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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 15 Dec 2012 08:46:58 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/15/t13555793015jmjjfi9uz7opuo.htm/, Retrieved Tue, 30 Apr 2024 18:56:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=199920, Retrieved Tue, 30 Apr 2024 18:56:18 +0000

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157

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [(Partial) Autocorrelation Function] [Births] [2010-11-29 09:36:27] [b98453cac15ba1066b407e146608df68]
- R PD          [(Partial) Autocorrelation Function] [WS9 3.1 ACF d=0, D=0] [2010-12-07 10:00:49] [afe9379cca749d06b3d6872e02cc47ed]
-   PD            [(Partial) Autocorrelation Function] [Apple Inc - ACF d...] [2010-12-14 15:49:43] [afe9379cca749d06b3d6872e02cc47ed]
- R PD                [(Partial) Autocorrelation Function] [] [2012-12-15 13:46:58] [14d0a7ecb926325afa0eb6a607fbc7a0] [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	'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199920&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199920&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199920&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.127778	-1.0061	0.159133
2	0.164288	1.2936	0.100301
3	-0.100572	-0.7919	0.215717
4	-0.175298	-1.3803	0.086226
5	0.020636	0.1625	0.435725
6	0.030147	0.2374	0.406573
7	0.157521	1.2403	0.109765
8	-0.136361	-1.0737	0.143558
9	0.171131	1.3475	0.091363
10	-0.233673	-1.8399	0.035282
11	0.06548	0.5156	0.303986
12	-0.161433	-1.2711	0.104217
13	0.111102	0.8748	0.192524
14	-0.072394	-0.57	0.285358
15	0.052793	0.4157	0.339534
16	0.001123	0.0088	0.496487
17	-0.075518	-0.5946	0.277127

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.127778 & -1.0061 & 0.159133 \tabularnewline
2 & 0.164288 & 1.2936 & 0.100301 \tabularnewline
3 & -0.100572 & -0.7919 & 0.215717 \tabularnewline
4 & -0.175298 & -1.3803 & 0.086226 \tabularnewline
5 & 0.020636 & 0.1625 & 0.435725 \tabularnewline
6 & 0.030147 & 0.2374 & 0.406573 \tabularnewline
7 & 0.157521 & 1.2403 & 0.109765 \tabularnewline
8 & -0.136361 & -1.0737 & 0.143558 \tabularnewline
9 & 0.171131 & 1.3475 & 0.091363 \tabularnewline
10 & -0.233673 & -1.8399 & 0.035282 \tabularnewline
11 & 0.06548 & 0.5156 & 0.303986 \tabularnewline
12 & -0.161433 & -1.2711 & 0.104217 \tabularnewline
13 & 0.111102 & 0.8748 & 0.192524 \tabularnewline
14 & -0.072394 & -0.57 & 0.285358 \tabularnewline
15 & 0.052793 & 0.4157 & 0.339534 \tabularnewline
16 & 0.001123 & 0.0088 & 0.496487 \tabularnewline
17 & -0.075518 & -0.5946 & 0.277127 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199920&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]-0.127778[/C][C]-1.0061[/C][C]0.159133[/C][/ROW]
[ROW][C]2[/C][C]0.164288[/C][C]1.2936[/C][C]0.100301[/C][/ROW]
[ROW][C]3[/C][C]-0.100572[/C][C]-0.7919[/C][C]0.215717[/C][/ROW]
[ROW][C]4[/C][C]-0.175298[/C][C]-1.3803[/C][C]0.086226[/C][/ROW]
[ROW][C]5[/C][C]0.020636[/C][C]0.1625[/C][C]0.435725[/C][/ROW]
[ROW][C]6[/C][C]0.030147[/C][C]0.2374[/C][C]0.406573[/C][/ROW]
[ROW][C]7[/C][C]0.157521[/C][C]1.2403[/C][C]0.109765[/C][/ROW]
[ROW][C]8[/C][C]-0.136361[/C][C]-1.0737[/C][C]0.143558[/C][/ROW]
[ROW][C]9[/C][C]0.171131[/C][C]1.3475[/C][C]0.091363[/C][/ROW]
[ROW][C]10[/C][C]-0.233673[/C][C]-1.8399[/C][C]0.035282[/C][/ROW]
[ROW][C]11[/C][C]0.06548[/C][C]0.5156[/C][C]0.303986[/C][/ROW]
[ROW][C]12[/C][C]-0.161433[/C][C]-1.2711[/C][C]0.104217[/C][/ROW]
[ROW][C]13[/C][C]0.111102[/C][C]0.8748[/C][C]0.192524[/C][/ROW]
[ROW][C]14[/C][C]-0.072394[/C][C]-0.57[/C][C]0.285358[/C][/ROW]
[ROW][C]15[/C][C]0.052793[/C][C]0.4157[/C][C]0.339534[/C][/ROW]
[ROW][C]16[/C][C]0.001123[/C][C]0.0088[/C][C]0.496487[/C][/ROW]
[ROW][C]17[/C][C]-0.075518[/C][C]-0.5946[/C][C]0.277127[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199920&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199920&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	-0.127778	-1.0061	0.159133
2	0.164288	1.2936	0.100301
3	-0.100572	-0.7919	0.215717
4	-0.175298	-1.3803	0.086226
5	0.020636	0.1625	0.435725
6	0.030147	0.2374	0.406573
7	0.157521	1.2403	0.109765
8	-0.136361	-1.0737	0.143558
9	0.171131	1.3475	0.091363
10	-0.233673	-1.8399	0.035282
11	0.06548	0.5156	0.303986
12	-0.161433	-1.2711	0.104217
13	0.111102	0.8748	0.192524
14	-0.072394	-0.57	0.285358
15	0.052793	0.4157	0.339534
16	0.001123	0.0088	0.496487
17	-0.075518	-0.5946	0.277127

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.127778	-1.0061	0.159133
2	0.150416	1.1844	0.120392
3	-0.066067	-0.5202	0.302385
4	-0.226898	-1.7866	0.039446
5	0.004332	0.0341	0.486449
6	0.101466	0.7989	0.213685
7	0.143092	1.1267	0.132104
8	-0.18678	-1.4707	0.073214
9	0.115841	0.9121	0.182616
10	-0.110695	-0.8716	0.193392
11	0.019484	0.1534	0.439284
12	-0.173452	-1.3658	0.088474
13	0.121025	0.9529	0.172158
14	-0.098606	-0.7764	0.220226
15	0.042064	0.3312	0.3708
16	-0.080702	-0.6355	0.263737
17	0.057022	0.449	0.327502

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.127778 & -1.0061 & 0.159133 \tabularnewline
2 & 0.150416 & 1.1844 & 0.120392 \tabularnewline
3 & -0.066067 & -0.5202 & 0.302385 \tabularnewline
4 & -0.226898 & -1.7866 & 0.039446 \tabularnewline
5 & 0.004332 & 0.0341 & 0.486449 \tabularnewline
6 & 0.101466 & 0.7989 & 0.213685 \tabularnewline
7 & 0.143092 & 1.1267 & 0.132104 \tabularnewline
8 & -0.18678 & -1.4707 & 0.073214 \tabularnewline
9 & 0.115841 & 0.9121 & 0.182616 \tabularnewline
10 & -0.110695 & -0.8716 & 0.193392 \tabularnewline
11 & 0.019484 & 0.1534 & 0.439284 \tabularnewline
12 & -0.173452 & -1.3658 & 0.088474 \tabularnewline
13 & 0.121025 & 0.9529 & 0.172158 \tabularnewline
14 & -0.098606 & -0.7764 & 0.220226 \tabularnewline
15 & 0.042064 & 0.3312 & 0.3708 \tabularnewline
16 & -0.080702 & -0.6355 & 0.263737 \tabularnewline
17 & 0.057022 & 0.449 & 0.327502 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199920&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]-0.127778[/C][C]-1.0061[/C][C]0.159133[/C][/ROW]
[ROW][C]2[/C][C]0.150416[/C][C]1.1844[/C][C]0.120392[/C][/ROW]
[ROW][C]3[/C][C]-0.066067[/C][C]-0.5202[/C][C]0.302385[/C][/ROW]
[ROW][C]4[/C][C]-0.226898[/C][C]-1.7866[/C][C]0.039446[/C][/ROW]
[ROW][C]5[/C][C]0.004332[/C][C]0.0341[/C][C]0.486449[/C][/ROW]
[ROW][C]6[/C][C]0.101466[/C][C]0.7989[/C][C]0.213685[/C][/ROW]
[ROW][C]7[/C][C]0.143092[/C][C]1.1267[/C][C]0.132104[/C][/ROW]
[ROW][C]8[/C][C]-0.18678[/C][C]-1.4707[/C][C]0.073214[/C][/ROW]
[ROW][C]9[/C][C]0.115841[/C][C]0.9121[/C][C]0.182616[/C][/ROW]
[ROW][C]10[/C][C]-0.110695[/C][C]-0.8716[/C][C]0.193392[/C][/ROW]
[ROW][C]11[/C][C]0.019484[/C][C]0.1534[/C][C]0.439284[/C][/ROW]
[ROW][C]12[/C][C]-0.173452[/C][C]-1.3658[/C][C]0.088474[/C][/ROW]
[ROW][C]13[/C][C]0.121025[/C][C]0.9529[/C][C]0.172158[/C][/ROW]
[ROW][C]14[/C][C]-0.098606[/C][C]-0.7764[/C][C]0.220226[/C][/ROW]
[ROW][C]15[/C][C]0.042064[/C][C]0.3312[/C][C]0.3708[/C][/ROW]
[ROW][C]16[/C][C]-0.080702[/C][C]-0.6355[/C][C]0.263737[/C][/ROW]
[ROW][C]17[/C][C]0.057022[/C][C]0.449[/C][C]0.327502[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199920&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199920&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	-0.127778	-1.0061	0.159133
2	0.150416	1.1844	0.120392
3	-0.066067	-0.5202	0.302385
4	-0.226898	-1.7866	0.039446
5	0.004332	0.0341	0.486449
6	0.101466	0.7989	0.213685
7	0.143092	1.1267	0.132104
8	-0.18678	-1.4707	0.073214
9	0.115841	0.9121	0.182616
10	-0.110695	-0.8716	0.193392
11	0.019484	0.1534	0.439284
12	-0.173452	-1.3658	0.088474
13	0.121025	0.9529	0.172158
14	-0.098606	-0.7764	0.220226
15	0.042064	0.3312	0.3708
16	-0.080702	-0.6355	0.263737
17	0.057022	0.449	0.327502

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 3 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 3 ; 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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),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,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code