Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

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

Tue, 15 Dec 2009 01:28:36 -0700

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/2009/Dec/15/t1260865805ig1wzs6rtzwfwza.htm/, Retrieved Wed, 08 May 2024 23:47:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67762, Retrieved Wed, 08 May 2024 23:47:12 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

152

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

-       [(Partial) Autocorrelation Function] [Autocorrelation (...] [2009-12-15 08:28:36] [91da2e1ebdd83187f2515f461585cbee] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	8 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 8 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67762&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]8 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67762&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67762&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	8 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.798926	9.179	0
2	0.706016	8.1115	0
3	0.755609	8.6813	0
4	0.752684	8.6477	0
5	0.722074	8.296	0
6	0.729751	8.3842	0
7	0.659752	7.58	0
8	0.64884	7.4546	0
9	0.578158	6.6425	0
10	0.508572	5.843	0
11	0.571497	6.566	0
12	0.676476	7.7721	0
13	0.512117	5.8838	0
14	0.424846	4.8811	1e-06
15	0.451568	5.1881	0
16	0.460689	5.2929	0
17	0.439002	5.0437	1e-06
18	0.443809	5.099	1e-06
19	0.393179	4.5173	7e-06
20	0.378653	4.3504	1.3e-05
21	0.31152	3.5791	0.000242

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.798926 & 9.179 & 0 \tabularnewline
2 & 0.706016 & 8.1115 & 0 \tabularnewline
3 & 0.755609 & 8.6813 & 0 \tabularnewline
4 & 0.752684 & 8.6477 & 0 \tabularnewline
5 & 0.722074 & 8.296 & 0 \tabularnewline
6 & 0.729751 & 8.3842 & 0 \tabularnewline
7 & 0.659752 & 7.58 & 0 \tabularnewline
8 & 0.64884 & 7.4546 & 0 \tabularnewline
9 & 0.578158 & 6.6425 & 0 \tabularnewline
10 & 0.508572 & 5.843 & 0 \tabularnewline
11 & 0.571497 & 6.566 & 0 \tabularnewline
12 & 0.676476 & 7.7721 & 0 \tabularnewline
13 & 0.512117 & 5.8838 & 0 \tabularnewline
14 & 0.424846 & 4.8811 & 1e-06 \tabularnewline
15 & 0.451568 & 5.1881 & 0 \tabularnewline
16 & 0.460689 & 5.2929 & 0 \tabularnewline
17 & 0.439002 & 5.0437 & 1e-06 \tabularnewline
18 & 0.443809 & 5.099 & 1e-06 \tabularnewline
19 & 0.393179 & 4.5173 & 7e-06 \tabularnewline
20 & 0.378653 & 4.3504 & 1.3e-05 \tabularnewline
21 & 0.31152 & 3.5791 & 0.000242 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67762&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]0.798926[/C][C]9.179[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.706016[/C][C]8.1115[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.755609[/C][C]8.6813[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.752684[/C][C]8.6477[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.722074[/C][C]8.296[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.729751[/C][C]8.3842[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.659752[/C][C]7.58[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.64884[/C][C]7.4546[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.578158[/C][C]6.6425[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.508572[/C][C]5.843[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.571497[/C][C]6.566[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.676476[/C][C]7.7721[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.512117[/C][C]5.8838[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.424846[/C][C]4.8811[/C][C]1e-06[/C][/ROW]
[ROW][C]15[/C][C]0.451568[/C][C]5.1881[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.460689[/C][C]5.2929[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.439002[/C][C]5.0437[/C][C]1e-06[/C][/ROW]
[ROW][C]18[/C][C]0.443809[/C][C]5.099[/C][C]1e-06[/C][/ROW]
[ROW][C]19[/C][C]0.393179[/C][C]4.5173[/C][C]7e-06[/C][/ROW]
[ROW][C]20[/C][C]0.378653[/C][C]4.3504[/C][C]1.3e-05[/C][/ROW]
[ROW][C]21[/C][C]0.31152[/C][C]3.5791[/C][C]0.000242[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67762&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67762&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	0.798926	9.179	0
2	0.706016	8.1115	0
3	0.755609	8.6813	0
4	0.752684	8.6477	0
5	0.722074	8.296	0
6	0.729751	8.3842	0
7	0.659752	7.58	0
8	0.64884	7.4546	0
9	0.578158	6.6425	0
10	0.508572	5.843	0
11	0.571497	6.566	0
12	0.676476	7.7721	0
13	0.512117	5.8838	0
14	0.424846	4.8811	1e-06
15	0.451568	5.1881	0
16	0.460689	5.2929	0
17	0.439002	5.0437	1e-06
18	0.443809	5.099	1e-06
19	0.393179	4.5173	7e-06
20	0.378653	4.3504	1.3e-05
21	0.31152	3.5791	0.000242

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.798926	9.179	0
2	0.187255	2.1514	0.016633
3	0.422805	4.8577	2e-06
4	0.159453	1.832	0.034605
5	0.133872	1.5381	0.063212
6	0.14799	1.7003	0.045717
7	-0.173556	-1.994	0.024106
8	0.070712	0.8124	0.209008
9	-0.345217	-3.9662	6e-05
10	-0.174622	-2.0062	0.023437
11	0.196514	2.2578	0.012801
12	0.502568	5.7741	0
13	-0.280291	-3.2203	0.000806
14	-0.176881	-2.0322	0.02207
15	-0.142747	-1.64	0.051689
16	0.068148	0.783	0.217528
17	0.044405	0.5102	0.305392
18	0.053045	0.6094	0.271641
19	0.014895	0.1711	0.432192
20	-0.057892	-0.6651	0.253566
21	-0.02064	-0.2371	0.406462

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.798926 & 9.179 & 0 \tabularnewline
2 & 0.187255 & 2.1514 & 0.016633 \tabularnewline
3 & 0.422805 & 4.8577 & 2e-06 \tabularnewline
4 & 0.159453 & 1.832 & 0.034605 \tabularnewline
5 & 0.133872 & 1.5381 & 0.063212 \tabularnewline
6 & 0.14799 & 1.7003 & 0.045717 \tabularnewline
7 & -0.173556 & -1.994 & 0.024106 \tabularnewline
8 & 0.070712 & 0.8124 & 0.209008 \tabularnewline
9 & -0.345217 & -3.9662 & 6e-05 \tabularnewline
10 & -0.174622 & -2.0062 & 0.023437 \tabularnewline
11 & 0.196514 & 2.2578 & 0.012801 \tabularnewline
12 & 0.502568 & 5.7741 & 0 \tabularnewline
13 & -0.280291 & -3.2203 & 0.000806 \tabularnewline
14 & -0.176881 & -2.0322 & 0.02207 \tabularnewline
15 & -0.142747 & -1.64 & 0.051689 \tabularnewline
16 & 0.068148 & 0.783 & 0.217528 \tabularnewline
17 & 0.044405 & 0.5102 & 0.305392 \tabularnewline
18 & 0.053045 & 0.6094 & 0.271641 \tabularnewline
19 & 0.014895 & 0.1711 & 0.432192 \tabularnewline
20 & -0.057892 & -0.6651 & 0.253566 \tabularnewline
21 & -0.02064 & -0.2371 & 0.406462 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67762&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]0.798926[/C][C]9.179[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.187255[/C][C]2.1514[/C][C]0.016633[/C][/ROW]
[ROW][C]3[/C][C]0.422805[/C][C]4.8577[/C][C]2e-06[/C][/ROW]
[ROW][C]4[/C][C]0.159453[/C][C]1.832[/C][C]0.034605[/C][/ROW]
[ROW][C]5[/C][C]0.133872[/C][C]1.5381[/C][C]0.063212[/C][/ROW]
[ROW][C]6[/C][C]0.14799[/C][C]1.7003[/C][C]0.045717[/C][/ROW]
[ROW][C]7[/C][C]-0.173556[/C][C]-1.994[/C][C]0.024106[/C][/ROW]
[ROW][C]8[/C][C]0.070712[/C][C]0.8124[/C][C]0.209008[/C][/ROW]
[ROW][C]9[/C][C]-0.345217[/C][C]-3.9662[/C][C]6e-05[/C][/ROW]
[ROW][C]10[/C][C]-0.174622[/C][C]-2.0062[/C][C]0.023437[/C][/ROW]
[ROW][C]11[/C][C]0.196514[/C][C]2.2578[/C][C]0.012801[/C][/ROW]
[ROW][C]12[/C][C]0.502568[/C][C]5.7741[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.280291[/C][C]-3.2203[/C][C]0.000806[/C][/ROW]
[ROW][C]14[/C][C]-0.176881[/C][C]-2.0322[/C][C]0.02207[/C][/ROW]
[ROW][C]15[/C][C]-0.142747[/C][C]-1.64[/C][C]0.051689[/C][/ROW]
[ROW][C]16[/C][C]0.068148[/C][C]0.783[/C][C]0.217528[/C][/ROW]
[ROW][C]17[/C][C]0.044405[/C][C]0.5102[/C][C]0.305392[/C][/ROW]
[ROW][C]18[/C][C]0.053045[/C][C]0.6094[/C][C]0.271641[/C][/ROW]
[ROW][C]19[/C][C]0.014895[/C][C]0.1711[/C][C]0.432192[/C][/ROW]
[ROW][C]20[/C][C]-0.057892[/C][C]-0.6651[/C][C]0.253566[/C][/ROW]
[ROW][C]21[/C][C]-0.02064[/C][C]-0.2371[/C][C]0.406462[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67762&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67762&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	0.798926	9.179	0
2	0.187255	2.1514	0.016633
3	0.422805	4.8577	2e-06
4	0.159453	1.832	0.034605
5	0.133872	1.5381	0.063212
6	0.14799	1.7003	0.045717
7	-0.173556	-1.994	0.024106
8	0.070712	0.8124	0.209008
9	-0.345217	-3.9662	6e-05
10	-0.174622	-2.0062	0.023437
11	0.196514	2.2578	0.012801
12	0.502568	5.7741	0
13	-0.280291	-3.2203	0.000806
14	-0.176881	-2.0322	0.02207
15	-0.142747	-1.64	0.051689
16	0.068148	0.783	0.217528
17	0.044405	0.5102	0.305392
18	0.053045	0.6094	0.271641
19	0.014895	0.1711	0.432192
20	-0.057892	-0.6651	0.253566
21	-0.02064	-0.2371	0.406462

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code