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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 computationTue, 07 Dec 2010 09:06:31 +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/07/t1291713208atduthv8rdvq7m1.htm/, Retrieved Fri, 03 May 2024 18:17:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106048, Retrieved Fri, 03 May 2024 18:17:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103

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]
-    D      [(Partial) Autocorrelation Function] [ws 9: acf] [2010-12-07 09:06:31] [09489ba95453d3f5c9e6f2eaeda915af] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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
89,1
104,5
105,1
95,1
88,7
86,3
91,8
111,5
99,7
97,5
111,7
86,2
95,4

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106048&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106048&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106048&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'George Udny Yule' @ 72.249.76.132






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.266612.19850.015659
20.0336530.27750.391116
30.1976551.62990.053873
40.1211190.99880.160723
50.3597112.96630.002078
60.4195113.45940.00047
70.2702822.22880.014568
80.0829960.68440.248024
90.0461170.38030.352459
10-0.131488-1.08430.141035
110.102520.84540.200426
120.5303724.37362.1e-05
130.0248330.20480.419179
14-0.202743-1.67190.049574
15-0.143557-1.18380.120306
16-0.099368-0.81940.207708
170.0822060.67790.250071
180.0601750.49620.31067

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.26661 & 2.1985 & 0.015659 \tabularnewline
2 & 0.033653 & 0.2775 & 0.391116 \tabularnewline
3 & 0.197655 & 1.6299 & 0.053873 \tabularnewline
4 & 0.121119 & 0.9988 & 0.160723 \tabularnewline
5 & 0.359711 & 2.9663 & 0.002078 \tabularnewline
6 & 0.419511 & 3.4594 & 0.00047 \tabularnewline
7 & 0.270282 & 2.2288 & 0.014568 \tabularnewline
8 & 0.082996 & 0.6844 & 0.248024 \tabularnewline
9 & 0.046117 & 0.3803 & 0.352459 \tabularnewline
10 & -0.131488 & -1.0843 & 0.141035 \tabularnewline
11 & 0.10252 & 0.8454 & 0.200426 \tabularnewline
12 & 0.530372 & 4.3736 & 2.1e-05 \tabularnewline
13 & 0.024833 & 0.2048 & 0.419179 \tabularnewline
14 & -0.202743 & -1.6719 & 0.049574 \tabularnewline
15 & -0.143557 & -1.1838 & 0.120306 \tabularnewline
16 & -0.099368 & -0.8194 & 0.207708 \tabularnewline
17 & 0.082206 & 0.6779 & 0.250071 \tabularnewline
18 & 0.060175 & 0.4962 & 0.31067 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106048&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]0.26661[/C][C]2.1985[/C][C]0.015659[/C][/ROW]
[ROW][C]2[/C][C]0.033653[/C][C]0.2775[/C][C]0.391116[/C][/ROW]
[ROW][C]3[/C][C]0.197655[/C][C]1.6299[/C][C]0.053873[/C][/ROW]
[ROW][C]4[/C][C]0.121119[/C][C]0.9988[/C][C]0.160723[/C][/ROW]
[ROW][C]5[/C][C]0.359711[/C][C]2.9663[/C][C]0.002078[/C][/ROW]
[ROW][C]6[/C][C]0.419511[/C][C]3.4594[/C][C]0.00047[/C][/ROW]
[ROW][C]7[/C][C]0.270282[/C][C]2.2288[/C][C]0.014568[/C][/ROW]
[ROW][C]8[/C][C]0.082996[/C][C]0.6844[/C][C]0.248024[/C][/ROW]
[ROW][C]9[/C][C]0.046117[/C][C]0.3803[/C][C]0.352459[/C][/ROW]
[ROW][C]10[/C][C]-0.131488[/C][C]-1.0843[/C][C]0.141035[/C][/ROW]
[ROW][C]11[/C][C]0.10252[/C][C]0.8454[/C][C]0.200426[/C][/ROW]
[ROW][C]12[/C][C]0.530372[/C][C]4.3736[/C][C]2.1e-05[/C][/ROW]
[ROW][C]13[/C][C]0.024833[/C][C]0.2048[/C][C]0.419179[/C][/ROW]
[ROW][C]14[/C][C]-0.202743[/C][C]-1.6719[/C][C]0.049574[/C][/ROW]
[ROW][C]15[/C][C]-0.143557[/C][C]-1.1838[/C][C]0.120306[/C][/ROW]
[ROW][C]16[/C][C]-0.099368[/C][C]-0.8194[/C][C]0.207708[/C][/ROW]
[ROW][C]17[/C][C]0.082206[/C][C]0.6779[/C][C]0.250071[/C][/ROW]
[ROW][C]18[/C][C]0.060175[/C][C]0.4962[/C][C]0.31067[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106048&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106048&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
10.266612.19850.015659
20.0336530.27750.391116
30.1976551.62990.053873
40.1211190.99880.160723
50.3597112.96630.002078
60.4195113.45940.00047
70.2702822.22880.014568
80.0829960.68440.248024
90.0461170.38030.352459
10-0.131488-1.08430.141035
110.102520.84540.200426
120.5303724.37362.1e-05
130.0248330.20480.419179
14-0.202743-1.67190.049574
15-0.143557-1.18380.120306
16-0.099368-0.81940.207708
170.0822060.67790.250071
180.0601750.49620.31067






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.266612.19850.015659
2-0.040292-0.33230.370359
30.2146451.770.040604
40.012120.09990.460341
50.3782023.11870.001332
60.2560462.11140.019208
70.2232921.84130.034969
8-0.075838-0.62540.26691
9-0.056518-0.46610.321332
10-0.495224-4.08376e-05
11-0.133528-1.10110.137368
120.350312.88870.002592
13-0.141596-1.16760.123518
14-0.198656-1.63820.053004
15-0.184667-1.52280.066222
160.1349881.11310.134784
170.0223640.18440.427118
18-0.086967-0.71710.23787

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.26661 & 2.1985 & 0.015659 \tabularnewline
2 & -0.040292 & -0.3323 & 0.370359 \tabularnewline
3 & 0.214645 & 1.77 & 0.040604 \tabularnewline
4 & 0.01212 & 0.0999 & 0.460341 \tabularnewline
5 & 0.378202 & 3.1187 & 0.001332 \tabularnewline
6 & 0.256046 & 2.1114 & 0.019208 \tabularnewline
7 & 0.223292 & 1.8413 & 0.034969 \tabularnewline
8 & -0.075838 & -0.6254 & 0.26691 \tabularnewline
9 & -0.056518 & -0.4661 & 0.321332 \tabularnewline
10 & -0.495224 & -4.0837 & 6e-05 \tabularnewline
11 & -0.133528 & -1.1011 & 0.137368 \tabularnewline
12 & 0.35031 & 2.8887 & 0.002592 \tabularnewline
13 & -0.141596 & -1.1676 & 0.123518 \tabularnewline
14 & -0.198656 & -1.6382 & 0.053004 \tabularnewline
15 & -0.184667 & -1.5228 & 0.066222 \tabularnewline
16 & 0.134988 & 1.1131 & 0.134784 \tabularnewline
17 & 0.022364 & 0.1844 & 0.427118 \tabularnewline
18 & -0.086967 & -0.7171 & 0.23787 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106048&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]0.26661[/C][C]2.1985[/C][C]0.015659[/C][/ROW]
[ROW][C]2[/C][C]-0.040292[/C][C]-0.3323[/C][C]0.370359[/C][/ROW]
[ROW][C]3[/C][C]0.214645[/C][C]1.77[/C][C]0.040604[/C][/ROW]
[ROW][C]4[/C][C]0.01212[/C][C]0.0999[/C][C]0.460341[/C][/ROW]
[ROW][C]5[/C][C]0.378202[/C][C]3.1187[/C][C]0.001332[/C][/ROW]
[ROW][C]6[/C][C]0.256046[/C][C]2.1114[/C][C]0.019208[/C][/ROW]
[ROW][C]7[/C][C]0.223292[/C][C]1.8413[/C][C]0.034969[/C][/ROW]
[ROW][C]8[/C][C]-0.075838[/C][C]-0.6254[/C][C]0.26691[/C][/ROW]
[ROW][C]9[/C][C]-0.056518[/C][C]-0.4661[/C][C]0.321332[/C][/ROW]
[ROW][C]10[/C][C]-0.495224[/C][C]-4.0837[/C][C]6e-05[/C][/ROW]
[ROW][C]11[/C][C]-0.133528[/C][C]-1.1011[/C][C]0.137368[/C][/ROW]
[ROW][C]12[/C][C]0.35031[/C][C]2.8887[/C][C]0.002592[/C][/ROW]
[ROW][C]13[/C][C]-0.141596[/C][C]-1.1676[/C][C]0.123518[/C][/ROW]
[ROW][C]14[/C][C]-0.198656[/C][C]-1.6382[/C][C]0.053004[/C][/ROW]
[ROW][C]15[/C][C]-0.184667[/C][C]-1.5228[/C][C]0.066222[/C][/ROW]
[ROW][C]16[/C][C]0.134988[/C][C]1.1131[/C][C]0.134784[/C][/ROW]
[ROW][C]17[/C][C]0.022364[/C][C]0.1844[/C][C]0.427118[/C][/ROW]
[ROW][C]18[/C][C]-0.086967[/C][C]-0.7171[/C][C]0.23787[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106048&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106048&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
10.266612.19850.015659
2-0.040292-0.33230.370359
30.2146451.770.040604
40.012120.09990.460341
50.3782023.11870.001332
60.2560462.11140.019208
70.2232921.84130.034969
8-0.075838-0.62540.26691
9-0.056518-0.46610.321332
10-0.495224-4.08376e-05
11-0.133528-1.10110.137368
120.350312.88870.002592
13-0.141596-1.16760.123518
14-0.198656-1.63820.053004
15-0.184667-1.52280.066222
160.1349881.11310.134784
170.0223640.18440.427118
18-0.086967-0.71710.23787


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 ;
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')