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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, 27 Dec 2009 03:30:59 -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/27/t1261909925vcnxyeehco8legb.htm/, Retrieved Thu, 02 May 2024 19:33:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70818, Retrieved Thu, 02 May 2024 19:33:19 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

182

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

-     [Spectral Analysis] [Spectraalanalyse ...] [2008-12-11 17:29:14] [12d343c4448a5f9e527bb31caeac580b]
- RMPD    [(Partial) Autocorrelation Function] [Paper PACF d=2] [2009-12-27 10:30:59] [eba9f01697e64705b70041e6f338cb22] [Current]
-   PD      [(Partial) Autocorrelation Function] [paper lambda 2] [2010-12-18 13:06:04] [d87a19cd5db53e12ea62bda70b3bb267] 

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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	'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70818&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]1 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=70818&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70818&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.589722	-8.6269	0
2	0.126607	1.8521	0.032694
3	0.080621	1.1794	0.119777
4	-0.118429	-1.7325	0.042316
5	0.072052	1.054	0.146529
6	-0.123196	-1.8022	0.03646
7	0.083872	1.2269	0.110595
8	-0.102328	-1.4969	0.067942
9	0.048071	0.7032	0.24134
10	0.001341	0.0196	0.492181
11	0.009417	0.1378	0.445279
12	0.033994	0.4973	0.309747
13	0.042923	0.6279	0.265365
14	0.008585	0.1256	0.450088
15	-0.08105	-1.1857	0.118537
16	0.093847	1.3729	0.085615
17	-0.073362	-1.0732	0.142197
18	-0.04866	-0.7118	0.238673
19	0.020494	0.2998	0.382312
20	-0.022594	-0.3305	0.370666
21	-0.017094	-0.2501	0.401391
22	0.045923	0.6718	0.251218
23	0.037824	0.5533	0.290311

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.589722 & -8.6269 & 0 \tabularnewline
2 & 0.126607 & 1.8521 & 0.032694 \tabularnewline
3 & 0.080621 & 1.1794 & 0.119777 \tabularnewline
4 & -0.118429 & -1.7325 & 0.042316 \tabularnewline
5 & 0.072052 & 1.054 & 0.146529 \tabularnewline
6 & -0.123196 & -1.8022 & 0.03646 \tabularnewline
7 & 0.083872 & 1.2269 & 0.110595 \tabularnewline
8 & -0.102328 & -1.4969 & 0.067942 \tabularnewline
9 & 0.048071 & 0.7032 & 0.24134 \tabularnewline
10 & 0.001341 & 0.0196 & 0.492181 \tabularnewline
11 & 0.009417 & 0.1378 & 0.445279 \tabularnewline
12 & 0.033994 & 0.4973 & 0.309747 \tabularnewline
13 & 0.042923 & 0.6279 & 0.265365 \tabularnewline
14 & 0.008585 & 0.1256 & 0.450088 \tabularnewline
15 & -0.08105 & -1.1857 & 0.118537 \tabularnewline
16 & 0.093847 & 1.3729 & 0.085615 \tabularnewline
17 & -0.073362 & -1.0732 & 0.142197 \tabularnewline
18 & -0.04866 & -0.7118 & 0.238673 \tabularnewline
19 & 0.020494 & 0.2998 & 0.382312 \tabularnewline
20 & -0.022594 & -0.3305 & 0.370666 \tabularnewline
21 & -0.017094 & -0.2501 & 0.401391 \tabularnewline
22 & 0.045923 & 0.6718 & 0.251218 \tabularnewline
23 & 0.037824 & 0.5533 & 0.290311 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70818&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]-0.589722[/C][C]-8.6269[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.126607[/C][C]1.8521[/C][C]0.032694[/C][/ROW]
[ROW][C]3[/C][C]0.080621[/C][C]1.1794[/C][C]0.119777[/C][/ROW]
[ROW][C]4[/C][C]-0.118429[/C][C]-1.7325[/C][C]0.042316[/C][/ROW]
[ROW][C]5[/C][C]0.072052[/C][C]1.054[/C][C]0.146529[/C][/ROW]
[ROW][C]6[/C][C]-0.123196[/C][C]-1.8022[/C][C]0.03646[/C][/ROW]
[ROW][C]7[/C][C]0.083872[/C][C]1.2269[/C][C]0.110595[/C][/ROW]
[ROW][C]8[/C][C]-0.102328[/C][C]-1.4969[/C][C]0.067942[/C][/ROW]
[ROW][C]9[/C][C]0.048071[/C][C]0.7032[/C][C]0.24134[/C][/ROW]
[ROW][C]10[/C][C]0.001341[/C][C]0.0196[/C][C]0.492181[/C][/ROW]
[ROW][C]11[/C][C]0.009417[/C][C]0.1378[/C][C]0.445279[/C][/ROW]
[ROW][C]12[/C][C]0.033994[/C][C]0.4973[/C][C]0.309747[/C][/ROW]
[ROW][C]13[/C][C]0.042923[/C][C]0.6279[/C][C]0.265365[/C][/ROW]
[ROW][C]14[/C][C]0.008585[/C][C]0.1256[/C][C]0.450088[/C][/ROW]
[ROW][C]15[/C][C]-0.08105[/C][C]-1.1857[/C][C]0.118537[/C][/ROW]
[ROW][C]16[/C][C]0.093847[/C][C]1.3729[/C][C]0.085615[/C][/ROW]
[ROW][C]17[/C][C]-0.073362[/C][C]-1.0732[/C][C]0.142197[/C][/ROW]
[ROW][C]18[/C][C]-0.04866[/C][C]-0.7118[/C][C]0.238673[/C][/ROW]
[ROW][C]19[/C][C]0.020494[/C][C]0.2998[/C][C]0.382312[/C][/ROW]
[ROW][C]20[/C][C]-0.022594[/C][C]-0.3305[/C][C]0.370666[/C][/ROW]
[ROW][C]21[/C][C]-0.017094[/C][C]-0.2501[/C][C]0.401391[/C][/ROW]
[ROW][C]22[/C][C]0.045923[/C][C]0.6718[/C][C]0.251218[/C][/ROW]
[ROW][C]23[/C][C]0.037824[/C][C]0.5533[/C][C]0.290311[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70818&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70818&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	-0.589722	-8.6269	0
2	0.126607	1.8521	0.032694
3	0.080621	1.1794	0.119777
4	-0.118429	-1.7325	0.042316
5	0.072052	1.054	0.146529
6	-0.123196	-1.8022	0.03646
7	0.083872	1.2269	0.110595
8	-0.102328	-1.4969	0.067942
9	0.048071	0.7032	0.24134
10	0.001341	0.0196	0.492181
11	0.009417	0.1378	0.445279
12	0.033994	0.4973	0.309747
13	0.042923	0.6279	0.265365
14	0.008585	0.1256	0.450088
15	-0.08105	-1.1857	0.118537
16	0.093847	1.3729	0.085615
17	-0.073362	-1.0732	0.142197
18	-0.04866	-0.7118	0.238673
19	0.020494	0.2998	0.382312
20	-0.022594	-0.3305	0.370666
21	-0.017094	-0.2501	0.401391
22	0.045923	0.6718	0.251218
23	0.037824	0.5533	0.290311

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.589722	-8.6269	0
2	-0.339093	-4.9605	1e-06
3	-0.033555	-0.4909	0.312012
4	-0.04743	-0.6938	0.244268
5	-0.0192	-0.2809	0.389538
6	-0.187481	-2.7426	0.003306
7	-0.137526	-2.0118	0.022746
8	-0.218199	-3.192	0.000813
9	-0.178915	-2.6173	0.004748
10	-0.147417	-2.1565	0.016079
11	-0.074648	-1.092	0.138028
12	-0.02644	-0.3868	0.349649
13	0.10214	1.4942	0.068301
14	0.162453	2.3765	0.00918
15	0.01765	0.2582	0.398249
16	0.034463	0.5042	0.307337
17	0.030265	0.4427	0.329201
18	-0.057972	-0.8481	0.198676
19	-0.097554	-1.4271	0.077506
20	-0.082376	-1.2051	0.114756
21	-0.112616	-1.6474	0.050469
22	-0.050939	-0.7452	0.228492
23	0.044644	0.6531	0.257202

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.589722 & -8.6269 & 0 \tabularnewline
2 & -0.339093 & -4.9605 & 1e-06 \tabularnewline
3 & -0.033555 & -0.4909 & 0.312012 \tabularnewline
4 & -0.04743 & -0.6938 & 0.244268 \tabularnewline
5 & -0.0192 & -0.2809 & 0.389538 \tabularnewline
6 & -0.187481 & -2.7426 & 0.003306 \tabularnewline
7 & -0.137526 & -2.0118 & 0.022746 \tabularnewline
8 & -0.218199 & -3.192 & 0.000813 \tabularnewline
9 & -0.178915 & -2.6173 & 0.004748 \tabularnewline
10 & -0.147417 & -2.1565 & 0.016079 \tabularnewline
11 & -0.074648 & -1.092 & 0.138028 \tabularnewline
12 & -0.02644 & -0.3868 & 0.349649 \tabularnewline
13 & 0.10214 & 1.4942 & 0.068301 \tabularnewline
14 & 0.162453 & 2.3765 & 0.00918 \tabularnewline
15 & 0.01765 & 0.2582 & 0.398249 \tabularnewline
16 & 0.034463 & 0.5042 & 0.307337 \tabularnewline
17 & 0.030265 & 0.4427 & 0.329201 \tabularnewline
18 & -0.057972 & -0.8481 & 0.198676 \tabularnewline
19 & -0.097554 & -1.4271 & 0.077506 \tabularnewline
20 & -0.082376 & -1.2051 & 0.114756 \tabularnewline
21 & -0.112616 & -1.6474 & 0.050469 \tabularnewline
22 & -0.050939 & -0.7452 & 0.228492 \tabularnewline
23 & 0.044644 & 0.6531 & 0.257202 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70818&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]-0.589722[/C][C]-8.6269[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.339093[/C][C]-4.9605[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]-0.033555[/C][C]-0.4909[/C][C]0.312012[/C][/ROW]
[ROW][C]4[/C][C]-0.04743[/C][C]-0.6938[/C][C]0.244268[/C][/ROW]
[ROW][C]5[/C][C]-0.0192[/C][C]-0.2809[/C][C]0.389538[/C][/ROW]
[ROW][C]6[/C][C]-0.187481[/C][C]-2.7426[/C][C]0.003306[/C][/ROW]
[ROW][C]7[/C][C]-0.137526[/C][C]-2.0118[/C][C]0.022746[/C][/ROW]
[ROW][C]8[/C][C]-0.218199[/C][C]-3.192[/C][C]0.000813[/C][/ROW]
[ROW][C]9[/C][C]-0.178915[/C][C]-2.6173[/C][C]0.004748[/C][/ROW]
[ROW][C]10[/C][C]-0.147417[/C][C]-2.1565[/C][C]0.016079[/C][/ROW]
[ROW][C]11[/C][C]-0.074648[/C][C]-1.092[/C][C]0.138028[/C][/ROW]
[ROW][C]12[/C][C]-0.02644[/C][C]-0.3868[/C][C]0.349649[/C][/ROW]
[ROW][C]13[/C][C]0.10214[/C][C]1.4942[/C][C]0.068301[/C][/ROW]
[ROW][C]14[/C][C]0.162453[/C][C]2.3765[/C][C]0.00918[/C][/ROW]
[ROW][C]15[/C][C]0.01765[/C][C]0.2582[/C][C]0.398249[/C][/ROW]
[ROW][C]16[/C][C]0.034463[/C][C]0.5042[/C][C]0.307337[/C][/ROW]
[ROW][C]17[/C][C]0.030265[/C][C]0.4427[/C][C]0.329201[/C][/ROW]
[ROW][C]18[/C][C]-0.057972[/C][C]-0.8481[/C][C]0.198676[/C][/ROW]
[ROW][C]19[/C][C]-0.097554[/C][C]-1.4271[/C][C]0.077506[/C][/ROW]
[ROW][C]20[/C][C]-0.082376[/C][C]-1.2051[/C][C]0.114756[/C][/ROW]
[ROW][C]21[/C][C]-0.112616[/C][C]-1.6474[/C][C]0.050469[/C][/ROW]
[ROW][C]22[/C][C]-0.050939[/C][C]-0.7452[/C][C]0.228492[/C][/ROW]
[ROW][C]23[/C][C]0.044644[/C][C]0.6531[/C][C]0.257202[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70818&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70818&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	-0.589722	-8.6269	0
2	-0.339093	-4.9605	1e-06
3	-0.033555	-0.4909	0.312012
4	-0.04743	-0.6938	0.244268
5	-0.0192	-0.2809	0.389538
6	-0.187481	-2.7426	0.003306
7	-0.137526	-2.0118	0.022746
8	-0.218199	-3.192	0.000813
9	-0.178915	-2.6173	0.004748
10	-0.147417	-2.1565	0.016079
11	-0.074648	-1.092	0.138028
12	-0.02644	-0.3868	0.349649
13	0.10214	1.4942	0.068301
14	0.162453	2.3765	0.00918
15	0.01765	0.2582	0.398249
16	0.034463	0.5042	0.307337
17	0.030265	0.4427	0.329201
18	-0.057972	-0.8481	0.198676
19	-0.097554	-1.4271	0.077506
20	-0.082376	-1.2051	0.114756
21	-0.112616	-1.6474	0.050469
22	-0.050939	-0.7452	0.228492
23	0.044644	0.6531	0.257202

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = -1.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = -1.0 ; par3 = 2 ; 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