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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 15:39:04 -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/t1227825609w4u2iybpu0zepch.htm/, Retrieved Sun, 19 May 2024 10:47:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25935, Retrieved Sun, 19 May 2024 10:47:23 +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

142

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 22:39:04] [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	3 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 & 3 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=25935&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]3 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=25935&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25935&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.435572	-3.3457	0.000716
2	-0.283589	-2.1783	0.016696
3	0.419751	3.2242	0.00103
4	-0.243683	-1.8718	0.033099
5	-0.092133	-0.7077	0.240962
6	0.350481	2.6921	0.004613
7	-0.274844	-2.1111	0.019504
8	-0.028387	-0.218	0.414074
9	0.243282	1.8687	0.033317
10	-0.273508	-2.1009	0.019968
11	-0.072404	-0.5561	0.290108
12	0.428344	3.2902	0.000846
13	-0.217706	-1.6722	0.049888
14	-0.088014	-0.676	0.250826
15	0.184301	1.4156	0.081068
16	-0.197139	-1.5143	0.06765
17	0.037235	0.286	0.387937

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.435572 & -3.3457 & 0.000716 \tabularnewline
2 & -0.283589 & -2.1783 & 0.016696 \tabularnewline
3 & 0.419751 & 3.2242 & 0.00103 \tabularnewline
4 & -0.243683 & -1.8718 & 0.033099 \tabularnewline
5 & -0.092133 & -0.7077 & 0.240962 \tabularnewline
6 & 0.350481 & 2.6921 & 0.004613 \tabularnewline
7 & -0.274844 & -2.1111 & 0.019504 \tabularnewline
8 & -0.028387 & -0.218 & 0.414074 \tabularnewline
9 & 0.243282 & 1.8687 & 0.033317 \tabularnewline
10 & -0.273508 & -2.1009 & 0.019968 \tabularnewline
11 & -0.072404 & -0.5561 & 0.290108 \tabularnewline
12 & 0.428344 & 3.2902 & 0.000846 \tabularnewline
13 & -0.217706 & -1.6722 & 0.049888 \tabularnewline
14 & -0.088014 & -0.676 & 0.250826 \tabularnewline
15 & 0.184301 & 1.4156 & 0.081068 \tabularnewline
16 & -0.197139 & -1.5143 & 0.06765 \tabularnewline
17 & 0.037235 & 0.286 & 0.387937 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25935&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]-0.435572[/C][C]-3.3457[/C][C]0.000716[/C][/ROW]
[ROW][C]2[/C][C]-0.283589[/C][C]-2.1783[/C][C]0.016696[/C][/ROW]
[ROW][C]3[/C][C]0.419751[/C][C]3.2242[/C][C]0.00103[/C][/ROW]
[ROW][C]4[/C][C]-0.243683[/C][C]-1.8718[/C][C]0.033099[/C][/ROW]
[ROW][C]5[/C][C]-0.092133[/C][C]-0.7077[/C][C]0.240962[/C][/ROW]
[ROW][C]6[/C][C]0.350481[/C][C]2.6921[/C][C]0.004613[/C][/ROW]
[ROW][C]7[/C][C]-0.274844[/C][C]-2.1111[/C][C]0.019504[/C][/ROW]
[ROW][C]8[/C][C]-0.028387[/C][C]-0.218[/C][C]0.414074[/C][/ROW]
[ROW][C]9[/C][C]0.243282[/C][C]1.8687[/C][C]0.033317[/C][/ROW]
[ROW][C]10[/C][C]-0.273508[/C][C]-2.1009[/C][C]0.019968[/C][/ROW]
[ROW][C]11[/C][C]-0.072404[/C][C]-0.5561[/C][C]0.290108[/C][/ROW]
[ROW][C]12[/C][C]0.428344[/C][C]3.2902[/C][C]0.000846[/C][/ROW]
[ROW][C]13[/C][C]-0.217706[/C][C]-1.6722[/C][C]0.049888[/C][/ROW]
[ROW][C]14[/C][C]-0.088014[/C][C]-0.676[/C][C]0.250826[/C][/ROW]
[ROW][C]15[/C][C]0.184301[/C][C]1.4156[/C][C]0.081068[/C][/ROW]
[ROW][C]16[/C][C]-0.197139[/C][C]-1.5143[/C][C]0.06765[/C][/ROW]
[ROW][C]17[/C][C]0.037235[/C][C]0.286[/C][C]0.387937[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25935&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25935&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	-0.435572	-3.3457	0.000716
2	-0.283589	-2.1783	0.016696
3	0.419751	3.2242	0.00103
4	-0.243683	-1.8718	0.033099
5	-0.092133	-0.7077	0.240962
6	0.350481	2.6921	0.004613
7	-0.274844	-2.1111	0.019504
8	-0.028387	-0.218	0.414074
9	0.243282	1.8687	0.033317
10	-0.273508	-2.1009	0.019968
11	-0.072404	-0.5561	0.290108
12	0.428344	3.2902	0.000846
13	-0.217706	-1.6722	0.049888
14	-0.088014	-0.676	0.250826
15	0.184301	1.4156	0.081068
16	-0.197139	-1.5143	0.06765
17	0.037235	0.286	0.387937

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.435572	-3.3457	0.000716
2	-0.584137	-4.4868	1.7e-05
3	-0.056878	-0.4369	0.331893
4	-0.266254	-2.0451	0.022655
5	-0.257792	-1.9801	0.026179
6	0.035642	0.2738	0.392609
7	-0.10707	-0.8224	0.207075
8	-0.068501	-0.5262	0.300372
9	-0.006134	-0.0471	0.48129
10	-0.170696	-1.3111	0.097445
11	-0.441561	-3.3917	0.000623
12	-0.102315	-0.7859	0.217537
13	0.040105	0.3081	0.379564
14	0.168654	1.2955	0.100105
15	0.129259	0.9929	0.162416
16	0.038088	0.2926	0.385444
17	-0.001625	-0.0125	0.495041

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.435572 & -3.3457 & 0.000716 \tabularnewline
2 & -0.584137 & -4.4868 & 1.7e-05 \tabularnewline
3 & -0.056878 & -0.4369 & 0.331893 \tabularnewline
4 & -0.266254 & -2.0451 & 0.022655 \tabularnewline
5 & -0.257792 & -1.9801 & 0.026179 \tabularnewline
6 & 0.035642 & 0.2738 & 0.392609 \tabularnewline
7 & -0.10707 & -0.8224 & 0.207075 \tabularnewline
8 & -0.068501 & -0.5262 & 0.300372 \tabularnewline
9 & -0.006134 & -0.0471 & 0.48129 \tabularnewline
10 & -0.170696 & -1.3111 & 0.097445 \tabularnewline
11 & -0.441561 & -3.3917 & 0.000623 \tabularnewline
12 & -0.102315 & -0.7859 & 0.217537 \tabularnewline
13 & 0.040105 & 0.3081 & 0.379564 \tabularnewline
14 & 0.168654 & 1.2955 & 0.100105 \tabularnewline
15 & 0.129259 & 0.9929 & 0.162416 \tabularnewline
16 & 0.038088 & 0.2926 & 0.385444 \tabularnewline
17 & -0.001625 & -0.0125 & 0.495041 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25935&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]-0.435572[/C][C]-3.3457[/C][C]0.000716[/C][/ROW]
[ROW][C]2[/C][C]-0.584137[/C][C]-4.4868[/C][C]1.7e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.056878[/C][C]-0.4369[/C][C]0.331893[/C][/ROW]
[ROW][C]4[/C][C]-0.266254[/C][C]-2.0451[/C][C]0.022655[/C][/ROW]
[ROW][C]5[/C][C]-0.257792[/C][C]-1.9801[/C][C]0.026179[/C][/ROW]
[ROW][C]6[/C][C]0.035642[/C][C]0.2738[/C][C]0.392609[/C][/ROW]
[ROW][C]7[/C][C]-0.10707[/C][C]-0.8224[/C][C]0.207075[/C][/ROW]
[ROW][C]8[/C][C]-0.068501[/C][C]-0.5262[/C][C]0.300372[/C][/ROW]
[ROW][C]9[/C][C]-0.006134[/C][C]-0.0471[/C][C]0.48129[/C][/ROW]
[ROW][C]10[/C][C]-0.170696[/C][C]-1.3111[/C][C]0.097445[/C][/ROW]
[ROW][C]11[/C][C]-0.441561[/C][C]-3.3917[/C][C]0.000623[/C][/ROW]
[ROW][C]12[/C][C]-0.102315[/C][C]-0.7859[/C][C]0.217537[/C][/ROW]
[ROW][C]13[/C][C]0.040105[/C][C]0.3081[/C][C]0.379564[/C][/ROW]
[ROW][C]14[/C][C]0.168654[/C][C]1.2955[/C][C]0.100105[/C][/ROW]
[ROW][C]15[/C][C]0.129259[/C][C]0.9929[/C][C]0.162416[/C][/ROW]
[ROW][C]16[/C][C]0.038088[/C][C]0.2926[/C][C]0.385444[/C][/ROW]
[ROW][C]17[/C][C]-0.001625[/C][C]-0.0125[/C][C]0.495041[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25935&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25935&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	-0.435572	-3.3457	0.000716
2	-0.584137	-4.4868	1.7e-05
3	-0.056878	-0.4369	0.331893
4	-0.266254	-2.0451	0.022655
5	-0.257792	-1.9801	0.026179
6	0.035642	0.2738	0.392609
7	-0.10707	-0.8224	0.207075
8	-0.068501	-0.5262	0.300372
9	-0.006134	-0.0471	0.48129
10	-0.170696	-1.3111	0.097445
11	-0.441561	-3.3917	0.000623
12	-0.102315	-0.7859	0.217537
13	0.040105	0.3081	0.379564
14	0.168654	1.2955	0.100105
15	0.129259	0.9929	0.162416
16	0.038088	0.2926	0.385444
17	-0.001625	-0.0125	0.495041

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code