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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

Sun, 18 Dec 2016 14:25:37 +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/18/t1482067553vvs4c8sx3ct78j5.htm/, Retrieved Wed, 08 May 2024 11:18:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301067, Retrieved Wed, 08 May 2024 11:18:48 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

104

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

-     [Exponential Smoothing] [] [2016-12-18 12:31:12] [683f400e1b95307fc738e729f07c4fce]
- RM D    [(Partial) Autocorrelation Function] [] [2016-12-18 13:25:37] [404ac5ee4f7301873f6a96ef36861981] [Current]
- R P       [(Partial) Autocorrelation Function] [] [2016-12-20 22:53:44] [683f400e1b95307fc738e729f07c4fce] 
-   P       [(Partial) Autocorrelation Function] [] [2016-12-20 22:57:51] [683f400e1b95307fc738e729f07c4fce] 
- RMP       [Spectral Analysis] [] [2016-12-20 23:03:30] [683f400e1b95307fc738e729f07c4fce] 

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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=301067&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=301067&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301067&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	-0.013819	-0.1409	0.4441
2	0.159309	1.6246	0.053633
3	-0.379578	-3.8709	9.5e-05
4	-0.150051	-1.5302	0.064499
5	-0.044428	-0.4531	0.325718
6	-0.127861	-1.3039	0.097568
7	0.0467	0.4762	0.31745
8	-0.109992	-1.1217	0.132286
9	-0.044855	-0.4574	0.324158
10	-0.007495	-0.0764	0.469609
11	0.069583	0.7096	0.239767
12	0.251811	2.568	0.005825
13	0.205948	2.1003	0.019062
14	-0.051201	-0.5221	0.30134
15	-0.104926	-1.07	0.143539
16	-0.169454	-1.7281	0.043469
17	0.06097	0.6218	0.267726
18	-0.041026	-0.4184	0.338264
19	0.034061	0.3474	0.364513
20	-0.068268	-0.6962	0.24393

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.013819 & -0.1409 & 0.4441 \tabularnewline
2 & 0.159309 & 1.6246 & 0.053633 \tabularnewline
3 & -0.379578 & -3.8709 & 9.5e-05 \tabularnewline
4 & -0.150051 & -1.5302 & 0.064499 \tabularnewline
5 & -0.044428 & -0.4531 & 0.325718 \tabularnewline
6 & -0.127861 & -1.3039 & 0.097568 \tabularnewline
7 & 0.0467 & 0.4762 & 0.31745 \tabularnewline
8 & -0.109992 & -1.1217 & 0.132286 \tabularnewline
9 & -0.044855 & -0.4574 & 0.324158 \tabularnewline
10 & -0.007495 & -0.0764 & 0.469609 \tabularnewline
11 & 0.069583 & 0.7096 & 0.239767 \tabularnewline
12 & 0.251811 & 2.568 & 0.005825 \tabularnewline
13 & 0.205948 & 2.1003 & 0.019062 \tabularnewline
14 & -0.051201 & -0.5221 & 0.30134 \tabularnewline
15 & -0.104926 & -1.07 & 0.143539 \tabularnewline
16 & -0.169454 & -1.7281 & 0.043469 \tabularnewline
17 & 0.06097 & 0.6218 & 0.267726 \tabularnewline
18 & -0.041026 & -0.4184 & 0.338264 \tabularnewline
19 & 0.034061 & 0.3474 & 0.364513 \tabularnewline
20 & -0.068268 & -0.6962 & 0.24393 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301067&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]-0.013819[/C][C]-0.1409[/C][C]0.4441[/C][/ROW]
[ROW][C]2[/C][C]0.159309[/C][C]1.6246[/C][C]0.053633[/C][/ROW]
[ROW][C]3[/C][C]-0.379578[/C][C]-3.8709[/C][C]9.5e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.150051[/C][C]-1.5302[/C][C]0.064499[/C][/ROW]
[ROW][C]5[/C][C]-0.044428[/C][C]-0.4531[/C][C]0.325718[/C][/ROW]
[ROW][C]6[/C][C]-0.127861[/C][C]-1.3039[/C][C]0.097568[/C][/ROW]
[ROW][C]7[/C][C]0.0467[/C][C]0.4762[/C][C]0.31745[/C][/ROW]
[ROW][C]8[/C][C]-0.109992[/C][C]-1.1217[/C][C]0.132286[/C][/ROW]
[ROW][C]9[/C][C]-0.044855[/C][C]-0.4574[/C][C]0.324158[/C][/ROW]
[ROW][C]10[/C][C]-0.007495[/C][C]-0.0764[/C][C]0.469609[/C][/ROW]
[ROW][C]11[/C][C]0.069583[/C][C]0.7096[/C][C]0.239767[/C][/ROW]
[ROW][C]12[/C][C]0.251811[/C][C]2.568[/C][C]0.005825[/C][/ROW]
[ROW][C]13[/C][C]0.205948[/C][C]2.1003[/C][C]0.019062[/C][/ROW]
[ROW][C]14[/C][C]-0.051201[/C][C]-0.5221[/C][C]0.30134[/C][/ROW]
[ROW][C]15[/C][C]-0.104926[/C][C]-1.07[/C][C]0.143539[/C][/ROW]
[ROW][C]16[/C][C]-0.169454[/C][C]-1.7281[/C][C]0.043469[/C][/ROW]
[ROW][C]17[/C][C]0.06097[/C][C]0.6218[/C][C]0.267726[/C][/ROW]
[ROW][C]18[/C][C]-0.041026[/C][C]-0.4184[/C][C]0.338264[/C][/ROW]
[ROW][C]19[/C][C]0.034061[/C][C]0.3474[/C][C]0.364513[/C][/ROW]
[ROW][C]20[/C][C]-0.068268[/C][C]-0.6962[/C][C]0.24393[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301067&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301067&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	-0.013819	-0.1409	0.4441
2	0.159309	1.6246	0.053633
3	-0.379578	-3.8709	9.5e-05
4	-0.150051	-1.5302	0.064499
5	-0.044428	-0.4531	0.325718
6	-0.127861	-1.3039	0.097568
7	0.0467	0.4762	0.31745
8	-0.109992	-1.1217	0.132286
9	-0.044855	-0.4574	0.324158
10	-0.007495	-0.0764	0.469609
11	0.069583	0.7096	0.239767
12	0.251811	2.568	0.005825
13	0.205948	2.1003	0.019062
14	-0.051201	-0.5221	0.30134
15	-0.104926	-1.07	0.143539
16	-0.169454	-1.7281	0.043469
17	0.06097	0.6218	0.267726
18	-0.041026	-0.4184	0.338264
19	0.034061	0.3474	0.364513
20	-0.068268	-0.6962	0.24393

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.013819	-0.1409	0.4441
2	0.159149	1.623	0.053808
3	-0.385359	-3.9299	7.7e-05
4	-0.194207	-1.9805	0.025142
5	0.099041	1.01	0.157413
6	-0.268725	-2.7405	0.003611
7	-0.119232	-1.2159	0.113381
8	-0.072446	-0.7388	0.230845
9	-0.270375	-2.7573	0.003443
10	-0.10381	-1.0587	0.146105
11	0.005591	0.057	0.477319
12	0.075651	0.7715	0.221083
13	0.189425	1.9318	0.028055
14	-0.153552	-1.5659	0.060201
15	-0.058295	-0.5945	0.276736
16	0.122024	1.2444	0.108073
17	0.071022	0.7243	0.235259
18	-0.046675	-0.476	0.317537
19	0.067031	0.6836	0.247878
20	-0.005757	-0.0587	0.476649

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.013819 & -0.1409 & 0.4441 \tabularnewline
2 & 0.159149 & 1.623 & 0.053808 \tabularnewline
3 & -0.385359 & -3.9299 & 7.7e-05 \tabularnewline
4 & -0.194207 & -1.9805 & 0.025142 \tabularnewline
5 & 0.099041 & 1.01 & 0.157413 \tabularnewline
6 & -0.268725 & -2.7405 & 0.003611 \tabularnewline
7 & -0.119232 & -1.2159 & 0.113381 \tabularnewline
8 & -0.072446 & -0.7388 & 0.230845 \tabularnewline
9 & -0.270375 & -2.7573 & 0.003443 \tabularnewline
10 & -0.10381 & -1.0587 & 0.146105 \tabularnewline
11 & 0.005591 & 0.057 & 0.477319 \tabularnewline
12 & 0.075651 & 0.7715 & 0.221083 \tabularnewline
13 & 0.189425 & 1.9318 & 0.028055 \tabularnewline
14 & -0.153552 & -1.5659 & 0.060201 \tabularnewline
15 & -0.058295 & -0.5945 & 0.276736 \tabularnewline
16 & 0.122024 & 1.2444 & 0.108073 \tabularnewline
17 & 0.071022 & 0.7243 & 0.235259 \tabularnewline
18 & -0.046675 & -0.476 & 0.317537 \tabularnewline
19 & 0.067031 & 0.6836 & 0.247878 \tabularnewline
20 & -0.005757 & -0.0587 & 0.476649 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301067&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]-0.013819[/C][C]-0.1409[/C][C]0.4441[/C][/ROW]
[ROW][C]2[/C][C]0.159149[/C][C]1.623[/C][C]0.053808[/C][/ROW]
[ROW][C]3[/C][C]-0.385359[/C][C]-3.9299[/C][C]7.7e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.194207[/C][C]-1.9805[/C][C]0.025142[/C][/ROW]
[ROW][C]5[/C][C]0.099041[/C][C]1.01[/C][C]0.157413[/C][/ROW]
[ROW][C]6[/C][C]-0.268725[/C][C]-2.7405[/C][C]0.003611[/C][/ROW]
[ROW][C]7[/C][C]-0.119232[/C][C]-1.2159[/C][C]0.113381[/C][/ROW]
[ROW][C]8[/C][C]-0.072446[/C][C]-0.7388[/C][C]0.230845[/C][/ROW]
[ROW][C]9[/C][C]-0.270375[/C][C]-2.7573[/C][C]0.003443[/C][/ROW]
[ROW][C]10[/C][C]-0.10381[/C][C]-1.0587[/C][C]0.146105[/C][/ROW]
[ROW][C]11[/C][C]0.005591[/C][C]0.057[/C][C]0.477319[/C][/ROW]
[ROW][C]12[/C][C]0.075651[/C][C]0.7715[/C][C]0.221083[/C][/ROW]
[ROW][C]13[/C][C]0.189425[/C][C]1.9318[/C][C]0.028055[/C][/ROW]
[ROW][C]14[/C][C]-0.153552[/C][C]-1.5659[/C][C]0.060201[/C][/ROW]
[ROW][C]15[/C][C]-0.058295[/C][C]-0.5945[/C][C]0.276736[/C][/ROW]
[ROW][C]16[/C][C]0.122024[/C][C]1.2444[/C][C]0.108073[/C][/ROW]
[ROW][C]17[/C][C]0.071022[/C][C]0.7243[/C][C]0.235259[/C][/ROW]
[ROW][C]18[/C][C]-0.046675[/C][C]-0.476[/C][C]0.317537[/C][/ROW]
[ROW][C]19[/C][C]0.067031[/C][C]0.6836[/C][C]0.247878[/C][/ROW]
[ROW][C]20[/C][C]-0.005757[/C][C]-0.0587[/C][C]0.476649[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301067&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301067&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	-0.013819	-0.1409	0.4441
2	0.159149	1.623	0.053808
3	-0.385359	-3.9299	7.7e-05
4	-0.194207	-1.9805	0.025142
5	0.099041	1.01	0.157413
6	-0.268725	-2.7405	0.003611
7	-0.119232	-1.2159	0.113381
8	-0.072446	-0.7388	0.230845
9	-0.270375	-2.7573	0.003443
10	-0.10381	-1.0587	0.146105
11	0.005591	0.057	0.477319
12	0.075651	0.7715	0.221083
13	0.189425	1.9318	0.028055
14	-0.153552	-1.5659	0.060201
15	-0.058295	-0.5945	0.276736
16	0.122024	1.2444	0.108073
17	0.071022	0.7243	0.235259
18	-0.046675	-0.476	0.317537
19	0.067031	0.6836	0.247878
20	-0.005757	-0.0587	0.476649

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 3 ; 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 <- '1'
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