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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 13:17:37 +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/t1482322705e9lqu8n7gseux91.htm/, Retrieved Mon, 06 May 2024 13:03:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302207, Retrieved Mon, 06 May 2024 13:03:04 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

N1954

Estimated Impact

103

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 12:17:37] [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=302207&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=302207&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302207&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	-0.421641	-4.7141	3e-06
2	-0.125028	-1.3979	0.082317
3	0.028807	0.3221	0.373967
4	0.044381	0.4962	0.310316
5	0.07727	0.8639	0.194648
6	-0.092815	-1.0377	0.150706
7	-0.025259	-0.2824	0.389051
8	-0.059826	-0.6689	0.252403
9	0.124878	1.3962	0.082567
10	-0.076327	-0.8534	0.197545
11	0.033184	0.371	0.355629
12	0.122819	1.3732	0.086081
13	-0.171566	-1.9182	0.028685
14	-0.012235	-0.1368	0.445706
15	0.146859	1.6419	0.051559
16	0.030563	0.3417	0.366574
17	-0.160807	-1.7979	0.037305
18	0.094714	1.0589	0.145835
19	-0.072877	-0.8148	0.20837
20	-0.080314	-0.8979	0.185471
21	0.276246	3.0885	0.001239

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.421641 & -4.7141 & 3e-06 \tabularnewline
2 & -0.125028 & -1.3979 & 0.082317 \tabularnewline
3 & 0.028807 & 0.3221 & 0.373967 \tabularnewline
4 & 0.044381 & 0.4962 & 0.310316 \tabularnewline
5 & 0.07727 & 0.8639 & 0.194648 \tabularnewline
6 & -0.092815 & -1.0377 & 0.150706 \tabularnewline
7 & -0.025259 & -0.2824 & 0.389051 \tabularnewline
8 & -0.059826 & -0.6689 & 0.252403 \tabularnewline
9 & 0.124878 & 1.3962 & 0.082567 \tabularnewline
10 & -0.076327 & -0.8534 & 0.197545 \tabularnewline
11 & 0.033184 & 0.371 & 0.355629 \tabularnewline
12 & 0.122819 & 1.3732 & 0.086081 \tabularnewline
13 & -0.171566 & -1.9182 & 0.028685 \tabularnewline
14 & -0.012235 & -0.1368 & 0.445706 \tabularnewline
15 & 0.146859 & 1.6419 & 0.051559 \tabularnewline
16 & 0.030563 & 0.3417 & 0.366574 \tabularnewline
17 & -0.160807 & -1.7979 & 0.037305 \tabularnewline
18 & 0.094714 & 1.0589 & 0.145835 \tabularnewline
19 & -0.072877 & -0.8148 & 0.20837 \tabularnewline
20 & -0.080314 & -0.8979 & 0.185471 \tabularnewline
21 & 0.276246 & 3.0885 & 0.001239 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302207&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]-0.421641[/C][C]-4.7141[/C][C]3e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.125028[/C][C]-1.3979[/C][C]0.082317[/C][/ROW]
[ROW][C]3[/C][C]0.028807[/C][C]0.3221[/C][C]0.373967[/C][/ROW]
[ROW][C]4[/C][C]0.044381[/C][C]0.4962[/C][C]0.310316[/C][/ROW]
[ROW][C]5[/C][C]0.07727[/C][C]0.8639[/C][C]0.194648[/C][/ROW]
[ROW][C]6[/C][C]-0.092815[/C][C]-1.0377[/C][C]0.150706[/C][/ROW]
[ROW][C]7[/C][C]-0.025259[/C][C]-0.2824[/C][C]0.389051[/C][/ROW]
[ROW][C]8[/C][C]-0.059826[/C][C]-0.6689[/C][C]0.252403[/C][/ROW]
[ROW][C]9[/C][C]0.124878[/C][C]1.3962[/C][C]0.082567[/C][/ROW]
[ROW][C]10[/C][C]-0.076327[/C][C]-0.8534[/C][C]0.197545[/C][/ROW]
[ROW][C]11[/C][C]0.033184[/C][C]0.371[/C][C]0.355629[/C][/ROW]
[ROW][C]12[/C][C]0.122819[/C][C]1.3732[/C][C]0.086081[/C][/ROW]
[ROW][C]13[/C][C]-0.171566[/C][C]-1.9182[/C][C]0.028685[/C][/ROW]
[ROW][C]14[/C][C]-0.012235[/C][C]-0.1368[/C][C]0.445706[/C][/ROW]
[ROW][C]15[/C][C]0.146859[/C][C]1.6419[/C][C]0.051559[/C][/ROW]
[ROW][C]16[/C][C]0.030563[/C][C]0.3417[/C][C]0.366574[/C][/ROW]
[ROW][C]17[/C][C]-0.160807[/C][C]-1.7979[/C][C]0.037305[/C][/ROW]
[ROW][C]18[/C][C]0.094714[/C][C]1.0589[/C][C]0.145835[/C][/ROW]
[ROW][C]19[/C][C]-0.072877[/C][C]-0.8148[/C][C]0.20837[/C][/ROW]
[ROW][C]20[/C][C]-0.080314[/C][C]-0.8979[/C][C]0.185471[/C][/ROW]
[ROW][C]21[/C][C]0.276246[/C][C]3.0885[/C][C]0.001239[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302207&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302207&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	-0.421641	-4.7141	3e-06
2	-0.125028	-1.3979	0.082317
3	0.028807	0.3221	0.373967
4	0.044381	0.4962	0.310316
5	0.07727	0.8639	0.194648
6	-0.092815	-1.0377	0.150706
7	-0.025259	-0.2824	0.389051
8	-0.059826	-0.6689	0.252403
9	0.124878	1.3962	0.082567
10	-0.076327	-0.8534	0.197545
11	0.033184	0.371	0.355629
12	0.122819	1.3732	0.086081
13	-0.171566	-1.9182	0.028685
14	-0.012235	-0.1368	0.445706
15	0.146859	1.6419	0.051559
16	0.030563	0.3417	0.366574
17	-0.160807	-1.7979	0.037305
18	0.094714	1.0589	0.145835
19	-0.072877	-0.8148	0.20837
20	-0.080314	-0.8979	0.185471
21	0.276246	3.0885	0.001239

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.421641	-4.7141	3e-06
2	-0.368282	-4.1175	3.5e-05
3	-0.279453	-3.1244	0.001108
4	-0.183252	-2.0488	0.021286
5	-3e-05	-3e-04	0.499866
6	-0.031281	-0.3497	0.363565
7	-0.056863	-0.6357	0.263051
8	-0.198861	-2.2233	0.013995
9	-0.087374	-0.9769	0.165261
10	-0.162841	-1.8206	0.035529
11	-0.070605	-0.7894	0.21569
12	0.17488	1.9552	0.026394
13	0.032285	0.361	0.359371
14	-0.089792	-1.0039	0.158682
15	0.043019	0.481	0.31569
16	0.144483	1.6154	0.054376
17	0.008943	0.1	0.46026
18	0.160447	1.7939	0.037627
19	0.046421	0.519	0.302339
20	-0.229807	-2.5693	0.005682
21	0.099973	1.1177	0.132914

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.421641 & -4.7141 & 3e-06 \tabularnewline
2 & -0.368282 & -4.1175 & 3.5e-05 \tabularnewline
3 & -0.279453 & -3.1244 & 0.001108 \tabularnewline
4 & -0.183252 & -2.0488 & 0.021286 \tabularnewline
5 & -3e-05 & -3e-04 & 0.499866 \tabularnewline
6 & -0.031281 & -0.3497 & 0.363565 \tabularnewline
7 & -0.056863 & -0.6357 & 0.263051 \tabularnewline
8 & -0.198861 & -2.2233 & 0.013995 \tabularnewline
9 & -0.087374 & -0.9769 & 0.165261 \tabularnewline
10 & -0.162841 & -1.8206 & 0.035529 \tabularnewline
11 & -0.070605 & -0.7894 & 0.21569 \tabularnewline
12 & 0.17488 & 1.9552 & 0.026394 \tabularnewline
13 & 0.032285 & 0.361 & 0.359371 \tabularnewline
14 & -0.089792 & -1.0039 & 0.158682 \tabularnewline
15 & 0.043019 & 0.481 & 0.31569 \tabularnewline
16 & 0.144483 & 1.6154 & 0.054376 \tabularnewline
17 & 0.008943 & 0.1 & 0.46026 \tabularnewline
18 & 0.160447 & 1.7939 & 0.037627 \tabularnewline
19 & 0.046421 & 0.519 & 0.302339 \tabularnewline
20 & -0.229807 & -2.5693 & 0.005682 \tabularnewline
21 & 0.099973 & 1.1177 & 0.132914 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302207&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]-0.421641[/C][C]-4.7141[/C][C]3e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.368282[/C][C]-4.1175[/C][C]3.5e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.279453[/C][C]-3.1244[/C][C]0.001108[/C][/ROW]
[ROW][C]4[/C][C]-0.183252[/C][C]-2.0488[/C][C]0.021286[/C][/ROW]
[ROW][C]5[/C][C]-3e-05[/C][C]-3e-04[/C][C]0.499866[/C][/ROW]
[ROW][C]6[/C][C]-0.031281[/C][C]-0.3497[/C][C]0.363565[/C][/ROW]
[ROW][C]7[/C][C]-0.056863[/C][C]-0.6357[/C][C]0.263051[/C][/ROW]
[ROW][C]8[/C][C]-0.198861[/C][C]-2.2233[/C][C]0.013995[/C][/ROW]
[ROW][C]9[/C][C]-0.087374[/C][C]-0.9769[/C][C]0.165261[/C][/ROW]
[ROW][C]10[/C][C]-0.162841[/C][C]-1.8206[/C][C]0.035529[/C][/ROW]
[ROW][C]11[/C][C]-0.070605[/C][C]-0.7894[/C][C]0.21569[/C][/ROW]
[ROW][C]12[/C][C]0.17488[/C][C]1.9552[/C][C]0.026394[/C][/ROW]
[ROW][C]13[/C][C]0.032285[/C][C]0.361[/C][C]0.359371[/C][/ROW]
[ROW][C]14[/C][C]-0.089792[/C][C]-1.0039[/C][C]0.158682[/C][/ROW]
[ROW][C]15[/C][C]0.043019[/C][C]0.481[/C][C]0.31569[/C][/ROW]
[ROW][C]16[/C][C]0.144483[/C][C]1.6154[/C][C]0.054376[/C][/ROW]
[ROW][C]17[/C][C]0.008943[/C][C]0.1[/C][C]0.46026[/C][/ROW]
[ROW][C]18[/C][C]0.160447[/C][C]1.7939[/C][C]0.037627[/C][/ROW]
[ROW][C]19[/C][C]0.046421[/C][C]0.519[/C][C]0.302339[/C][/ROW]
[ROW][C]20[/C][C]-0.229807[/C][C]-2.5693[/C][C]0.005682[/C][/ROW]
[ROW][C]21[/C][C]0.099973[/C][C]1.1177[/C][C]0.132914[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302207&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302207&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	-0.421641	-4.7141	3e-06
2	-0.368282	-4.1175	3.5e-05
3	-0.279453	-3.1244	0.001108
4	-0.183252	-2.0488	0.021286
5	-3e-05	-3e-04	0.499866
6	-0.031281	-0.3497	0.363565
7	-0.056863	-0.6357	0.263051
8	-0.198861	-2.2233	0.013995
9	-0.087374	-0.9769	0.165261
10	-0.162841	-1.8206	0.035529
11	-0.070605	-0.7894	0.21569
12	0.17488	1.9552	0.026394
13	0.032285	0.361	0.359371
14	-0.089792	-1.0039	0.158682
15	0.043019	0.481	0.31569
16	0.144483	1.6154	0.054376
17	0.008943	0.1	0.46026
18	0.160447	1.7939	0.037627
19	0.046421	0.519	0.302339
20	-0.229807	-2.5693	0.005682
21	0.099973	1.1177	0.132914

Figure 1

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Figure 2

PNG link

Postscript 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 = 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