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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, 20 Dec 2009 02:46:37 -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/20/t1261302547dvk4xt4z66hq596.htm/, Retrieved Sat, 27 Apr 2024 06:13:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69803, Retrieved Sat, 27 Apr 2024 06:13:37 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

146

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

-       [(Partial) Autocorrelation Function] [Paper: Differenti...] [2009-12-20 09:46:37] [762da55b2e2304daaed24a7cc507d14d] [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	'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=69803&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=69803&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69803&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	0.955069	15.1913	0
2	0.883093	14.0464	0
3	0.828653	13.1805	0
4	0.799038	12.7095	0
5	0.789353	12.5554	0
6	0.776843	12.3564	0
7	0.750998	11.9454	0
8	0.721179	11.4711	0
9	0.714051	11.3577	0
10	0.732863	11.6569	0
11	0.769456	12.239	0
12	0.779984	12.4064	0
13	0.715247	11.3767	0
14	0.626324	9.9623	0
15	0.554446	8.819	0
16	0.508568	8.0893	0
17	0.483713	7.6939	0
18	0.458034	7.2855	0
19	0.421105	6.6981	0
20	0.381177	6.063	0
21	0.36401	5.7899	0
22	0.371296	5.9058	0
23	0.395691	6.2939	0
24	0.394786	6.2795	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.955069 & 15.1913 & 0 \tabularnewline
2 & 0.883093 & 14.0464 & 0 \tabularnewline
3 & 0.828653 & 13.1805 & 0 \tabularnewline
4 & 0.799038 & 12.7095 & 0 \tabularnewline
5 & 0.789353 & 12.5554 & 0 \tabularnewline
6 & 0.776843 & 12.3564 & 0 \tabularnewline
7 & 0.750998 & 11.9454 & 0 \tabularnewline
8 & 0.721179 & 11.4711 & 0 \tabularnewline
9 & 0.714051 & 11.3577 & 0 \tabularnewline
10 & 0.732863 & 11.6569 & 0 \tabularnewline
11 & 0.769456 & 12.239 & 0 \tabularnewline
12 & 0.779984 & 12.4064 & 0 \tabularnewline
13 & 0.715247 & 11.3767 & 0 \tabularnewline
14 & 0.626324 & 9.9623 & 0 \tabularnewline
15 & 0.554446 & 8.819 & 0 \tabularnewline
16 & 0.508568 & 8.0893 & 0 \tabularnewline
17 & 0.483713 & 7.6939 & 0 \tabularnewline
18 & 0.458034 & 7.2855 & 0 \tabularnewline
19 & 0.421105 & 6.6981 & 0 \tabularnewline
20 & 0.381177 & 6.063 & 0 \tabularnewline
21 & 0.36401 & 5.7899 & 0 \tabularnewline
22 & 0.371296 & 5.9058 & 0 \tabularnewline
23 & 0.395691 & 6.2939 & 0 \tabularnewline
24 & 0.394786 & 6.2795 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69803&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]0.955069[/C][C]15.1913[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.883093[/C][C]14.0464[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.828653[/C][C]13.1805[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.799038[/C][C]12.7095[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.789353[/C][C]12.5554[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.776843[/C][C]12.3564[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.750998[/C][C]11.9454[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.721179[/C][C]11.4711[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.714051[/C][C]11.3577[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.732863[/C][C]11.6569[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.769456[/C][C]12.239[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.779984[/C][C]12.4064[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.715247[/C][C]11.3767[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.626324[/C][C]9.9623[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.554446[/C][C]8.819[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.508568[/C][C]8.0893[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.483713[/C][C]7.6939[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.458034[/C][C]7.2855[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.421105[/C][C]6.6981[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.381177[/C][C]6.063[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.36401[/C][C]5.7899[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.371296[/C][C]5.9058[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.395691[/C][C]6.2939[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]0.394786[/C][C]6.2795[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69803&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69803&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	0.955069	15.1913	0
2	0.883093	14.0464	0
3	0.828653	13.1805	0
4	0.799038	12.7095	0
5	0.789353	12.5554	0
6	0.776843	12.3564	0
7	0.750998	11.9454	0
8	0.721179	11.4711	0
9	0.714051	11.3577	0
10	0.732863	11.6569	0
11	0.769456	12.239	0
12	0.779984	12.4064	0
13	0.715247	11.3767	0
14	0.626324	9.9623	0
15	0.554446	8.819	0
16	0.508568	8.0893	0
17	0.483713	7.6939	0
18	0.458034	7.2855	0
19	0.421105	6.6981	0
20	0.381177	6.063	0
21	0.36401	5.7899	0
22	0.371296	5.9058	0
23	0.395691	6.2939	0
24	0.394786	6.2795	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.955069	15.1913	0
2	-0.33087	-5.2628	0
3	0.283559	4.5103	5e-06
4	0.106652	1.6964	0.04552
5	0.153904	2.448	0.007523
6	-0.088825	-1.4129	0.079464
7	-0.012946	-0.2059	0.418508
8	0.043715	0.6953	0.243744
9	0.284145	4.5196	5e-06
10	0.123037	1.957	0.025722
11	0.243895	3.8794	6.7e-05
12	-0.33436	-5.3183	0
13	-0.73717	-11.7254	0
14	0.046703	0.7429	0.229128
15	-0.029508	-0.4694	0.319608
16	0.052571	0.8362	0.201916
17	0.100073	1.5918	0.056345
18	0.004471	0.0711	0.471678
19	0.08916	1.4182	0.078685
20	0.002571	0.0409	0.483705
21	-0.052491	-0.8349	0.202276
22	-0.099522	-1.583	0.057336
23	-0.008028	-0.1277	0.449247
24	-0.060743	-0.9662	0.167439

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.955069 & 15.1913 & 0 \tabularnewline
2 & -0.33087 & -5.2628 & 0 \tabularnewline
3 & 0.283559 & 4.5103 & 5e-06 \tabularnewline
4 & 0.106652 & 1.6964 & 0.04552 \tabularnewline
5 & 0.153904 & 2.448 & 0.007523 \tabularnewline
6 & -0.088825 & -1.4129 & 0.079464 \tabularnewline
7 & -0.012946 & -0.2059 & 0.418508 \tabularnewline
8 & 0.043715 & 0.6953 & 0.243744 \tabularnewline
9 & 0.284145 & 4.5196 & 5e-06 \tabularnewline
10 & 0.123037 & 1.957 & 0.025722 \tabularnewline
11 & 0.243895 & 3.8794 & 6.7e-05 \tabularnewline
12 & -0.33436 & -5.3183 & 0 \tabularnewline
13 & -0.73717 & -11.7254 & 0 \tabularnewline
14 & 0.046703 & 0.7429 & 0.229128 \tabularnewline
15 & -0.029508 & -0.4694 & 0.319608 \tabularnewline
16 & 0.052571 & 0.8362 & 0.201916 \tabularnewline
17 & 0.100073 & 1.5918 & 0.056345 \tabularnewline
18 & 0.004471 & 0.0711 & 0.471678 \tabularnewline
19 & 0.08916 & 1.4182 & 0.078685 \tabularnewline
20 & 0.002571 & 0.0409 & 0.483705 \tabularnewline
21 & -0.052491 & -0.8349 & 0.202276 \tabularnewline
22 & -0.099522 & -1.583 & 0.057336 \tabularnewline
23 & -0.008028 & -0.1277 & 0.449247 \tabularnewline
24 & -0.060743 & -0.9662 & 0.167439 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69803&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]0.955069[/C][C]15.1913[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.33087[/C][C]-5.2628[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.283559[/C][C]4.5103[/C][C]5e-06[/C][/ROW]
[ROW][C]4[/C][C]0.106652[/C][C]1.6964[/C][C]0.04552[/C][/ROW]
[ROW][C]5[/C][C]0.153904[/C][C]2.448[/C][C]0.007523[/C][/ROW]
[ROW][C]6[/C][C]-0.088825[/C][C]-1.4129[/C][C]0.079464[/C][/ROW]
[ROW][C]7[/C][C]-0.012946[/C][C]-0.2059[/C][C]0.418508[/C][/ROW]
[ROW][C]8[/C][C]0.043715[/C][C]0.6953[/C][C]0.243744[/C][/ROW]
[ROW][C]9[/C][C]0.284145[/C][C]4.5196[/C][C]5e-06[/C][/ROW]
[ROW][C]10[/C][C]0.123037[/C][C]1.957[/C][C]0.025722[/C][/ROW]
[ROW][C]11[/C][C]0.243895[/C][C]3.8794[/C][C]6.7e-05[/C][/ROW]
[ROW][C]12[/C][C]-0.33436[/C][C]-5.3183[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.73717[/C][C]-11.7254[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.046703[/C][C]0.7429[/C][C]0.229128[/C][/ROW]
[ROW][C]15[/C][C]-0.029508[/C][C]-0.4694[/C][C]0.319608[/C][/ROW]
[ROW][C]16[/C][C]0.052571[/C][C]0.8362[/C][C]0.201916[/C][/ROW]
[ROW][C]17[/C][C]0.100073[/C][C]1.5918[/C][C]0.056345[/C][/ROW]
[ROW][C]18[/C][C]0.004471[/C][C]0.0711[/C][C]0.471678[/C][/ROW]
[ROW][C]19[/C][C]0.08916[/C][C]1.4182[/C][C]0.078685[/C][/ROW]
[ROW][C]20[/C][C]0.002571[/C][C]0.0409[/C][C]0.483705[/C][/ROW]
[ROW][C]21[/C][C]-0.052491[/C][C]-0.8349[/C][C]0.202276[/C][/ROW]
[ROW][C]22[/C][C]-0.099522[/C][C]-1.583[/C][C]0.057336[/C][/ROW]
[ROW][C]23[/C][C]-0.008028[/C][C]-0.1277[/C][C]0.449247[/C][/ROW]
[ROW][C]24[/C][C]-0.060743[/C][C]-0.9662[/C][C]0.167439[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69803&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69803&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	0.955069	15.1913	0
2	-0.33087	-5.2628	0
3	0.283559	4.5103	5e-06
4	0.106652	1.6964	0.04552
5	0.153904	2.448	0.007523
6	-0.088825	-1.4129	0.079464
7	-0.012946	-0.2059	0.418508
8	0.043715	0.6953	0.243744
9	0.284145	4.5196	5e-06
10	0.123037	1.957	0.025722
11	0.243895	3.8794	6.7e-05
12	-0.33436	-5.3183	0
13	-0.73717	-11.7254	0
14	0.046703	0.7429	0.229128
15	-0.029508	-0.4694	0.319608
16	0.052571	0.8362	0.201916
17	0.100073	1.5918	0.056345
18	0.004471	0.0711	0.471678
19	0.08916	1.4182	0.078685
20	0.002571	0.0409	0.483705
21	-0.052491	-0.8349	0.202276
22	-0.099522	-1.583	0.057336
23	-0.008028	-0.1277	0.449247
24	-0.060743	-0.9662	0.167439

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