19	-0.024072	-0.2502	0.401469
20	-0.127987	-1.3301	0.093146

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.457523 & -4.7547 & 3e-06 \tabularnewline
2 & -0.374005 & -3.8868 & 8.8e-05 \tabularnewline
3 & -0.255087 & -2.6509 & 0.004617 \tabularnewline
4 & -0.159229 & -1.6548 & 0.050438 \tabularnewline
5 & -0.079641 & -0.8277 & 0.204846 \tabularnewline
6 & 0.006325 & 0.0657 & 0.473857 \tabularnewline
7 & -0.055952 & -0.5815 & 0.281066 \tabularnewline
8 & 0.134267 & 1.3953 & 0.082887 \tabularnewline
9 & -0.036476 & -0.3791 & 0.35269 \tabularnewline
10 & -0.029228 & -0.3037 & 0.380954 \tabularnewline
11 & 0.32487 & 3.3762 & 0.000511 \tabularnewline
12 & -0.167875 & -1.7446 & 0.041949 \tabularnewline
13 & -0.116538 & -1.2111 & 0.114251 \tabularnewline
14 & -0.088084 & -0.9154 & 0.181012 \tabularnewline
15 & -0.031913 & -0.3316 & 0.370398 \tabularnewline
16 & -0.047457 & -0.4932 & 0.31144 \tabularnewline
17 & -0.010236 & -0.1064 & 0.457741 \tabularnewline
18 & -0.019459 & -0.2022 & 0.420063 \tabularnewline
19 & -0.024072 & -0.2502 & 0.401469 \tabularnewline
20 & -0.127987 & -1.3301 & 0.093146 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297679&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]-0.457523[/C][C]-4.7547[/C][C]3e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.374005[/C][C]-3.8868[/C][C]8.8e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.255087[/C][C]-2.6509[/C][C]0.004617[/C][/ROW]
[ROW][C]4[/C][C]-0.159229[/C][C]-1.6548[/C][C]0.050438[/C][/ROW]
[ROW][C]5[/C][C]-0.079641[/C][C]-0.8277[/C][C]0.204846[/C][/ROW]
[ROW][C]6[/C][C]0.006325[/C][C]0.0657[/C][C]0.473857[/C][/ROW]
[ROW][C]7[/C][C]-0.055952[/C][C]-0.5815[/C][C]0.281066[/C][/ROW]
[ROW][C]8[/C][C]0.134267[/C][C]1.3953[/C][C]0.082887[/C][/ROW]
[ROW][C]9[/C][C]-0.036476[/C][C]-0.3791[/C][C]0.35269[/C][/ROW]
[ROW][C]10[/C][C]-0.029228[/C][C]-0.3037[/C][C]0.380954[/C][/ROW]
[ROW][C]11[/C][C]0.32487[/C][C]3.3762[/C][C]0.000511[/C][/ROW]
[ROW][C]12[/C][C]-0.167875[/C][C]-1.7446[/C][C]0.041949[/C][/ROW]
[ROW][C]13[/C][C]-0.116538[/C][C]-1.2111[/C][C]0.114251[/C][/ROW]
[ROW][C]14[/C][C]-0.088084[/C][C]-0.9154[/C][C]0.181012[/C][/ROW]
[ROW][C]15[/C][C]-0.031913[/C][C]-0.3316[/C][C]0.370398[/C][/ROW]
[ROW][C]16[/C][C]-0.047457[/C][C]-0.4932[/C][C]0.31144[/C][/ROW]
[ROW][C]17[/C][C]-0.010236[/C][C]-0.1064[/C][C]0.457741[/C][/ROW]
[ROW][C]18[/C][C]-0.019459[/C][C]-0.2022[/C][C]0.420063[/C][/ROW]
[ROW][C]19[/C][C]-0.024072[/C][C]-0.2502[/C][C]0.401469[/C][/ROW]
[ROW][C]20[/C][C]-0.127987[/C][C]-1.3301[/C][C]0.093146[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297679&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297679&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	-0.457523	-4.7547	3e-06
2	-0.374005	-3.8868	8.8e-05
3	-0.255087	-2.6509	0.004617
4	-0.159229	-1.6548	0.050438
5	-0.079641	-0.8277	0.204846
6	0.006325	0.0657	0.473857
7	-0.055952	-0.5815	0.281066
8	0.134267	1.3953	0.082887
9	-0.036476	-0.3791	0.35269
10	-0.029228	-0.3037	0.380954
11	0.32487	3.3762	0.000511
12	-0.167875	-1.7446	0.041949
13	-0.116538	-1.2111	0.114251
14	-0.088084	-0.9154	0.181012
15	-0.031913	-0.3316	0.370398
16	-0.047457	-0.4932	0.31144
17	-0.010236	-0.1064	0.457741
18	-0.019459	-0.2022	0.420063
19	-0.024072	-0.2502	0.401469
20	-0.127987	-1.3301	0.093146

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

PDF link

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 = 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