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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 21 Dec 2016 13:35:07 +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/21/t1482323756gpjo5dip33cjcyb.htm/, Retrieved Mon, 06 May 2024 21:48:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302230, Retrieved Mon, 06 May 2024 21:48:35 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

N2054

Estimated Impact

107

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

-     [ML Fitting and QQ Plot- Normal Distribution] [Normal distribution] [2016-12-15 09:27:42] [061bcad4f8cbfaa4a6cadfe6faec1e5a]
- RMPD  [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Chisquared simula...] [2016-12-15 10:38:18] [061bcad4f8cbfaa4a6cadfe6faec1e5a]
- RMPD      [(Partial) Autocorrelation Function] [Partial autocorre...] [2016-12-21 12:35:07] [9a9519454d094169f95f881e5b6f16f7] [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=302230&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=302230&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302230&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	-0.2728	-2.8999	0.002243
2	-0.160092	-1.7018	0.045772
3	0.145981	1.5518	0.061754
4	-0.118325	-1.2578	0.105526
5	0.082736	0.8795	0.1905
6	0.057791	0.6143	0.270116
7	-0.278385	-2.9593	0.001879
8	0.00575	0.0611	0.475685
9	0.242183	2.5744	0.005666
10	-0.020209	-0.2148	0.415145
11	-0.097266	-1.0339	0.151684
12	-0.080668	-0.8575	0.196488
13	-0.126726	-1.3471	0.09032
14	0.205373	2.1831	0.015547
15	-0.115654	-1.2294	0.110735
16	-0.228996	-2.4343	0.008244
17	0.155382	1.6517	0.050682
18	0.104444	1.1103	0.134622
19	-0.103568	-1.1009	0.13663
20	0.217461	2.3116	0.011305
21	-0.055448	-0.5894	0.278379

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.2728 & -2.8999 & 0.002243 \tabularnewline
2 & -0.160092 & -1.7018 & 0.045772 \tabularnewline
3 & 0.145981 & 1.5518 & 0.061754 \tabularnewline
4 & -0.118325 & -1.2578 & 0.105526 \tabularnewline
5 & 0.082736 & 0.8795 & 0.1905 \tabularnewline
6 & 0.057791 & 0.6143 & 0.270116 \tabularnewline
7 & -0.278385 & -2.9593 & 0.001879 \tabularnewline
8 & 0.00575 & 0.0611 & 0.475685 \tabularnewline
9 & 0.242183 & 2.5744 & 0.005666 \tabularnewline
10 & -0.020209 & -0.2148 & 0.415145 \tabularnewline
11 & -0.097266 & -1.0339 & 0.151684 \tabularnewline
12 & -0.080668 & -0.8575 & 0.196488 \tabularnewline
13 & -0.126726 & -1.3471 & 0.09032 \tabularnewline
14 & 0.205373 & 2.1831 & 0.015547 \tabularnewline
15 & -0.115654 & -1.2294 & 0.110735 \tabularnewline
16 & -0.228996 & -2.4343 & 0.008244 \tabularnewline
17 & 0.155382 & 1.6517 & 0.050682 \tabularnewline
18 & 0.104444 & 1.1103 & 0.134622 \tabularnewline
19 & -0.103568 & -1.1009 & 0.13663 \tabularnewline
20 & 0.217461 & 2.3116 & 0.011305 \tabularnewline
21 & -0.055448 & -0.5894 & 0.278379 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302230&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]-0.2728[/C][C]-2.8999[/C][C]0.002243[/C][/ROW]
[ROW][C]2[/C][C]-0.160092[/C][C]-1.7018[/C][C]0.045772[/C][/ROW]
[ROW][C]3[/C][C]0.145981[/C][C]1.5518[/C][C]0.061754[/C][/ROW]
[ROW][C]4[/C][C]-0.118325[/C][C]-1.2578[/C][C]0.105526[/C][/ROW]
[ROW][C]5[/C][C]0.082736[/C][C]0.8795[/C][C]0.1905[/C][/ROW]
[ROW][C]6[/C][C]0.057791[/C][C]0.6143[/C][C]0.270116[/C][/ROW]
[ROW][C]7[/C][C]-0.278385[/C][C]-2.9593[/C][C]0.001879[/C][/ROW]
[ROW][C]8[/C][C]0.00575[/C][C]0.0611[/C][C]0.475685[/C][/ROW]
[ROW][C]9[/C][C]0.242183[/C][C]2.5744[/C][C]0.005666[/C][/ROW]
[ROW][C]10[/C][C]-0.020209[/C][C]-0.2148[/C][C]0.415145[/C][/ROW]
[ROW][C]11[/C][C]-0.097266[/C][C]-1.0339[/C][C]0.151684[/C][/ROW]
[ROW][C]12[/C][C]-0.080668[/C][C]-0.8575[/C][C]0.196488[/C][/ROW]
[ROW][C]13[/C][C]-0.126726[/C][C]-1.3471[/C][C]0.09032[/C][/ROW]
[ROW][C]14[/C][C]0.205373[/C][C]2.1831[/C][C]0.015547[/C][/ROW]
[ROW][C]15[/C][C]-0.115654[/C][C]-1.2294[/C][C]0.110735[/C][/ROW]
[ROW][C]16[/C][C]-0.228996[/C][C]-2.4343[/C][C]0.008244[/C][/ROW]
[ROW][C]17[/C][C]0.155382[/C][C]1.6517[/C][C]0.050682[/C][/ROW]
[ROW][C]18[/C][C]0.104444[/C][C]1.1103[/C][C]0.134622[/C][/ROW]
[ROW][C]19[/C][C]-0.103568[/C][C]-1.1009[/C][C]0.13663[/C][/ROW]
[ROW][C]20[/C][C]0.217461[/C][C]2.3116[/C][C]0.011305[/C][/ROW]
[ROW][C]21[/C][C]-0.055448[/C][C]-0.5894[/C][C]0.278379[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302230&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302230&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	-0.2728	-2.8999	0.002243
2	-0.160092	-1.7018	0.045772
3	0.145981	1.5518	0.061754
4	-0.118325	-1.2578	0.105526
5	0.082736	0.8795	0.1905
6	0.057791	0.6143	0.270116
7	-0.278385	-2.9593	0.001879
8	0.00575	0.0611	0.475685
9	0.242183	2.5744	0.005666
10	-0.020209	-0.2148	0.415145
11	-0.097266	-1.0339	0.151684
12	-0.080668	-0.8575	0.196488
13	-0.126726	-1.3471	0.09032
14	0.205373	2.1831	0.015547
15	-0.115654	-1.2294	0.110735
16	-0.228996	-2.4343	0.008244
17	0.155382	1.6517	0.050682
18	0.104444	1.1103	0.134622
19	-0.103568	-1.1009	0.13663
20	0.217461	2.3116	0.011305
21	-0.055448	-0.5894	0.278379

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.2728	-2.8999	0.002243
2	-0.253367	-2.6933	0.004076
3	0.025543	0.2715	0.393243
4	-0.117321	-1.2471	0.107463
5	0.057496	0.6112	0.271149
6	0.061321	0.6518	0.257911
7	-0.231306	-2.4588	0.007728
8	-0.178926	-1.902	0.029858
9	0.126602	1.3458	0.090531
10	0.140299	1.4914	0.069321
11	-0.038001	-0.404	0.343503
12	-0.161454	-1.7163	0.044426
13	-0.253732	-2.6972	0.004032
14	0.005491	0.0584	0.476778
15	-0.150154	-1.5962	0.056623
16	-0.24171	-2.5694	0.005745
17	-0.03365	-0.3577	0.360616
18	0.087129	0.9262	0.178161
19	-0.185618	-1.9731	0.02546
20	0.083439	0.887	0.188491
21	0.208616	2.2176	0.014291

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.2728 & -2.8999 & 0.002243 \tabularnewline
2 & -0.253367 & -2.6933 & 0.004076 \tabularnewline
3 & 0.025543 & 0.2715 & 0.393243 \tabularnewline
4 & -0.117321 & -1.2471 & 0.107463 \tabularnewline
5 & 0.057496 & 0.6112 & 0.271149 \tabularnewline
6 & 0.061321 & 0.6518 & 0.257911 \tabularnewline
7 & -0.231306 & -2.4588 & 0.007728 \tabularnewline
8 & -0.178926 & -1.902 & 0.029858 \tabularnewline
9 & 0.126602 & 1.3458 & 0.090531 \tabularnewline
10 & 0.140299 & 1.4914 & 0.069321 \tabularnewline
11 & -0.038001 & -0.404 & 0.343503 \tabularnewline
12 & -0.161454 & -1.7163 & 0.044426 \tabularnewline
13 & -0.253732 & -2.6972 & 0.004032 \tabularnewline
14 & 0.005491 & 0.0584 & 0.476778 \tabularnewline
15 & -0.150154 & -1.5962 & 0.056623 \tabularnewline
16 & -0.24171 & -2.5694 & 0.005745 \tabularnewline
17 & -0.03365 & -0.3577 & 0.360616 \tabularnewline
18 & 0.087129 & 0.9262 & 0.178161 \tabularnewline
19 & -0.185618 & -1.9731 & 0.02546 \tabularnewline
20 & 0.083439 & 0.887 & 0.188491 \tabularnewline
21 & 0.208616 & 2.2176 & 0.014291 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302230&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]-0.2728[/C][C]-2.8999[/C][C]0.002243[/C][/ROW]
[ROW][C]2[/C][C]-0.253367[/C][C]-2.6933[/C][C]0.004076[/C][/ROW]
[ROW][C]3[/C][C]0.025543[/C][C]0.2715[/C][C]0.393243[/C][/ROW]
[ROW][C]4[/C][C]-0.117321[/C][C]-1.2471[/C][C]0.107463[/C][/ROW]
[ROW][C]5[/C][C]0.057496[/C][C]0.6112[/C][C]0.271149[/C][/ROW]
[ROW][C]6[/C][C]0.061321[/C][C]0.6518[/C][C]0.257911[/C][/ROW]
[ROW][C]7[/C][C]-0.231306[/C][C]-2.4588[/C][C]0.007728[/C][/ROW]
[ROW][C]8[/C][C]-0.178926[/C][C]-1.902[/C][C]0.029858[/C][/ROW]
[ROW][C]9[/C][C]0.126602[/C][C]1.3458[/C][C]0.090531[/C][/ROW]
[ROW][C]10[/C][C]0.140299[/C][C]1.4914[/C][C]0.069321[/C][/ROW]
[ROW][C]11[/C][C]-0.038001[/C][C]-0.404[/C][C]0.343503[/C][/ROW]
[ROW][C]12[/C][C]-0.161454[/C][C]-1.7163[/C][C]0.044426[/C][/ROW]
[ROW][C]13[/C][C]-0.253732[/C][C]-2.6972[/C][C]0.004032[/C][/ROW]
[ROW][C]14[/C][C]0.005491[/C][C]0.0584[/C][C]0.476778[/C][/ROW]
[ROW][C]15[/C][C]-0.150154[/C][C]-1.5962[/C][C]0.056623[/C][/ROW]
[ROW][C]16[/C][C]-0.24171[/C][C]-2.5694[/C][C]0.005745[/C][/ROW]
[ROW][C]17[/C][C]-0.03365[/C][C]-0.3577[/C][C]0.360616[/C][/ROW]
[ROW][C]18[/C][C]0.087129[/C][C]0.9262[/C][C]0.178161[/C][/ROW]
[ROW][C]19[/C][C]-0.185618[/C][C]-1.9731[/C][C]0.02546[/C][/ROW]
[ROW][C]20[/C][C]0.083439[/C][C]0.887[/C][C]0.188491[/C][/ROW]
[ROW][C]21[/C][C]0.208616[/C][C]2.2176[/C][C]0.014291[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302230&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302230&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	-0.2728	-2.8999	0.002243
2	-0.253367	-2.6933	0.004076
3	0.025543	0.2715	0.393243
4	-0.117321	-1.2471	0.107463
5	0.057496	0.6112	0.271149
6	0.061321	0.6518	0.257911
7	-0.231306	-2.4588	0.007728
8	-0.178926	-1.902	0.029858
9	0.126602	1.3458	0.090531
10	0.140299	1.4914	0.069321
11	-0.038001	-0.404	0.343503
12	-0.161454	-1.7163	0.044426
13	-0.253732	-2.6972	0.004032
14	0.005491	0.0584	0.476778
15	-0.150154	-1.5962	0.056623
16	-0.24171	-2.5694	0.005745
17	-0.03365	-0.3577	0.360616
18	0.087129	0.9262	0.178161
19	-0.185618	-1.9731	0.02546
20	0.083439	0.887	0.188491
21	0.208616	2.2176	0.014291

Figure 1

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PDF link

Figure 2

PNG link

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Figure 3

PNG link

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Parameters (Session):

par1 = 12 ;

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