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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 06 Dec 2016 17:47:13 +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/06/t1481043367kzjg3etkrscng41.htm/, Retrieved Sat, 04 May 2024 12:28:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297876, Retrieved Sat, 04 May 2024 12:28:27 +0000

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User-defined keywords

2e x gedifferentieerd

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2016-12-06 16:47:13] [e6dc02234f5305f92311fb16bc25f73e] [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=297876&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=297876&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297876&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	-0.117782	-1.1895	0.118495
2	0.043607	0.4404	0.330287
3	0.143808	1.4524	0.074732
4	-0.094361	-0.953	0.171421
5	-0.132928	-1.3425	0.091206
6	0.041094	0.415	0.339497
7	0.025289	0.2554	0.39946
8	0.034014	0.3435	0.365956
9	0.02995	0.3025	0.38145
10	0.008927	0.0902	0.464167
11	0.101346	1.0235	0.154235
12	-0.342004	-3.4541	0.000403
13	0.102495	1.0352	0.151523
14	-0.049048	-0.4954	0.310706
15	-0.149059	-1.5054	0.067653
16	-0.022381	-0.226	0.410813
17	-0.048738	-0.4922	0.311809
18	-0.134182	-1.3552	0.089178
19	0.04347	0.439	0.330787
20	-0.018143	-0.1832	0.427488
21	-0.08488	-0.8572	0.196659

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.117782 & -1.1895 & 0.118495 \tabularnewline
2 & 0.043607 & 0.4404 & 0.330287 \tabularnewline
3 & 0.143808 & 1.4524 & 0.074732 \tabularnewline
4 & -0.094361 & -0.953 & 0.171421 \tabularnewline
5 & -0.132928 & -1.3425 & 0.091206 \tabularnewline
6 & 0.041094 & 0.415 & 0.339497 \tabularnewline
7 & 0.025289 & 0.2554 & 0.39946 \tabularnewline
8 & 0.034014 & 0.3435 & 0.365956 \tabularnewline
9 & 0.02995 & 0.3025 & 0.38145 \tabularnewline
10 & 0.008927 & 0.0902 & 0.464167 \tabularnewline
11 & 0.101346 & 1.0235 & 0.154235 \tabularnewline
12 & -0.342004 & -3.4541 & 0.000403 \tabularnewline
13 & 0.102495 & 1.0352 & 0.151523 \tabularnewline
14 & -0.049048 & -0.4954 & 0.310706 \tabularnewline
15 & -0.149059 & -1.5054 & 0.067653 \tabularnewline
16 & -0.022381 & -0.226 & 0.410813 \tabularnewline
17 & -0.048738 & -0.4922 & 0.311809 \tabularnewline
18 & -0.134182 & -1.3552 & 0.089178 \tabularnewline
19 & 0.04347 & 0.439 & 0.330787 \tabularnewline
20 & -0.018143 & -0.1832 & 0.427488 \tabularnewline
21 & -0.08488 & -0.8572 & 0.196659 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297876&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]-0.117782[/C][C]-1.1895[/C][C]0.118495[/C][/ROW]
[ROW][C]2[/C][C]0.043607[/C][C]0.4404[/C][C]0.330287[/C][/ROW]
[ROW][C]3[/C][C]0.143808[/C][C]1.4524[/C][C]0.074732[/C][/ROW]
[ROW][C]4[/C][C]-0.094361[/C][C]-0.953[/C][C]0.171421[/C][/ROW]
[ROW][C]5[/C][C]-0.132928[/C][C]-1.3425[/C][C]0.091206[/C][/ROW]
[ROW][C]6[/C][C]0.041094[/C][C]0.415[/C][C]0.339497[/C][/ROW]
[ROW][C]7[/C][C]0.025289[/C][C]0.2554[/C][C]0.39946[/C][/ROW]
[ROW][C]8[/C][C]0.034014[/C][C]0.3435[/C][C]0.365956[/C][/ROW]
[ROW][C]9[/C][C]0.02995[/C][C]0.3025[/C][C]0.38145[/C][/ROW]
[ROW][C]10[/C][C]0.008927[/C][C]0.0902[/C][C]0.464167[/C][/ROW]
[ROW][C]11[/C][C]0.101346[/C][C]1.0235[/C][C]0.154235[/C][/ROW]
[ROW][C]12[/C][C]-0.342004[/C][C]-3.4541[/C][C]0.000403[/C][/ROW]
[ROW][C]13[/C][C]0.102495[/C][C]1.0352[/C][C]0.151523[/C][/ROW]
[ROW][C]14[/C][C]-0.049048[/C][C]-0.4954[/C][C]0.310706[/C][/ROW]
[ROW][C]15[/C][C]-0.149059[/C][C]-1.5054[/C][C]0.067653[/C][/ROW]
[ROW][C]16[/C][C]-0.022381[/C][C]-0.226[/C][C]0.410813[/C][/ROW]
[ROW][C]17[/C][C]-0.048738[/C][C]-0.4922[/C][C]0.311809[/C][/ROW]
[ROW][C]18[/C][C]-0.134182[/C][C]-1.3552[/C][C]0.089178[/C][/ROW]
[ROW][C]19[/C][C]0.04347[/C][C]0.439[/C][C]0.330787[/C][/ROW]
[ROW][C]20[/C][C]-0.018143[/C][C]-0.1832[/C][C]0.427488[/C][/ROW]
[ROW][C]21[/C][C]-0.08488[/C][C]-0.8572[/C][C]0.196659[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297876&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297876&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	-0.117782	-1.1895	0.118495
2	0.043607	0.4404	0.330287
3	0.143808	1.4524	0.074732
4	-0.094361	-0.953	0.171421
5	-0.132928	-1.3425	0.091206
6	0.041094	0.415	0.339497
7	0.025289	0.2554	0.39946
8	0.034014	0.3435	0.365956
9	0.02995	0.3025	0.38145
10	0.008927	0.0902	0.464167
11	0.101346	1.0235	0.154235
12	-0.342004	-3.4541	0.000403
13	0.102495	1.0352	0.151523
14	-0.049048	-0.4954	0.310706
15	-0.149059	-1.5054	0.067653
16	-0.022381	-0.226	0.410813
17	-0.048738	-0.4922	0.311809
18	-0.134182	-1.3552	0.089178
19	0.04347	0.439	0.330787
20	-0.018143	-0.1832	0.427488
21	-0.08488	-0.8572	0.196659

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.117782	-1.1895	0.118495
2	0.030153	0.3045	0.380674
3	0.154624	1.5616	0.060737
4	-0.063573	-0.6421	0.261138
5	-0.17168	-1.7339	0.04298
6	-0.007219	-0.0729	0.471012
7	0.079123	0.7991	0.213045
8	0.087825	0.887	0.188586
9	0.002489	0.0251	0.489996
10	-0.036952	-0.3732	0.354887
11	0.103097	1.0412	0.150115
12	-0.322421	-3.2563	0.000766
13	0.043436	0.4387	0.330909
14	-0.014287	-0.1443	0.442779
15	-0.0629	-0.6353	0.263341
16	-0.112791	-1.1391	0.128657
17	-0.15898	-1.6056	0.055725
18	-0.105191	-1.0624	0.145287
19	0.046788	0.4725	0.318778
20	0.004849	0.049	0.480518
21	-0.092996	-0.9392	0.174919

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.117782 & -1.1895 & 0.118495 \tabularnewline
2 & 0.030153 & 0.3045 & 0.380674 \tabularnewline
3 & 0.154624 & 1.5616 & 0.060737 \tabularnewline
4 & -0.063573 & -0.6421 & 0.261138 \tabularnewline
5 & -0.17168 & -1.7339 & 0.04298 \tabularnewline
6 & -0.007219 & -0.0729 & 0.471012 \tabularnewline
7 & 0.079123 & 0.7991 & 0.213045 \tabularnewline
8 & 0.087825 & 0.887 & 0.188586 \tabularnewline
9 & 0.002489 & 0.0251 & 0.489996 \tabularnewline
10 & -0.036952 & -0.3732 & 0.354887 \tabularnewline
11 & 0.103097 & 1.0412 & 0.150115 \tabularnewline
12 & -0.322421 & -3.2563 & 0.000766 \tabularnewline
13 & 0.043436 & 0.4387 & 0.330909 \tabularnewline
14 & -0.014287 & -0.1443 & 0.442779 \tabularnewline
15 & -0.0629 & -0.6353 & 0.263341 \tabularnewline
16 & -0.112791 & -1.1391 & 0.128657 \tabularnewline
17 & -0.15898 & -1.6056 & 0.055725 \tabularnewline
18 & -0.105191 & -1.0624 & 0.145287 \tabularnewline
19 & 0.046788 & 0.4725 & 0.318778 \tabularnewline
20 & 0.004849 & 0.049 & 0.480518 \tabularnewline
21 & -0.092996 & -0.9392 & 0.174919 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297876&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]-0.117782[/C][C]-1.1895[/C][C]0.118495[/C][/ROW]
[ROW][C]2[/C][C]0.030153[/C][C]0.3045[/C][C]0.380674[/C][/ROW]
[ROW][C]3[/C][C]0.154624[/C][C]1.5616[/C][C]0.060737[/C][/ROW]
[ROW][C]4[/C][C]-0.063573[/C][C]-0.6421[/C][C]0.261138[/C][/ROW]
[ROW][C]5[/C][C]-0.17168[/C][C]-1.7339[/C][C]0.04298[/C][/ROW]
[ROW][C]6[/C][C]-0.007219[/C][C]-0.0729[/C][C]0.471012[/C][/ROW]
[ROW][C]7[/C][C]0.079123[/C][C]0.7991[/C][C]0.213045[/C][/ROW]
[ROW][C]8[/C][C]0.087825[/C][C]0.887[/C][C]0.188586[/C][/ROW]
[ROW][C]9[/C][C]0.002489[/C][C]0.0251[/C][C]0.489996[/C][/ROW]
[ROW][C]10[/C][C]-0.036952[/C][C]-0.3732[/C][C]0.354887[/C][/ROW]
[ROW][C]11[/C][C]0.103097[/C][C]1.0412[/C][C]0.150115[/C][/ROW]
[ROW][C]12[/C][C]-0.322421[/C][C]-3.2563[/C][C]0.000766[/C][/ROW]
[ROW][C]13[/C][C]0.043436[/C][C]0.4387[/C][C]0.330909[/C][/ROW]
[ROW][C]14[/C][C]-0.014287[/C][C]-0.1443[/C][C]0.442779[/C][/ROW]
[ROW][C]15[/C][C]-0.0629[/C][C]-0.6353[/C][C]0.263341[/C][/ROW]
[ROW][C]16[/C][C]-0.112791[/C][C]-1.1391[/C][C]0.128657[/C][/ROW]
[ROW][C]17[/C][C]-0.15898[/C][C]-1.6056[/C][C]0.055725[/C][/ROW]
[ROW][C]18[/C][C]-0.105191[/C][C]-1.0624[/C][C]0.145287[/C][/ROW]
[ROW][C]19[/C][C]0.046788[/C][C]0.4725[/C][C]0.318778[/C][/ROW]
[ROW][C]20[/C][C]0.004849[/C][C]0.049[/C][C]0.480518[/C][/ROW]
[ROW][C]21[/C][C]-0.092996[/C][C]-0.9392[/C][C]0.174919[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297876&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297876&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	-0.117782	-1.1895	0.118495
2	0.030153	0.3045	0.380674
3	0.154624	1.5616	0.060737
4	-0.063573	-0.6421	0.261138
5	-0.17168	-1.7339	0.04298
6	-0.007219	-0.0729	0.471012
7	0.079123	0.7991	0.213045
8	0.087825	0.887	0.188586
9	0.002489	0.0251	0.489996
10	-0.036952	-0.3732	0.354887
11	0.103097	1.0412	0.150115
12	-0.322421	-3.2563	0.000766
13	0.043436	0.4387	0.330909
14	-0.014287	-0.1443	0.442779
15	-0.0629	-0.6353	0.263341
16	-0.112791	-1.1391	0.128657
17	-0.15898	-1.6056	0.055725
18	-0.105191	-1.0624	0.145287
19	0.046788	0.4725	0.318778
20	0.004849	0.049	0.480518
21	-0.092996	-0.9392	0.174919

Figure 1

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Postscript link

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Figure 2

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Figure 3

PNG link

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Parameters (Session):

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '2'
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