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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 computationSun, 17 Dec 2017 15:30:00 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/17/t151352103286vxec46h94z769.htm/, Retrieved Wed, 15 May 2024 12:57:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309985, Retrieved Wed, 15 May 2024 12:57:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105

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] [] [2017-12-17 14:30:00] [9daa1cf3c40a2e57e8b63b2aa362ac76] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
97.7
88.9
96.5
89.5
85.4
84.3
83.7
86.2
90.7
95.7
95.6
97
97.2
86.6
88.4
81.4
86.9
84.9
83.7
86.8
88.3
92.5
94.7
94.5
98.7
88.6
95.2
91.3
91.7
89.3
88.7
91.2
88.6
94.6
96
94.3
102
93.4
96.7
93.7
91.6
89.6
92.9
94.1
92
97.5
92.7
100.7
105.9
95.3
99.8
91.3
90.8
87.1
91.4
86.1
87.1
92.6
96.6
105.3
102.4
98.2
98.6
92.6
87.9
84.1
86.7
84.4
86
90.4
92.9
105.8
106
99.1
99.9
88.1
87.8
87.1
85.9
86.5
84.1
92.1
93.3
98.9
103
98.4
100.7
92.3
89
88.9
85.5
90.1
87
97.1
101.5
103
106.1
96.1
94.2
89.1
85.2
86.5
88
88.4
87.9
95.7
94.8
105.2
108.7
96.1
98.3
88.6
90.8
88.1
91.9
98.5
98.6
100.3
98.7
110.7
115.4
105.4
108
94.5
96.5
91
94.1
96.4
93.1
97.5
102.5
105.7
109.1
97.2
100.3
91.3
94.3
89.5
89.3
93.4
91.9
92.9
93.7
100.1
105.5
110.5
89.5
90.4
89.9
84.6
86.2
83.4
82.9
81.8
87.6
94.6
99.6
96.7
99.8
83.8
82.4
86.8
91
85.3
83.6
94
100.3
107.1
100.7
95.5
92.9
79.2
82
79.3
81.5
76
73.1
80.4
82.1
90.5
98.1
89.5
86.5
77
74.7
73.4
72.5
69.3
75.2
83.5
90.5
92.2
110.5
101.8
107.4
95.5
84.5
81.1
86.2
91.5
84.7
92.2
99.2
104.5
113
100.4
101
84.8
86.5
91.7
94.8
95

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309985&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309985&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309985&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Autocorrelation Function
Time lag kACF(k)T-STATP-value
1-0.31638-4.46317e-06
2-0.048086-0.67830.249172
3-0.070325-0.99210.161188
4-0.016415-0.23160.408557
50.124841.76110.03988
6-0.086181-1.21570.112764
7-0.001862-0.02630.489536
8-0.037016-0.52220.301067
90.08091.14120.127572
10-0.027552-0.38870.348971
110.1539772.17210.015515
12-0.382006-5.38890
130.0874821.23410.109314
140.0556030.78440.216874
150.0421730.59490.276287
16-0.083114-1.17250.121205
17-0.059099-0.83370.202726
180.1010021.42480.07789
19-0.070525-0.99490.160501
200.0157730.22250.412072
21-0.045597-0.64320.260408
220.1024021.44460.075077
230.0399360.56340.286909

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.31638 & -4.4631 & 7e-06 \tabularnewline
2 & -0.048086 & -0.6783 & 0.249172 \tabularnewline
3 & -0.070325 & -0.9921 & 0.161188 \tabularnewline
4 & -0.016415 & -0.2316 & 0.408557 \tabularnewline
5 & 0.12484 & 1.7611 & 0.03988 \tabularnewline
6 & -0.086181 & -1.2157 & 0.112764 \tabularnewline
7 & -0.001862 & -0.0263 & 0.489536 \tabularnewline
8 & -0.037016 & -0.5222 & 0.301067 \tabularnewline
9 & 0.0809 & 1.1412 & 0.127572 \tabularnewline
10 & -0.027552 & -0.3887 & 0.348971 \tabularnewline
11 & 0.153977 & 2.1721 & 0.015515 \tabularnewline
12 & -0.382006 & -5.3889 & 0 \tabularnewline
13 & 0.087482 & 1.2341 & 0.109314 \tabularnewline
14 & 0.055603 & 0.7844 & 0.216874 \tabularnewline
15 & 0.042173 & 0.5949 & 0.276287 \tabularnewline
16 & -0.083114 & -1.1725 & 0.121205 \tabularnewline
17 & -0.059099 & -0.8337 & 0.202726 \tabularnewline
18 & 0.101002 & 1.4248 & 0.07789 \tabularnewline
19 & -0.070525 & -0.9949 & 0.160501 \tabularnewline
20 & 0.015773 & 0.2225 & 0.412072 \tabularnewline
21 & -0.045597 & -0.6432 & 0.260408 \tabularnewline
22 & 0.102402 & 1.4446 & 0.075077 \tabularnewline
23 & 0.039936 & 0.5634 & 0.286909 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309985&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]-0.31638[/C][C]-4.4631[/C][C]7e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.048086[/C][C]-0.6783[/C][C]0.249172[/C][/ROW]
[ROW][C]3[/C][C]-0.070325[/C][C]-0.9921[/C][C]0.161188[/C][/ROW]
[ROW][C]4[/C][C]-0.016415[/C][C]-0.2316[/C][C]0.408557[/C][/ROW]
[ROW][C]5[/C][C]0.12484[/C][C]1.7611[/C][C]0.03988[/C][/ROW]
[ROW][C]6[/C][C]-0.086181[/C][C]-1.2157[/C][C]0.112764[/C][/ROW]
[ROW][C]7[/C][C]-0.001862[/C][C]-0.0263[/C][C]0.489536[/C][/ROW]
[ROW][C]8[/C][C]-0.037016[/C][C]-0.5222[/C][C]0.301067[/C][/ROW]
[ROW][C]9[/C][C]0.0809[/C][C]1.1412[/C][C]0.127572[/C][/ROW]
[ROW][C]10[/C][C]-0.027552[/C][C]-0.3887[/C][C]0.348971[/C][/ROW]
[ROW][C]11[/C][C]0.153977[/C][C]2.1721[/C][C]0.015515[/C][/ROW]
[ROW][C]12[/C][C]-0.382006[/C][C]-5.3889[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.087482[/C][C]1.2341[/C][C]0.109314[/C][/ROW]
[ROW][C]14[/C][C]0.055603[/C][C]0.7844[/C][C]0.216874[/C][/ROW]
[ROW][C]15[/C][C]0.042173[/C][C]0.5949[/C][C]0.276287[/C][/ROW]
[ROW][C]16[/C][C]-0.083114[/C][C]-1.1725[/C][C]0.121205[/C][/ROW]
[ROW][C]17[/C][C]-0.059099[/C][C]-0.8337[/C][C]0.202726[/C][/ROW]
[ROW][C]18[/C][C]0.101002[/C][C]1.4248[/C][C]0.07789[/C][/ROW]
[ROW][C]19[/C][C]-0.070525[/C][C]-0.9949[/C][C]0.160501[/C][/ROW]
[ROW][C]20[/C][C]0.015773[/C][C]0.2225[/C][C]0.412072[/C][/ROW]
[ROW][C]21[/C][C]-0.045597[/C][C]-0.6432[/C][C]0.260408[/C][/ROW]
[ROW][C]22[/C][C]0.102402[/C][C]1.4446[/C][C]0.075077[/C][/ROW]
[ROW][C]23[/C][C]0.039936[/C][C]0.5634[/C][C]0.286909[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309985&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309985&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
1-0.31638-4.46317e-06
2-0.048086-0.67830.249172
3-0.070325-0.99210.161188
4-0.016415-0.23160.408557
50.124841.76110.03988
6-0.086181-1.21570.112764
7-0.001862-0.02630.489536
8-0.037016-0.52220.301067
90.08091.14120.127572
10-0.027552-0.38870.348971
110.1539772.17210.015515
12-0.382006-5.38890
130.0874821.23410.109314
140.0556030.78440.216874
150.0421730.59490.276287
16-0.083114-1.17250.121205
17-0.059099-0.83370.202726
180.1010021.42480.07789
19-0.070525-0.99490.160501
200.0157730.22250.412072
21-0.045597-0.64320.260408
220.1024021.44460.075077
230.0399360.56340.286909






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.31638-4.46317e-06
2-0.164665-2.32290.010598
3-0.160068-2.2580.012514
4-0.123763-1.74590.041187
50.06090.85910.19566
6-0.045837-0.64660.259314
7-0.03574-0.50420.30735
8-0.055855-0.78790.215837
90.0454490.64110.261086
10-0.012111-0.17080.432262
110.1927152.71860.003568
12-0.310616-4.38181e-05
13-0.130331-1.83850.033737
14-0.0549-0.77450.219787
150.0037650.05310.478848
16-0.161002-2.27120.012102
17-0.051743-0.72990.233146
18-0.009455-0.13340.447013
19-0.09647-1.36090.087545
20-0.111273-1.56970.059037
21-0.03557-0.50180.308191
220.0458360.64660.259319
230.1840432.59620.005064

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.31638 & -4.4631 & 7e-06 \tabularnewline
2 & -0.164665 & -2.3229 & 0.010598 \tabularnewline
3 & -0.160068 & -2.258 & 0.012514 \tabularnewline
4 & -0.123763 & -1.7459 & 0.041187 \tabularnewline
5 & 0.0609 & 0.8591 & 0.19566 \tabularnewline
6 & -0.045837 & -0.6466 & 0.259314 \tabularnewline
7 & -0.03574 & -0.5042 & 0.30735 \tabularnewline
8 & -0.055855 & -0.7879 & 0.215837 \tabularnewline
9 & 0.045449 & 0.6411 & 0.261086 \tabularnewline
10 & -0.012111 & -0.1708 & 0.432262 \tabularnewline
11 & 0.192715 & 2.7186 & 0.003568 \tabularnewline
12 & -0.310616 & -4.3818 & 1e-05 \tabularnewline
13 & -0.130331 & -1.8385 & 0.033737 \tabularnewline
14 & -0.0549 & -0.7745 & 0.219787 \tabularnewline
15 & 0.003765 & 0.0531 & 0.478848 \tabularnewline
16 & -0.161002 & -2.2712 & 0.012102 \tabularnewline
17 & -0.051743 & -0.7299 & 0.233146 \tabularnewline
18 & -0.009455 & -0.1334 & 0.447013 \tabularnewline
19 & -0.09647 & -1.3609 & 0.087545 \tabularnewline
20 & -0.111273 & -1.5697 & 0.059037 \tabularnewline
21 & -0.03557 & -0.5018 & 0.308191 \tabularnewline
22 & 0.045836 & 0.6466 & 0.259319 \tabularnewline
23 & 0.184043 & 2.5962 & 0.005064 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309985&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]-0.31638[/C][C]-4.4631[/C][C]7e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.164665[/C][C]-2.3229[/C][C]0.010598[/C][/ROW]
[ROW][C]3[/C][C]-0.160068[/C][C]-2.258[/C][C]0.012514[/C][/ROW]
[ROW][C]4[/C][C]-0.123763[/C][C]-1.7459[/C][C]0.041187[/C][/ROW]
[ROW][C]5[/C][C]0.0609[/C][C]0.8591[/C][C]0.19566[/C][/ROW]
[ROW][C]6[/C][C]-0.045837[/C][C]-0.6466[/C][C]0.259314[/C][/ROW]
[ROW][C]7[/C][C]-0.03574[/C][C]-0.5042[/C][C]0.30735[/C][/ROW]
[ROW][C]8[/C][C]-0.055855[/C][C]-0.7879[/C][C]0.215837[/C][/ROW]
[ROW][C]9[/C][C]0.045449[/C][C]0.6411[/C][C]0.261086[/C][/ROW]
[ROW][C]10[/C][C]-0.012111[/C][C]-0.1708[/C][C]0.432262[/C][/ROW]
[ROW][C]11[/C][C]0.192715[/C][C]2.7186[/C][C]0.003568[/C][/ROW]
[ROW][C]12[/C][C]-0.310616[/C][C]-4.3818[/C][C]1e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.130331[/C][C]-1.8385[/C][C]0.033737[/C][/ROW]
[ROW][C]14[/C][C]-0.0549[/C][C]-0.7745[/C][C]0.219787[/C][/ROW]
[ROW][C]15[/C][C]0.003765[/C][C]0.0531[/C][C]0.478848[/C][/ROW]
[ROW][C]16[/C][C]-0.161002[/C][C]-2.2712[/C][C]0.012102[/C][/ROW]
[ROW][C]17[/C][C]-0.051743[/C][C]-0.7299[/C][C]0.233146[/C][/ROW]
[ROW][C]18[/C][C]-0.009455[/C][C]-0.1334[/C][C]0.447013[/C][/ROW]
[ROW][C]19[/C][C]-0.09647[/C][C]-1.3609[/C][C]0.087545[/C][/ROW]
[ROW][C]20[/C][C]-0.111273[/C][C]-1.5697[/C][C]0.059037[/C][/ROW]
[ROW][C]21[/C][C]-0.03557[/C][C]-0.5018[/C][C]0.308191[/C][/ROW]
[ROW][C]22[/C][C]0.045836[/C][C]0.6466[/C][C]0.259319[/C][/ROW]
[ROW][C]23[/C][C]0.184043[/C][C]2.5962[/C][C]0.005064[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309985&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309985&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
1-0.31638-4.46317e-06
2-0.164665-2.32290.010598
3-0.160068-2.2580.012514
4-0.123763-1.74590.041187
50.06090.85910.19566
6-0.045837-0.64660.259314
7-0.03574-0.50420.30735
8-0.055855-0.78790.215837
90.0454490.64110.261086
10-0.012111-0.17080.432262
110.1927152.71860.003568
12-0.310616-4.38181e-05
13-0.130331-1.83850.033737
14-0.0549-0.77450.219787
150.0037650.05310.478848
16-0.161002-2.27120.012102
17-0.051743-0.72990.233146
18-0.009455-0.13340.447013
19-0.09647-1.36090.087545
20-0.111273-1.56970.059037
21-0.03557-0.50180.308191
220.0458360.64660.259319
230.1840432.59620.005064


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;
R code (references can be found in the software module):
par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '1'
par2 <- '1'
par1 <- 'Default'
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,'ACF(k)',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,'PACF(k)',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')