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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, 15 Dec 2015 14:45:41 +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/2015/Dec/15/t1450190785ekq3l8x2yegj1pe.htm/, Retrieved Sat, 18 May 2024 15:27:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286515, Retrieved Sat, 18 May 2024 15:27:46 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71

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-       [(Partial) Autocorrelation Function] [Autocorrelatie] [2015-12-15 14:45:41] [6c9172abf40f1c7e1d0d83ef980264f4] [Current]
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Dataset

Dataseries X:
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Histogram
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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' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286515&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286515&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286515&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' @ jenkins.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.48649112.49820
20.123253.16630.000807
3-0.130437-3.3510.000426
4-0.268091-6.88740
5-0.312755-8.03480
6-0.326721-8.39360
7-0.307378-7.89670
8-0.242255-6.22370
9-0.106186-2.7280.003271
100.0937742.40910.008132
110.42993811.04530
120.58337914.98730
130.41629910.69490
140.1298113.33490.000451
15-0.117791-3.02610.001287
16-0.239554-6.15430
17-0.306309-7.86920
18-0.317315-8.1520
19-0.307594-7.90220
20-0.244808-6.28920
21-0.103279-2.65330.004082
220.1032282.6520.004097
230.43865111.26920
240.56100314.41240
250.3546919.11220
260.0921212.36660.009119
27-0.101329-2.60320.004722
28-0.226284-5.81330

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.486491 & 12.4982 & 0 \tabularnewline
2 & 0.12325 & 3.1663 & 0.000807 \tabularnewline
3 & -0.130437 & -3.351 & 0.000426 \tabularnewline
4 & -0.268091 & -6.8874 & 0 \tabularnewline
5 & -0.312755 & -8.0348 & 0 \tabularnewline
6 & -0.326721 & -8.3936 & 0 \tabularnewline
7 & -0.307378 & -7.8967 & 0 \tabularnewline
8 & -0.242255 & -6.2237 & 0 \tabularnewline
9 & -0.106186 & -2.728 & 0.003271 \tabularnewline
10 & 0.093774 & 2.4091 & 0.008132 \tabularnewline
11 & 0.429938 & 11.0453 & 0 \tabularnewline
12 & 0.583379 & 14.9873 & 0 \tabularnewline
13 & 0.416299 & 10.6949 & 0 \tabularnewline
14 & 0.129811 & 3.3349 & 0.000451 \tabularnewline
15 & -0.117791 & -3.0261 & 0.001287 \tabularnewline
16 & -0.239554 & -6.1543 & 0 \tabularnewline
17 & -0.306309 & -7.8692 & 0 \tabularnewline
18 & -0.317315 & -8.152 & 0 \tabularnewline
19 & -0.307594 & -7.9022 & 0 \tabularnewline
20 & -0.244808 & -6.2892 & 0 \tabularnewline
21 & -0.103279 & -2.6533 & 0.004082 \tabularnewline
22 & 0.103228 & 2.652 & 0.004097 \tabularnewline
23 & 0.438651 & 11.2692 & 0 \tabularnewline
24 & 0.561003 & 14.4124 & 0 \tabularnewline
25 & 0.354691 & 9.1122 & 0 \tabularnewline
26 & 0.092121 & 2.3666 & 0.009119 \tabularnewline
27 & -0.101329 & -2.6032 & 0.004722 \tabularnewline
28 & -0.226284 & -5.8133 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286515&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]0.486491[/C][C]12.4982[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.12325[/C][C]3.1663[/C][C]0.000807[/C][/ROW]
[ROW][C]3[/C][C]-0.130437[/C][C]-3.351[/C][C]0.000426[/C][/ROW]
[ROW][C]4[/C][C]-0.268091[/C][C]-6.8874[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]-0.312755[/C][C]-8.0348[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]-0.326721[/C][C]-8.3936[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.307378[/C][C]-7.8967[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]-0.242255[/C][C]-6.2237[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]-0.106186[/C][C]-2.728[/C][C]0.003271[/C][/ROW]
[ROW][C]10[/C][C]0.093774[/C][C]2.4091[/C][C]0.008132[/C][/ROW]
[ROW][C]11[/C][C]0.429938[/C][C]11.0453[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.583379[/C][C]14.9873[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.416299[/C][C]10.6949[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.129811[/C][C]3.3349[/C][C]0.000451[/C][/ROW]
[ROW][C]15[/C][C]-0.117791[/C][C]-3.0261[/C][C]0.001287[/C][/ROW]
[ROW][C]16[/C][C]-0.239554[/C][C]-6.1543[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]-0.306309[/C][C]-7.8692[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]-0.317315[/C][C]-8.152[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]-0.307594[/C][C]-7.9022[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]-0.244808[/C][C]-6.2892[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]-0.103279[/C][C]-2.6533[/C][C]0.004082[/C][/ROW]
[ROW][C]22[/C][C]0.103228[/C][C]2.652[/C][C]0.004097[/C][/ROW]
[ROW][C]23[/C][C]0.438651[/C][C]11.2692[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]0.561003[/C][C]14.4124[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]0.354691[/C][C]9.1122[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]0.092121[/C][C]2.3666[/C][C]0.009119[/C][/ROW]
[ROW][C]27[/C][C]-0.101329[/C][C]-2.6032[/C][C]0.004722[/C][/ROW]
[ROW][C]28[/C][C]-0.226284[/C][C]-5.8133[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286515&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286515&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
10.48649112.49820
20.123253.16630.000807
3-0.130437-3.3510.000426
4-0.268091-6.88740
5-0.312755-8.03480
6-0.326721-8.39360
7-0.307378-7.89670
8-0.242255-6.22370
9-0.106186-2.7280.003271
100.0937742.40910.008132
110.42993811.04530
120.58337914.98730
130.41629910.69490
140.1298113.33490.000451
15-0.117791-3.02610.001287
16-0.239554-6.15430
17-0.306309-7.86920
18-0.317315-8.1520
19-0.307594-7.90220
20-0.244808-6.28920
21-0.103279-2.65330.004082
220.1032282.6520.004097
230.43865111.26920
240.56100314.41240
250.3546919.11220
260.0921212.36660.009119
27-0.101329-2.60320.004722
28-0.226284-5.81330






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.48649112.49820
2-0.148592-3.81747.4e-05
3-0.170158-4.37147e-06
4-0.150551-3.86776e-05
5-0.141599-3.63770.000148
6-0.185445-4.76421e-06
7-0.19633-5.04380
8-0.184909-4.75041e-06
9-0.119764-3.07680.001089
10-0.013741-0.3530.362098
110.3010657.73450
120.2639266.78040
130.0429111.10240.135343
14-0.032859-0.84420.199442
15-0.043763-1.12430.130648
16-0.00412-0.10590.457866
17-0.050097-1.2870.09927
18-0.040911-1.0510.146819
19-0.07487-1.92350.027427
20-0.077578-1.9930.023336
21-0.033452-0.85940.195214
22-0.034883-0.89620.185249
230.1865584.79281e-06
240.1254883.22380.000664
25-0.088453-2.27240.011692
26-0.040234-1.03360.150843
270.0147630.37930.352302
28-0.012292-0.31580.376128

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.486491 & 12.4982 & 0 \tabularnewline
2 & -0.148592 & -3.8174 & 7.4e-05 \tabularnewline
3 & -0.170158 & -4.3714 & 7e-06 \tabularnewline
4 & -0.150551 & -3.8677 & 6e-05 \tabularnewline
5 & -0.141599 & -3.6377 & 0.000148 \tabularnewline
6 & -0.185445 & -4.7642 & 1e-06 \tabularnewline
7 & -0.19633 & -5.0438 & 0 \tabularnewline
8 & -0.184909 & -4.7504 & 1e-06 \tabularnewline
9 & -0.119764 & -3.0768 & 0.001089 \tabularnewline
10 & -0.013741 & -0.353 & 0.362098 \tabularnewline
11 & 0.301065 & 7.7345 & 0 \tabularnewline
12 & 0.263926 & 6.7804 & 0 \tabularnewline
13 & 0.042911 & 1.1024 & 0.135343 \tabularnewline
14 & -0.032859 & -0.8442 & 0.199442 \tabularnewline
15 & -0.043763 & -1.1243 & 0.130648 \tabularnewline
16 & -0.00412 & -0.1059 & 0.457866 \tabularnewline
17 & -0.050097 & -1.287 & 0.09927 \tabularnewline
18 & -0.040911 & -1.051 & 0.146819 \tabularnewline
19 & -0.07487 & -1.9235 & 0.027427 \tabularnewline
20 & -0.077578 & -1.993 & 0.023336 \tabularnewline
21 & -0.033452 & -0.8594 & 0.195214 \tabularnewline
22 & -0.034883 & -0.8962 & 0.185249 \tabularnewline
23 & 0.186558 & 4.7928 & 1e-06 \tabularnewline
24 & 0.125488 & 3.2238 & 0.000664 \tabularnewline
25 & -0.088453 & -2.2724 & 0.011692 \tabularnewline
26 & -0.040234 & -1.0336 & 0.150843 \tabularnewline
27 & 0.014763 & 0.3793 & 0.352302 \tabularnewline
28 & -0.012292 & -0.3158 & 0.376128 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286515&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]0.486491[/C][C]12.4982[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.148592[/C][C]-3.8174[/C][C]7.4e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.170158[/C][C]-4.3714[/C][C]7e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.150551[/C][C]-3.8677[/C][C]6e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.141599[/C][C]-3.6377[/C][C]0.000148[/C][/ROW]
[ROW][C]6[/C][C]-0.185445[/C][C]-4.7642[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]-0.19633[/C][C]-5.0438[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]-0.184909[/C][C]-4.7504[/C][C]1e-06[/C][/ROW]
[ROW][C]9[/C][C]-0.119764[/C][C]-3.0768[/C][C]0.001089[/C][/ROW]
[ROW][C]10[/C][C]-0.013741[/C][C]-0.353[/C][C]0.362098[/C][/ROW]
[ROW][C]11[/C][C]0.301065[/C][C]7.7345[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.263926[/C][C]6.7804[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.042911[/C][C]1.1024[/C][C]0.135343[/C][/ROW]
[ROW][C]14[/C][C]-0.032859[/C][C]-0.8442[/C][C]0.199442[/C][/ROW]
[ROW][C]15[/C][C]-0.043763[/C][C]-1.1243[/C][C]0.130648[/C][/ROW]
[ROW][C]16[/C][C]-0.00412[/C][C]-0.1059[/C][C]0.457866[/C][/ROW]
[ROW][C]17[/C][C]-0.050097[/C][C]-1.287[/C][C]0.09927[/C][/ROW]
[ROW][C]18[/C][C]-0.040911[/C][C]-1.051[/C][C]0.146819[/C][/ROW]
[ROW][C]19[/C][C]-0.07487[/C][C]-1.9235[/C][C]0.027427[/C][/ROW]
[ROW][C]20[/C][C]-0.077578[/C][C]-1.993[/C][C]0.023336[/C][/ROW]
[ROW][C]21[/C][C]-0.033452[/C][C]-0.8594[/C][C]0.195214[/C][/ROW]
[ROW][C]22[/C][C]-0.034883[/C][C]-0.8962[/C][C]0.185249[/C][/ROW]
[ROW][C]23[/C][C]0.186558[/C][C]4.7928[/C][C]1e-06[/C][/ROW]
[ROW][C]24[/C][C]0.125488[/C][C]3.2238[/C][C]0.000664[/C][/ROW]
[ROW][C]25[/C][C]-0.088453[/C][C]-2.2724[/C][C]0.011692[/C][/ROW]
[ROW][C]26[/C][C]-0.040234[/C][C]-1.0336[/C][C]0.150843[/C][/ROW]
[ROW][C]27[/C][C]0.014763[/C][C]0.3793[/C][C]0.352302[/C][/ROW]
[ROW][C]28[/C][C]-0.012292[/C][C]-0.3158[/C][C]0.376128[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286515&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286515&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
10.48649112.49820
2-0.148592-3.81747.4e-05
3-0.170158-4.37147e-06
4-0.150551-3.86776e-05
5-0.141599-3.63770.000148
6-0.185445-4.76421e-06
7-0.19633-5.04380
8-0.184909-4.75041e-06
9-0.119764-3.07680.001089
10-0.013741-0.3530.362098
110.3010657.73450
120.2639266.78040
130.0429111.10240.135343
14-0.032859-0.84420.199442
15-0.043763-1.12430.130648
16-0.00412-0.10590.457866
17-0.050097-1.2870.09927
18-0.040911-1.0510.146819
19-0.07487-1.92350.027427
20-0.077578-1.9930.023336
21-0.033452-0.85940.195214
22-0.034883-0.89620.185249
230.1865584.79281e-06
240.1254883.22380.000664
25-0.088453-2.27240.011692
26-0.040234-1.03360.150843
270.0147630.37930.352302
28-0.012292-0.31580.376128


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 0,99 ; par4 = two.sided ; par5 = paired ; par6 = 0 ;
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)
x <- na.omit(x)
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')