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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 computationSun, 15 Jan 2012 12:00:15 -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/2012/Jan/15/t1326646860nz3ctmslfkrvi64.htm/, Retrieved Fri, 03 May 2024 07:34:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=161105, Retrieved Fri, 03 May 2024 07:34:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W12
Estimated Impact110

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Notched Boxplots] [boxplot] [2011-10-11 16:58:56] [0f3802131247472a006387bf3e5d274d]
- RMPD    [(Partial) Autocorrelation Function] [] [2012-01-15 17:00:15] [9bda411d6223d16f0472c7feaae49b5f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
113,25
104,54
132,78
122,99
133,14
125,83
122,99
125,7
148,47
120,75
136,7
139,17
123,47
112,76
137,99
139,75
140,22
121,6
132,33
130,34
149,05
130,47
139,29
146,55
137,79
122,95
139,51
155,77
143,95
125,07
142,35
144,34
145,87
156,01
146,74
156,45
152,29
122,56
154,59
149,68
118,75
109,22
104,19
107,33
114,07
107,92
103,53
117,3
112,09
95,08
123,28
121,98
121,74
119,93
113,31
117,19
141,13
130,18
127,47
148,33
131,24
119,99
146,49
142,98
140,65
131,15

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'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161105&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161105&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161105&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'AstonUniversity' @ aston.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.5205684.22913.7e-05
20.3467732.81720.003192
30.4600483.73740.000195
40.4119983.34710.000676
50.2808422.28160.012874
60.279532.27090.013211
70.076320.620.268689
80.1056090.8580.197006
9-0.047235-0.38370.351202
10-0.238143-1.93470.028659
11-0.126881-1.03080.153202
120.1038460.84360.200957
13-0.208851-1.69670.047232
14-0.352009-2.85970.002835
15-0.291483-2.3680.010411
16-0.213298-1.73280.043897
17-0.249144-2.02410.023508
18-0.240856-1.95670.027306

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.520568 & 4.2291 & 3.7e-05 \tabularnewline
2 & 0.346773 & 2.8172 & 0.003192 \tabularnewline
3 & 0.460048 & 3.7374 & 0.000195 \tabularnewline
4 & 0.411998 & 3.3471 & 0.000676 \tabularnewline
5 & 0.280842 & 2.2816 & 0.012874 \tabularnewline
6 & 0.27953 & 2.2709 & 0.013211 \tabularnewline
7 & 0.07632 & 0.62 & 0.268689 \tabularnewline
8 & 0.105609 & 0.858 & 0.197006 \tabularnewline
9 & -0.047235 & -0.3837 & 0.351202 \tabularnewline
10 & -0.238143 & -1.9347 & 0.028659 \tabularnewline
11 & -0.126881 & -1.0308 & 0.153202 \tabularnewline
12 & 0.103846 & 0.8436 & 0.200957 \tabularnewline
13 & -0.208851 & -1.6967 & 0.047232 \tabularnewline
14 & -0.352009 & -2.8597 & 0.002835 \tabularnewline
15 & -0.291483 & -2.368 & 0.010411 \tabularnewline
16 & -0.213298 & -1.7328 & 0.043897 \tabularnewline
17 & -0.249144 & -2.0241 & 0.023508 \tabularnewline
18 & -0.240856 & -1.9567 & 0.027306 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161105&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]0.520568[/C][C]4.2291[/C][C]3.7e-05[/C][/ROW]
[ROW][C]2[/C][C]0.346773[/C][C]2.8172[/C][C]0.003192[/C][/ROW]
[ROW][C]3[/C][C]0.460048[/C][C]3.7374[/C][C]0.000195[/C][/ROW]
[ROW][C]4[/C][C]0.411998[/C][C]3.3471[/C][C]0.000676[/C][/ROW]
[ROW][C]5[/C][C]0.280842[/C][C]2.2816[/C][C]0.012874[/C][/ROW]
[ROW][C]6[/C][C]0.27953[/C][C]2.2709[/C][C]0.013211[/C][/ROW]
[ROW][C]7[/C][C]0.07632[/C][C]0.62[/C][C]0.268689[/C][/ROW]
[ROW][C]8[/C][C]0.105609[/C][C]0.858[/C][C]0.197006[/C][/ROW]
[ROW][C]9[/C][C]-0.047235[/C][C]-0.3837[/C][C]0.351202[/C][/ROW]
[ROW][C]10[/C][C]-0.238143[/C][C]-1.9347[/C][C]0.028659[/C][/ROW]
[ROW][C]11[/C][C]-0.126881[/C][C]-1.0308[/C][C]0.153202[/C][/ROW]
[ROW][C]12[/C][C]0.103846[/C][C]0.8436[/C][C]0.200957[/C][/ROW]
[ROW][C]13[/C][C]-0.208851[/C][C]-1.6967[/C][C]0.047232[/C][/ROW]
[ROW][C]14[/C][C]-0.352009[/C][C]-2.8597[/C][C]0.002835[/C][/ROW]
[ROW][C]15[/C][C]-0.291483[/C][C]-2.368[/C][C]0.010411[/C][/ROW]
[ROW][C]16[/C][C]-0.213298[/C][C]-1.7328[/C][C]0.043897[/C][/ROW]
[ROW][C]17[/C][C]-0.249144[/C][C]-2.0241[/C][C]0.023508[/C][/ROW]
[ROW][C]18[/C][C]-0.240856[/C][C]-1.9567[/C][C]0.027306[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161105&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161105&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
10.5205684.22913.7e-05
20.3467732.81720.003192
30.4600483.73740.000195
40.4119983.34710.000676
50.2808422.28160.012874
60.279532.27090.013211
70.076320.620.268689
80.1056090.8580.197006
9-0.047235-0.38370.351202
10-0.238143-1.93470.028659
11-0.126881-1.03080.153202
120.1038460.84360.200957
13-0.208851-1.69670.047232
14-0.352009-2.85970.002835
15-0.291483-2.3680.010411
16-0.213298-1.73280.043897
17-0.249144-2.02410.023508
18-0.240856-1.95670.027306






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.5205684.22913.7e-05
20.1039530.84450.200716
30.3386072.75090.003832
40.0877990.71330.239093
5-0.018819-0.15290.439478
60.0364120.29580.384152
7-0.307237-2.4960.007533
80.0878240.71350.23903
9-0.347843-2.82590.003116
10-0.215172-1.74810.042551
110.118270.96080.170072
120.4071123.30740.000763
13-0.163598-1.32910.094199
14-0.266121-2.1620.017125
15-0.214653-1.74380.042921
160.0219210.17810.4296
170.0035460.02880.488551
18-0.004543-0.03690.485334

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.520568 & 4.2291 & 3.7e-05 \tabularnewline
2 & 0.103953 & 0.8445 & 0.200716 \tabularnewline
3 & 0.338607 & 2.7509 & 0.003832 \tabularnewline
4 & 0.087799 & 0.7133 & 0.239093 \tabularnewline
5 & -0.018819 & -0.1529 & 0.439478 \tabularnewline
6 & 0.036412 & 0.2958 & 0.384152 \tabularnewline
7 & -0.307237 & -2.496 & 0.007533 \tabularnewline
8 & 0.087824 & 0.7135 & 0.23903 \tabularnewline
9 & -0.347843 & -2.8259 & 0.003116 \tabularnewline
10 & -0.215172 & -1.7481 & 0.042551 \tabularnewline
11 & 0.11827 & 0.9608 & 0.170072 \tabularnewline
12 & 0.407112 & 3.3074 & 0.000763 \tabularnewline
13 & -0.163598 & -1.3291 & 0.094199 \tabularnewline
14 & -0.266121 & -2.162 & 0.017125 \tabularnewline
15 & -0.214653 & -1.7438 & 0.042921 \tabularnewline
16 & 0.021921 & 0.1781 & 0.4296 \tabularnewline
17 & 0.003546 & 0.0288 & 0.488551 \tabularnewline
18 & -0.004543 & -0.0369 & 0.485334 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161105&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]0.520568[/C][C]4.2291[/C][C]3.7e-05[/C][/ROW]
[ROW][C]2[/C][C]0.103953[/C][C]0.8445[/C][C]0.200716[/C][/ROW]
[ROW][C]3[/C][C]0.338607[/C][C]2.7509[/C][C]0.003832[/C][/ROW]
[ROW][C]4[/C][C]0.087799[/C][C]0.7133[/C][C]0.239093[/C][/ROW]
[ROW][C]5[/C][C]-0.018819[/C][C]-0.1529[/C][C]0.439478[/C][/ROW]
[ROW][C]6[/C][C]0.036412[/C][C]0.2958[/C][C]0.384152[/C][/ROW]
[ROW][C]7[/C][C]-0.307237[/C][C]-2.496[/C][C]0.007533[/C][/ROW]
[ROW][C]8[/C][C]0.087824[/C][C]0.7135[/C][C]0.23903[/C][/ROW]
[ROW][C]9[/C][C]-0.347843[/C][C]-2.8259[/C][C]0.003116[/C][/ROW]
[ROW][C]10[/C][C]-0.215172[/C][C]-1.7481[/C][C]0.042551[/C][/ROW]
[ROW][C]11[/C][C]0.11827[/C][C]0.9608[/C][C]0.170072[/C][/ROW]
[ROW][C]12[/C][C]0.407112[/C][C]3.3074[/C][C]0.000763[/C][/ROW]
[ROW][C]13[/C][C]-0.163598[/C][C]-1.3291[/C][C]0.094199[/C][/ROW]
[ROW][C]14[/C][C]-0.266121[/C][C]-2.162[/C][C]0.017125[/C][/ROW]
[ROW][C]15[/C][C]-0.214653[/C][C]-1.7438[/C][C]0.042921[/C][/ROW]
[ROW][C]16[/C][C]0.021921[/C][C]0.1781[/C][C]0.4296[/C][/ROW]
[ROW][C]17[/C][C]0.003546[/C][C]0.0288[/C][C]0.488551[/C][/ROW]
[ROW][C]18[/C][C]-0.004543[/C][C]-0.0369[/C][C]0.485334[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161105&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161105&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
10.5205684.22913.7e-05
20.1039530.84450.200716
30.3386072.75090.003832
40.0877990.71330.239093
5-0.018819-0.15290.439478
60.0364120.29580.384152
7-0.307237-2.4960.007533
80.0878240.71350.23903
9-0.347843-2.82590.003116
10-0.215172-1.74810.042551
110.118270.96080.170072
120.4071123.30740.000763
13-0.163598-1.32910.094199
14-0.266121-2.1620.017125
15-0.214653-1.74380.042921
160.0219210.17810.4296
170.0035460.02880.488551
18-0.004543-0.03690.485334


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')