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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 19 Dec 2010 16:00:59 +0000

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/2010/Dec/19/t12927743631twqcrdlqc1fklc.htm/, Retrieved Sun, 05 May 2024 06:20:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112535, Retrieved Sun, 05 May 2024 06:20:23 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

143

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-    D    [(Partial) Autocorrelation Function] [Autocorrelation WS9] [2010-12-06 11:15:00] [f4dc4aa51d65be851b8508203d9f6001]
-    D      [(Partial) Autocorrelation Function] [Autocorrelation B...] [2010-12-19 15:56:02] [f4dc4aa51d65be851b8508203d9f6001]
-   P           [(Partial) Autocorrelation Function] [Autocorrelation B...] [2010-12-19 16:00:59] [7a87ed98a7b21a29d6a45388a9b7b229] [Current]
-   P             [(Partial) Autocorrelation Function] [Autocorrelation B...] [2010-12-19 16:15:04] [f4dc4aa51d65be851b8508203d9f6001] 

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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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112535&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112535&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112535&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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.927461	6.4256	0
2	0.857959	5.9441	0
3	0.793464	5.4973	1e-06
4	0.700219	4.8513	7e-06
5	0.57148	3.9593	0.000124
6	0.459215	3.1815	0.001284
7	0.342779	2.3748	0.0108
8	0.206666	1.4318	0.079337
9	0.067881	0.4703	0.320138
10	-0.047656	-0.3302	0.371355
11	-0.151027	-1.0463	0.150321
12	-0.254799	-1.7653	0.041937
13	-0.310607	-2.152	0.01823
14	-0.334819	-2.3197	0.012329
15	-0.368891	-2.5558	0.006909
16	-0.372518	-2.5809	0.006484
17	-0.365744	-2.5339	0.007298

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.927461 & 6.4256 & 0 \tabularnewline
2 & 0.857959 & 5.9441 & 0 \tabularnewline
3 & 0.793464 & 5.4973 & 1e-06 \tabularnewline
4 & 0.700219 & 4.8513 & 7e-06 \tabularnewline
5 & 0.57148 & 3.9593 & 0.000124 \tabularnewline
6 & 0.459215 & 3.1815 & 0.001284 \tabularnewline
7 & 0.342779 & 2.3748 & 0.0108 \tabularnewline
8 & 0.206666 & 1.4318 & 0.079337 \tabularnewline
9 & 0.067881 & 0.4703 & 0.320138 \tabularnewline
10 & -0.047656 & -0.3302 & 0.371355 \tabularnewline
11 & -0.151027 & -1.0463 & 0.150321 \tabularnewline
12 & -0.254799 & -1.7653 & 0.041937 \tabularnewline
13 & -0.310607 & -2.152 & 0.01823 \tabularnewline
14 & -0.334819 & -2.3197 & 0.012329 \tabularnewline
15 & -0.368891 & -2.5558 & 0.006909 \tabularnewline
16 & -0.372518 & -2.5809 & 0.006484 \tabularnewline
17 & -0.365744 & -2.5339 & 0.007298 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112535&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]0.927461[/C][C]6.4256[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.857959[/C][C]5.9441[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.793464[/C][C]5.4973[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]0.700219[/C][C]4.8513[/C][C]7e-06[/C][/ROW]
[ROW][C]5[/C][C]0.57148[/C][C]3.9593[/C][C]0.000124[/C][/ROW]
[ROW][C]6[/C][C]0.459215[/C][C]3.1815[/C][C]0.001284[/C][/ROW]
[ROW][C]7[/C][C]0.342779[/C][C]2.3748[/C][C]0.0108[/C][/ROW]
[ROW][C]8[/C][C]0.206666[/C][C]1.4318[/C][C]0.079337[/C][/ROW]
[ROW][C]9[/C][C]0.067881[/C][C]0.4703[/C][C]0.320138[/C][/ROW]
[ROW][C]10[/C][C]-0.047656[/C][C]-0.3302[/C][C]0.371355[/C][/ROW]
[ROW][C]11[/C][C]-0.151027[/C][C]-1.0463[/C][C]0.150321[/C][/ROW]
[ROW][C]12[/C][C]-0.254799[/C][C]-1.7653[/C][C]0.041937[/C][/ROW]
[ROW][C]13[/C][C]-0.310607[/C][C]-2.152[/C][C]0.01823[/C][/ROW]
[ROW][C]14[/C][C]-0.334819[/C][C]-2.3197[/C][C]0.012329[/C][/ROW]
[ROW][C]15[/C][C]-0.368891[/C][C]-2.5558[/C][C]0.006909[/C][/ROW]
[ROW][C]16[/C][C]-0.372518[/C][C]-2.5809[/C][C]0.006484[/C][/ROW]
[ROW][C]17[/C][C]-0.365744[/C][C]-2.5339[/C][C]0.007298[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112535&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112535&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	0.927461	6.4256	0
2	0.857959	5.9441	0
3	0.793464	5.4973	1e-06
4	0.700219	4.8513	7e-06
5	0.57148	3.9593	0.000124
6	0.459215	3.1815	0.001284
7	0.342779	2.3748	0.0108
8	0.206666	1.4318	0.079337
9	0.067881	0.4703	0.320138
10	-0.047656	-0.3302	0.371355
11	-0.151027	-1.0463	0.150321
12	-0.254799	-1.7653	0.041937
13	-0.310607	-2.152	0.01823
14	-0.334819	-2.3197	0.012329
15	-0.368891	-2.5558	0.006909
16	-0.372518	-2.5809	0.006484
17	-0.365744	-2.5339	0.007298

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.927461	6.4256	0
2	-0.015912	-0.1102	0.45634
3	-0.001163	-0.0081	0.496802
4	-0.240321	-1.665	0.051214
5	-0.333096	-2.3078	0.012684
6	-0.008111	-0.0562	0.477709
7	-0.089675	-0.6213	0.268676
8	-0.149786	-1.0377	0.152294
9	-0.136359	-0.9447	0.174765
10	-0.007033	-0.0487	0.480669
11	0.053929	0.3736	0.355162
12	-0.035539	-0.2462	0.40328
13	0.250085	1.7326	0.044791
14	0.1607	1.1134	0.135548
15	-0.102908	-0.713	0.23966
16	0.101854	0.7057	0.241903
17	-0.222566	-1.542	0.064822

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.927461 & 6.4256 & 0 \tabularnewline
2 & -0.015912 & -0.1102 & 0.45634 \tabularnewline
3 & -0.001163 & -0.0081 & 0.496802 \tabularnewline
4 & -0.240321 & -1.665 & 0.051214 \tabularnewline
5 & -0.333096 & -2.3078 & 0.012684 \tabularnewline
6 & -0.008111 & -0.0562 & 0.477709 \tabularnewline
7 & -0.089675 & -0.6213 & 0.268676 \tabularnewline
8 & -0.149786 & -1.0377 & 0.152294 \tabularnewline
9 & -0.136359 & -0.9447 & 0.174765 \tabularnewline
10 & -0.007033 & -0.0487 & 0.480669 \tabularnewline
11 & 0.053929 & 0.3736 & 0.355162 \tabularnewline
12 & -0.035539 & -0.2462 & 0.40328 \tabularnewline
13 & 0.250085 & 1.7326 & 0.044791 \tabularnewline
14 & 0.1607 & 1.1134 & 0.135548 \tabularnewline
15 & -0.102908 & -0.713 & 0.23966 \tabularnewline
16 & 0.101854 & 0.7057 & 0.241903 \tabularnewline
17 & -0.222566 & -1.542 & 0.064822 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112535&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]0.927461[/C][C]6.4256[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.015912[/C][C]-0.1102[/C][C]0.45634[/C][/ROW]
[ROW][C]3[/C][C]-0.001163[/C][C]-0.0081[/C][C]0.496802[/C][/ROW]
[ROW][C]4[/C][C]-0.240321[/C][C]-1.665[/C][C]0.051214[/C][/ROW]
[ROW][C]5[/C][C]-0.333096[/C][C]-2.3078[/C][C]0.012684[/C][/ROW]
[ROW][C]6[/C][C]-0.008111[/C][C]-0.0562[/C][C]0.477709[/C][/ROW]
[ROW][C]7[/C][C]-0.089675[/C][C]-0.6213[/C][C]0.268676[/C][/ROW]
[ROW][C]8[/C][C]-0.149786[/C][C]-1.0377[/C][C]0.152294[/C][/ROW]
[ROW][C]9[/C][C]-0.136359[/C][C]-0.9447[/C][C]0.174765[/C][/ROW]
[ROW][C]10[/C][C]-0.007033[/C][C]-0.0487[/C][C]0.480669[/C][/ROW]
[ROW][C]11[/C][C]0.053929[/C][C]0.3736[/C][C]0.355162[/C][/ROW]
[ROW][C]12[/C][C]-0.035539[/C][C]-0.2462[/C][C]0.40328[/C][/ROW]
[ROW][C]13[/C][C]0.250085[/C][C]1.7326[/C][C]0.044791[/C][/ROW]
[ROW][C]14[/C][C]0.1607[/C][C]1.1134[/C][C]0.135548[/C][/ROW]
[ROW][C]15[/C][C]-0.102908[/C][C]-0.713[/C][C]0.23966[/C][/ROW]
[ROW][C]16[/C][C]0.101854[/C][C]0.7057[/C][C]0.241903[/C][/ROW]
[ROW][C]17[/C][C]-0.222566[/C][C]-1.542[/C][C]0.064822[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112535&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112535&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	0.927461	6.4256	0
2	-0.015912	-0.1102	0.45634
3	-0.001163	-0.0081	0.496802
4	-0.240321	-1.665	0.051214
5	-0.333096	-2.3078	0.012684
6	-0.008111	-0.0562	0.477709
7	-0.089675	-0.6213	0.268676
8	-0.149786	-1.0377	0.152294
9	-0.136359	-0.9447	0.174765
10	-0.007033	-0.0487	0.480669
11	0.053929	0.3736	0.355162
12	-0.035539	-0.2462	0.40328
13	0.250085	1.7326	0.044791
14	0.1607	1.1134	0.135548
15	-0.102908	-0.713	0.23966
16	0.101854	0.7057	0.241903
17	-0.222566	-1.542	0.064822

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 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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