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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationWed, 04 Apr 2012 16:29:50 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Apr/04/t1333571461ve59vqfd3xsj3lr.htm/, Retrieved Mon, 29 Apr 2024 01:02:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=164314, Retrieved Mon, 29 Apr 2024 01:02:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [autocorrelatiefun...] [2012-04-04 20:29:50] [6aa41422895d0082cb99bdd8f056be10] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
86,9
85,8
84,4
80,4
84,4
90,7
91,6
91,9
92,5
92,5
92
92
94,5
95,5
96,3
100
103,1
109,2
108,7
107,5
104,5
103,8
102,5
100,8
100,7
102,7
106,5
105,5
110,1
110,1
109
106,9
108
106,1
101,7
100,6
102,6
100,5
105,2
104,3
104,1
104,8
105,2
102,7
101
93,9
90,2
92,4
94,4
93,3
93,9
95,1
97,6
99,3
101,1
100,6
99,3
97
96,4
98,7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164314&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164314&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164314&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.9127717.07030
20.7858336.0870
30.6482745.02152e-06
40.5023673.89130.000126
50.3816622.95630.002223
60.312842.42320.009208
70.2655042.05660.022041
80.2433181.88470.032156
90.2368371.83450.035767
100.2313251.79180.039101
110.1973981.5290.065756
120.1229520.95240.172362
130.0126280.09780.461202
14-0.104881-0.81240.209885
15-0.206739-1.60140.057271
16-0.284011-2.19990.015837
17-0.337969-2.61790.005591

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.912771 & 7.0703 & 0 \tabularnewline
2 & 0.785833 & 6.087 & 0 \tabularnewline
3 & 0.648274 & 5.0215 & 2e-06 \tabularnewline
4 & 0.502367 & 3.8913 & 0.000126 \tabularnewline
5 & 0.381662 & 2.9563 & 0.002223 \tabularnewline
6 & 0.31284 & 2.4232 & 0.009208 \tabularnewline
7 & 0.265504 & 2.0566 & 0.022041 \tabularnewline
8 & 0.243318 & 1.8847 & 0.032156 \tabularnewline
9 & 0.236837 & 1.8345 & 0.035767 \tabularnewline
10 & 0.231325 & 1.7918 & 0.039101 \tabularnewline
11 & 0.197398 & 1.529 & 0.065756 \tabularnewline
12 & 0.122952 & 0.9524 & 0.172362 \tabularnewline
13 & 0.012628 & 0.0978 & 0.461202 \tabularnewline
14 & -0.104881 & -0.8124 & 0.209885 \tabularnewline
15 & -0.206739 & -1.6014 & 0.057271 \tabularnewline
16 & -0.284011 & -2.1999 & 0.015837 \tabularnewline
17 & -0.337969 & -2.6179 & 0.005591 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164314&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]0.912771[/C][C]7.0703[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.785833[/C][C]6.087[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.648274[/C][C]5.0215[/C][C]2e-06[/C][/ROW]
[ROW][C]4[/C][C]0.502367[/C][C]3.8913[/C][C]0.000126[/C][/ROW]
[ROW][C]5[/C][C]0.381662[/C][C]2.9563[/C][C]0.002223[/C][/ROW]
[ROW][C]6[/C][C]0.31284[/C][C]2.4232[/C][C]0.009208[/C][/ROW]
[ROW][C]7[/C][C]0.265504[/C][C]2.0566[/C][C]0.022041[/C][/ROW]
[ROW][C]8[/C][C]0.243318[/C][C]1.8847[/C][C]0.032156[/C][/ROW]
[ROW][C]9[/C][C]0.236837[/C][C]1.8345[/C][C]0.035767[/C][/ROW]
[ROW][C]10[/C][C]0.231325[/C][C]1.7918[/C][C]0.039101[/C][/ROW]
[ROW][C]11[/C][C]0.197398[/C][C]1.529[/C][C]0.065756[/C][/ROW]
[ROW][C]12[/C][C]0.122952[/C][C]0.9524[/C][C]0.172362[/C][/ROW]
[ROW][C]13[/C][C]0.012628[/C][C]0.0978[/C][C]0.461202[/C][/ROW]
[ROW][C]14[/C][C]-0.104881[/C][C]-0.8124[/C][C]0.209885[/C][/ROW]
[ROW][C]15[/C][C]-0.206739[/C][C]-1.6014[/C][C]0.057271[/C][/ROW]
[ROW][C]16[/C][C]-0.284011[/C][C]-2.1999[/C][C]0.015837[/C][/ROW]
[ROW][C]17[/C][C]-0.337969[/C][C]-2.6179[/C][C]0.005591[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164314&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164314&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
10.9127717.07030
20.7858336.0870
30.6482745.02152e-06
40.5023673.89130.000126
50.3816622.95630.002223
60.312842.42320.009208
70.2655042.05660.022041
80.2433181.88470.032156
90.2368371.83450.035767
100.2313251.79180.039101
110.1973981.5290.065756
120.1229520.95240.172362
130.0126280.09780.461202
14-0.104881-0.81240.209885
15-0.206739-1.60140.057271
16-0.284011-2.19990.015837
17-0.337969-2.61790.005591






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9127717.07030
2-0.283595-2.19670.015957
3-0.088467-0.68530.247908
4-0.123158-0.9540.171962
50.0876750.67910.249835
60.1913191.4820.071793
7-0.044005-0.34090.367198
80.0502560.38930.349224
9-0.009938-0.0770.469449
100.0048280.03740.485146
11-0.16324-1.26450.105479
12-0.225158-1.74410.043134
13-0.167746-1.29940.099397
14-0.00945-0.07320.470944
150.0560560.43420.332847
16-0.030625-0.23720.406646
17-0.105029-0.81360.209559

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.912771 & 7.0703 & 0 \tabularnewline
2 & -0.283595 & -2.1967 & 0.015957 \tabularnewline
3 & -0.088467 & -0.6853 & 0.247908 \tabularnewline
4 & -0.123158 & -0.954 & 0.171962 \tabularnewline
5 & 0.087675 & 0.6791 & 0.249835 \tabularnewline
6 & 0.191319 & 1.482 & 0.071793 \tabularnewline
7 & -0.044005 & -0.3409 & 0.367198 \tabularnewline
8 & 0.050256 & 0.3893 & 0.349224 \tabularnewline
9 & -0.009938 & -0.077 & 0.469449 \tabularnewline
10 & 0.004828 & 0.0374 & 0.485146 \tabularnewline
11 & -0.16324 & -1.2645 & 0.105479 \tabularnewline
12 & -0.225158 & -1.7441 & 0.043134 \tabularnewline
13 & -0.167746 & -1.2994 & 0.099397 \tabularnewline
14 & -0.00945 & -0.0732 & 0.470944 \tabularnewline
15 & 0.056056 & 0.4342 & 0.332847 \tabularnewline
16 & -0.030625 & -0.2372 & 0.406646 \tabularnewline
17 & -0.105029 & -0.8136 & 0.209559 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164314&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]0.912771[/C][C]7.0703[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.283595[/C][C]-2.1967[/C][C]0.015957[/C][/ROW]
[ROW][C]3[/C][C]-0.088467[/C][C]-0.6853[/C][C]0.247908[/C][/ROW]
[ROW][C]4[/C][C]-0.123158[/C][C]-0.954[/C][C]0.171962[/C][/ROW]
[ROW][C]5[/C][C]0.087675[/C][C]0.6791[/C][C]0.249835[/C][/ROW]
[ROW][C]6[/C][C]0.191319[/C][C]1.482[/C][C]0.071793[/C][/ROW]
[ROW][C]7[/C][C]-0.044005[/C][C]-0.3409[/C][C]0.367198[/C][/ROW]
[ROW][C]8[/C][C]0.050256[/C][C]0.3893[/C][C]0.349224[/C][/ROW]
[ROW][C]9[/C][C]-0.009938[/C][C]-0.077[/C][C]0.469449[/C][/ROW]
[ROW][C]10[/C][C]0.004828[/C][C]0.0374[/C][C]0.485146[/C][/ROW]
[ROW][C]11[/C][C]-0.16324[/C][C]-1.2645[/C][C]0.105479[/C][/ROW]
[ROW][C]12[/C][C]-0.225158[/C][C]-1.7441[/C][C]0.043134[/C][/ROW]
[ROW][C]13[/C][C]-0.167746[/C][C]-1.2994[/C][C]0.099397[/C][/ROW]
[ROW][C]14[/C][C]-0.00945[/C][C]-0.0732[/C][C]0.470944[/C][/ROW]
[ROW][C]15[/C][C]0.056056[/C][C]0.4342[/C][C]0.332847[/C][/ROW]
[ROW][C]16[/C][C]-0.030625[/C][C]-0.2372[/C][C]0.406646[/C][/ROW]
[ROW][C]17[/C][C]-0.105029[/C][C]-0.8136[/C][C]0.209559[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164314&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164314&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
10.9127717.07030
2-0.283595-2.19670.015957
3-0.088467-0.68530.247908
4-0.123158-0.9540.171962
50.0876750.67910.249835
60.1913191.4820.071793
7-0.044005-0.34090.367198
80.0502560.38930.349224
9-0.009938-0.0770.469449
100.0048280.03740.485146
11-0.16324-1.26450.105479
12-0.225158-1.74410.043134
13-0.167746-1.29940.099397
14-0.00945-0.07320.470944
150.0560560.43420.332847
16-0.030625-0.23720.406646
17-0.105029-0.81360.209559


Figures (Output of Computation)

Input Parameters & R Code

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 ; 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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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')