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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 17 Dec 2016 08:18:22 +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/17/t1481959256r530gsplgo4eteo.htm/, Retrieved Fri, 01 Nov 2024 03:34:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300600, Retrieved Fri, 01 Nov 2024 03:34:36 +0000

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User-defined keywords

Estimated Impact

145

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

-       [(Partial) Autocorrelation Function] [N 2460- ACF (1)] [2016-12-17 07:18:22] [86c7fb9c8a0af864c0a27e2f433e80d7] [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	2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300600&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300600&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300600&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	2 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.730242	8.1969	0
2	0.595486	6.6843	0
3	0.571767	6.4181	0
4	0.53191	5.9707	0
5	0.520994	5.8481	0
6	0.492782	5.5315	0
7	0.483297	5.425	0
8	0.442574	4.9679	1e-06
9	0.451292	5.0657	1e-06
10	0.443021	4.9729	1e-06
11	0.553709	6.2154	0
12	0.763631	8.5717	0
13	0.529314	5.9415	0
14	0.417625	4.6878	4e-06
15	0.395129	4.4353	1e-05
16	0.345021	3.8729	8.6e-05
17	0.337458	3.788	0.000117
18	0.31132	3.4946	0.000328
19	0.296499	3.3282	0.000573
20	0.25545	2.8674	0.002426
21	0.261879	2.9396	0.001955

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.730242 & 8.1969 & 0 \tabularnewline
2 & 0.595486 & 6.6843 & 0 \tabularnewline
3 & 0.571767 & 6.4181 & 0 \tabularnewline
4 & 0.53191 & 5.9707 & 0 \tabularnewline
5 & 0.520994 & 5.8481 & 0 \tabularnewline
6 & 0.492782 & 5.5315 & 0 \tabularnewline
7 & 0.483297 & 5.425 & 0 \tabularnewline
8 & 0.442574 & 4.9679 & 1e-06 \tabularnewline
9 & 0.451292 & 5.0657 & 1e-06 \tabularnewline
10 & 0.443021 & 4.9729 & 1e-06 \tabularnewline
11 & 0.553709 & 6.2154 & 0 \tabularnewline
12 & 0.763631 & 8.5717 & 0 \tabularnewline
13 & 0.529314 & 5.9415 & 0 \tabularnewline
14 & 0.417625 & 4.6878 & 4e-06 \tabularnewline
15 & 0.395129 & 4.4353 & 1e-05 \tabularnewline
16 & 0.345021 & 3.8729 & 8.6e-05 \tabularnewline
17 & 0.337458 & 3.788 & 0.000117 \tabularnewline
18 & 0.31132 & 3.4946 & 0.000328 \tabularnewline
19 & 0.296499 & 3.3282 & 0.000573 \tabularnewline
20 & 0.25545 & 2.8674 & 0.002426 \tabularnewline
21 & 0.261879 & 2.9396 & 0.001955 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300600&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]0.730242[/C][C]8.1969[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.595486[/C][C]6.6843[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.571767[/C][C]6.4181[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.53191[/C][C]5.9707[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.520994[/C][C]5.8481[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.492782[/C][C]5.5315[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.483297[/C][C]5.425[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.442574[/C][C]4.9679[/C][C]1e-06[/C][/ROW]
[ROW][C]9[/C][C]0.451292[/C][C]5.0657[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.443021[/C][C]4.9729[/C][C]1e-06[/C][/ROW]
[ROW][C]11[/C][C]0.553709[/C][C]6.2154[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.763631[/C][C]8.5717[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.529314[/C][C]5.9415[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.417625[/C][C]4.6878[/C][C]4e-06[/C][/ROW]
[ROW][C]15[/C][C]0.395129[/C][C]4.4353[/C][C]1e-05[/C][/ROW]
[ROW][C]16[/C][C]0.345021[/C][C]3.8729[/C][C]8.6e-05[/C][/ROW]
[ROW][C]17[/C][C]0.337458[/C][C]3.788[/C][C]0.000117[/C][/ROW]
[ROW][C]18[/C][C]0.31132[/C][C]3.4946[/C][C]0.000328[/C][/ROW]
[ROW][C]19[/C][C]0.296499[/C][C]3.3282[/C][C]0.000573[/C][/ROW]
[ROW][C]20[/C][C]0.25545[/C][C]2.8674[/C][C]0.002426[/C][/ROW]
[ROW][C]21[/C][C]0.261879[/C][C]2.9396[/C][C]0.001955[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300600&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300600&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	0.730242	8.1969	0
2	0.595486	6.6843	0
3	0.571767	6.4181	0
4	0.53191	5.9707	0
5	0.520994	5.8481	0
6	0.492782	5.5315	0
7	0.483297	5.425	0
8	0.442574	4.9679	1e-06
9	0.451292	5.0657	1e-06
10	0.443021	4.9729	1e-06
11	0.553709	6.2154	0
12	0.763631	8.5717	0
13	0.529314	5.9415	0
14	0.417625	4.6878	4e-06
15	0.395129	4.4353	1e-05
16	0.345021	3.8729	8.6e-05
17	0.337458	3.788	0.000117
18	0.31132	3.4946	0.000328
19	0.296499	3.3282	0.000573
20	0.25545	2.8674	0.002426
21	0.261879	2.9396	0.001955

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.730242	8.1969	0
2	0.133334	1.4967	0.06849
3	0.212744	2.388	0.009212
4	0.072414	0.8128	0.208921
5	0.125948	1.4138	0.079949
6	0.034935	0.3921	0.347807
7	0.085649	0.9614	0.169093
8	-0.026537	-0.2979	0.383145
9	0.110421	1.2395	0.108737
10	0.013799	0.1549	0.438578
11	0.344899	3.8715	8.6e-05
12	0.560792	6.2949	0
13	-0.640167	-7.1859	0
14	-0.131945	-1.4811	0.070541
15	-0.094441	-1.0601	0.145564
16	-0.124505	-1.3976	0.08235
17	0.128015	1.437	0.076604
18	-0.000805	-0.009	0.4964
19	0.009268	0.104	0.458656
20	0.116048	1.3026	0.097537
21	-0.037936	-0.4258	0.33548

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.730242 & 8.1969 & 0 \tabularnewline
2 & 0.133334 & 1.4967 & 0.06849 \tabularnewline
3 & 0.212744 & 2.388 & 0.009212 \tabularnewline
4 & 0.072414 & 0.8128 & 0.208921 \tabularnewline
5 & 0.125948 & 1.4138 & 0.079949 \tabularnewline
6 & 0.034935 & 0.3921 & 0.347807 \tabularnewline
7 & 0.085649 & 0.9614 & 0.169093 \tabularnewline
8 & -0.026537 & -0.2979 & 0.383145 \tabularnewline
9 & 0.110421 & 1.2395 & 0.108737 \tabularnewline
10 & 0.013799 & 0.1549 & 0.438578 \tabularnewline
11 & 0.344899 & 3.8715 & 8.6e-05 \tabularnewline
12 & 0.560792 & 6.2949 & 0 \tabularnewline
13 & -0.640167 & -7.1859 & 0 \tabularnewline
14 & -0.131945 & -1.4811 & 0.070541 \tabularnewline
15 & -0.094441 & -1.0601 & 0.145564 \tabularnewline
16 & -0.124505 & -1.3976 & 0.08235 \tabularnewline
17 & 0.128015 & 1.437 & 0.076604 \tabularnewline
18 & -0.000805 & -0.009 & 0.4964 \tabularnewline
19 & 0.009268 & 0.104 & 0.458656 \tabularnewline
20 & 0.116048 & 1.3026 & 0.097537 \tabularnewline
21 & -0.037936 & -0.4258 & 0.33548 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300600&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]0.730242[/C][C]8.1969[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.133334[/C][C]1.4967[/C][C]0.06849[/C][/ROW]
[ROW][C]3[/C][C]0.212744[/C][C]2.388[/C][C]0.009212[/C][/ROW]
[ROW][C]4[/C][C]0.072414[/C][C]0.8128[/C][C]0.208921[/C][/ROW]
[ROW][C]5[/C][C]0.125948[/C][C]1.4138[/C][C]0.079949[/C][/ROW]
[ROW][C]6[/C][C]0.034935[/C][C]0.3921[/C][C]0.347807[/C][/ROW]
[ROW][C]7[/C][C]0.085649[/C][C]0.9614[/C][C]0.169093[/C][/ROW]
[ROW][C]8[/C][C]-0.026537[/C][C]-0.2979[/C][C]0.383145[/C][/ROW]
[ROW][C]9[/C][C]0.110421[/C][C]1.2395[/C][C]0.108737[/C][/ROW]
[ROW][C]10[/C][C]0.013799[/C][C]0.1549[/C][C]0.438578[/C][/ROW]
[ROW][C]11[/C][C]0.344899[/C][C]3.8715[/C][C]8.6e-05[/C][/ROW]
[ROW][C]12[/C][C]0.560792[/C][C]6.2949[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.640167[/C][C]-7.1859[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]-0.131945[/C][C]-1.4811[/C][C]0.070541[/C][/ROW]
[ROW][C]15[/C][C]-0.094441[/C][C]-1.0601[/C][C]0.145564[/C][/ROW]
[ROW][C]16[/C][C]-0.124505[/C][C]-1.3976[/C][C]0.08235[/C][/ROW]
[ROW][C]17[/C][C]0.128015[/C][C]1.437[/C][C]0.076604[/C][/ROW]
[ROW][C]18[/C][C]-0.000805[/C][C]-0.009[/C][C]0.4964[/C][/ROW]
[ROW][C]19[/C][C]0.009268[/C][C]0.104[/C][C]0.458656[/C][/ROW]
[ROW][C]20[/C][C]0.116048[/C][C]1.3026[/C][C]0.097537[/C][/ROW]
[ROW][C]21[/C][C]-0.037936[/C][C]-0.4258[/C][C]0.33548[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300600&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300600&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	0.730242	8.1969	0
2	0.133334	1.4967	0.06849
3	0.212744	2.388	0.009212
4	0.072414	0.8128	0.208921
5	0.125948	1.4138	0.079949
6	0.034935	0.3921	0.347807
7	0.085649	0.9614	0.169093
8	-0.026537	-0.2979	0.383145
9	0.110421	1.2395	0.108737
10	0.013799	0.1549	0.438578
11	0.344899	3.8715	8.6e-05
12	0.560792	6.2949	0
13	-0.640167	-7.1859	0
14	-0.131945	-1.4811	0.070541
15	-0.094441	-1.0601	0.145564
16	-0.124505	-1.3976	0.08235
17	0.128015	1.437	0.076604
18	-0.000805	-0.009	0.4964
19	0.009268	0.104	0.458656
20	0.116048	1.3026	0.097537
21	-0.037936	-0.4258	0.33548

Figure 1

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Figure 2

PNG link

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Figure 3

PNG link

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PDF link

Parameters (Session):

par4 = 12 ;

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