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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 computationWed, 13 Dec 2017 14:27:51 +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/13/t15131717212xyb86yybuv0vk3.htm/, Retrieved Wed, 15 May 2024 17:09:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309296, Retrieved Wed, 15 May 2024 17:09:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact55

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] [(Partial) Autocor...] [2017-12-13 13:27:51] [bd83e7d2022b632a928e3cc7dd68d98c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
58.5
59.8
64.6
62.2
68
64.3
58.9
64.8
67.5
76.2
73.7
70.4
67.7
63.7
72.4
66
70.1
70.4
66.6
72.6
74
79
76.1
72.3
71.6
67.2
73.8
70.8
71.4
70.4
70.7
70.6
75.5
82.1
74.3
76.3
74.5
71.1
73.3
73.8
69
71.1
71.9
69
77.3
82.8
74
77.6
72.3
70.7
81
76.4
72.3
79.5
73.3
74.5
82.7
83.8
81.6
85.5
76.7
71.8
80.2
76.8
76.1
80.7
71.3
80.9
85
84.5
87.7
87.7
80.2
74.4
85.8
77
84.5
83.6
77.7
85.7
87.9
93.7
92.3
87
89.1
81.3
92.7
83.9
87.3
89.1
86.9
91.7
93
105.3
101.6
94.2
100.5
95.8
95.8
102.1
96
96.8
98.9
93.4
105.5
110.9
98.6
102.6
93.5
90.8
99.7
97.8
91.1
98.1
96
93.5
101.2
105.2
98.9
101.3
92.1
90.6
105.4
98.4
92.7
101.2
93.4
98.3
104.3
107
107.7
108.9
99.6
96.1
109
99.5
104.6
99.9
94.1
105.3
110.4
110.5
110
108.5
104.3
101.2
109.2
99.6
105.6
106.2
102.2
107.5
105.8
120.5
113.2
104.3
107.7
99.2
105.1
104.3
106.1
100.8
106.7
101.6
104.4
114.8
105.4
104
102
96.5
102.3
105.3
101.9
102.2
102.8
100.4
110.7
116.4
106
109.2
103
99.8
109.8
107.3
101.2
111.8
106.9
103.5
113.1
119.4
113.3
115
104.7
107.2
116.6
111.3
111.4
115
102.4
111.4
113.2
112.9
114.2
115.6
107.1
102.3
117.9
105.8
114.3
113.1
102.9
112.2

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309296&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309296&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309296&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 time2 seconds
R ServerBig Analytics Cloud Computing Center






Autocorrelation Function
Time lag kACF(k)T-STATP-value
1-0.398613-5.79020
2-0.13052-1.89590.029669
30.2777744.03493.8e-05
4-0.444802-6.46110
50.1135661.64960.050253
60.2700343.92255.9e-05
7-0.131553-1.91090.028686
8-0.176825-2.56850.005452
90.2060072.99240.001549
10-0.289796-4.20951.9e-05
11-0.028324-0.41140.340586
120.590168.57260
13-0.336337-4.88561e-06
140.1150421.67110.048093
150.0480560.6980.242958
16-0.436309-6.33780
170.2700493.92275.9e-05
180.1260251.83060.034284
19-0.149772-2.17560.01535
200.0168010.2440.403717
21-0.017497-0.25420.399809
22-0.254739-3.70030.000137
230.2162493.14120.000962

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.398613 & -5.7902 & 0 \tabularnewline
2 & -0.13052 & -1.8959 & 0.029669 \tabularnewline
3 & 0.277774 & 4.0349 & 3.8e-05 \tabularnewline
4 & -0.444802 & -6.4611 & 0 \tabularnewline
5 & 0.113566 & 1.6496 & 0.050253 \tabularnewline
6 & 0.270034 & 3.9225 & 5.9e-05 \tabularnewline
7 & -0.131553 & -1.9109 & 0.028686 \tabularnewline
8 & -0.176825 & -2.5685 & 0.005452 \tabularnewline
9 & 0.206007 & 2.9924 & 0.001549 \tabularnewline
10 & -0.289796 & -4.2095 & 1.9e-05 \tabularnewline
11 & -0.028324 & -0.4114 & 0.340586 \tabularnewline
12 & 0.59016 & 8.5726 & 0 \tabularnewline
13 & -0.336337 & -4.8856 & 1e-06 \tabularnewline
14 & 0.115042 & 1.6711 & 0.048093 \tabularnewline
15 & 0.048056 & 0.698 & 0.242958 \tabularnewline
16 & -0.436309 & -6.3378 & 0 \tabularnewline
17 & 0.270049 & 3.9227 & 5.9e-05 \tabularnewline
18 & 0.126025 & 1.8306 & 0.034284 \tabularnewline
19 & -0.149772 & -2.1756 & 0.01535 \tabularnewline
20 & 0.016801 & 0.244 & 0.403717 \tabularnewline
21 & -0.017497 & -0.2542 & 0.399809 \tabularnewline
22 & -0.254739 & -3.7003 & 0.000137 \tabularnewline
23 & 0.216249 & 3.1412 & 0.000962 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309296&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]-0.398613[/C][C]-5.7902[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.13052[/C][C]-1.8959[/C][C]0.029669[/C][/ROW]
[ROW][C]3[/C][C]0.277774[/C][C]4.0349[/C][C]3.8e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.444802[/C][C]-6.4611[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.113566[/C][C]1.6496[/C][C]0.050253[/C][/ROW]
[ROW][C]6[/C][C]0.270034[/C][C]3.9225[/C][C]5.9e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.131553[/C][C]-1.9109[/C][C]0.028686[/C][/ROW]
[ROW][C]8[/C][C]-0.176825[/C][C]-2.5685[/C][C]0.005452[/C][/ROW]
[ROW][C]9[/C][C]0.206007[/C][C]2.9924[/C][C]0.001549[/C][/ROW]
[ROW][C]10[/C][C]-0.289796[/C][C]-4.2095[/C][C]1.9e-05[/C][/ROW]
[ROW][C]11[/C][C]-0.028324[/C][C]-0.4114[/C][C]0.340586[/C][/ROW]
[ROW][C]12[/C][C]0.59016[/C][C]8.5726[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.336337[/C][C]-4.8856[/C][C]1e-06[/C][/ROW]
[ROW][C]14[/C][C]0.115042[/C][C]1.6711[/C][C]0.048093[/C][/ROW]
[ROW][C]15[/C][C]0.048056[/C][C]0.698[/C][C]0.242958[/C][/ROW]
[ROW][C]16[/C][C]-0.436309[/C][C]-6.3378[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.270049[/C][C]3.9227[/C][C]5.9e-05[/C][/ROW]
[ROW][C]18[/C][C]0.126025[/C][C]1.8306[/C][C]0.034284[/C][/ROW]
[ROW][C]19[/C][C]-0.149772[/C][C]-2.1756[/C][C]0.01535[/C][/ROW]
[ROW][C]20[/C][C]0.016801[/C][C]0.244[/C][C]0.403717[/C][/ROW]
[ROW][C]21[/C][C]-0.017497[/C][C]-0.2542[/C][C]0.399809[/C][/ROW]
[ROW][C]22[/C][C]-0.254739[/C][C]-3.7003[/C][C]0.000137[/C][/ROW]
[ROW][C]23[/C][C]0.216249[/C][C]3.1412[/C][C]0.000962[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309296&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309296&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
1-0.398613-5.79020
2-0.13052-1.89590.029669
30.2777744.03493.8e-05
4-0.444802-6.46110
50.1135661.64960.050253
60.2700343.92255.9e-05
7-0.131553-1.91090.028686
8-0.176825-2.56850.005452
90.2060072.99240.001549
10-0.289796-4.20951.9e-05
11-0.028324-0.41140.340586
120.590168.57260
13-0.336337-4.88561e-06
140.1150421.67110.048093
150.0480560.6980.242958
16-0.436309-6.33780
170.2700493.92275.9e-05
180.1260251.83060.034284
19-0.149772-2.17560.01535
200.0168010.2440.403717
21-0.017497-0.25420.399809
22-0.254739-3.70030.000137
230.2162493.14120.000962






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.398613-5.79020
2-0.344084-4.99811e-06
30.095331.38470.083797
4-0.415542-6.03610
5-0.25958-3.77060.000106
60.0447410.64990.258231
70.183542.66610.004134
8-0.388869-5.64860
9-0.109171-1.58580.057142
10-0.289975-4.21211.9e-05
11-0.385983-5.60670
120.207633.0160.001438
130.2233513.24440.000684
140.3380534.91051e-06
150.1136121.65030.050184
16-0.067015-0.97340.165724
17-0.042172-0.61260.270407
180.0070320.10210.459371
190.0001280.00190.499262
20-0.041989-0.60990.271285
21-0.115673-1.68020.047195
22-0.170448-2.47590.007038
23-0.024106-0.35020.363283

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.398613 & -5.7902 & 0 \tabularnewline
2 & -0.344084 & -4.9981 & 1e-06 \tabularnewline
3 & 0.09533 & 1.3847 & 0.083797 \tabularnewline
4 & -0.415542 & -6.0361 & 0 \tabularnewline
5 & -0.25958 & -3.7706 & 0.000106 \tabularnewline
6 & 0.044741 & 0.6499 & 0.258231 \tabularnewline
7 & 0.18354 & 2.6661 & 0.004134 \tabularnewline
8 & -0.388869 & -5.6486 & 0 \tabularnewline
9 & -0.109171 & -1.5858 & 0.057142 \tabularnewline
10 & -0.289975 & -4.2121 & 1.9e-05 \tabularnewline
11 & -0.385983 & -5.6067 & 0 \tabularnewline
12 & 0.20763 & 3.016 & 0.001438 \tabularnewline
13 & 0.223351 & 3.2444 & 0.000684 \tabularnewline
14 & 0.338053 & 4.9105 & 1e-06 \tabularnewline
15 & 0.113612 & 1.6503 & 0.050184 \tabularnewline
16 & -0.067015 & -0.9734 & 0.165724 \tabularnewline
17 & -0.042172 & -0.6126 & 0.270407 \tabularnewline
18 & 0.007032 & 0.1021 & 0.459371 \tabularnewline
19 & 0.000128 & 0.0019 & 0.499262 \tabularnewline
20 & -0.041989 & -0.6099 & 0.271285 \tabularnewline
21 & -0.115673 & -1.6802 & 0.047195 \tabularnewline
22 & -0.170448 & -2.4759 & 0.007038 \tabularnewline
23 & -0.024106 & -0.3502 & 0.363283 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309296&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]-0.398613[/C][C]-5.7902[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.344084[/C][C]-4.9981[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.09533[/C][C]1.3847[/C][C]0.083797[/C][/ROW]
[ROW][C]4[/C][C]-0.415542[/C][C]-6.0361[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]-0.25958[/C][C]-3.7706[/C][C]0.000106[/C][/ROW]
[ROW][C]6[/C][C]0.044741[/C][C]0.6499[/C][C]0.258231[/C][/ROW]
[ROW][C]7[/C][C]0.18354[/C][C]2.6661[/C][C]0.004134[/C][/ROW]
[ROW][C]8[/C][C]-0.388869[/C][C]-5.6486[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]-0.109171[/C][C]-1.5858[/C][C]0.057142[/C][/ROW]
[ROW][C]10[/C][C]-0.289975[/C][C]-4.2121[/C][C]1.9e-05[/C][/ROW]
[ROW][C]11[/C][C]-0.385983[/C][C]-5.6067[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.20763[/C][C]3.016[/C][C]0.001438[/C][/ROW]
[ROW][C]13[/C][C]0.223351[/C][C]3.2444[/C][C]0.000684[/C][/ROW]
[ROW][C]14[/C][C]0.338053[/C][C]4.9105[/C][C]1e-06[/C][/ROW]
[ROW][C]15[/C][C]0.113612[/C][C]1.6503[/C][C]0.050184[/C][/ROW]
[ROW][C]16[/C][C]-0.067015[/C][C]-0.9734[/C][C]0.165724[/C][/ROW]
[ROW][C]17[/C][C]-0.042172[/C][C]-0.6126[/C][C]0.270407[/C][/ROW]
[ROW][C]18[/C][C]0.007032[/C][C]0.1021[/C][C]0.459371[/C][/ROW]
[ROW][C]19[/C][C]0.000128[/C][C]0.0019[/C][C]0.499262[/C][/ROW]
[ROW][C]20[/C][C]-0.041989[/C][C]-0.6099[/C][C]0.271285[/C][/ROW]
[ROW][C]21[/C][C]-0.115673[/C][C]-1.6802[/C][C]0.047195[/C][/ROW]
[ROW][C]22[/C][C]-0.170448[/C][C]-2.4759[/C][C]0.007038[/C][/ROW]
[ROW][C]23[/C][C]-0.024106[/C][C]-0.3502[/C][C]0.363283[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309296&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309296&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
1-0.398613-5.79020
2-0.344084-4.99811e-06
30.095331.38470.083797
4-0.415542-6.03610
5-0.25958-3.77060.000106
60.0447410.64990.258231
70.183542.66610.004134
8-0.388869-5.64860
9-0.109171-1.58580.057142
10-0.289975-4.21211.9e-05
11-0.385983-5.60670
120.207633.0160.001438
130.2233513.24440.000684
140.3380534.91051e-06
150.1136121.65030.050184
16-0.067015-0.97340.165724
17-0.042172-0.61260.270407
180.0070320.10210.459371
190.0001280.00190.499262
20-0.041989-0.60990.271285
21-0.115673-1.68020.047195
22-0.170448-2.47590.007038
23-0.024106-0.35020.363283


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 1 ; 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,'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')