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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, 03 Dec 2010 15:23:40 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/03/t1291389704wa6di08bnmfqvj6.htm/, Retrieved Tue, 07 May 2024 12:48:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=104863, Retrieved Tue, 07 May 2024 12:48:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140

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] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-   PD      [(Partial) Autocorrelation Function] [WS9] [2010-12-03 15:23:40] [0cadca125c925bcc9e6efbdd1941e458] [Current]
-    D        [(Partial) Autocorrelation Function] [WS9] [2010-12-03 15:28:44] [c7506ced21a6c0dca45d37c8a93c80e0]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
101,79
101,78
102,04
102,05
101,97
102,2
102,18
102,09
101,79
101,79
101,79
101,91
101,84
101,91
103,21
103,21
104,17
103,86
104,97
104,91
104,02
104,02
103,8
103,8
104,28
103,79
103,81
103,74
105,05
104,92
104,72
104,65
104,72
104,59
104,59
104,55
104,47
104,48
104,35
104,09
104,52
104,88
105,16
105,19
105,23
105,21
105,2
105,16
105,06
105,09
105,8
105,76
105,72
105,82
105,82
105,71

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=104863&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=104863&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104863&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
10.9184386.8730
20.8435836.31280
30.7640775.71780
40.6928765.1852e-06
50.6132354.5891.3e-05
60.5350574.0049.3e-05
70.4864153.640.000298
80.4451023.33080.000769
90.4035753.02010.001901
100.3615332.70550.004511
110.2997592.24320.014429
120.2567141.92110.029909
130.1946641.45670.075387
140.1262390.94470.17444
150.070440.52710.300094
160.0301550.22570.411144
170.016860.12620.450024

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.918438 & 6.873 & 0 \tabularnewline
2 & 0.843583 & 6.3128 & 0 \tabularnewline
3 & 0.764077 & 5.7178 & 0 \tabularnewline
4 & 0.692876 & 5.185 & 2e-06 \tabularnewline
5 & 0.613235 & 4.589 & 1.3e-05 \tabularnewline
6 & 0.535057 & 4.004 & 9.3e-05 \tabularnewline
7 & 0.486415 & 3.64 & 0.000298 \tabularnewline
8 & 0.445102 & 3.3308 & 0.000769 \tabularnewline
9 & 0.403575 & 3.0201 & 0.001901 \tabularnewline
10 & 0.361533 & 2.7055 & 0.004511 \tabularnewline
11 & 0.299759 & 2.2432 & 0.014429 \tabularnewline
12 & 0.256714 & 1.9211 & 0.029909 \tabularnewline
13 & 0.194664 & 1.4567 & 0.075387 \tabularnewline
14 & 0.126239 & 0.9447 & 0.17444 \tabularnewline
15 & 0.07044 & 0.5271 & 0.300094 \tabularnewline
16 & 0.030155 & 0.2257 & 0.411144 \tabularnewline
17 & 0.01686 & 0.1262 & 0.450024 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104863&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]0.918438[/C][C]6.873[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.843583[/C][C]6.3128[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.764077[/C][C]5.7178[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.692876[/C][C]5.185[/C][C]2e-06[/C][/ROW]
[ROW][C]5[/C][C]0.613235[/C][C]4.589[/C][C]1.3e-05[/C][/ROW]
[ROW][C]6[/C][C]0.535057[/C][C]4.004[/C][C]9.3e-05[/C][/ROW]
[ROW][C]7[/C][C]0.486415[/C][C]3.64[/C][C]0.000298[/C][/ROW]
[ROW][C]8[/C][C]0.445102[/C][C]3.3308[/C][C]0.000769[/C][/ROW]
[ROW][C]9[/C][C]0.403575[/C][C]3.0201[/C][C]0.001901[/C][/ROW]
[ROW][C]10[/C][C]0.361533[/C][C]2.7055[/C][C]0.004511[/C][/ROW]
[ROW][C]11[/C][C]0.299759[/C][C]2.2432[/C][C]0.014429[/C][/ROW]
[ROW][C]12[/C][C]0.256714[/C][C]1.9211[/C][C]0.029909[/C][/ROW]
[ROW][C]13[/C][C]0.194664[/C][C]1.4567[/C][C]0.075387[/C][/ROW]
[ROW][C]14[/C][C]0.126239[/C][C]0.9447[/C][C]0.17444[/C][/ROW]
[ROW][C]15[/C][C]0.07044[/C][C]0.5271[/C][C]0.300094[/C][/ROW]
[ROW][C]16[/C][C]0.030155[/C][C]0.2257[/C][C]0.411144[/C][/ROW]
[ROW][C]17[/C][C]0.01686[/C][C]0.1262[/C][C]0.450024[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104863&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104863&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
10.9184386.8730
20.8435836.31280
30.7640775.71780
40.6928765.1852e-06
50.6132354.5891.3e-05
60.5350574.0049.3e-05
70.4864153.640.000298
80.4451023.33080.000769
90.4035753.02010.001901
100.3615332.70550.004511
110.2997592.24320.014429
120.2567141.92110.029909
130.1946641.45670.075387
140.1262390.94470.17444
150.070440.52710.300094
160.0301550.22570.411144
170.016860.12620.450024






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9184386.8730
20.0003520.00260.498954
3-0.068717-0.51420.304556
40.0060470.04530.482033
5-0.091784-0.68680.247507
6-0.046247-0.34610.365289
70.1461631.09380.139367
80.0212790.15920.437029
9-0.0387-0.28960.386593
10-0.022151-0.16580.43447
11-0.180415-1.35010.091208
120.0633330.47390.318692
13-0.11321-0.84720.200249
14-0.103697-0.7760.220509
150.0672240.50310.308448
160.0380620.28480.388412
170.1056060.79030.216348

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.918438 & 6.873 & 0 \tabularnewline
2 & 0.000352 & 0.0026 & 0.498954 \tabularnewline
3 & -0.068717 & -0.5142 & 0.304556 \tabularnewline
4 & 0.006047 & 0.0453 & 0.482033 \tabularnewline
5 & -0.091784 & -0.6868 & 0.247507 \tabularnewline
6 & -0.046247 & -0.3461 & 0.365289 \tabularnewline
7 & 0.146163 & 1.0938 & 0.139367 \tabularnewline
8 & 0.021279 & 0.1592 & 0.437029 \tabularnewline
9 & -0.0387 & -0.2896 & 0.386593 \tabularnewline
10 & -0.022151 & -0.1658 & 0.43447 \tabularnewline
11 & -0.180415 & -1.3501 & 0.091208 \tabularnewline
12 & 0.063333 & 0.4739 & 0.318692 \tabularnewline
13 & -0.11321 & -0.8472 & 0.200249 \tabularnewline
14 & -0.103697 & -0.776 & 0.220509 \tabularnewline
15 & 0.067224 & 0.5031 & 0.308448 \tabularnewline
16 & 0.038062 & 0.2848 & 0.388412 \tabularnewline
17 & 0.105606 & 0.7903 & 0.216348 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104863&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]0.918438[/C][C]6.873[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.000352[/C][C]0.0026[/C][C]0.498954[/C][/ROW]
[ROW][C]3[/C][C]-0.068717[/C][C]-0.5142[/C][C]0.304556[/C][/ROW]
[ROW][C]4[/C][C]0.006047[/C][C]0.0453[/C][C]0.482033[/C][/ROW]
[ROW][C]5[/C][C]-0.091784[/C][C]-0.6868[/C][C]0.247507[/C][/ROW]
[ROW][C]6[/C][C]-0.046247[/C][C]-0.3461[/C][C]0.365289[/C][/ROW]
[ROW][C]7[/C][C]0.146163[/C][C]1.0938[/C][C]0.139367[/C][/ROW]
[ROW][C]8[/C][C]0.021279[/C][C]0.1592[/C][C]0.437029[/C][/ROW]
[ROW][C]9[/C][C]-0.0387[/C][C]-0.2896[/C][C]0.386593[/C][/ROW]
[ROW][C]10[/C][C]-0.022151[/C][C]-0.1658[/C][C]0.43447[/C][/ROW]
[ROW][C]11[/C][C]-0.180415[/C][C]-1.3501[/C][C]0.091208[/C][/ROW]
[ROW][C]12[/C][C]0.063333[/C][C]0.4739[/C][C]0.318692[/C][/ROW]
[ROW][C]13[/C][C]-0.11321[/C][C]-0.8472[/C][C]0.200249[/C][/ROW]
[ROW][C]14[/C][C]-0.103697[/C][C]-0.776[/C][C]0.220509[/C][/ROW]
[ROW][C]15[/C][C]0.067224[/C][C]0.5031[/C][C]0.308448[/C][/ROW]
[ROW][C]16[/C][C]0.038062[/C][C]0.2848[/C][C]0.388412[/C][/ROW]
[ROW][C]17[/C][C]0.105606[/C][C]0.7903[/C][C]0.216348[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104863&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104863&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
10.9184386.8730
20.0003520.00260.498954
3-0.068717-0.51420.304556
40.0060470.04530.482033
5-0.091784-0.68680.247507
6-0.046247-0.34610.365289
70.1461631.09380.139367
80.0212790.15920.437029
9-0.0387-0.28960.386593
10-0.022151-0.16580.43447
11-0.180415-1.35010.091208
120.0633330.47390.318692
13-0.11321-0.84720.200249
14-0.103697-0.7760.220509
150.0672240.50310.308448
160.0380620.28480.388412
170.1056060.79030.216348


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 2 ; par4 = 1 ;
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')