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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

Tue, 14 Dec 2010 13:10:00 +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/14/t1292332173o9260dnoo897jef.htm/, Retrieved Thu, 02 May 2024 22:12:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=109563, Retrieved Thu, 02 May 2024 22:12:17 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Workshop 6

Estimated Impact

144

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

-       [(Partial) Autocorrelation Function] [Workshop 6: ACF] [2010-12-14 13:10:00] [f76239c595e4d455b3b05a43389f68d5] [Current]
- R  D    [(Partial) Autocorrelation Function] [ACF] [2011-12-22 12:45:46] [74be16979710d4c4e7c6647856088456] 

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Boxplots

-5
-1
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-2
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1
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1
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-1
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-7
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-11
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-17
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-11
-11
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-15
-15
-15
-13
-8
-13
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0

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=109563&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=109563&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109563&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	0.891009	6.9017	0
2	0.815533	6.3171	0
3	0.760451	5.8904	0
4	0.692561	5.3646	1e-06
5	0.622528	4.8221	5e-06
6	0.546383	4.2323	4e-05
7	0.498261	3.8595	0.00014
8	0.417267	3.2321	0.000999
9	0.343559	2.6612	0.004988
10	0.294208	2.2789	0.013122
11	0.259499	2.0101	0.024463
12	0.198284	1.5359	0.06491
13	0.129739	1.005	0.159478
14	0.053604	0.4152	0.339734
15	-0.016424	-0.1272	0.449595
16	-0.106871	-0.8278	0.205528
17	-0.179361	-1.3893	0.084935

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.891009 & 6.9017 & 0 \tabularnewline
2 & 0.815533 & 6.3171 & 0 \tabularnewline
3 & 0.760451 & 5.8904 & 0 \tabularnewline
4 & 0.692561 & 5.3646 & 1e-06 \tabularnewline
5 & 0.622528 & 4.8221 & 5e-06 \tabularnewline
6 & 0.546383 & 4.2323 & 4e-05 \tabularnewline
7 & 0.498261 & 3.8595 & 0.00014 \tabularnewline
8 & 0.417267 & 3.2321 & 0.000999 \tabularnewline
9 & 0.343559 & 2.6612 & 0.004988 \tabularnewline
10 & 0.294208 & 2.2789 & 0.013122 \tabularnewline
11 & 0.259499 & 2.0101 & 0.024463 \tabularnewline
12 & 0.198284 & 1.5359 & 0.06491 \tabularnewline
13 & 0.129739 & 1.005 & 0.159478 \tabularnewline
14 & 0.053604 & 0.4152 & 0.339734 \tabularnewline
15 & -0.016424 & -0.1272 & 0.449595 \tabularnewline
16 & -0.106871 & -0.8278 & 0.205528 \tabularnewline
17 & -0.179361 & -1.3893 & 0.084935 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109563&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]0.891009[/C][C]6.9017[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.815533[/C][C]6.3171[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.760451[/C][C]5.8904[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.692561[/C][C]5.3646[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]0.622528[/C][C]4.8221[/C][C]5e-06[/C][/ROW]
[ROW][C]6[/C][C]0.546383[/C][C]4.2323[/C][C]4e-05[/C][/ROW]
[ROW][C]7[/C][C]0.498261[/C][C]3.8595[/C][C]0.00014[/C][/ROW]
[ROW][C]8[/C][C]0.417267[/C][C]3.2321[/C][C]0.000999[/C][/ROW]
[ROW][C]9[/C][C]0.343559[/C][C]2.6612[/C][C]0.004988[/C][/ROW]
[ROW][C]10[/C][C]0.294208[/C][C]2.2789[/C][C]0.013122[/C][/ROW]
[ROW][C]11[/C][C]0.259499[/C][C]2.0101[/C][C]0.024463[/C][/ROW]
[ROW][C]12[/C][C]0.198284[/C][C]1.5359[/C][C]0.06491[/C][/ROW]
[ROW][C]13[/C][C]0.129739[/C][C]1.005[/C][C]0.159478[/C][/ROW]
[ROW][C]14[/C][C]0.053604[/C][C]0.4152[/C][C]0.339734[/C][/ROW]
[ROW][C]15[/C][C]-0.016424[/C][C]-0.1272[/C][C]0.449595[/C][/ROW]
[ROW][C]16[/C][C]-0.106871[/C][C]-0.8278[/C][C]0.205528[/C][/ROW]
[ROW][C]17[/C][C]-0.179361[/C][C]-1.3893[/C][C]0.084935[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109563&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109563&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	0.891009	6.9017	0
2	0.815533	6.3171	0
3	0.760451	5.8904	0
4	0.692561	5.3646	1e-06
5	0.622528	4.8221	5e-06
6	0.546383	4.2323	4e-05
7	0.498261	3.8595	0.00014
8	0.417267	3.2321	0.000999
9	0.343559	2.6612	0.004988
10	0.294208	2.2789	0.013122
11	0.259499	2.0101	0.024463
12	0.198284	1.5359	0.06491
13	0.129739	1.005	0.159478
14	0.053604	0.4152	0.339734
15	-0.016424	-0.1272	0.449595
16	-0.106871	-0.8278	0.205528
17	-0.179361	-1.3893	0.084935

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.891009	6.9017	0
2	0.104982	0.8132	0.209663
3	0.08119	0.6289	0.265903
4	-0.061969	-0.48	0.316483
5	-0.053106	-0.4114	0.341138
6	-0.086477	-0.6698	0.252763
7	0.078776	0.6102	0.272017
8	-0.165966	-1.2856	0.101767
9	-0.030654	-0.2374	0.406561
10	0.03818	0.2957	0.384223
11	0.082125	0.6361	0.263554
12	-0.131105	-1.0155	0.156965
13	-0.088165	-0.6829	0.248641
14	-0.179869	-1.3933	0.084341
15	-0.038853	-0.301	0.382245
16	-0.18083	-1.4007	0.083227
17	-0.006218	-0.0482	0.480872

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.891009 & 6.9017 & 0 \tabularnewline
2 & 0.104982 & 0.8132 & 0.209663 \tabularnewline
3 & 0.08119 & 0.6289 & 0.265903 \tabularnewline
4 & -0.061969 & -0.48 & 0.316483 \tabularnewline
5 & -0.053106 & -0.4114 & 0.341138 \tabularnewline
6 & -0.086477 & -0.6698 & 0.252763 \tabularnewline
7 & 0.078776 & 0.6102 & 0.272017 \tabularnewline
8 & -0.165966 & -1.2856 & 0.101767 \tabularnewline
9 & -0.030654 & -0.2374 & 0.406561 \tabularnewline
10 & 0.03818 & 0.2957 & 0.384223 \tabularnewline
11 & 0.082125 & 0.6361 & 0.263554 \tabularnewline
12 & -0.131105 & -1.0155 & 0.156965 \tabularnewline
13 & -0.088165 & -0.6829 & 0.248641 \tabularnewline
14 & -0.179869 & -1.3933 & 0.084341 \tabularnewline
15 & -0.038853 & -0.301 & 0.382245 \tabularnewline
16 & -0.18083 & -1.4007 & 0.083227 \tabularnewline
17 & -0.006218 & -0.0482 & 0.480872 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109563&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]0.891009[/C][C]6.9017[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.104982[/C][C]0.8132[/C][C]0.209663[/C][/ROW]
[ROW][C]3[/C][C]0.08119[/C][C]0.6289[/C][C]0.265903[/C][/ROW]
[ROW][C]4[/C][C]-0.061969[/C][C]-0.48[/C][C]0.316483[/C][/ROW]
[ROW][C]5[/C][C]-0.053106[/C][C]-0.4114[/C][C]0.341138[/C][/ROW]
[ROW][C]6[/C][C]-0.086477[/C][C]-0.6698[/C][C]0.252763[/C][/ROW]
[ROW][C]7[/C][C]0.078776[/C][C]0.6102[/C][C]0.272017[/C][/ROW]
[ROW][C]8[/C][C]-0.165966[/C][C]-1.2856[/C][C]0.101767[/C][/ROW]
[ROW][C]9[/C][C]-0.030654[/C][C]-0.2374[/C][C]0.406561[/C][/ROW]
[ROW][C]10[/C][C]0.03818[/C][C]0.2957[/C][C]0.384223[/C][/ROW]
[ROW][C]11[/C][C]0.082125[/C][C]0.6361[/C][C]0.263554[/C][/ROW]
[ROW][C]12[/C][C]-0.131105[/C][C]-1.0155[/C][C]0.156965[/C][/ROW]
[ROW][C]13[/C][C]-0.088165[/C][C]-0.6829[/C][C]0.248641[/C][/ROW]
[ROW][C]14[/C][C]-0.179869[/C][C]-1.3933[/C][C]0.084341[/C][/ROW]
[ROW][C]15[/C][C]-0.038853[/C][C]-0.301[/C][C]0.382245[/C][/ROW]
[ROW][C]16[/C][C]-0.18083[/C][C]-1.4007[/C][C]0.083227[/C][/ROW]
[ROW][C]17[/C][C]-0.006218[/C][C]-0.0482[/C][C]0.480872[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109563&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109563&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	0.891009	6.9017	0
2	0.104982	0.8132	0.209663
3	0.08119	0.6289	0.265903
4	-0.061969	-0.48	0.316483
5	-0.053106	-0.4114	0.341138
6	-0.086477	-0.6698	0.252763
7	0.078776	0.6102	0.272017
8	-0.165966	-1.2856	0.101767
9	-0.030654	-0.2374	0.406561
10	0.03818	0.2957	0.384223
11	0.082125	0.6361	0.263554
12	-0.131105	-1.0155	0.156965
13	-0.088165	-0.6829	0.248641
14	-0.179869	-1.3933	0.084341
15	-0.038853	-0.301	0.382245
16	-0.18083	-1.4007	0.083227
17	-0.006218	-0.0482	0.480872

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code