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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

Thu, 27 Nov 2008 15:41:03 -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/2008/Nov/27/t1227825709b1i07kmpzzj8lgm.htm/, Retrieved Sun, 19 May 2024 09:23:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25937, Retrieved Sun, 19 May 2024 09:23:37 +0000

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Original text written by user:

d=0 D=1

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

168

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

F     [Law of Averages] [Random Walk Simul...] [2008-11-25 18:40:39] [b98453cac15ba1066b407e146608df68]
F       [Law of Averages] [Random Walk Simul...] [2008-11-27 19:45:04] [58bf45a666dc5198906262e8815a9722]
F RMPD    [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-11-27 22:08:29] [58bf45a666dc5198906262e8815a9722]
- RMPD        [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2008-11-27 22:41:03] [63db34dadd44fb018112addcdefe949f] [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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25937&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25937&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25937&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.116992	-0.8105	0.210813
2	-0.029948	-0.2075	0.418253
3	0.362526	2.5117	0.007717
4	0.002755	0.0191	0.492426
5	-0.081067	-0.5616	0.288485
6	0.201814	1.3982	0.084239
7	-0.086268	-0.5977	0.276432
8	0.061918	0.429	0.334927
9	0.176561	1.2233	0.113603
10	-0.09896	-0.6856	0.248126
11	-0.036105	-0.2501	0.401773
12	0.051666	0.358	0.360974
13	-0.183566	-1.2718	0.104788
14	-0.01818	-0.126	0.450147
15	0.129596	0.8979	0.186869
16	-0.168064	-1.1644	0.125012
17	0.030791	0.2133	0.415989

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.116992 & -0.8105 & 0.210813 \tabularnewline
2 & -0.029948 & -0.2075 & 0.418253 \tabularnewline
3 & 0.362526 & 2.5117 & 0.007717 \tabularnewline
4 & 0.002755 & 0.0191 & 0.492426 \tabularnewline
5 & -0.081067 & -0.5616 & 0.288485 \tabularnewline
6 & 0.201814 & 1.3982 & 0.084239 \tabularnewline
7 & -0.086268 & -0.5977 & 0.276432 \tabularnewline
8 & 0.061918 & 0.429 & 0.334927 \tabularnewline
9 & 0.176561 & 1.2233 & 0.113603 \tabularnewline
10 & -0.09896 & -0.6856 & 0.248126 \tabularnewline
11 & -0.036105 & -0.2501 & 0.401773 \tabularnewline
12 & 0.051666 & 0.358 & 0.360974 \tabularnewline
13 & -0.183566 & -1.2718 & 0.104788 \tabularnewline
14 & -0.01818 & -0.126 & 0.450147 \tabularnewline
15 & 0.129596 & 0.8979 & 0.186869 \tabularnewline
16 & -0.168064 & -1.1644 & 0.125012 \tabularnewline
17 & 0.030791 & 0.2133 & 0.415989 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25937&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]-0.116992[/C][C]-0.8105[/C][C]0.210813[/C][/ROW]
[ROW][C]2[/C][C]-0.029948[/C][C]-0.2075[/C][C]0.418253[/C][/ROW]
[ROW][C]3[/C][C]0.362526[/C][C]2.5117[/C][C]0.007717[/C][/ROW]
[ROW][C]4[/C][C]0.002755[/C][C]0.0191[/C][C]0.492426[/C][/ROW]
[ROW][C]5[/C][C]-0.081067[/C][C]-0.5616[/C][C]0.288485[/C][/ROW]
[ROW][C]6[/C][C]0.201814[/C][C]1.3982[/C][C]0.084239[/C][/ROW]
[ROW][C]7[/C][C]-0.086268[/C][C]-0.5977[/C][C]0.276432[/C][/ROW]
[ROW][C]8[/C][C]0.061918[/C][C]0.429[/C][C]0.334927[/C][/ROW]
[ROW][C]9[/C][C]0.176561[/C][C]1.2233[/C][C]0.113603[/C][/ROW]
[ROW][C]10[/C][C]-0.09896[/C][C]-0.6856[/C][C]0.248126[/C][/ROW]
[ROW][C]11[/C][C]-0.036105[/C][C]-0.2501[/C][C]0.401773[/C][/ROW]
[ROW][C]12[/C][C]0.051666[/C][C]0.358[/C][C]0.360974[/C][/ROW]
[ROW][C]13[/C][C]-0.183566[/C][C]-1.2718[/C][C]0.104788[/C][/ROW]
[ROW][C]14[/C][C]-0.01818[/C][C]-0.126[/C][C]0.450147[/C][/ROW]
[ROW][C]15[/C][C]0.129596[/C][C]0.8979[/C][C]0.186869[/C][/ROW]
[ROW][C]16[/C][C]-0.168064[/C][C]-1.1644[/C][C]0.125012[/C][/ROW]
[ROW][C]17[/C][C]0.030791[/C][C]0.2133[/C][C]0.415989[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25937&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25937&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	-0.116992	-0.8105	0.210813
2	-0.029948	-0.2075	0.418253
3	0.362526	2.5117	0.007717
4	0.002755	0.0191	0.492426
5	-0.081067	-0.5616	0.288485
6	0.201814	1.3982	0.084239
7	-0.086268	-0.5977	0.276432
8	0.061918	0.429	0.334927
9	0.176561	1.2233	0.113603
10	-0.09896	-0.6856	0.248126
11	-0.036105	-0.2501	0.401773
12	0.051666	0.358	0.360974
13	-0.183566	-1.2718	0.104788
14	-0.01818	-0.126	0.450147
15	0.129596	0.8979	0.186869
16	-0.168064	-1.1644	0.125012
17	0.030791	0.2133	0.415989

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.116992	-0.8105	0.210813
2	-0.044241	-0.3065	0.380271
3	0.359303	2.4893	0.008159
4	0.097173	0.6732	0.252013
5	-0.068448	-0.4742	0.318746
6	0.060882	0.4218	0.337526
7	-0.101146	-0.7008	0.243417
8	0.105215	0.729	0.234786
9	0.137377	0.9518	0.17299
10	-0.035107	-0.2432	0.404433
11	-0.105055	-0.7278	0.235123
12	-0.120999	-0.8383	0.203008
13	-0.161579	-1.1195	0.134259
14	-0.004294	-0.0297	0.488195
15	0.178445	1.2363	0.111181
16	-0.003679	-0.0255	0.489886
17	0.00089	0.0062	0.497552

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.116992 & -0.8105 & 0.210813 \tabularnewline
2 & -0.044241 & -0.3065 & 0.380271 \tabularnewline
3 & 0.359303 & 2.4893 & 0.008159 \tabularnewline
4 & 0.097173 & 0.6732 & 0.252013 \tabularnewline
5 & -0.068448 & -0.4742 & 0.318746 \tabularnewline
6 & 0.060882 & 0.4218 & 0.337526 \tabularnewline
7 & -0.101146 & -0.7008 & 0.243417 \tabularnewline
8 & 0.105215 & 0.729 & 0.234786 \tabularnewline
9 & 0.137377 & 0.9518 & 0.17299 \tabularnewline
10 & -0.035107 & -0.2432 & 0.404433 \tabularnewline
11 & -0.105055 & -0.7278 & 0.235123 \tabularnewline
12 & -0.120999 & -0.8383 & 0.203008 \tabularnewline
13 & -0.161579 & -1.1195 & 0.134259 \tabularnewline
14 & -0.004294 & -0.0297 & 0.488195 \tabularnewline
15 & 0.178445 & 1.2363 & 0.111181 \tabularnewline
16 & -0.003679 & -0.0255 & 0.489886 \tabularnewline
17 & 0.00089 & 0.0062 & 0.497552 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25937&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]-0.116992[/C][C]-0.8105[/C][C]0.210813[/C][/ROW]
[ROW][C]2[/C][C]-0.044241[/C][C]-0.3065[/C][C]0.380271[/C][/ROW]
[ROW][C]3[/C][C]0.359303[/C][C]2.4893[/C][C]0.008159[/C][/ROW]
[ROW][C]4[/C][C]0.097173[/C][C]0.6732[/C][C]0.252013[/C][/ROW]
[ROW][C]5[/C][C]-0.068448[/C][C]-0.4742[/C][C]0.318746[/C][/ROW]
[ROW][C]6[/C][C]0.060882[/C][C]0.4218[/C][C]0.337526[/C][/ROW]
[ROW][C]7[/C][C]-0.101146[/C][C]-0.7008[/C][C]0.243417[/C][/ROW]
[ROW][C]8[/C][C]0.105215[/C][C]0.729[/C][C]0.234786[/C][/ROW]
[ROW][C]9[/C][C]0.137377[/C][C]0.9518[/C][C]0.17299[/C][/ROW]
[ROW][C]10[/C][C]-0.035107[/C][C]-0.2432[/C][C]0.404433[/C][/ROW]
[ROW][C]11[/C][C]-0.105055[/C][C]-0.7278[/C][C]0.235123[/C][/ROW]
[ROW][C]12[/C][C]-0.120999[/C][C]-0.8383[/C][C]0.203008[/C][/ROW]
[ROW][C]13[/C][C]-0.161579[/C][C]-1.1195[/C][C]0.134259[/C][/ROW]
[ROW][C]14[/C][C]-0.004294[/C][C]-0.0297[/C][C]0.488195[/C][/ROW]
[ROW][C]15[/C][C]0.178445[/C][C]1.2363[/C][C]0.111181[/C][/ROW]
[ROW][C]16[/C][C]-0.003679[/C][C]-0.0255[/C][C]0.489886[/C][/ROW]
[ROW][C]17[/C][C]0.00089[/C][C]0.0062[/C][C]0.497552[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25937&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25937&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	-0.116992	-0.8105	0.210813
2	-0.044241	-0.3065	0.380271
3	0.359303	2.4893	0.008159
4	0.097173	0.6732	0.252013
5	-0.068448	-0.4742	0.318746
6	0.060882	0.4218	0.337526
7	-0.101146	-0.7008	0.243417
8	0.105215	0.729	0.234786
9	0.137377	0.9518	0.17299
10	-0.035107	-0.2432	0.404433
11	-0.105055	-0.7278	0.235123
12	-0.120999	-0.8383	0.203008
13	-0.161579	-1.1195	0.134259
14	-0.004294	-0.0297	0.488195
15	0.178445	1.2363	0.111181
16	-0.003679	-0.0255	0.489886
17	0.00089	0.0062	0.497552

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 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code