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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 16:30:48 +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/16/t1481902336tf75jcl5mz2nflp.htm/, Retrieved Thu, 02 May 2024 14:07:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300367, Retrieved Thu, 02 May 2024 14:07:32 +0000

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User-defined keywords

Estimated Impact

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

-     [ARIMA Backward Selection] [] [2016-12-16 13:36:55] [683f400e1b95307fc738e729f07c4fce]
-    D  [ARIMA Backward Selection] [] [2016-12-16 14:17:56] [683f400e1b95307fc738e729f07c4fce]
- R  D    [ARIMA Backward Selection] [] [2016-12-16 14:51:40] [683f400e1b95307fc738e729f07c4fce]
- RM D        [(Partial) Autocorrelation Function] [] [2016-12-16 15:30:48] [404ac5ee4f7301873f6a96ef36861981] [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=300367&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=300367&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300367&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	-0.579429	-5.0513	1e-06
2	0.262952	2.2924	0.012327
3	0.000115	0.001	0.499601
4	-0.19714	-1.7186	0.044877
5	0.175157	1.527	0.065459
6	-0.237605	-2.0714	0.020858
7	0.02433	0.2121	0.416295
8	-0.0954	-0.8317	0.204098
9	0.03028	0.264	0.396256
10	-0.000246	-0.0021	0.499148
11	0.164891	1.4375	0.077342
12	-0.073329	-0.6393	0.262285
13	0.123401	1.0758	0.142713
14	0.019365	0.1688	0.433192
15	0.048825	0.4256	0.335786
16	-0.127874	-1.1148	0.134229
17	0.018118	0.1579	0.437458
18	-0.075134	-0.655	0.25722
19	-0.085379	-0.7443	0.229491
20	0.077455	0.6752	0.250788
21	-0.163977	-1.4295	0.078477
22	0.24576	2.1425	0.017678
23	-0.164742	-1.4362	0.077526
24	0.139981	1.2203	0.113057

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.579429 & -5.0513 & 1e-06 \tabularnewline
2 & 0.262952 & 2.2924 & 0.012327 \tabularnewline
3 & 0.000115 & 0.001 & 0.499601 \tabularnewline
4 & -0.19714 & -1.7186 & 0.044877 \tabularnewline
5 & 0.175157 & 1.527 & 0.065459 \tabularnewline
6 & -0.237605 & -2.0714 & 0.020858 \tabularnewline
7 & 0.02433 & 0.2121 & 0.416295 \tabularnewline
8 & -0.0954 & -0.8317 & 0.204098 \tabularnewline
9 & 0.03028 & 0.264 & 0.396256 \tabularnewline
10 & -0.000246 & -0.0021 & 0.499148 \tabularnewline
11 & 0.164891 & 1.4375 & 0.077342 \tabularnewline
12 & -0.073329 & -0.6393 & 0.262285 \tabularnewline
13 & 0.123401 & 1.0758 & 0.142713 \tabularnewline
14 & 0.019365 & 0.1688 & 0.433192 \tabularnewline
15 & 0.048825 & 0.4256 & 0.335786 \tabularnewline
16 & -0.127874 & -1.1148 & 0.134229 \tabularnewline
17 & 0.018118 & 0.1579 & 0.437458 \tabularnewline
18 & -0.075134 & -0.655 & 0.25722 \tabularnewline
19 & -0.085379 & -0.7443 & 0.229491 \tabularnewline
20 & 0.077455 & 0.6752 & 0.250788 \tabularnewline
21 & -0.163977 & -1.4295 & 0.078477 \tabularnewline
22 & 0.24576 & 2.1425 & 0.017678 \tabularnewline
23 & -0.164742 & -1.4362 & 0.077526 \tabularnewline
24 & 0.139981 & 1.2203 & 0.113057 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300367&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]-0.579429[/C][C]-5.0513[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.262952[/C][C]2.2924[/C][C]0.012327[/C][/ROW]
[ROW][C]3[/C][C]0.000115[/C][C]0.001[/C][C]0.499601[/C][/ROW]
[ROW][C]4[/C][C]-0.19714[/C][C]-1.7186[/C][C]0.044877[/C][/ROW]
[ROW][C]5[/C][C]0.175157[/C][C]1.527[/C][C]0.065459[/C][/ROW]
[ROW][C]6[/C][C]-0.237605[/C][C]-2.0714[/C][C]0.020858[/C][/ROW]
[ROW][C]7[/C][C]0.02433[/C][C]0.2121[/C][C]0.416295[/C][/ROW]
[ROW][C]8[/C][C]-0.0954[/C][C]-0.8317[/C][C]0.204098[/C][/ROW]
[ROW][C]9[/C][C]0.03028[/C][C]0.264[/C][C]0.396256[/C][/ROW]
[ROW][C]10[/C][C]-0.000246[/C][C]-0.0021[/C][C]0.499148[/C][/ROW]
[ROW][C]11[/C][C]0.164891[/C][C]1.4375[/C][C]0.077342[/C][/ROW]
[ROW][C]12[/C][C]-0.073329[/C][C]-0.6393[/C][C]0.262285[/C][/ROW]
[ROW][C]13[/C][C]0.123401[/C][C]1.0758[/C][C]0.142713[/C][/ROW]
[ROW][C]14[/C][C]0.019365[/C][C]0.1688[/C][C]0.433192[/C][/ROW]
[ROW][C]15[/C][C]0.048825[/C][C]0.4256[/C][C]0.335786[/C][/ROW]
[ROW][C]16[/C][C]-0.127874[/C][C]-1.1148[/C][C]0.134229[/C][/ROW]
[ROW][C]17[/C][C]0.018118[/C][C]0.1579[/C][C]0.437458[/C][/ROW]
[ROW][C]18[/C][C]-0.075134[/C][C]-0.655[/C][C]0.25722[/C][/ROW]
[ROW][C]19[/C][C]-0.085379[/C][C]-0.7443[/C][C]0.229491[/C][/ROW]
[ROW][C]20[/C][C]0.077455[/C][C]0.6752[/C][C]0.250788[/C][/ROW]
[ROW][C]21[/C][C]-0.163977[/C][C]-1.4295[/C][C]0.078477[/C][/ROW]
[ROW][C]22[/C][C]0.24576[/C][C]2.1425[/C][C]0.017678[/C][/ROW]
[ROW][C]23[/C][C]-0.164742[/C][C]-1.4362[/C][C]0.077526[/C][/ROW]
[ROW][C]24[/C][C]0.139981[/C][C]1.2203[/C][C]0.113057[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300367&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300367&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	-0.579429	-5.0513	1e-06
2	0.262952	2.2924	0.012327
3	0.000115	0.001	0.499601
4	-0.19714	-1.7186	0.044877
5	0.175157	1.527	0.065459
6	-0.237605	-2.0714	0.020858
7	0.02433	0.2121	0.416295
8	-0.0954	-0.8317	0.204098
9	0.03028	0.264	0.396256
10	-0.000246	-0.0021	0.499148
11	0.164891	1.4375	0.077342
12	-0.073329	-0.6393	0.262285
13	0.123401	1.0758	0.142713
14	0.019365	0.1688	0.433192
15	0.048825	0.4256	0.335786
16	-0.127874	-1.1148	0.134229
17	0.018118	0.1579	0.437458
18	-0.075134	-0.655	0.25722
19	-0.085379	-0.7443	0.229491
20	0.077455	0.6752	0.250788
21	-0.163977	-1.4295	0.078477
22	0.24576	2.1425	0.017678
23	-0.164742	-1.4362	0.077526
24	0.139981	1.2203	0.113057

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.579429	-5.0513	1e-06
2	-0.109576	-0.9553	0.171238
3	0.161028	1.4038	0.082224
4	-0.159829	-1.3934	0.083787
5	-0.083009	-0.7237	0.235751
6	-0.19986	-1.7423	0.042747
7	-0.277767	-2.4215	0.00892
8	-0.374068	-3.2611	0.000831
9	-0.270512	-2.3583	0.010466
10	-0.272106	-2.3722	0.010108
11	0.034021	0.2966	0.383794
12	0.004521	0.0394	0.484333
13	-0.007958	-0.0694	0.472437
14	0.005522	0.0481	0.480866
15	0.20685	1.8033	0.037654
16	-0.061248	-0.5339	0.297469
17	-0.079821	-0.6959	0.244318
18	-0.009707	-0.0846	0.466391
19	-0.022925	-0.1999	0.421063
20	0.028745	0.2506	0.401404
21	-0.069532	-0.6062	0.273106
22	0.138678	1.209	0.115211
23	0.037322	0.3254	0.3729
24	-0.124909	-1.0889	0.139813

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.579429 & -5.0513 & 1e-06 \tabularnewline
2 & -0.109576 & -0.9553 & 0.171238 \tabularnewline
3 & 0.161028 & 1.4038 & 0.082224 \tabularnewline
4 & -0.159829 & -1.3934 & 0.083787 \tabularnewline
5 & -0.083009 & -0.7237 & 0.235751 \tabularnewline
6 & -0.19986 & -1.7423 & 0.042747 \tabularnewline
7 & -0.277767 & -2.4215 & 0.00892 \tabularnewline
8 & -0.374068 & -3.2611 & 0.000831 \tabularnewline
9 & -0.270512 & -2.3583 & 0.010466 \tabularnewline
10 & -0.272106 & -2.3722 & 0.010108 \tabularnewline
11 & 0.034021 & 0.2966 & 0.383794 \tabularnewline
12 & 0.004521 & 0.0394 & 0.484333 \tabularnewline
13 & -0.007958 & -0.0694 & 0.472437 \tabularnewline
14 & 0.005522 & 0.0481 & 0.480866 \tabularnewline
15 & 0.20685 & 1.8033 & 0.037654 \tabularnewline
16 & -0.061248 & -0.5339 & 0.297469 \tabularnewline
17 & -0.079821 & -0.6959 & 0.244318 \tabularnewline
18 & -0.009707 & -0.0846 & 0.466391 \tabularnewline
19 & -0.022925 & -0.1999 & 0.421063 \tabularnewline
20 & 0.028745 & 0.2506 & 0.401404 \tabularnewline
21 & -0.069532 & -0.6062 & 0.273106 \tabularnewline
22 & 0.138678 & 1.209 & 0.115211 \tabularnewline
23 & 0.037322 & 0.3254 & 0.3729 \tabularnewline
24 & -0.124909 & -1.0889 & 0.139813 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300367&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]-0.579429[/C][C]-5.0513[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.109576[/C][C]-0.9553[/C][C]0.171238[/C][/ROW]
[ROW][C]3[/C][C]0.161028[/C][C]1.4038[/C][C]0.082224[/C][/ROW]
[ROW][C]4[/C][C]-0.159829[/C][C]-1.3934[/C][C]0.083787[/C][/ROW]
[ROW][C]5[/C][C]-0.083009[/C][C]-0.7237[/C][C]0.235751[/C][/ROW]
[ROW][C]6[/C][C]-0.19986[/C][C]-1.7423[/C][C]0.042747[/C][/ROW]
[ROW][C]7[/C][C]-0.277767[/C][C]-2.4215[/C][C]0.00892[/C][/ROW]
[ROW][C]8[/C][C]-0.374068[/C][C]-3.2611[/C][C]0.000831[/C][/ROW]
[ROW][C]9[/C][C]-0.270512[/C][C]-2.3583[/C][C]0.010466[/C][/ROW]
[ROW][C]10[/C][C]-0.272106[/C][C]-2.3722[/C][C]0.010108[/C][/ROW]
[ROW][C]11[/C][C]0.034021[/C][C]0.2966[/C][C]0.383794[/C][/ROW]
[ROW][C]12[/C][C]0.004521[/C][C]0.0394[/C][C]0.484333[/C][/ROW]
[ROW][C]13[/C][C]-0.007958[/C][C]-0.0694[/C][C]0.472437[/C][/ROW]
[ROW][C]14[/C][C]0.005522[/C][C]0.0481[/C][C]0.480866[/C][/ROW]
[ROW][C]15[/C][C]0.20685[/C][C]1.8033[/C][C]0.037654[/C][/ROW]
[ROW][C]16[/C][C]-0.061248[/C][C]-0.5339[/C][C]0.297469[/C][/ROW]
[ROW][C]17[/C][C]-0.079821[/C][C]-0.6959[/C][C]0.244318[/C][/ROW]
[ROW][C]18[/C][C]-0.009707[/C][C]-0.0846[/C][C]0.466391[/C][/ROW]
[ROW][C]19[/C][C]-0.022925[/C][C]-0.1999[/C][C]0.421063[/C][/ROW]
[ROW][C]20[/C][C]0.028745[/C][C]0.2506[/C][C]0.401404[/C][/ROW]
[ROW][C]21[/C][C]-0.069532[/C][C]-0.6062[/C][C]0.273106[/C][/ROW]
[ROW][C]22[/C][C]0.138678[/C][C]1.209[/C][C]0.115211[/C][/ROW]
[ROW][C]23[/C][C]0.037322[/C][C]0.3254[/C][C]0.3729[/C][/ROW]
[ROW][C]24[/C][C]-0.124909[/C][C]-1.0889[/C][C]0.139813[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300367&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300367&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	-0.579429	-5.0513	1e-06
2	-0.109576	-0.9553	0.171238
3	0.161028	1.4038	0.082224
4	-0.159829	-1.3934	0.083787
5	-0.083009	-0.7237	0.235751
6	-0.19986	-1.7423	0.042747
7	-0.277767	-2.4215	0.00892
8	-0.374068	-3.2611	0.000831
9	-0.270512	-2.3583	0.010466
10	-0.272106	-2.3722	0.010108
11	0.034021	0.2966	0.383794
12	0.004521	0.0394	0.484333
13	-0.007958	-0.0694	0.472437
14	0.005522	0.0481	0.480866
15	0.20685	1.8033	0.037654
16	-0.061248	-0.5339	0.297469
17	-0.079821	-0.6959	0.244318
18	-0.009707	-0.0846	0.466391
19	-0.022925	-0.1999	0.421063
20	0.028745	0.2506	0.401404
21	-0.069532	-0.6062	0.273106
22	0.138678	1.209	0.115211
23	0.037322	0.3254	0.3729
24	-0.124909	-1.0889	0.139813

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 0 ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; 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 <- '1'
par4 <- '0'
par3 <- '2'
par2 <- '1'
par1 <- '48'
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