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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationFri, 11 Dec 2009 05:33:45 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/11/t1260534880w7k0imh87frmsyk.htm/, Retrieved Sun, 28 Apr 2024 22:48:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=66088, Retrieved Sun, 28 Apr 2024 22:48:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120

Tree of Dependent Computations

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] [] [2009-11-27 14:46:03] [b98453cac15ba1066b407e146608df68]
-   PD    [(Partial) Autocorrelation Function] [WS9: ACF] [2009-12-04 17:46:09] [5c968c05ca472afa314d272082b56b09]
-   PD        [(Partial) Autocorrelation Function] [ws9-3] [2009-12-11 12:33:45] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
96,8
114,1
110,3
103,9
101,6
94,6
95,9
104,7
102,8
98,1
113,9
80,9
95,7
113,2
105,9
108,8
102,3
99
100,7
115,5
100,7
109,9
114,6
85,4
100,5
114,8
116,5
112,9
102
106
105,3
118,8
106,1
109,3
117,2
92,5
104,2
112,5
122,4
113,3
100
110,7
112,8
109,8
117,3
109,1
115,9
96
99,8
116,8
115,7
99,4
94,3
91
93,2
103,1
94,1
91,8
102,7
82,6

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66088&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66088&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66088&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.5194923.59910.000377
20.6147794.25934.7e-05
30.6573794.55451.8e-05
40.3536142.44990.008994
50.4038172.79770.003693
60.3372022.33620.011852
70.1166080.80790.211572
80.2029621.40620.083058
90.0380170.26340.396688
100.0276660.19170.424403
110.083910.58130.281865
12-0.063451-0.43960.331098

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.519492 & 3.5991 & 0.000377 \tabularnewline
2 & 0.614779 & 4.2593 & 4.7e-05 \tabularnewline
3 & 0.657379 & 4.5545 & 1.8e-05 \tabularnewline
4 & 0.353614 & 2.4499 & 0.008994 \tabularnewline
5 & 0.403817 & 2.7977 & 0.003693 \tabularnewline
6 & 0.337202 & 2.3362 & 0.011852 \tabularnewline
7 & 0.116608 & 0.8079 & 0.211572 \tabularnewline
8 & 0.202962 & 1.4062 & 0.083058 \tabularnewline
9 & 0.038017 & 0.2634 & 0.396688 \tabularnewline
10 & 0.027666 & 0.1917 & 0.424403 \tabularnewline
11 & 0.08391 & 0.5813 & 0.281865 \tabularnewline
12 & -0.063451 & -0.4396 & 0.331098 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66088&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]0.519492[/C][C]3.5991[/C][C]0.000377[/C][/ROW]
[ROW][C]2[/C][C]0.614779[/C][C]4.2593[/C][C]4.7e-05[/C][/ROW]
[ROW][C]3[/C][C]0.657379[/C][C]4.5545[/C][C]1.8e-05[/C][/ROW]
[ROW][C]4[/C][C]0.353614[/C][C]2.4499[/C][C]0.008994[/C][/ROW]
[ROW][C]5[/C][C]0.403817[/C][C]2.7977[/C][C]0.003693[/C][/ROW]
[ROW][C]6[/C][C]0.337202[/C][C]2.3362[/C][C]0.011852[/C][/ROW]
[ROW][C]7[/C][C]0.116608[/C][C]0.8079[/C][C]0.211572[/C][/ROW]
[ROW][C]8[/C][C]0.202962[/C][C]1.4062[/C][C]0.083058[/C][/ROW]
[ROW][C]9[/C][C]0.038017[/C][C]0.2634[/C][C]0.396688[/C][/ROW]
[ROW][C]10[/C][C]0.027666[/C][C]0.1917[/C][C]0.424403[/C][/ROW]
[ROW][C]11[/C][C]0.08391[/C][C]0.5813[/C][C]0.281865[/C][/ROW]
[ROW][C]12[/C][C]-0.063451[/C][C]-0.4396[/C][C]0.331098[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66088&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66088&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.5194923.59910.000377
20.6147794.25934.7e-05
30.6573794.55451.8e-05
40.3536142.44990.008994
50.4038172.79770.003693
60.3372022.33620.011852
70.1166080.80790.211572
80.2029621.40620.083058
90.0380170.26340.396688
100.0276660.19170.424403
110.083910.58130.281865
12-0.063451-0.43960.331098






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.5194923.59910.000377
20.4723933.27280.000989
30.4292542.9740.002294
4-0.290359-2.01170.024944
5-0.217548-1.50720.069154
6-0.021898-0.15170.440025
7-0.121794-0.84380.201479
80.0496960.34430.36606
9-0.080936-0.56070.288791
100.1181030.81820.208631
110.1641341.13720.13056
12-0.061246-0.42430.336612

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.519492 & 3.5991 & 0.000377 \tabularnewline
2 & 0.472393 & 3.2728 & 0.000989 \tabularnewline
3 & 0.429254 & 2.974 & 0.002294 \tabularnewline
4 & -0.290359 & -2.0117 & 0.024944 \tabularnewline
5 & -0.217548 & -1.5072 & 0.069154 \tabularnewline
6 & -0.021898 & -0.1517 & 0.440025 \tabularnewline
7 & -0.121794 & -0.8438 & 0.201479 \tabularnewline
8 & 0.049696 & 0.3443 & 0.36606 \tabularnewline
9 & -0.080936 & -0.5607 & 0.288791 \tabularnewline
10 & 0.118103 & 0.8182 & 0.208631 \tabularnewline
11 & 0.164134 & 1.1372 & 0.13056 \tabularnewline
12 & -0.061246 & -0.4243 & 0.336612 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66088&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]0.519492[/C][C]3.5991[/C][C]0.000377[/C][/ROW]
[ROW][C]2[/C][C]0.472393[/C][C]3.2728[/C][C]0.000989[/C][/ROW]
[ROW][C]3[/C][C]0.429254[/C][C]2.974[/C][C]0.002294[/C][/ROW]
[ROW][C]4[/C][C]-0.290359[/C][C]-2.0117[/C][C]0.024944[/C][/ROW]
[ROW][C]5[/C][C]-0.217548[/C][C]-1.5072[/C][C]0.069154[/C][/ROW]
[ROW][C]6[/C][C]-0.021898[/C][C]-0.1517[/C][C]0.440025[/C][/ROW]
[ROW][C]7[/C][C]-0.121794[/C][C]-0.8438[/C][C]0.201479[/C][/ROW]
[ROW][C]8[/C][C]0.049696[/C][C]0.3443[/C][C]0.36606[/C][/ROW]
[ROW][C]9[/C][C]-0.080936[/C][C]-0.5607[/C][C]0.288791[/C][/ROW]
[ROW][C]10[/C][C]0.118103[/C][C]0.8182[/C][C]0.208631[/C][/ROW]
[ROW][C]11[/C][C]0.164134[/C][C]1.1372[/C][C]0.13056[/C][/ROW]
[ROW][C]12[/C][C]-0.061246[/C][C]-0.4243[/C][C]0.336612[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66088&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66088&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.5194923.59910.000377
20.4723933.27280.000989
30.4292542.9740.002294
4-0.290359-2.01170.024944
5-0.217548-1.50720.069154
6-0.021898-0.15170.440025
7-0.121794-0.84380.201479
80.0496960.34430.36606
9-0.080936-0.56070.288791
100.1181030.81820.208631
110.1641341.13720.13056
12-0.061246-0.42430.336612


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = 1.0 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = 1.0 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; 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')