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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, 10 Dec 2017 13:54:52 +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/10/t151291066413vwxihbuomgo4k.htm/, Retrieved Wed, 15 May 2024 02:00:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308913, Retrieved Wed, 15 May 2024 02:00:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89

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] [] [2017-12-10 12:54:52] [8829069b4432872c842806a35f4fa8df] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
63.2
68.6
77.7
68.1
75.1
73.3
60.5
65.9
77.7
77.1
77.7
71.3
76
75.3
81.7
72.5
77.4
81.1
65.1
68.7
75.6
79.7
75.3
67.7
73.2
72.2
79.3
77.5
75.6
77.4
69.2
67.1
77.9
82.7
75.7
70.1
76.4
74.3
80.5
78
73.5
78.8
71.2
66.2
82.7
83.8
75
80.4
74.6
77.7
89.8
82.4
77
89.6
75.7
75.1
89.9
88.8
86.5
90
84
82.7
91.7
87.5
82
92.2
73.1
75.6
91.6
87.5
90.1
91.3
87.6
88.4
100.7
85.3
92
96.8
77.9
80.9
95.3
99.3
96.1
92.5
93.7
92.1
103.6
92.5
95.7
103.4
89
89.1
98.7
109.4
101.1
95.4
101.4
102.1
103.6
106
98.4
106.6
95.8
87.2
108.5
107
92
94.9
84.4
85
94
84.5
88.2
92.1
81.1
81.2
96.1
95.3
92.1
91.7
90.3
96.1
108.7
95.9
95.1
109.4
91.2
91.4
107.4
105.6
105.3
103.7
99.5
103.2
123.1
102.2
110
106.2
91.3
99.3
111.8
104.4
102.4
101
100.6
104.5
117.4
97.4
99.5
106.4
95.2
94
104.1
105.8
101.1
93.5
97.9
96.8
108.4
103.5
101.3
107.4
100.7
91.1
105
112.8
105.6
101
101.9
103.5
109.5
105
102.9
108.5
96.9
88.4
112.4
111.3
101.6
101.2
101.8
98.8
114.4
104.5
97.6
109.1
94.5
90.4
111.8
110.5
106.8
101.8
103.7
107.4
117.5
109.6
102.8
115.5
97.8
100.2
112.9
108.7
109
113.9
106.9
109.6
124.5
104.2
110.8
118.7
102.1
105.1

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=308913&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=308913&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308913&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
10.5625687.95590
20.5619177.94670
30.6269158.86590
40.4016585.68030
50.4369876.17990
60.3510254.96421e-06
70.1422982.01240.02276
80.1305461.84620.033171
90.0433110.61250.270449
10-0.060562-0.85650.19638
11-0.093269-1.3190.094335
12-0.275033-3.88966.8e-05
13-0.257832-3.64630.00017
14-0.261854-3.70320.000138
15-0.313919-4.43957e-06
16-0.342573-4.84471e-06
17-0.329354-4.65783e-06
18-0.341798-4.83381e-06
19-0.386566-5.46690
20-0.304334-4.30391.3e-05
21-0.299421-4.23451.7e-05
22-0.345074-4.88011e-06
23-0.176613-2.49770.006654

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.562568 & 7.9559 & 0 \tabularnewline
2 & 0.561917 & 7.9467 & 0 \tabularnewline
3 & 0.626915 & 8.8659 & 0 \tabularnewline
4 & 0.401658 & 5.6803 & 0 \tabularnewline
5 & 0.436987 & 6.1799 & 0 \tabularnewline
6 & 0.351025 & 4.9642 & 1e-06 \tabularnewline
7 & 0.142298 & 2.0124 & 0.02276 \tabularnewline
8 & 0.130546 & 1.8462 & 0.033171 \tabularnewline
9 & 0.043311 & 0.6125 & 0.270449 \tabularnewline
10 & -0.060562 & -0.8565 & 0.19638 \tabularnewline
11 & -0.093269 & -1.319 & 0.094335 \tabularnewline
12 & -0.275033 & -3.8896 & 6.8e-05 \tabularnewline
13 & -0.257832 & -3.6463 & 0.00017 \tabularnewline
14 & -0.261854 & -3.7032 & 0.000138 \tabularnewline
15 & -0.313919 & -4.4395 & 7e-06 \tabularnewline
16 & -0.342573 & -4.8447 & 1e-06 \tabularnewline
17 & -0.329354 & -4.6578 & 3e-06 \tabularnewline
18 & -0.341798 & -4.8338 & 1e-06 \tabularnewline
19 & -0.386566 & -5.4669 & 0 \tabularnewline
20 & -0.304334 & -4.3039 & 1.3e-05 \tabularnewline
21 & -0.299421 & -4.2345 & 1.7e-05 \tabularnewline
22 & -0.345074 & -4.8801 & 1e-06 \tabularnewline
23 & -0.176613 & -2.4977 & 0.006654 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308913&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]0.562568[/C][C]7.9559[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.561917[/C][C]7.9467[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.626915[/C][C]8.8659[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.401658[/C][C]5.6803[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.436987[/C][C]6.1799[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.351025[/C][C]4.9642[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.142298[/C][C]2.0124[/C][C]0.02276[/C][/ROW]
[ROW][C]8[/C][C]0.130546[/C][C]1.8462[/C][C]0.033171[/C][/ROW]
[ROW][C]9[/C][C]0.043311[/C][C]0.6125[/C][C]0.270449[/C][/ROW]
[ROW][C]10[/C][C]-0.060562[/C][C]-0.8565[/C][C]0.19638[/C][/ROW]
[ROW][C]11[/C][C]-0.093269[/C][C]-1.319[/C][C]0.094335[/C][/ROW]
[ROW][C]12[/C][C]-0.275033[/C][C]-3.8896[/C][C]6.8e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.257832[/C][C]-3.6463[/C][C]0.00017[/C][/ROW]
[ROW][C]14[/C][C]-0.261854[/C][C]-3.7032[/C][C]0.000138[/C][/ROW]
[ROW][C]15[/C][C]-0.313919[/C][C]-4.4395[/C][C]7e-06[/C][/ROW]
[ROW][C]16[/C][C]-0.342573[/C][C]-4.8447[/C][C]1e-06[/C][/ROW]
[ROW][C]17[/C][C]-0.329354[/C][C]-4.6578[/C][C]3e-06[/C][/ROW]
[ROW][C]18[/C][C]-0.341798[/C][C]-4.8338[/C][C]1e-06[/C][/ROW]
[ROW][C]19[/C][C]-0.386566[/C][C]-5.4669[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]-0.304334[/C][C]-4.3039[/C][C]1.3e-05[/C][/ROW]
[ROW][C]21[/C][C]-0.299421[/C][C]-4.2345[/C][C]1.7e-05[/C][/ROW]
[ROW][C]22[/C][C]-0.345074[/C][C]-4.8801[/C][C]1e-06[/C][/ROW]
[ROW][C]23[/C][C]-0.176613[/C][C]-2.4977[/C][C]0.006654[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308913&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308913&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
10.5625687.95590
20.5619177.94670
30.6269158.86590
40.4016585.68030
50.4369876.17990
60.3510254.96421e-06
70.1422982.01240.02276
80.1305461.84620.033171
90.0433110.61250.270449
10-0.060562-0.85650.19638
11-0.093269-1.3190.094335
12-0.275033-3.88966.8e-05
13-0.257832-3.64630.00017
14-0.261854-3.70320.000138
15-0.313919-4.43957e-06
16-0.342573-4.84471e-06
17-0.329354-4.65783e-06
18-0.341798-4.83381e-06
19-0.386566-5.46690
20-0.304334-4.30391.3e-05
21-0.299421-4.23451.7e-05
22-0.345074-4.88011e-06
23-0.176613-2.49770.006654






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.5625687.95590
20.3590765.07810
30.3733765.28030
4-0.149313-2.11160.017981
50.0341130.48240.315014
6-0.10434-1.47560.070813
7-0.26181-3.70250.000138
8-0.166475-2.35430.009763
9-0.062551-0.88460.188717
10-0.015472-0.21880.413513
11-0.032576-0.46070.322761
12-0.237001-3.35170.00048
130.0198130.28020.389808
140.0583060.82460.2053
150.112681.59350.05631
16-0.104764-1.48160.070013
170.0282660.39970.344885
18-0.012683-0.17940.428914
19-0.223788-3.16480.000897
20-0.054359-0.76880.221472
210.0392920.55570.289528
22-0.072316-1.02270.153842
230.1563462.21110.014082

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.562568 & 7.9559 & 0 \tabularnewline
2 & 0.359076 & 5.0781 & 0 \tabularnewline
3 & 0.373376 & 5.2803 & 0 \tabularnewline
4 & -0.149313 & -2.1116 & 0.017981 \tabularnewline
5 & 0.034113 & 0.4824 & 0.315014 \tabularnewline
6 & -0.10434 & -1.4756 & 0.070813 \tabularnewline
7 & -0.26181 & -3.7025 & 0.000138 \tabularnewline
8 & -0.166475 & -2.3543 & 0.009763 \tabularnewline
9 & -0.062551 & -0.8846 & 0.188717 \tabularnewline
10 & -0.015472 & -0.2188 & 0.413513 \tabularnewline
11 & -0.032576 & -0.4607 & 0.322761 \tabularnewline
12 & -0.237001 & -3.3517 & 0.00048 \tabularnewline
13 & 0.019813 & 0.2802 & 0.389808 \tabularnewline
14 & 0.058306 & 0.8246 & 0.2053 \tabularnewline
15 & 0.11268 & 1.5935 & 0.05631 \tabularnewline
16 & -0.104764 & -1.4816 & 0.070013 \tabularnewline
17 & 0.028266 & 0.3997 & 0.344885 \tabularnewline
18 & -0.012683 & -0.1794 & 0.428914 \tabularnewline
19 & -0.223788 & -3.1648 & 0.000897 \tabularnewline
20 & -0.054359 & -0.7688 & 0.221472 \tabularnewline
21 & 0.039292 & 0.5557 & 0.289528 \tabularnewline
22 & -0.072316 & -1.0227 & 0.153842 \tabularnewline
23 & 0.156346 & 2.2111 & 0.014082 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308913&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]0.562568[/C][C]7.9559[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.359076[/C][C]5.0781[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.373376[/C][C]5.2803[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.149313[/C][C]-2.1116[/C][C]0.017981[/C][/ROW]
[ROW][C]5[/C][C]0.034113[/C][C]0.4824[/C][C]0.315014[/C][/ROW]
[ROW][C]6[/C][C]-0.10434[/C][C]-1.4756[/C][C]0.070813[/C][/ROW]
[ROW][C]7[/C][C]-0.26181[/C][C]-3.7025[/C][C]0.000138[/C][/ROW]
[ROW][C]8[/C][C]-0.166475[/C][C]-2.3543[/C][C]0.009763[/C][/ROW]
[ROW][C]9[/C][C]-0.062551[/C][C]-0.8846[/C][C]0.188717[/C][/ROW]
[ROW][C]10[/C][C]-0.015472[/C][C]-0.2188[/C][C]0.413513[/C][/ROW]
[ROW][C]11[/C][C]-0.032576[/C][C]-0.4607[/C][C]0.322761[/C][/ROW]
[ROW][C]12[/C][C]-0.237001[/C][C]-3.3517[/C][C]0.00048[/C][/ROW]
[ROW][C]13[/C][C]0.019813[/C][C]0.2802[/C][C]0.389808[/C][/ROW]
[ROW][C]14[/C][C]0.058306[/C][C]0.8246[/C][C]0.2053[/C][/ROW]
[ROW][C]15[/C][C]0.11268[/C][C]1.5935[/C][C]0.05631[/C][/ROW]
[ROW][C]16[/C][C]-0.104764[/C][C]-1.4816[/C][C]0.070013[/C][/ROW]
[ROW][C]17[/C][C]0.028266[/C][C]0.3997[/C][C]0.344885[/C][/ROW]
[ROW][C]18[/C][C]-0.012683[/C][C]-0.1794[/C][C]0.428914[/C][/ROW]
[ROW][C]19[/C][C]-0.223788[/C][C]-3.1648[/C][C]0.000897[/C][/ROW]
[ROW][C]20[/C][C]-0.054359[/C][C]-0.7688[/C][C]0.221472[/C][/ROW]
[ROW][C]21[/C][C]0.039292[/C][C]0.5557[/C][C]0.289528[/C][/ROW]
[ROW][C]22[/C][C]-0.072316[/C][C]-1.0227[/C][C]0.153842[/C][/ROW]
[ROW][C]23[/C][C]0.156346[/C][C]2.2111[/C][C]0.014082[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308913&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308913&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
10.5625687.95590
20.3590765.07810
30.3733765.28030
4-0.149313-2.11160.017981
50.0341130.48240.315014
6-0.10434-1.47560.070813
7-0.26181-3.70250.000138
8-0.166475-2.35430.009763
9-0.062551-0.88460.188717
10-0.015472-0.21880.413513
11-0.032576-0.46070.322761
12-0.237001-3.35170.00048
130.0198130.28020.389808
140.0583060.82460.2053
150.112681.59350.05631
16-0.104764-1.48160.070013
170.0282660.39970.344885
18-0.012683-0.17940.428914
19-0.223788-3.16480.000897
20-0.054359-0.76880.221472
210.0392920.55570.289528
22-0.072316-1.02270.153842
230.1563462.21110.014082


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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,'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')