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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 15:29:15 -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/t12278250174e80dm16u3x7zzo.htm/, Retrieved Sun, 19 May 2024 10:19:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25931, Retrieved Sun, 19 May 2024 10:19:14 +0000

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Original text written by user:

d=1 D=0

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

159

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]
- RMP         [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2008-11-27 22:29:15] [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	4 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25931&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25931&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25931&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	4 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.383753	-2.9477	0.00229
2	-0.306943	-2.3577	0.010863
3	0.195122	1.4988	0.069634
4	0.011851	0.091	0.463888
5	-0.12223	-0.9389	0.175814
6	0.274409	2.1078	0.019654
7	-0.255243	-1.9606	0.027329
8	0.112908	0.8673	0.194655
9	0.123688	0.9501	0.172978
10	-0.28629	-2.199	0.015904
11	-0.129866	-0.9975	0.161293
12	0.558295	4.2883	3.4e-05
13	-0.219713	-1.6876	0.04838
14	-0.146847	-1.128	0.131952
15	0.052557	0.4037	0.343949
16	0.007227	0.0555	0.47796
17	-0.032591	-0.2503	0.401598

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.383753 & -2.9477 & 0.00229 \tabularnewline
2 & -0.306943 & -2.3577 & 0.010863 \tabularnewline
3 & 0.195122 & 1.4988 & 0.069634 \tabularnewline
4 & 0.011851 & 0.091 & 0.463888 \tabularnewline
5 & -0.12223 & -0.9389 & 0.175814 \tabularnewline
6 & 0.274409 & 2.1078 & 0.019654 \tabularnewline
7 & -0.255243 & -1.9606 & 0.027329 \tabularnewline
8 & 0.112908 & 0.8673 & 0.194655 \tabularnewline
9 & 0.123688 & 0.9501 & 0.172978 \tabularnewline
10 & -0.28629 & -2.199 & 0.015904 \tabularnewline
11 & -0.129866 & -0.9975 & 0.161293 \tabularnewline
12 & 0.558295 & 4.2883 & 3.4e-05 \tabularnewline
13 & -0.219713 & -1.6876 & 0.04838 \tabularnewline
14 & -0.146847 & -1.128 & 0.131952 \tabularnewline
15 & 0.052557 & 0.4037 & 0.343949 \tabularnewline
16 & 0.007227 & 0.0555 & 0.47796 \tabularnewline
17 & -0.032591 & -0.2503 & 0.401598 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25931&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]-0.383753[/C][C]-2.9477[/C][C]0.00229[/C][/ROW]
[ROW][C]2[/C][C]-0.306943[/C][C]-2.3577[/C][C]0.010863[/C][/ROW]
[ROW][C]3[/C][C]0.195122[/C][C]1.4988[/C][C]0.069634[/C][/ROW]
[ROW][C]4[/C][C]0.011851[/C][C]0.091[/C][C]0.463888[/C][/ROW]
[ROW][C]5[/C][C]-0.12223[/C][C]-0.9389[/C][C]0.175814[/C][/ROW]
[ROW][C]6[/C][C]0.274409[/C][C]2.1078[/C][C]0.019654[/C][/ROW]
[ROW][C]7[/C][C]-0.255243[/C][C]-1.9606[/C][C]0.027329[/C][/ROW]
[ROW][C]8[/C][C]0.112908[/C][C]0.8673[/C][C]0.194655[/C][/ROW]
[ROW][C]9[/C][C]0.123688[/C][C]0.9501[/C][C]0.172978[/C][/ROW]
[ROW][C]10[/C][C]-0.28629[/C][C]-2.199[/C][C]0.015904[/C][/ROW]
[ROW][C]11[/C][C]-0.129866[/C][C]-0.9975[/C][C]0.161293[/C][/ROW]
[ROW][C]12[/C][C]0.558295[/C][C]4.2883[/C][C]3.4e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.219713[/C][C]-1.6876[/C][C]0.04838[/C][/ROW]
[ROW][C]14[/C][C]-0.146847[/C][C]-1.128[/C][C]0.131952[/C][/ROW]
[ROW][C]15[/C][C]0.052557[/C][C]0.4037[/C][C]0.343949[/C][/ROW]
[ROW][C]16[/C][C]0.007227[/C][C]0.0555[/C][C]0.47796[/C][/ROW]
[ROW][C]17[/C][C]-0.032591[/C][C]-0.2503[/C][C]0.401598[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25931&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25931&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	-0.383753	-2.9477	0.00229
2	-0.306943	-2.3577	0.010863
3	0.195122	1.4988	0.069634
4	0.011851	0.091	0.463888
5	-0.12223	-0.9389	0.175814
6	0.274409	2.1078	0.019654
7	-0.255243	-1.9606	0.027329
8	0.112908	0.8673	0.194655
9	0.123688	0.9501	0.172978
10	-0.28629	-2.199	0.015904
11	-0.129866	-0.9975	0.161293
12	0.558295	4.2883	3.4e-05
13	-0.219713	-1.6876	0.04838
14	-0.146847	-1.128	0.131952
15	0.052557	0.4037	0.343949
16	0.007227	0.0555	0.47796
17	-0.032591	-0.2503	0.401598

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.383753	-2.9477	0.00229
2	-0.532651	-4.0914	6.6e-05
3	-0.310767	-2.387	0.010104
4	-0.326093	-2.5048	0.007518
5	-0.452098	-3.4726	0.000486
6	-0.086271	-0.6627	0.255065
7	-0.385609	-2.9619	0.0022
8	-0.031998	-0.2458	0.403352
9	0.233411	1.7929	0.039061
10	0.105857	0.8131	0.209714
11	-0.414097	-3.1807	0.001171
12	-0.138175	-1.0613	0.146429
13	-0.122809	-0.9433	0.174684
14	0.034419	0.2644	0.396205
15	0.04237	0.3254	0.372997
16	0.158413	1.2168	0.114264
17	0.124217	0.9541	0.171957

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.383753 & -2.9477 & 0.00229 \tabularnewline
2 & -0.532651 & -4.0914 & 6.6e-05 \tabularnewline
3 & -0.310767 & -2.387 & 0.010104 \tabularnewline
4 & -0.326093 & -2.5048 & 0.007518 \tabularnewline
5 & -0.452098 & -3.4726 & 0.000486 \tabularnewline
6 & -0.086271 & -0.6627 & 0.255065 \tabularnewline
7 & -0.385609 & -2.9619 & 0.0022 \tabularnewline
8 & -0.031998 & -0.2458 & 0.403352 \tabularnewline
9 & 0.233411 & 1.7929 & 0.039061 \tabularnewline
10 & 0.105857 & 0.8131 & 0.209714 \tabularnewline
11 & -0.414097 & -3.1807 & 0.001171 \tabularnewline
12 & -0.138175 & -1.0613 & 0.146429 \tabularnewline
13 & -0.122809 & -0.9433 & 0.174684 \tabularnewline
14 & 0.034419 & 0.2644 & 0.396205 \tabularnewline
15 & 0.04237 & 0.3254 & 0.372997 \tabularnewline
16 & 0.158413 & 1.2168 & 0.114264 \tabularnewline
17 & 0.124217 & 0.9541 & 0.171957 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25931&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]-0.383753[/C][C]-2.9477[/C][C]0.00229[/C][/ROW]
[ROW][C]2[/C][C]-0.532651[/C][C]-4.0914[/C][C]6.6e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.310767[/C][C]-2.387[/C][C]0.010104[/C][/ROW]
[ROW][C]4[/C][C]-0.326093[/C][C]-2.5048[/C][C]0.007518[/C][/ROW]
[ROW][C]5[/C][C]-0.452098[/C][C]-3.4726[/C][C]0.000486[/C][/ROW]
[ROW][C]6[/C][C]-0.086271[/C][C]-0.6627[/C][C]0.255065[/C][/ROW]
[ROW][C]7[/C][C]-0.385609[/C][C]-2.9619[/C][C]0.0022[/C][/ROW]
[ROW][C]8[/C][C]-0.031998[/C][C]-0.2458[/C][C]0.403352[/C][/ROW]
[ROW][C]9[/C][C]0.233411[/C][C]1.7929[/C][C]0.039061[/C][/ROW]
[ROW][C]10[/C][C]0.105857[/C][C]0.8131[/C][C]0.209714[/C][/ROW]
[ROW][C]11[/C][C]-0.414097[/C][C]-3.1807[/C][C]0.001171[/C][/ROW]
[ROW][C]12[/C][C]-0.138175[/C][C]-1.0613[/C][C]0.146429[/C][/ROW]
[ROW][C]13[/C][C]-0.122809[/C][C]-0.9433[/C][C]0.174684[/C][/ROW]
[ROW][C]14[/C][C]0.034419[/C][C]0.2644[/C][C]0.396205[/C][/ROW]
[ROW][C]15[/C][C]0.04237[/C][C]0.3254[/C][C]0.372997[/C][/ROW]
[ROW][C]16[/C][C]0.158413[/C][C]1.2168[/C][C]0.114264[/C][/ROW]
[ROW][C]17[/C][C]0.124217[/C][C]0.9541[/C][C]0.171957[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25931&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25931&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	-0.383753	-2.9477	0.00229
2	-0.532651	-4.0914	6.6e-05
3	-0.310767	-2.387	0.010104
4	-0.326093	-2.5048	0.007518
5	-0.452098	-3.4726	0.000486
6	-0.086271	-0.6627	0.255065
7	-0.385609	-2.9619	0.0022
8	-0.031998	-0.2458	0.403352
9	0.233411	1.7929	0.039061
10	0.105857	0.8131	0.209714
11	-0.414097	-3.1807	0.001171
12	-0.138175	-1.0613	0.146429
13	-0.122809	-0.9433	0.174684
14	0.034419	0.2644	0.396205
15	0.04237	0.3254	0.372997
16	0.158413	1.2168	0.114264
17	0.124217	0.9541	0.171957

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 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; 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')

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Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code