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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 computationSat, 09 Dec 2017 14:28:38 +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/09/t1512826134qxbjkmchwsoisnk.htm/, Retrieved Tue, 14 May 2024 15:13:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308853, Retrieved Tue, 14 May 2024 15:13:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88

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] [] [2017-12-09 13:28:38] [20141777ecd6b11d9726230b5f8289b4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
62
67.1
75.9
67
74.2
72.2
60.2
65.8
76.2
76.6
76.8
70.6
74.5
73.5
80.2
71.5
76.6
79.6
65.5
69.2
74.8
79.4
75
67.7
72.5
71.2
78.3
76.6
74.9
76.5
69.4
67.4
77.2
82.2
75.1
70.6
75.6
73.5
79.4
77.5
72.9
78
71.5
66.6
81.8
83.5
74.6
79.8
73.9
76.6
88.9
81.7
76.5
88.8
75.5
75.2
89
87.9
85.7
89.2
82.7
81
90.3
86.3
81.5
91.1
73.1
76.4
91
86.9
89.6
90.5
86.3
86.5
98.8
84.3
91.2
95.5
78.1
81.5
94.4
98.5
95.3
91.6
92.8
90.5
102.2
91.5
94.9
102.1
88.8
89.4
97.8
108.8
100.8
95
101
101
102.5
105.6
98.3
105.5
96.4
88
108.1
107.2
92.5
95.7
84.8
85.4
94.6
86
88.6
93.3
83.1
82.6
96.7
96.2
92.6
92.7
89.9
95.4
108.4
96.2
95
109
91.9
92.2
107.1
105.6
105.4
103.9
99.2
102.4
121.8
102.3
110.1
106
91.9
100.1
112
105
103.3
101.8
100.9
104.2
116.8
97.8
100.7
107.2
96.3
95.9
104.6
107.5
102.5
94.9
98.7
96.8
108.3
103.9
102.4
107.3
101.9
92.5
105.4
113.2
105.7
101.7
101.8
102.9
109.2
105.6
103.4
108.8
98.1
90
112.8
112.2
102.2
102.5
101.8
98.8
114.3
105.2
98.3
110.1
96.4
92.1
112.2
111.6
107.6
103.4
103.6
107.7
117.9
110.4
104.4
116.2
98.9
102.1
113.7
109.5
110.3
114.5
107
109.4
124.6
104.8
112
119.2
103
106.5

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=308853&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=308853&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308853&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
1-0.334312-4.85621e-06
2-0.390757-5.67610
30.3878125.63330
4-0.242454-3.52180.000263
5-0.085424-1.24090.108017
60.4046875.87840
7-0.203582-2.95720.001729
8-0.104275-1.51470.065675
90.315794.58714e-06
10-0.438513-6.36980
11-0.131351-1.9080.028876
120.71663610.40970
13-0.261372-3.79669.6e-05
14-0.273387-3.97124.9e-05
150.2410993.50220.000282
16-0.192002-2.7890.002885
17-0.026683-0.38760.349352
180.3121794.53475e-06
19-0.195908-2.84570.002434
20-0.029972-0.43540.33187
210.2309433.35460.000471
22-0.420439-6.10720
23-0.03473-0.50450.307222

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.334312 & -4.8562 & 1e-06 \tabularnewline
2 & -0.390757 & -5.6761 & 0 \tabularnewline
3 & 0.387812 & 5.6333 & 0 \tabularnewline
4 & -0.242454 & -3.5218 & 0.000263 \tabularnewline
5 & -0.085424 & -1.2409 & 0.108017 \tabularnewline
6 & 0.404687 & 5.8784 & 0 \tabularnewline
7 & -0.203582 & -2.9572 & 0.001729 \tabularnewline
8 & -0.104275 & -1.5147 & 0.065675 \tabularnewline
9 & 0.31579 & 4.5871 & 4e-06 \tabularnewline
10 & -0.438513 & -6.3698 & 0 \tabularnewline
11 & -0.131351 & -1.908 & 0.028876 \tabularnewline
12 & 0.716636 & 10.4097 & 0 \tabularnewline
13 & -0.261372 & -3.7966 & 9.6e-05 \tabularnewline
14 & -0.273387 & -3.9712 & 4.9e-05 \tabularnewline
15 & 0.241099 & 3.5022 & 0.000282 \tabularnewline
16 & -0.192002 & -2.789 & 0.002885 \tabularnewline
17 & -0.026683 & -0.3876 & 0.349352 \tabularnewline
18 & 0.312179 & 4.5347 & 5e-06 \tabularnewline
19 & -0.195908 & -2.8457 & 0.002434 \tabularnewline
20 & -0.029972 & -0.4354 & 0.33187 \tabularnewline
21 & 0.230943 & 3.3546 & 0.000471 \tabularnewline
22 & -0.420439 & -6.1072 & 0 \tabularnewline
23 & -0.03473 & -0.5045 & 0.307222 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308853&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]-0.334312[/C][C]-4.8562[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.390757[/C][C]-5.6761[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.387812[/C][C]5.6333[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.242454[/C][C]-3.5218[/C][C]0.000263[/C][/ROW]
[ROW][C]5[/C][C]-0.085424[/C][C]-1.2409[/C][C]0.108017[/C][/ROW]
[ROW][C]6[/C][C]0.404687[/C][C]5.8784[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.203582[/C][C]-2.9572[/C][C]0.001729[/C][/ROW]
[ROW][C]8[/C][C]-0.104275[/C][C]-1.5147[/C][C]0.065675[/C][/ROW]
[ROW][C]9[/C][C]0.31579[/C][C]4.5871[/C][C]4e-06[/C][/ROW]
[ROW][C]10[/C][C]-0.438513[/C][C]-6.3698[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]-0.131351[/C][C]-1.908[/C][C]0.028876[/C][/ROW]
[ROW][C]12[/C][C]0.716636[/C][C]10.4097[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.261372[/C][C]-3.7966[/C][C]9.6e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.273387[/C][C]-3.9712[/C][C]4.9e-05[/C][/ROW]
[ROW][C]15[/C][C]0.241099[/C][C]3.5022[/C][C]0.000282[/C][/ROW]
[ROW][C]16[/C][C]-0.192002[/C][C]-2.789[/C][C]0.002885[/C][/ROW]
[ROW][C]17[/C][C]-0.026683[/C][C]-0.3876[/C][C]0.349352[/C][/ROW]
[ROW][C]18[/C][C]0.312179[/C][C]4.5347[/C][C]5e-06[/C][/ROW]
[ROW][C]19[/C][C]-0.195908[/C][C]-2.8457[/C][C]0.002434[/C][/ROW]
[ROW][C]20[/C][C]-0.029972[/C][C]-0.4354[/C][C]0.33187[/C][/ROW]
[ROW][C]21[/C][C]0.230943[/C][C]3.3546[/C][C]0.000471[/C][/ROW]
[ROW][C]22[/C][C]-0.420439[/C][C]-6.1072[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]-0.03473[/C][C]-0.5045[/C][C]0.307222[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308853&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308853&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
1-0.334312-4.85621e-06
2-0.390757-5.67610
30.3878125.63330
4-0.242454-3.52180.000263
5-0.085424-1.24090.108017
60.4046875.87840
7-0.203582-2.95720.001729
8-0.104275-1.51470.065675
90.315794.58714e-06
10-0.438513-6.36980
11-0.131351-1.9080.028876
120.71663610.40970
13-0.261372-3.79669.6e-05
14-0.273387-3.97124.9e-05
150.2410993.50220.000282
16-0.192002-2.7890.002885
17-0.026683-0.38760.349352
180.3121794.53475e-06
19-0.195908-2.84570.002434
20-0.029972-0.43540.33187
210.2309433.35460.000471
22-0.420439-6.10720
23-0.03473-0.50450.307222






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.334312-4.85621e-06
2-0.565753-8.2180
3-0.009717-0.14110.443945
4-0.436563-6.34140
5-0.279577-4.06113.4e-05
6-0.01441-0.20930.417199
7-0.03231-0.46930.319659
80.07791.13160.129553
90.3536895.13760
10-0.194198-2.82090.002623
11-0.498784-7.24530
120.1579922.2950.011359
130.2322413.37350.000442
140.1866662.71150.003625
15-0.144246-2.09530.018669
16-0.005752-0.08360.466746
17-0.065437-0.95050.171467
18-0.076543-1.11190.133734
19-0.108747-1.57960.057844
20-0.044644-0.64850.258685
21-0.009624-0.13980.444476
22-0.101963-1.48110.070037
23-0.13651-1.98290.024337

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.334312 & -4.8562 & 1e-06 \tabularnewline
2 & -0.565753 & -8.218 & 0 \tabularnewline
3 & -0.009717 & -0.1411 & 0.443945 \tabularnewline
4 & -0.436563 & -6.3414 & 0 \tabularnewline
5 & -0.279577 & -4.0611 & 3.4e-05 \tabularnewline
6 & -0.01441 & -0.2093 & 0.417199 \tabularnewline
7 & -0.03231 & -0.4693 & 0.319659 \tabularnewline
8 & 0.0779 & 1.1316 & 0.129553 \tabularnewline
9 & 0.353689 & 5.1376 & 0 \tabularnewline
10 & -0.194198 & -2.8209 & 0.002623 \tabularnewline
11 & -0.498784 & -7.2453 & 0 \tabularnewline
12 & 0.157992 & 2.295 & 0.011359 \tabularnewline
13 & 0.232241 & 3.3735 & 0.000442 \tabularnewline
14 & 0.186666 & 2.7115 & 0.003625 \tabularnewline
15 & -0.144246 & -2.0953 & 0.018669 \tabularnewline
16 & -0.005752 & -0.0836 & 0.466746 \tabularnewline
17 & -0.065437 & -0.9505 & 0.171467 \tabularnewline
18 & -0.076543 & -1.1119 & 0.133734 \tabularnewline
19 & -0.108747 & -1.5796 & 0.057844 \tabularnewline
20 & -0.044644 & -0.6485 & 0.258685 \tabularnewline
21 & -0.009624 & -0.1398 & 0.444476 \tabularnewline
22 & -0.101963 & -1.4811 & 0.070037 \tabularnewline
23 & -0.13651 & -1.9829 & 0.024337 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308853&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]-0.334312[/C][C]-4.8562[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.565753[/C][C]-8.218[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.009717[/C][C]-0.1411[/C][C]0.443945[/C][/ROW]
[ROW][C]4[/C][C]-0.436563[/C][C]-6.3414[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]-0.279577[/C][C]-4.0611[/C][C]3.4e-05[/C][/ROW]
[ROW][C]6[/C][C]-0.01441[/C][C]-0.2093[/C][C]0.417199[/C][/ROW]
[ROW][C]7[/C][C]-0.03231[/C][C]-0.4693[/C][C]0.319659[/C][/ROW]
[ROW][C]8[/C][C]0.0779[/C][C]1.1316[/C][C]0.129553[/C][/ROW]
[ROW][C]9[/C][C]0.353689[/C][C]5.1376[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]-0.194198[/C][C]-2.8209[/C][C]0.002623[/C][/ROW]
[ROW][C]11[/C][C]-0.498784[/C][C]-7.2453[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.157992[/C][C]2.295[/C][C]0.011359[/C][/ROW]
[ROW][C]13[/C][C]0.232241[/C][C]3.3735[/C][C]0.000442[/C][/ROW]
[ROW][C]14[/C][C]0.186666[/C][C]2.7115[/C][C]0.003625[/C][/ROW]
[ROW][C]15[/C][C]-0.144246[/C][C]-2.0953[/C][C]0.018669[/C][/ROW]
[ROW][C]16[/C][C]-0.005752[/C][C]-0.0836[/C][C]0.466746[/C][/ROW]
[ROW][C]17[/C][C]-0.065437[/C][C]-0.9505[/C][C]0.171467[/C][/ROW]
[ROW][C]18[/C][C]-0.076543[/C][C]-1.1119[/C][C]0.133734[/C][/ROW]
[ROW][C]19[/C][C]-0.108747[/C][C]-1.5796[/C][C]0.057844[/C][/ROW]
[ROW][C]20[/C][C]-0.044644[/C][C]-0.6485[/C][C]0.258685[/C][/ROW]
[ROW][C]21[/C][C]-0.009624[/C][C]-0.1398[/C][C]0.444476[/C][/ROW]
[ROW][C]22[/C][C]-0.101963[/C][C]-1.4811[/C][C]0.070037[/C][/ROW]
[ROW][C]23[/C][C]-0.13651[/C][C]-1.9829[/C][C]0.024337[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308853&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308853&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
1-0.334312-4.85621e-06
2-0.565753-8.2180
3-0.009717-0.14110.443945
4-0.436563-6.34140
5-0.279577-4.06113.4e-05
6-0.01441-0.20930.417199
7-0.03231-0.46930.319659
80.07791.13160.129553
90.3536895.13760
10-0.194198-2.82090.002623
11-0.498784-7.24530
120.1579922.2950.011359
130.2322413.37350.000442
140.1866662.71150.003625
15-0.144246-2.09530.018669
16-0.005752-0.08360.466746
17-0.065437-0.95050.171467
18-0.076543-1.11190.133734
19-0.108747-1.57960.057844
20-0.044644-0.64850.258685
21-0.009624-0.13980.444476
22-0.101963-1.48110.070037
23-0.13651-1.98290.024337


Figures (Output of Computation)

Input Parameters & R Code

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