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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 27 Nov 2009 12:01:50 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/27/t1259348596n0wqwtsjmu1sqsb.htm/, Retrieved Sun, 28 Apr 2024 21:43:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61137, Retrieved Sun, 28 Apr 2024 21:43:48 +0000

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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 Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:16:10] [b98453cac15ba1066b407e146608df68]
-   PD          [(Partial) Autocorrelation Function] [Shwws8_v1] [2009-11-27 19:01:50] [93b66894f6318f3da4fcda772f2ffa6f] [Current]
-   PD            [(Partial) Autocorrelation Function] [Review WS 8 autoc...] [2009-11-29 15:11:12] [12f02da0296cb21dc23d82ae014a8b71] 
-    D            [(Partial) Autocorrelation Function] [Paper] [2009-12-16 00:26:22] [5f89c040fdf1f8599c99d7f78a662321] 
-   PD            [(Partial) Autocorrelation Function] [Paper] [2009-12-16 00:35:46] [5f89c040fdf1f8599c99d7f78a662321] 
-    D              [(Partial) Autocorrelation Function] [Paper] [2009-12-16 00:42:44] [5f89c040fdf1f8599c99d7f78a662321] 
-   PD                [(Partial) Autocorrelation Function] [] [2009-12-16 13:33:00] [5f89c040fdf1f8599c99d7f78a662321] 

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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=61137&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=61137&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61137&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	0.947183	6.3539	0
2	0.897254	6.019	0
3	0.839757	5.6333	1e-06
4	0.776192	5.2069	2e-06
5	0.71849	4.8198	8e-06
6	0.653221	4.3819	3.5e-05
7	0.583276	3.9127	0.000153
8	0.51352	3.4448	0.000624
9	0.448473	3.0084	0.002145
10	0.38068	2.5537	0.007059
11	0.320627	2.1508	0.018448
12	0.252064	1.6909	0.048886
13	0.187407	1.2572	0.107591
14	0.122015	0.8185	0.208692
15	0.048706	0.3267	0.372695
16	-0.012128	-0.0814	0.467759

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.947183 & 6.3539 & 0 \tabularnewline
2 & 0.897254 & 6.019 & 0 \tabularnewline
3 & 0.839757 & 5.6333 & 1e-06 \tabularnewline
4 & 0.776192 & 5.2069 & 2e-06 \tabularnewline
5 & 0.71849 & 4.8198 & 8e-06 \tabularnewline
6 & 0.653221 & 4.3819 & 3.5e-05 \tabularnewline
7 & 0.583276 & 3.9127 & 0.000153 \tabularnewline
8 & 0.51352 & 3.4448 & 0.000624 \tabularnewline
9 & 0.448473 & 3.0084 & 0.002145 \tabularnewline
10 & 0.38068 & 2.5537 & 0.007059 \tabularnewline
11 & 0.320627 & 2.1508 & 0.018448 \tabularnewline
12 & 0.252064 & 1.6909 & 0.048886 \tabularnewline
13 & 0.187407 & 1.2572 & 0.107591 \tabularnewline
14 & 0.122015 & 0.8185 & 0.208692 \tabularnewline
15 & 0.048706 & 0.3267 & 0.372695 \tabularnewline
16 & -0.012128 & -0.0814 & 0.467759 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61137&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]0.947183[/C][C]6.3539[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.897254[/C][C]6.019[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.839757[/C][C]5.6333[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]0.776192[/C][C]5.2069[/C][C]2e-06[/C][/ROW]
[ROW][C]5[/C][C]0.71849[/C][C]4.8198[/C][C]8e-06[/C][/ROW]
[ROW][C]6[/C][C]0.653221[/C][C]4.3819[/C][C]3.5e-05[/C][/ROW]
[ROW][C]7[/C][C]0.583276[/C][C]3.9127[/C][C]0.000153[/C][/ROW]
[ROW][C]8[/C][C]0.51352[/C][C]3.4448[/C][C]0.000624[/C][/ROW]
[ROW][C]9[/C][C]0.448473[/C][C]3.0084[/C][C]0.002145[/C][/ROW]
[ROW][C]10[/C][C]0.38068[/C][C]2.5537[/C][C]0.007059[/C][/ROW]
[ROW][C]11[/C][C]0.320627[/C][C]2.1508[/C][C]0.018448[/C][/ROW]
[ROW][C]12[/C][C]0.252064[/C][C]1.6909[/C][C]0.048886[/C][/ROW]
[ROW][C]13[/C][C]0.187407[/C][C]1.2572[/C][C]0.107591[/C][/ROW]
[ROW][C]14[/C][C]0.122015[/C][C]0.8185[/C][C]0.208692[/C][/ROW]
[ROW][C]15[/C][C]0.048706[/C][C]0.3267[/C][C]0.372695[/C][/ROW]
[ROW][C]16[/C][C]-0.012128[/C][C]-0.0814[/C][C]0.467759[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61137&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61137&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	0.947183	6.3539	0
2	0.897254	6.019	0
3	0.839757	5.6333	1e-06
4	0.776192	5.2069	2e-06
5	0.71849	4.8198	8e-06
6	0.653221	4.3819	3.5e-05
7	0.583276	3.9127	0.000153
8	0.51352	3.4448	0.000624
9	0.448473	3.0084	0.002145
10	0.38068	2.5537	0.007059
11	0.320627	2.1508	0.018448
12	0.252064	1.6909	0.048886
13	0.187407	1.2572	0.107591
14	0.122015	0.8185	0.208692
15	0.048706	0.3267	0.372695
16	-0.012128	-0.0814	0.467759

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.947183	6.3539	0
2	0.000956	0.0064	0.497456
3	-0.099171	-0.6653	0.254639
4	-0.094831	-0.6361	0.263951
5	0.023245	0.1559	0.438393
6	-0.096582	-0.6479	0.260174
7	-0.095199	-0.6386	0.263156
8	-0.04335	-0.2908	0.386269
9	0.018605	0.1248	0.450617
10	-0.072035	-0.4832	0.315638
11	0.017744	0.119	0.452891
12	-0.12245	-0.8214	0.20787
13	-0.017478	-0.1172	0.453592
14	-0.067809	-0.4549	0.325692
15	-0.130425	-0.8749	0.193133
16	0.03581	0.2402	0.405626

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.947183 & 6.3539 & 0 \tabularnewline
2 & 0.000956 & 0.0064 & 0.497456 \tabularnewline
3 & -0.099171 & -0.6653 & 0.254639 \tabularnewline
4 & -0.094831 & -0.6361 & 0.263951 \tabularnewline
5 & 0.023245 & 0.1559 & 0.438393 \tabularnewline
6 & -0.096582 & -0.6479 & 0.260174 \tabularnewline
7 & -0.095199 & -0.6386 & 0.263156 \tabularnewline
8 & -0.04335 & -0.2908 & 0.386269 \tabularnewline
9 & 0.018605 & 0.1248 & 0.450617 \tabularnewline
10 & -0.072035 & -0.4832 & 0.315638 \tabularnewline
11 & 0.017744 & 0.119 & 0.452891 \tabularnewline
12 & -0.12245 & -0.8214 & 0.20787 \tabularnewline
13 & -0.017478 & -0.1172 & 0.453592 \tabularnewline
14 & -0.067809 & -0.4549 & 0.325692 \tabularnewline
15 & -0.130425 & -0.8749 & 0.193133 \tabularnewline
16 & 0.03581 & 0.2402 & 0.405626 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61137&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]0.947183[/C][C]6.3539[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.000956[/C][C]0.0064[/C][C]0.497456[/C][/ROW]
[ROW][C]3[/C][C]-0.099171[/C][C]-0.6653[/C][C]0.254639[/C][/ROW]
[ROW][C]4[/C][C]-0.094831[/C][C]-0.6361[/C][C]0.263951[/C][/ROW]
[ROW][C]5[/C][C]0.023245[/C][C]0.1559[/C][C]0.438393[/C][/ROW]
[ROW][C]6[/C][C]-0.096582[/C][C]-0.6479[/C][C]0.260174[/C][/ROW]
[ROW][C]7[/C][C]-0.095199[/C][C]-0.6386[/C][C]0.263156[/C][/ROW]
[ROW][C]8[/C][C]-0.04335[/C][C]-0.2908[/C][C]0.386269[/C][/ROW]
[ROW][C]9[/C][C]0.018605[/C][C]0.1248[/C][C]0.450617[/C][/ROW]
[ROW][C]10[/C][C]-0.072035[/C][C]-0.4832[/C][C]0.315638[/C][/ROW]
[ROW][C]11[/C][C]0.017744[/C][C]0.119[/C][C]0.452891[/C][/ROW]
[ROW][C]12[/C][C]-0.12245[/C][C]-0.8214[/C][C]0.20787[/C][/ROW]
[ROW][C]13[/C][C]-0.017478[/C][C]-0.1172[/C][C]0.453592[/C][/ROW]
[ROW][C]14[/C][C]-0.067809[/C][C]-0.4549[/C][C]0.325692[/C][/ROW]
[ROW][C]15[/C][C]-0.130425[/C][C]-0.8749[/C][C]0.193133[/C][/ROW]
[ROW][C]16[/C][C]0.03581[/C][C]0.2402[/C][C]0.405626[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61137&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61137&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	0.947183	6.3539	0
2	0.000956	0.0064	0.497456
3	-0.099171	-0.6653	0.254639
4	-0.094831	-0.6361	0.263951
5	0.023245	0.1559	0.438393
6	-0.096582	-0.6479	0.260174
7	-0.095199	-0.6386	0.263156
8	-0.04335	-0.2908	0.386269
9	0.018605	0.1248	0.450617
10	-0.072035	-0.4832	0.315638
11	0.017744	0.119	0.452891
12	-0.12245	-0.8214	0.20787
13	-0.017478	-0.1172	0.453592
14	-0.067809	-0.4549	0.325692
15	-0.130425	-0.8749	0.193133
16	0.03581	0.2402	0.405626

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 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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