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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 computationThu, 21 Dec 2017 11:48:09 +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/21/t1513853322oe6sfa0rer1kdpm.htm/, Retrieved Tue, 14 May 2024 18:44:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310613, Retrieved Tue, 14 May 2024 18:44:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103

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] [] [2017-12-21 10:48:09] [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 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=310613&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=310613&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310613&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
1-0.545493-7.69510
2-0.108387-1.5290.063929
30.3928915.54240
4-0.321046-4.52895e-06
50.0799581.12790.13035
60.1967342.77530.003021
7-0.305259-4.30621.3e-05
80.1066091.50390.067096
90.1948062.74810.003273
10-0.254339-3.58790.00021
110.1422472.00660.023071
12-9.1e-05-0.00130.499487
13-0.213493-3.01170.001468
140.2609243.68080.00015
15-0.015799-0.22290.411931
16-0.290878-4.10333e-05
170.2463063.47460.000314
180.078211.10330.135619
19-0.292128-4.1212.8e-05
200.2599613.66720.000157
21-0.041753-0.5890.278267
22-0.285894-4.0333.9e-05
230.4791646.75940

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.545493 & -7.6951 & 0 \tabularnewline
2 & -0.108387 & -1.529 & 0.063929 \tabularnewline
3 & 0.392891 & 5.5424 & 0 \tabularnewline
4 & -0.321046 & -4.5289 & 5e-06 \tabularnewline
5 & 0.079958 & 1.1279 & 0.13035 \tabularnewline
6 & 0.196734 & 2.7753 & 0.003021 \tabularnewline
7 & -0.305259 & -4.3062 & 1.3e-05 \tabularnewline
8 & 0.106609 & 1.5039 & 0.067096 \tabularnewline
9 & 0.194806 & 2.7481 & 0.003273 \tabularnewline
10 & -0.254339 & -3.5879 & 0.00021 \tabularnewline
11 & 0.142247 & 2.0066 & 0.023071 \tabularnewline
12 & -9.1e-05 & -0.0013 & 0.499487 \tabularnewline
13 & -0.213493 & -3.0117 & 0.001468 \tabularnewline
14 & 0.260924 & 3.6808 & 0.00015 \tabularnewline
15 & -0.015799 & -0.2229 & 0.411931 \tabularnewline
16 & -0.290878 & -4.1033 & 3e-05 \tabularnewline
17 & 0.246306 & 3.4746 & 0.000314 \tabularnewline
18 & 0.07821 & 1.1033 & 0.135619 \tabularnewline
19 & -0.292128 & -4.121 & 2.8e-05 \tabularnewline
20 & 0.259961 & 3.6672 & 0.000157 \tabularnewline
21 & -0.041753 & -0.589 & 0.278267 \tabularnewline
22 & -0.285894 & -4.033 & 3.9e-05 \tabularnewline
23 & 0.479164 & 6.7594 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310613&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]-0.545493[/C][C]-7.6951[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.108387[/C][C]-1.529[/C][C]0.063929[/C][/ROW]
[ROW][C]3[/C][C]0.392891[/C][C]5.5424[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.321046[/C][C]-4.5289[/C][C]5e-06[/C][/ROW]
[ROW][C]5[/C][C]0.079958[/C][C]1.1279[/C][C]0.13035[/C][/ROW]
[ROW][C]6[/C][C]0.196734[/C][C]2.7753[/C][C]0.003021[/C][/ROW]
[ROW][C]7[/C][C]-0.305259[/C][C]-4.3062[/C][C]1.3e-05[/C][/ROW]
[ROW][C]8[/C][C]0.106609[/C][C]1.5039[/C][C]0.067096[/C][/ROW]
[ROW][C]9[/C][C]0.194806[/C][C]2.7481[/C][C]0.003273[/C][/ROW]
[ROW][C]10[/C][C]-0.254339[/C][C]-3.5879[/C][C]0.00021[/C][/ROW]
[ROW][C]11[/C][C]0.142247[/C][C]2.0066[/C][C]0.023071[/C][/ROW]
[ROW][C]12[/C][C]-9.1e-05[/C][C]-0.0013[/C][C]0.499487[/C][/ROW]
[ROW][C]13[/C][C]-0.213493[/C][C]-3.0117[/C][C]0.001468[/C][/ROW]
[ROW][C]14[/C][C]0.260924[/C][C]3.6808[/C][C]0.00015[/C][/ROW]
[ROW][C]15[/C][C]-0.015799[/C][C]-0.2229[/C][C]0.411931[/C][/ROW]
[ROW][C]16[/C][C]-0.290878[/C][C]-4.1033[/C][C]3e-05[/C][/ROW]
[ROW][C]17[/C][C]0.246306[/C][C]3.4746[/C][C]0.000314[/C][/ROW]
[ROW][C]18[/C][C]0.07821[/C][C]1.1033[/C][C]0.135619[/C][/ROW]
[ROW][C]19[/C][C]-0.292128[/C][C]-4.121[/C][C]2.8e-05[/C][/ROW]
[ROW][C]20[/C][C]0.259961[/C][C]3.6672[/C][C]0.000157[/C][/ROW]
[ROW][C]21[/C][C]-0.041753[/C][C]-0.589[/C][C]0.278267[/C][/ROW]
[ROW][C]22[/C][C]-0.285894[/C][C]-4.033[/C][C]3.9e-05[/C][/ROW]
[ROW][C]23[/C][C]0.479164[/C][C]6.7594[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310613&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310613&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
1-0.545493-7.69510
2-0.108387-1.5290.063929
30.3928915.54240
4-0.321046-4.52895e-06
50.0799581.12790.13035
60.1967342.77530.003021
7-0.305259-4.30621.3e-05
80.1066091.50390.067096
90.1948062.74810.003273
10-0.254339-3.58790.00021
110.1422472.00660.023071
12-9.1e-05-0.00130.499487
13-0.213493-3.01170.001468
140.2609243.68080.00015
15-0.015799-0.22290.411931
16-0.290878-4.10333e-05
170.2463063.47460.000314
180.078211.10330.135619
19-0.292128-4.1212.8e-05
200.2599613.66720.000157
21-0.041753-0.5890.278267
22-0.285894-4.0333.9e-05
230.4791646.75940






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.545493-7.69510
2-0.577916-8.15250
3-0.033456-0.4720.31874
4-0.126856-1.78950.037525
5-0.044074-0.62170.267413
60.1594612.24950.012789
7-0.014043-0.19810.421584
8-0.145728-2.05570.020556
90.0728591.02780.152645
100.0839381.18410.118894
110.1356691.91380.028538
120.0195410.27570.391547
13-0.232219-3.27590.000621
14-0.150811-2.12740.017307
150.0943691.33120.092316
16-0.104075-1.46820.071819
17-0.205539-2.89950.002079
180.1109461.56510.059576
19-0.008595-0.12130.451806
20-0.026484-0.37360.354548
210.1336231.8850.030445
22-0.147084-2.07490.019642
230.1487872.09890.018544

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.545493 & -7.6951 & 0 \tabularnewline
2 & -0.577916 & -8.1525 & 0 \tabularnewline
3 & -0.033456 & -0.472 & 0.31874 \tabularnewline
4 & -0.126856 & -1.7895 & 0.037525 \tabularnewline
5 & -0.044074 & -0.6217 & 0.267413 \tabularnewline
6 & 0.159461 & 2.2495 & 0.012789 \tabularnewline
7 & -0.014043 & -0.1981 & 0.421584 \tabularnewline
8 & -0.145728 & -2.0557 & 0.020556 \tabularnewline
9 & 0.072859 & 1.0278 & 0.152645 \tabularnewline
10 & 0.083938 & 1.1841 & 0.118894 \tabularnewline
11 & 0.135669 & 1.9138 & 0.028538 \tabularnewline
12 & 0.019541 & 0.2757 & 0.391547 \tabularnewline
13 & -0.232219 & -3.2759 & 0.000621 \tabularnewline
14 & -0.150811 & -2.1274 & 0.017307 \tabularnewline
15 & 0.094369 & 1.3312 & 0.092316 \tabularnewline
16 & -0.104075 & -1.4682 & 0.071819 \tabularnewline
17 & -0.205539 & -2.8995 & 0.002079 \tabularnewline
18 & 0.110946 & 1.5651 & 0.059576 \tabularnewline
19 & -0.008595 & -0.1213 & 0.451806 \tabularnewline
20 & -0.026484 & -0.3736 & 0.354548 \tabularnewline
21 & 0.133623 & 1.885 & 0.030445 \tabularnewline
22 & -0.147084 & -2.0749 & 0.019642 \tabularnewline
23 & 0.148787 & 2.0989 & 0.018544 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310613&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]-0.545493[/C][C]-7.6951[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.577916[/C][C]-8.1525[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.033456[/C][C]-0.472[/C][C]0.31874[/C][/ROW]
[ROW][C]4[/C][C]-0.126856[/C][C]-1.7895[/C][C]0.037525[/C][/ROW]
[ROW][C]5[/C][C]-0.044074[/C][C]-0.6217[/C][C]0.267413[/C][/ROW]
[ROW][C]6[/C][C]0.159461[/C][C]2.2495[/C][C]0.012789[/C][/ROW]
[ROW][C]7[/C][C]-0.014043[/C][C]-0.1981[/C][C]0.421584[/C][/ROW]
[ROW][C]8[/C][C]-0.145728[/C][C]-2.0557[/C][C]0.020556[/C][/ROW]
[ROW][C]9[/C][C]0.072859[/C][C]1.0278[/C][C]0.152645[/C][/ROW]
[ROW][C]10[/C][C]0.083938[/C][C]1.1841[/C][C]0.118894[/C][/ROW]
[ROW][C]11[/C][C]0.135669[/C][C]1.9138[/C][C]0.028538[/C][/ROW]
[ROW][C]12[/C][C]0.019541[/C][C]0.2757[/C][C]0.391547[/C][/ROW]
[ROW][C]13[/C][C]-0.232219[/C][C]-3.2759[/C][C]0.000621[/C][/ROW]
[ROW][C]14[/C][C]-0.150811[/C][C]-2.1274[/C][C]0.017307[/C][/ROW]
[ROW][C]15[/C][C]0.094369[/C][C]1.3312[/C][C]0.092316[/C][/ROW]
[ROW][C]16[/C][C]-0.104075[/C][C]-1.4682[/C][C]0.071819[/C][/ROW]
[ROW][C]17[/C][C]-0.205539[/C][C]-2.8995[/C][C]0.002079[/C][/ROW]
[ROW][C]18[/C][C]0.110946[/C][C]1.5651[/C][C]0.059576[/C][/ROW]
[ROW][C]19[/C][C]-0.008595[/C][C]-0.1213[/C][C]0.451806[/C][/ROW]
[ROW][C]20[/C][C]-0.026484[/C][C]-0.3736[/C][C]0.354548[/C][/ROW]
[ROW][C]21[/C][C]0.133623[/C][C]1.885[/C][C]0.030445[/C][/ROW]
[ROW][C]22[/C][C]-0.147084[/C][C]-2.0749[/C][C]0.019642[/C][/ROW]
[ROW][C]23[/C][C]0.148787[/C][C]2.0989[/C][C]0.018544[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310613&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310613&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
1-0.545493-7.69510
2-0.577916-8.15250
3-0.033456-0.4720.31874
4-0.126856-1.78950.037525
5-0.044074-0.62170.267413
60.1594612.24950.012789
7-0.014043-0.19810.421584
8-0.145728-2.05570.020556
90.0728591.02780.152645
100.0839381.18410.118894
110.1356691.91380.028538
120.0195410.27570.391547
13-0.232219-3.27590.000621
14-0.150811-2.12740.017307
150.0943691.33120.092316
16-0.104075-1.46820.071819
17-0.205539-2.89950.002079
180.1109461.56510.059576
19-0.008595-0.12130.451806
20-0.026484-0.37360.354548
210.1336231.8850.030445
22-0.147084-2.07490.019642
230.1487872.09890.018544


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 0.5 ; par3 = 1 ; 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')