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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, 27 Nov 2009 06:42:37 -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/Nov/27/t1259329402dsk4rom8ndih9t5.htm/, Retrieved Mon, 29 Apr 2024 19:04:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60756, Retrieved Mon, 29 Apr 2024 19:04:52 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

shwws8

Estimated Impact

141

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

-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [] [2009-11-20 13:47:03] [5482608004c1d7bbf873930172393a2d]
- RMPD        [(Partial) Autocorrelation Function] [] [2009-11-27 13:42:37] [efdfe680cd785c4af09f858b30f777ec] [Current]
-   P           [(Partial) Autocorrelation Function] [workshop 8] [2009-11-28 12:46:05] [eaf42bcf5162b5692bb3c7f9d4636222] 

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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=60756&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=60756&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60756&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	-0.027614	-0.1893	0.425333
2	0.378214	2.5929	0.006323
3	0.114496	0.7849	0.218212
4	0.327191	2.2431	0.014822
5	-0.029249	-0.2005	0.420969
6	0.049869	0.3419	0.36698
7	0.134612	0.9229	0.180399
8	-0.028859	-0.1978	0.422009
9	0.021126	0.1448	0.442731
10	-0.200754	-1.3763	0.087625
11	0.304306	2.0862	0.021206
12	-0.330168	-2.2635	0.014131
13	0.099491	0.6821	0.249269
14	-0.124561	-0.8539	0.198732
15	0.197232	1.3522	0.091398
16	-0.170265	-1.1673	0.124493
17	0.113973	0.7814	0.219254

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.027614 & -0.1893 & 0.425333 \tabularnewline
2 & 0.378214 & 2.5929 & 0.006323 \tabularnewline
3 & 0.114496 & 0.7849 & 0.218212 \tabularnewline
4 & 0.327191 & 2.2431 & 0.014822 \tabularnewline
5 & -0.029249 & -0.2005 & 0.420969 \tabularnewline
6 & 0.049869 & 0.3419 & 0.36698 \tabularnewline
7 & 0.134612 & 0.9229 & 0.180399 \tabularnewline
8 & -0.028859 & -0.1978 & 0.422009 \tabularnewline
9 & 0.021126 & 0.1448 & 0.442731 \tabularnewline
10 & -0.200754 & -1.3763 & 0.087625 \tabularnewline
11 & 0.304306 & 2.0862 & 0.021206 \tabularnewline
12 & -0.330168 & -2.2635 & 0.014131 \tabularnewline
13 & 0.099491 & 0.6821 & 0.249269 \tabularnewline
14 & -0.124561 & -0.8539 & 0.198732 \tabularnewline
15 & 0.197232 & 1.3522 & 0.091398 \tabularnewline
16 & -0.170265 & -1.1673 & 0.124493 \tabularnewline
17 & 0.113973 & 0.7814 & 0.219254 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60756&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]-0.027614[/C][C]-0.1893[/C][C]0.425333[/C][/ROW]
[ROW][C]2[/C][C]0.378214[/C][C]2.5929[/C][C]0.006323[/C][/ROW]
[ROW][C]3[/C][C]0.114496[/C][C]0.7849[/C][C]0.218212[/C][/ROW]
[ROW][C]4[/C][C]0.327191[/C][C]2.2431[/C][C]0.014822[/C][/ROW]
[ROW][C]5[/C][C]-0.029249[/C][C]-0.2005[/C][C]0.420969[/C][/ROW]
[ROW][C]6[/C][C]0.049869[/C][C]0.3419[/C][C]0.36698[/C][/ROW]
[ROW][C]7[/C][C]0.134612[/C][C]0.9229[/C][C]0.180399[/C][/ROW]
[ROW][C]8[/C][C]-0.028859[/C][C]-0.1978[/C][C]0.422009[/C][/ROW]
[ROW][C]9[/C][C]0.021126[/C][C]0.1448[/C][C]0.442731[/C][/ROW]
[ROW][C]10[/C][C]-0.200754[/C][C]-1.3763[/C][C]0.087625[/C][/ROW]
[ROW][C]11[/C][C]0.304306[/C][C]2.0862[/C][C]0.021206[/C][/ROW]
[ROW][C]12[/C][C]-0.330168[/C][C]-2.2635[/C][C]0.014131[/C][/ROW]
[ROW][C]13[/C][C]0.099491[/C][C]0.6821[/C][C]0.249269[/C][/ROW]
[ROW][C]14[/C][C]-0.124561[/C][C]-0.8539[/C][C]0.198732[/C][/ROW]
[ROW][C]15[/C][C]0.197232[/C][C]1.3522[/C][C]0.091398[/C][/ROW]
[ROW][C]16[/C][C]-0.170265[/C][C]-1.1673[/C][C]0.124493[/C][/ROW]
[ROW][C]17[/C][C]0.113973[/C][C]0.7814[/C][C]0.219254[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60756&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60756&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	-0.027614	-0.1893	0.425333
2	0.378214	2.5929	0.006323
3	0.114496	0.7849	0.218212
4	0.327191	2.2431	0.014822
5	-0.029249	-0.2005	0.420969
6	0.049869	0.3419	0.36698
7	0.134612	0.9229	0.180399
8	-0.028859	-0.1978	0.422009
9	0.021126	0.1448	0.442731
10	-0.200754	-1.3763	0.087625
11	0.304306	2.0862	0.021206
12	-0.330168	-2.2635	0.014131
13	0.099491	0.6821	0.249269
14	-0.124561	-0.8539	0.198732
15	0.197232	1.3522	0.091398
16	-0.170265	-1.1673	0.124493
17	0.113973	0.7814	0.219254

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.027614	-0.1893	0.425333
2	0.377739	2.5896	0.006375
3	0.153416	1.0518	0.149141
4	0.23451	1.6077	0.057297
5	-0.106826	-0.7324	0.233793
6	-0.21011	-1.4404	0.078186
7	0.105641	0.7242	0.236254
8	-0.024915	-0.1708	0.432553
9	0.000424	0.0029	0.498847
10	-0.237281	-1.6267	0.055242
11	0.296131	2.0302	0.02401
12	-0.188439	-1.2919	0.101359
13	-0.028482	-0.1953	0.423014
14	0.048243	0.3307	0.371155
15	0.134545	0.9224	0.180517
16	0.011472	0.0786	0.468823
17	0.031785	0.2179	0.414223

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.027614 & -0.1893 & 0.425333 \tabularnewline
2 & 0.377739 & 2.5896 & 0.006375 \tabularnewline
3 & 0.153416 & 1.0518 & 0.149141 \tabularnewline
4 & 0.23451 & 1.6077 & 0.057297 \tabularnewline
5 & -0.106826 & -0.7324 & 0.233793 \tabularnewline
6 & -0.21011 & -1.4404 & 0.078186 \tabularnewline
7 & 0.105641 & 0.7242 & 0.236254 \tabularnewline
8 & -0.024915 & -0.1708 & 0.432553 \tabularnewline
9 & 0.000424 & 0.0029 & 0.498847 \tabularnewline
10 & -0.237281 & -1.6267 & 0.055242 \tabularnewline
11 & 0.296131 & 2.0302 & 0.02401 \tabularnewline
12 & -0.188439 & -1.2919 & 0.101359 \tabularnewline
13 & -0.028482 & -0.1953 & 0.423014 \tabularnewline
14 & 0.048243 & 0.3307 & 0.371155 \tabularnewline
15 & 0.134545 & 0.9224 & 0.180517 \tabularnewline
16 & 0.011472 & 0.0786 & 0.468823 \tabularnewline
17 & 0.031785 & 0.2179 & 0.414223 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60756&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]-0.027614[/C][C]-0.1893[/C][C]0.425333[/C][/ROW]
[ROW][C]2[/C][C]0.377739[/C][C]2.5896[/C][C]0.006375[/C][/ROW]
[ROW][C]3[/C][C]0.153416[/C][C]1.0518[/C][C]0.149141[/C][/ROW]
[ROW][C]4[/C][C]0.23451[/C][C]1.6077[/C][C]0.057297[/C][/ROW]
[ROW][C]5[/C][C]-0.106826[/C][C]-0.7324[/C][C]0.233793[/C][/ROW]
[ROW][C]6[/C][C]-0.21011[/C][C]-1.4404[/C][C]0.078186[/C][/ROW]
[ROW][C]7[/C][C]0.105641[/C][C]0.7242[/C][C]0.236254[/C][/ROW]
[ROW][C]8[/C][C]-0.024915[/C][C]-0.1708[/C][C]0.432553[/C][/ROW]
[ROW][C]9[/C][C]0.000424[/C][C]0.0029[/C][C]0.498847[/C][/ROW]
[ROW][C]10[/C][C]-0.237281[/C][C]-1.6267[/C][C]0.055242[/C][/ROW]
[ROW][C]11[/C][C]0.296131[/C][C]2.0302[/C][C]0.02401[/C][/ROW]
[ROW][C]12[/C][C]-0.188439[/C][C]-1.2919[/C][C]0.101359[/C][/ROW]
[ROW][C]13[/C][C]-0.028482[/C][C]-0.1953[/C][C]0.423014[/C][/ROW]
[ROW][C]14[/C][C]0.048243[/C][C]0.3307[/C][C]0.371155[/C][/ROW]
[ROW][C]15[/C][C]0.134545[/C][C]0.9224[/C][C]0.180517[/C][/ROW]
[ROW][C]16[/C][C]0.011472[/C][C]0.0786[/C][C]0.468823[/C][/ROW]
[ROW][C]17[/C][C]0.031785[/C][C]0.2179[/C][C]0.414223[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60756&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60756&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	-0.027614	-0.1893	0.425333
2	0.377739	2.5896	0.006375
3	0.153416	1.0518	0.149141
4	0.23451	1.6077	0.057297
5	-0.106826	-0.7324	0.233793
6	-0.21011	-1.4404	0.078186
7	0.105641	0.7242	0.236254
8	-0.024915	-0.1708	0.432553
9	0.000424	0.0029	0.498847
10	-0.237281	-1.6267	0.055242
11	0.296131	2.0302	0.02401
12	-0.188439	-1.2919	0.101359
13	-0.028482	-0.1953	0.423014
14	0.048243	0.3307	0.371155
15	0.134545	0.9224	0.180517
16	0.011472	0.0786	0.468823
17	0.031785	0.2179	0.414223

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code