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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 computationMon, 13 Dec 2010 08:20:15 +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/13/t1292228363tsvbdjfdi2vq1z2.htm/, Retrieved Tue, 07 May 2024 03:22:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108695, Retrieved Tue, 07 May 2024 03:22:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact177

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] [] [2010-12-13 08:20:15] [81d69fb83507cea26168920232cdff1b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
62.36
59.71
60.93
68.00
68.61
68.29
72.51
71.81
61.97
57.95
58.13
61.00
53.40
57.58
60.60
65.10
65.10
68.19
73.67
70.13
76.91
82.15
91.27
89.43
90.82
93.75
101.84
109.05
122.77
131.52
132.55
114.57
99.29
72.69
54.04
41.53
43.91
41.76
46.95
50.28
58.10
69.13
64.65
71.63
68.38
74.08
77.56
74.88
77.09
74.70
79.30
84.19
75.56
74.73
74.49
75.93
76.14

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108695&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108695&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108695&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.9262416.9930
20.7752225.85280
30.5686294.29313.5e-05
40.3535332.66910.004944
50.1487231.12280.133107
6-0.020498-0.15480.438781
7-0.13609-1.02750.154274
8-0.219968-1.66070.051131
9-0.283701-2.14190.018244
10-0.322602-2.43560.009009
11-0.347862-2.62630.005533
12-0.363016-2.74070.004087
13-0.368713-2.78370.003639
14-0.356217-2.68940.004686
15-0.333938-2.52120.007259
16-0.309644-2.33780.011467
17-0.273502-2.06490.021746

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.926241 & 6.993 & 0 \tabularnewline
2 & 0.775222 & 5.8528 & 0 \tabularnewline
3 & 0.568629 & 4.2931 & 3.5e-05 \tabularnewline
4 & 0.353533 & 2.6691 & 0.004944 \tabularnewline
5 & 0.148723 & 1.1228 & 0.133107 \tabularnewline
6 & -0.020498 & -0.1548 & 0.438781 \tabularnewline
7 & -0.13609 & -1.0275 & 0.154274 \tabularnewline
8 & -0.219968 & -1.6607 & 0.051131 \tabularnewline
9 & -0.283701 & -2.1419 & 0.018244 \tabularnewline
10 & -0.322602 & -2.4356 & 0.009009 \tabularnewline
11 & -0.347862 & -2.6263 & 0.005533 \tabularnewline
12 & -0.363016 & -2.7407 & 0.004087 \tabularnewline
13 & -0.368713 & -2.7837 & 0.003639 \tabularnewline
14 & -0.356217 & -2.6894 & 0.004686 \tabularnewline
15 & -0.333938 & -2.5212 & 0.007259 \tabularnewline
16 & -0.309644 & -2.3378 & 0.011467 \tabularnewline
17 & -0.273502 & -2.0649 & 0.021746 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108695&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]0.926241[/C][C]6.993[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.775222[/C][C]5.8528[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.568629[/C][C]4.2931[/C][C]3.5e-05[/C][/ROW]
[ROW][C]4[/C][C]0.353533[/C][C]2.6691[/C][C]0.004944[/C][/ROW]
[ROW][C]5[/C][C]0.148723[/C][C]1.1228[/C][C]0.133107[/C][/ROW]
[ROW][C]6[/C][C]-0.020498[/C][C]-0.1548[/C][C]0.438781[/C][/ROW]
[ROW][C]7[/C][C]-0.13609[/C][C]-1.0275[/C][C]0.154274[/C][/ROW]
[ROW][C]8[/C][C]-0.219968[/C][C]-1.6607[/C][C]0.051131[/C][/ROW]
[ROW][C]9[/C][C]-0.283701[/C][C]-2.1419[/C][C]0.018244[/C][/ROW]
[ROW][C]10[/C][C]-0.322602[/C][C]-2.4356[/C][C]0.009009[/C][/ROW]
[ROW][C]11[/C][C]-0.347862[/C][C]-2.6263[/C][C]0.005533[/C][/ROW]
[ROW][C]12[/C][C]-0.363016[/C][C]-2.7407[/C][C]0.004087[/C][/ROW]
[ROW][C]13[/C][C]-0.368713[/C][C]-2.7837[/C][C]0.003639[/C][/ROW]
[ROW][C]14[/C][C]-0.356217[/C][C]-2.6894[/C][C]0.004686[/C][/ROW]
[ROW][C]15[/C][C]-0.333938[/C][C]-2.5212[/C][C]0.007259[/C][/ROW]
[ROW][C]16[/C][C]-0.309644[/C][C]-2.3378[/C][C]0.011467[/C][/ROW]
[ROW][C]17[/C][C]-0.273502[/C][C]-2.0649[/C][C]0.021746[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108695&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108695&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
10.9262416.9930
20.7752225.85280
30.5686294.29313.5e-05
40.3535332.66910.004944
50.1487231.12280.133107
6-0.020498-0.15480.438781
7-0.13609-1.02750.154274
8-0.219968-1.66070.051131
9-0.283701-2.14190.018244
10-0.322602-2.43560.009009
11-0.347862-2.62630.005533
12-0.363016-2.74070.004087
13-0.368713-2.78370.003639
14-0.356217-2.68940.004686
15-0.333938-2.52120.007259
16-0.309644-2.33780.011467
17-0.273502-2.06490.021746






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9262416.9930
2-0.582071-4.39452.4e-05
3-0.300476-2.26850.013551
40.0928720.70120.243025
5-0.052212-0.39420.347454
60.0207860.15690.437928
70.1254360.9470.173813
8-0.285916-2.15860.017552
9-0.194417-1.46780.073826
100.1870141.41190.081704
11-0.141486-1.06820.144968
12-0.12462-0.94090.175373
130.1080980.81610.208913
14-0.073953-0.55830.289402
15-0.210174-1.58680.059048
160.0370040.27940.390485
170.1041250.78610.217524

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.926241 & 6.993 & 0 \tabularnewline
2 & -0.582071 & -4.3945 & 2.4e-05 \tabularnewline
3 & -0.300476 & -2.2685 & 0.013551 \tabularnewline
4 & 0.092872 & 0.7012 & 0.243025 \tabularnewline
5 & -0.052212 & -0.3942 & 0.347454 \tabularnewline
6 & 0.020786 & 0.1569 & 0.437928 \tabularnewline
7 & 0.125436 & 0.947 & 0.173813 \tabularnewline
8 & -0.285916 & -2.1586 & 0.017552 \tabularnewline
9 & -0.194417 & -1.4678 & 0.073826 \tabularnewline
10 & 0.187014 & 1.4119 & 0.081704 \tabularnewline
11 & -0.141486 & -1.0682 & 0.144968 \tabularnewline
12 & -0.12462 & -0.9409 & 0.175373 \tabularnewline
13 & 0.108098 & 0.8161 & 0.208913 \tabularnewline
14 & -0.073953 & -0.5583 & 0.289402 \tabularnewline
15 & -0.210174 & -1.5868 & 0.059048 \tabularnewline
16 & 0.037004 & 0.2794 & 0.390485 \tabularnewline
17 & 0.104125 & 0.7861 & 0.217524 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108695&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]0.926241[/C][C]6.993[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.582071[/C][C]-4.3945[/C][C]2.4e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.300476[/C][C]-2.2685[/C][C]0.013551[/C][/ROW]
[ROW][C]4[/C][C]0.092872[/C][C]0.7012[/C][C]0.243025[/C][/ROW]
[ROW][C]5[/C][C]-0.052212[/C][C]-0.3942[/C][C]0.347454[/C][/ROW]
[ROW][C]6[/C][C]0.020786[/C][C]0.1569[/C][C]0.437928[/C][/ROW]
[ROW][C]7[/C][C]0.125436[/C][C]0.947[/C][C]0.173813[/C][/ROW]
[ROW][C]8[/C][C]-0.285916[/C][C]-2.1586[/C][C]0.017552[/C][/ROW]
[ROW][C]9[/C][C]-0.194417[/C][C]-1.4678[/C][C]0.073826[/C][/ROW]
[ROW][C]10[/C][C]0.187014[/C][C]1.4119[/C][C]0.081704[/C][/ROW]
[ROW][C]11[/C][C]-0.141486[/C][C]-1.0682[/C][C]0.144968[/C][/ROW]
[ROW][C]12[/C][C]-0.12462[/C][C]-0.9409[/C][C]0.175373[/C][/ROW]
[ROW][C]13[/C][C]0.108098[/C][C]0.8161[/C][C]0.208913[/C][/ROW]
[ROW][C]14[/C][C]-0.073953[/C][C]-0.5583[/C][C]0.289402[/C][/ROW]
[ROW][C]15[/C][C]-0.210174[/C][C]-1.5868[/C][C]0.059048[/C][/ROW]
[ROW][C]16[/C][C]0.037004[/C][C]0.2794[/C][C]0.390485[/C][/ROW]
[ROW][C]17[/C][C]0.104125[/C][C]0.7861[/C][C]0.217524[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108695&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108695&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
10.9262416.9930
2-0.582071-4.39452.4e-05
3-0.300476-2.26850.013551
40.0928720.70120.243025
5-0.052212-0.39420.347454
60.0207860.15690.437928
70.1254360.9470.173813
8-0.285916-2.15860.017552
9-0.194417-1.46780.073826
100.1870141.41190.081704
11-0.141486-1.06820.144968
12-0.12462-0.94090.175373
130.1080980.81610.208913
14-0.073953-0.55830.289402
15-0.210174-1.58680.059048
160.0370040.27940.390485
170.1041250.78610.217524


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')