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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 04 Dec 2009 07:44:24 -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/04/t1259937893lftvqygh7pxuctn.htm/, Retrieved Sun, 28 Apr 2024 09:42:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63651, Retrieved Sun, 28 Apr 2024 09:42:25 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Lambda=-2 d=1

Estimated Impact

103

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

-     [Notched Boxplots] [3/11/2009] [2009-11-02 21:10:41] [b98453cac15ba1066b407e146608df68]
- RMPD  [Multiple Regression] [Paper:Bryan Beute...] [2009-12-04 12:54:13] [408e92805dcb18620260f240a7fb9d53]
- RMPD    [(Partial) Autocorrelation Function] [] [2009-12-04 14:39:07] [408e92805dcb18620260f240a7fb9d53]
-             [(Partial) Autocorrelation Function] [Paper:Bryan Beute...] [2009-12-04 14:44:24] [b32ceebc68d054278e6bda97f3d57f91] [Current]
-   PD          [(Partial) Autocorrelation Function] [CVM Paper: ACF (W...] [2009-12-17 13:43:25] [03d5b865e91ca35b5a5d21b8d6da5aba] 

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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	'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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63651&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63651&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63651&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.380223	-2.4047	0.010452
2	0.139091	0.8797	0.192141
3	-0.159336	-1.0077	0.159821
4	0.094822	0.5997	0.276041
5	-0.212583	-1.3445	0.093182
6	-0.023415	-0.1481	0.441508
7	0.034969	0.2212	0.413046
8	-0.020785	-0.1315	0.448037
9	-0.040761	-0.2578	0.398943
10	0.035748	0.2261	0.411142
11	0.003797	0.024	0.490479
12	-0.005769	-0.0365	0.485537
13	0.163614	1.0348	0.153492
14	-0.137027	-0.8666	0.195655
15	0.082552	0.5221	0.302239
16	-0.043149	-0.2729	0.393168

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.380223 & -2.4047 & 0.010452 \tabularnewline
2 & 0.139091 & 0.8797 & 0.192141 \tabularnewline
3 & -0.159336 & -1.0077 & 0.159821 \tabularnewline
4 & 0.094822 & 0.5997 & 0.276041 \tabularnewline
5 & -0.212583 & -1.3445 & 0.093182 \tabularnewline
6 & -0.023415 & -0.1481 & 0.441508 \tabularnewline
7 & 0.034969 & 0.2212 & 0.413046 \tabularnewline
8 & -0.020785 & -0.1315 & 0.448037 \tabularnewline
9 & -0.040761 & -0.2578 & 0.398943 \tabularnewline
10 & 0.035748 & 0.2261 & 0.411142 \tabularnewline
11 & 0.003797 & 0.024 & 0.490479 \tabularnewline
12 & -0.005769 & -0.0365 & 0.485537 \tabularnewline
13 & 0.163614 & 1.0348 & 0.153492 \tabularnewline
14 & -0.137027 & -0.8666 & 0.195655 \tabularnewline
15 & 0.082552 & 0.5221 & 0.302239 \tabularnewline
16 & -0.043149 & -0.2729 & 0.393168 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63651&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]-0.380223[/C][C]-2.4047[/C][C]0.010452[/C][/ROW]
[ROW][C]2[/C][C]0.139091[/C][C]0.8797[/C][C]0.192141[/C][/ROW]
[ROW][C]3[/C][C]-0.159336[/C][C]-1.0077[/C][C]0.159821[/C][/ROW]
[ROW][C]4[/C][C]0.094822[/C][C]0.5997[/C][C]0.276041[/C][/ROW]
[ROW][C]5[/C][C]-0.212583[/C][C]-1.3445[/C][C]0.093182[/C][/ROW]
[ROW][C]6[/C][C]-0.023415[/C][C]-0.1481[/C][C]0.441508[/C][/ROW]
[ROW][C]7[/C][C]0.034969[/C][C]0.2212[/C][C]0.413046[/C][/ROW]
[ROW][C]8[/C][C]-0.020785[/C][C]-0.1315[/C][C]0.448037[/C][/ROW]
[ROW][C]9[/C][C]-0.040761[/C][C]-0.2578[/C][C]0.398943[/C][/ROW]
[ROW][C]10[/C][C]0.035748[/C][C]0.2261[/C][C]0.411142[/C][/ROW]
[ROW][C]11[/C][C]0.003797[/C][C]0.024[/C][C]0.490479[/C][/ROW]
[ROW][C]12[/C][C]-0.005769[/C][C]-0.0365[/C][C]0.485537[/C][/ROW]
[ROW][C]13[/C][C]0.163614[/C][C]1.0348[/C][C]0.153492[/C][/ROW]
[ROW][C]14[/C][C]-0.137027[/C][C]-0.8666[/C][C]0.195655[/C][/ROW]
[ROW][C]15[/C][C]0.082552[/C][C]0.5221[/C][C]0.302239[/C][/ROW]
[ROW][C]16[/C][C]-0.043149[/C][C]-0.2729[/C][C]0.393168[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63651&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63651&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	-0.380223	-2.4047	0.010452
2	0.139091	0.8797	0.192141
3	-0.159336	-1.0077	0.159821
4	0.094822	0.5997	0.276041
5	-0.212583	-1.3445	0.093182
6	-0.023415	-0.1481	0.441508
7	0.034969	0.2212	0.413046
8	-0.020785	-0.1315	0.448037
9	-0.040761	-0.2578	0.398943
10	0.035748	0.2261	0.411142
11	0.003797	0.024	0.490479
12	-0.005769	-0.0365	0.485537
13	0.163614	1.0348	0.153492
14	-0.137027	-0.8666	0.195655
15	0.082552	0.5221	0.302239
16	-0.043149	-0.2729	0.393168

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.380223	-2.4047	0.010452
2	-0.006404	-0.0405	0.483946
3	-0.126897	-0.8026	0.213484
4	-0.008178	-0.0517	0.479504
5	-0.201975	-1.2774	0.104413
6	-0.229326	-1.4504	0.077374
7	-0.057126	-0.3613	0.359888
8	-0.090371	-0.5716	0.285411
9	-0.145391	-0.9195	0.181665
10	-0.103429	-0.6541	0.258383
11	-0.116868	-0.7391	0.23207
12	-0.110239	-0.6972	0.244852
13	0.127228	0.8047	0.212885
14	-0.101837	-0.6441	0.261601
15	-0.048115	-0.3043	0.381237
16	0.00699	0.0442	0.482479

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.380223 & -2.4047 & 0.010452 \tabularnewline
2 & -0.006404 & -0.0405 & 0.483946 \tabularnewline
3 & -0.126897 & -0.8026 & 0.213484 \tabularnewline
4 & -0.008178 & -0.0517 & 0.479504 \tabularnewline
5 & -0.201975 & -1.2774 & 0.104413 \tabularnewline
6 & -0.229326 & -1.4504 & 0.077374 \tabularnewline
7 & -0.057126 & -0.3613 & 0.359888 \tabularnewline
8 & -0.090371 & -0.5716 & 0.285411 \tabularnewline
9 & -0.145391 & -0.9195 & 0.181665 \tabularnewline
10 & -0.103429 & -0.6541 & 0.258383 \tabularnewline
11 & -0.116868 & -0.7391 & 0.23207 \tabularnewline
12 & -0.110239 & -0.6972 & 0.244852 \tabularnewline
13 & 0.127228 & 0.8047 & 0.212885 \tabularnewline
14 & -0.101837 & -0.6441 & 0.261601 \tabularnewline
15 & -0.048115 & -0.3043 & 0.381237 \tabularnewline
16 & 0.00699 & 0.0442 & 0.482479 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63651&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]-0.380223[/C][C]-2.4047[/C][C]0.010452[/C][/ROW]
[ROW][C]2[/C][C]-0.006404[/C][C]-0.0405[/C][C]0.483946[/C][/ROW]
[ROW][C]3[/C][C]-0.126897[/C][C]-0.8026[/C][C]0.213484[/C][/ROW]
[ROW][C]4[/C][C]-0.008178[/C][C]-0.0517[/C][C]0.479504[/C][/ROW]
[ROW][C]5[/C][C]-0.201975[/C][C]-1.2774[/C][C]0.104413[/C][/ROW]
[ROW][C]6[/C][C]-0.229326[/C][C]-1.4504[/C][C]0.077374[/C][/ROW]
[ROW][C]7[/C][C]-0.057126[/C][C]-0.3613[/C][C]0.359888[/C][/ROW]
[ROW][C]8[/C][C]-0.090371[/C][C]-0.5716[/C][C]0.285411[/C][/ROW]
[ROW][C]9[/C][C]-0.145391[/C][C]-0.9195[/C][C]0.181665[/C][/ROW]
[ROW][C]10[/C][C]-0.103429[/C][C]-0.6541[/C][C]0.258383[/C][/ROW]
[ROW][C]11[/C][C]-0.116868[/C][C]-0.7391[/C][C]0.23207[/C][/ROW]
[ROW][C]12[/C][C]-0.110239[/C][C]-0.6972[/C][C]0.244852[/C][/ROW]
[ROW][C]13[/C][C]0.127228[/C][C]0.8047[/C][C]0.212885[/C][/ROW]
[ROW][C]14[/C][C]-0.101837[/C][C]-0.6441[/C][C]0.261601[/C][/ROW]
[ROW][C]15[/C][C]-0.048115[/C][C]-0.3043[/C][C]0.381237[/C][/ROW]
[ROW][C]16[/C][C]0.00699[/C][C]0.0442[/C][C]0.482479[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63651&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63651&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	-0.380223	-2.4047	0.010452
2	-0.006404	-0.0405	0.483946
3	-0.126897	-0.8026	0.213484
4	-0.008178	-0.0517	0.479504
5	-0.201975	-1.2774	0.104413
6	-0.229326	-1.4504	0.077374
7	-0.057126	-0.3613	0.359888
8	-0.090371	-0.5716	0.285411
9	-0.145391	-0.9195	0.181665
10	-0.103429	-0.6541	0.258383
11	-0.116868	-0.7391	0.23207
12	-0.110239	-0.6972	0.244852
13	0.127228	0.8047	0.212885
14	-0.101837	-0.6441	0.261601
15	-0.048115	-0.3043	0.381237
16	0.00699	0.0442	0.482479

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ;

Parameters (R input):

par1 = Default ; par2 = -2.0 ; par3 = 1 ; par4 = 0 ; par5 = 1 ; 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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code