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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 computationThu, 22 Dec 2011 19:22:43 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/22/t13245998162ttca5dab9umu3g.htm/, Retrieved Fri, 03 May 2024 06:21:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160111, Retrieved Fri, 03 May 2024 06:21:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113

Tree of Dependent Computations

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       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [(Partial) Autocorrelation Function] [Births] [2010-11-29 09:36:27] [b98453cac15ba1066b407e146608df68]
- R PD          [(Partial) Autocorrelation Function] [WS9 3.1 ACF d=0, D=0] [2010-12-07 10:00:49] [afe9379cca749d06b3d6872e02cc47ed]
- R PD            [(Partial) Autocorrelation Function] [PAPER: aantal fai...] [2011-12-22 23:47:48] [f0cb027b41af06223bae4ee77475f3bc]
-    D                [(Partial) Autocorrelation Function] [PAPER: werklooshe...] [2011-12-23 00:22:43] [6baf48ba14bcb50d9e72b77bece8a45b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0,072
0,073
0,073
0,073
0,074
0,073
0,074
0,074
0,076
0,076
0,077
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0,089
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0,086
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0,083
0,082
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0,079
0,076
0,073
0,071
0,070
0,070
0,070
0,070
0,069
0,068
0,067
0,066

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'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160111&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160111&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160111&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'Gertrude Mary Cox' @ cox.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.94018810.29920
20.8491349.30180
30.7550728.27140
40.6849127.50280
50.6406947.01850
60.5970816.54070
70.5389275.90370
80.459395.03241e-06
90.3693884.04644.6e-05
100.280343.0710.00132
110.2008862.20060.01484
120.1316321.4420.07596
130.0720960.78980.215608
140.0194050.21260.416011
15-0.026691-0.29240.385248
16-0.065231-0.71460.238133
17-0.102329-1.1210.132273
18-0.131862-1.44450.075606
19-0.156946-1.71930.044073
20-0.178667-1.95720.026323

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.940188 & 10.2992 & 0 \tabularnewline
2 & 0.849134 & 9.3018 & 0 \tabularnewline
3 & 0.755072 & 8.2714 & 0 \tabularnewline
4 & 0.684912 & 7.5028 & 0 \tabularnewline
5 & 0.640694 & 7.0185 & 0 \tabularnewline
6 & 0.597081 & 6.5407 & 0 \tabularnewline
7 & 0.538927 & 5.9037 & 0 \tabularnewline
8 & 0.45939 & 5.0324 & 1e-06 \tabularnewline
9 & 0.369388 & 4.0464 & 4.6e-05 \tabularnewline
10 & 0.28034 & 3.071 & 0.00132 \tabularnewline
11 & 0.200886 & 2.2006 & 0.01484 \tabularnewline
12 & 0.131632 & 1.442 & 0.07596 \tabularnewline
13 & 0.072096 & 0.7898 & 0.215608 \tabularnewline
14 & 0.019405 & 0.2126 & 0.416011 \tabularnewline
15 & -0.026691 & -0.2924 & 0.385248 \tabularnewline
16 & -0.065231 & -0.7146 & 0.238133 \tabularnewline
17 & -0.102329 & -1.121 & 0.132273 \tabularnewline
18 & -0.131862 & -1.4445 & 0.075606 \tabularnewline
19 & -0.156946 & -1.7193 & 0.044073 \tabularnewline
20 & -0.178667 & -1.9572 & 0.026323 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160111&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]0.940188[/C][C]10.2992[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.849134[/C][C]9.3018[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.755072[/C][C]8.2714[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.684912[/C][C]7.5028[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.640694[/C][C]7.0185[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.597081[/C][C]6.5407[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.538927[/C][C]5.9037[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.45939[/C][C]5.0324[/C][C]1e-06[/C][/ROW]
[ROW][C]9[/C][C]0.369388[/C][C]4.0464[/C][C]4.6e-05[/C][/ROW]
[ROW][C]10[/C][C]0.28034[/C][C]3.071[/C][C]0.00132[/C][/ROW]
[ROW][C]11[/C][C]0.200886[/C][C]2.2006[/C][C]0.01484[/C][/ROW]
[ROW][C]12[/C][C]0.131632[/C][C]1.442[/C][C]0.07596[/C][/ROW]
[ROW][C]13[/C][C]0.072096[/C][C]0.7898[/C][C]0.215608[/C][/ROW]
[ROW][C]14[/C][C]0.019405[/C][C]0.2126[/C][C]0.416011[/C][/ROW]
[ROW][C]15[/C][C]-0.026691[/C][C]-0.2924[/C][C]0.385248[/C][/ROW]
[ROW][C]16[/C][C]-0.065231[/C][C]-0.7146[/C][C]0.238133[/C][/ROW]
[ROW][C]17[/C][C]-0.102329[/C][C]-1.121[/C][C]0.132273[/C][/ROW]
[ROW][C]18[/C][C]-0.131862[/C][C]-1.4445[/C][C]0.075606[/C][/ROW]
[ROW][C]19[/C][C]-0.156946[/C][C]-1.7193[/C][C]0.044073[/C][/ROW]
[ROW][C]20[/C][C]-0.178667[/C][C]-1.9572[/C][C]0.026323[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160111&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160111&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
10.94018810.29920
20.8491349.30180
30.7550728.27140
40.6849127.50280
50.6406947.01850
60.5970816.54070
70.5389275.90370
80.459395.03241e-06
90.3693884.04644.6e-05
100.280343.0710.00132
110.2008862.20060.01484
120.1316321.4420.07596
130.0720960.78980.215608
140.0194050.21260.416011
15-0.026691-0.29240.385248
16-0.065231-0.71460.238133
17-0.102329-1.1210.132273
18-0.131862-1.44450.075606
19-0.156946-1.71930.044073
20-0.178667-1.95720.026323






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.94018810.29920
2-0.30006-3.2870.000664
3-0.00675-0.07390.470587
40.1671351.83090.0348
50.0918271.00590.15824
6-0.129688-1.42070.079004
7-0.12244-1.34130.091185
8-0.118955-1.30310.097521
9-0.061016-0.66840.25258
10-0.069954-0.76630.222498
11-0.049809-0.54560.293165
12-0.042668-0.46740.32053
130.0079570.08720.465345
140.010860.1190.452751
150.0256410.28090.389642
160.0300480.32920.371304
17-0.040292-0.44140.329869
180.0395170.43290.332938
19-0.015075-0.16510.434556
20-0.039935-0.43750.331281

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.940188 & 10.2992 & 0 \tabularnewline
2 & -0.30006 & -3.287 & 0.000664 \tabularnewline
3 & -0.00675 & -0.0739 & 0.470587 \tabularnewline
4 & 0.167135 & 1.8309 & 0.0348 \tabularnewline
5 & 0.091827 & 1.0059 & 0.15824 \tabularnewline
6 & -0.129688 & -1.4207 & 0.079004 \tabularnewline
7 & -0.12244 & -1.3413 & 0.091185 \tabularnewline
8 & -0.118955 & -1.3031 & 0.097521 \tabularnewline
9 & -0.061016 & -0.6684 & 0.25258 \tabularnewline
10 & -0.069954 & -0.7663 & 0.222498 \tabularnewline
11 & -0.049809 & -0.5456 & 0.293165 \tabularnewline
12 & -0.042668 & -0.4674 & 0.32053 \tabularnewline
13 & 0.007957 & 0.0872 & 0.465345 \tabularnewline
14 & 0.01086 & 0.119 & 0.452751 \tabularnewline
15 & 0.025641 & 0.2809 & 0.389642 \tabularnewline
16 & 0.030048 & 0.3292 & 0.371304 \tabularnewline
17 & -0.040292 & -0.4414 & 0.329869 \tabularnewline
18 & 0.039517 & 0.4329 & 0.332938 \tabularnewline
19 & -0.015075 & -0.1651 & 0.434556 \tabularnewline
20 & -0.039935 & -0.4375 & 0.331281 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160111&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]0.940188[/C][C]10.2992[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.30006[/C][C]-3.287[/C][C]0.000664[/C][/ROW]
[ROW][C]3[/C][C]-0.00675[/C][C]-0.0739[/C][C]0.470587[/C][/ROW]
[ROW][C]4[/C][C]0.167135[/C][C]1.8309[/C][C]0.0348[/C][/ROW]
[ROW][C]5[/C][C]0.091827[/C][C]1.0059[/C][C]0.15824[/C][/ROW]
[ROW][C]6[/C][C]-0.129688[/C][C]-1.4207[/C][C]0.079004[/C][/ROW]
[ROW][C]7[/C][C]-0.12244[/C][C]-1.3413[/C][C]0.091185[/C][/ROW]
[ROW][C]8[/C][C]-0.118955[/C][C]-1.3031[/C][C]0.097521[/C][/ROW]
[ROW][C]9[/C][C]-0.061016[/C][C]-0.6684[/C][C]0.25258[/C][/ROW]
[ROW][C]10[/C][C]-0.069954[/C][C]-0.7663[/C][C]0.222498[/C][/ROW]
[ROW][C]11[/C][C]-0.049809[/C][C]-0.5456[/C][C]0.293165[/C][/ROW]
[ROW][C]12[/C][C]-0.042668[/C][C]-0.4674[/C][C]0.32053[/C][/ROW]
[ROW][C]13[/C][C]0.007957[/C][C]0.0872[/C][C]0.465345[/C][/ROW]
[ROW][C]14[/C][C]0.01086[/C][C]0.119[/C][C]0.452751[/C][/ROW]
[ROW][C]15[/C][C]0.025641[/C][C]0.2809[/C][C]0.389642[/C][/ROW]
[ROW][C]16[/C][C]0.030048[/C][C]0.3292[/C][C]0.371304[/C][/ROW]
[ROW][C]17[/C][C]-0.040292[/C][C]-0.4414[/C][C]0.329869[/C][/ROW]
[ROW][C]18[/C][C]0.039517[/C][C]0.4329[/C][C]0.332938[/C][/ROW]
[ROW][C]19[/C][C]-0.015075[/C][C]-0.1651[/C][C]0.434556[/C][/ROW]
[ROW][C]20[/C][C]-0.039935[/C][C]-0.4375[/C][C]0.331281[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160111&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160111&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
10.94018810.29920
2-0.30006-3.2870.000664
3-0.00675-0.07390.470587
40.1671351.83090.0348
50.0918271.00590.15824
6-0.129688-1.42070.079004
7-0.12244-1.34130.091185
8-0.118955-1.30310.097521
9-0.061016-0.66840.25258
10-0.069954-0.76630.222498
11-0.049809-0.54560.293165
12-0.042668-0.46740.32053
130.0079570.08720.465345
140.010860.1190.452751
150.0256410.28090.389642
160.0300480.32920.371304
17-0.040292-0.44140.329869
180.0395170.43290.332938
19-0.015075-0.16510.434556
20-0.039935-0.43750.331281


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = multiplicative ; par2 = 12 ;
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')