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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 computationMon, 18 Dec 2017 13:59:33 +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/18/t1513602002v4xqy9o5z7nm3ih.htm/, Retrieved Tue, 14 May 2024 18:34:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310157, Retrieved Tue, 14 May 2024 18:34:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact39

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] [Autocorrelatie (D...] [2017-12-18 12:59:33] [0687db01a969247b131332e81d79dad3] [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=310157&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=310157&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310157&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
1-0.323977-4.7062e-06
2-0.401627-5.8340
30.3788185.50260
4-0.210594-3.0590.001254
5-0.094709-1.37570.085183
60.3779625.49020
7-0.200892-2.91810.001951
8-0.087611-1.27260.102277
90.3099024.50166e-06
10-0.439746-6.38770
11-0.138283-2.00870.022923
120.72842710.5810
13-0.248581-3.61090.000191
14-0.30137-4.37779e-06
150.2456573.56840.000222
16-0.158476-2.3020.011156
17-0.048248-0.70080.242086
180.2940664.27161.5e-05
19-0.187894-2.72930.003441
20-0.030308-0.44030.330102
210.2394033.47750.000307
22-0.418541-6.07970
23-0.058972-0.85660.196315

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.323977 & -4.706 & 2e-06 \tabularnewline
2 & -0.401627 & -5.834 & 0 \tabularnewline
3 & 0.378818 & 5.5026 & 0 \tabularnewline
4 & -0.210594 & -3.059 & 0.001254 \tabularnewline
5 & -0.094709 & -1.3757 & 0.085183 \tabularnewline
6 & 0.377962 & 5.4902 & 0 \tabularnewline
7 & -0.200892 & -2.9181 & 0.001951 \tabularnewline
8 & -0.087611 & -1.2726 & 0.102277 \tabularnewline
9 & 0.309902 & 4.5016 & 6e-06 \tabularnewline
10 & -0.439746 & -6.3877 & 0 \tabularnewline
11 & -0.138283 & -2.0087 & 0.022923 \tabularnewline
12 & 0.728427 & 10.581 & 0 \tabularnewline
13 & -0.248581 & -3.6109 & 0.000191 \tabularnewline
14 & -0.30137 & -4.3777 & 9e-06 \tabularnewline
15 & 0.245657 & 3.5684 & 0.000222 \tabularnewline
16 & -0.158476 & -2.302 & 0.011156 \tabularnewline
17 & -0.048248 & -0.7008 & 0.242086 \tabularnewline
18 & 0.294066 & 4.2716 & 1.5e-05 \tabularnewline
19 & -0.187894 & -2.7293 & 0.003441 \tabularnewline
20 & -0.030308 & -0.4403 & 0.330102 \tabularnewline
21 & 0.239403 & 3.4775 & 0.000307 \tabularnewline
22 & -0.418541 & -6.0797 & 0 \tabularnewline
23 & -0.058972 & -0.8566 & 0.196315 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310157&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]-0.323977[/C][C]-4.706[/C][C]2e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.401627[/C][C]-5.834[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.378818[/C][C]5.5026[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.210594[/C][C]-3.059[/C][C]0.001254[/C][/ROW]
[ROW][C]5[/C][C]-0.094709[/C][C]-1.3757[/C][C]0.085183[/C][/ROW]
[ROW][C]6[/C][C]0.377962[/C][C]5.4902[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.200892[/C][C]-2.9181[/C][C]0.001951[/C][/ROW]
[ROW][C]8[/C][C]-0.087611[/C][C]-1.2726[/C][C]0.102277[/C][/ROW]
[ROW][C]9[/C][C]0.309902[/C][C]4.5016[/C][C]6e-06[/C][/ROW]
[ROW][C]10[/C][C]-0.439746[/C][C]-6.3877[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]-0.138283[/C][C]-2.0087[/C][C]0.022923[/C][/ROW]
[ROW][C]12[/C][C]0.728427[/C][C]10.581[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.248581[/C][C]-3.6109[/C][C]0.000191[/C][/ROW]
[ROW][C]14[/C][C]-0.30137[/C][C]-4.3777[/C][C]9e-06[/C][/ROW]
[ROW][C]15[/C][C]0.245657[/C][C]3.5684[/C][C]0.000222[/C][/ROW]
[ROW][C]16[/C][C]-0.158476[/C][C]-2.302[/C][C]0.011156[/C][/ROW]
[ROW][C]17[/C][C]-0.048248[/C][C]-0.7008[/C][C]0.242086[/C][/ROW]
[ROW][C]18[/C][C]0.294066[/C][C]4.2716[/C][C]1.5e-05[/C][/ROW]
[ROW][C]19[/C][C]-0.187894[/C][C]-2.7293[/C][C]0.003441[/C][/ROW]
[ROW][C]20[/C][C]-0.030308[/C][C]-0.4403[/C][C]0.330102[/C][/ROW]
[ROW][C]21[/C][C]0.239403[/C][C]3.4775[/C][C]0.000307[/C][/ROW]
[ROW][C]22[/C][C]-0.418541[/C][C]-6.0797[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]-0.058972[/C][C]-0.8566[/C][C]0.196315[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310157&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310157&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
1-0.323977-4.7062e-06
2-0.401627-5.8340
30.3788185.50260
4-0.210594-3.0590.001254
5-0.094709-1.37570.085183
60.3779625.49020
7-0.200892-2.91810.001951
8-0.087611-1.27260.102277
90.3099024.50166e-06
10-0.439746-6.38770
11-0.138283-2.00870.022923
120.72842710.5810
13-0.248581-3.61090.000191
14-0.30137-4.37779e-06
150.2456573.56840.000222
16-0.158476-2.3020.011156
17-0.048248-0.70080.242086
180.2940664.27161.5e-05
19-0.187894-2.72930.003441
20-0.030308-0.44030.330102
210.2394033.47750.000307
22-0.418541-6.07970
23-0.058972-0.85660.196315






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.323977-4.7062e-06
2-0.565996-8.22160
3-0.013671-0.19860.421389
4-0.411057-5.97090
5-0.241011-3.50090.000283
60.0067020.09740.46127
7-0.059703-0.86720.1934
80.076921.11730.132562
90.3109174.51635e-06
10-0.247081-3.58910.000206
11-0.511676-7.43250
120.2057532.98870.001567
130.260463.78340.000101
140.1870032.71640.003574
15-0.141845-2.06040.020293
160.0046650.06780.473018
17-0.070653-1.02630.152964
18-0.091547-1.32980.092511
19-0.113542-1.64930.050287
20-0.063369-0.92050.179183
21-0.015731-0.22850.409737
22-0.097008-1.40910.080137
23-0.135672-1.97070.02503

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.323977 & -4.706 & 2e-06 \tabularnewline
2 & -0.565996 & -8.2216 & 0 \tabularnewline
3 & -0.013671 & -0.1986 & 0.421389 \tabularnewline
4 & -0.411057 & -5.9709 & 0 \tabularnewline
5 & -0.241011 & -3.5009 & 0.000283 \tabularnewline
6 & 0.006702 & 0.0974 & 0.46127 \tabularnewline
7 & -0.059703 & -0.8672 & 0.1934 \tabularnewline
8 & 0.07692 & 1.1173 & 0.132562 \tabularnewline
9 & 0.310917 & 4.5163 & 5e-06 \tabularnewline
10 & -0.247081 & -3.5891 & 0.000206 \tabularnewline
11 & -0.511676 & -7.4325 & 0 \tabularnewline
12 & 0.205753 & 2.9887 & 0.001567 \tabularnewline
13 & 0.26046 & 3.7834 & 0.000101 \tabularnewline
14 & 0.187003 & 2.7164 & 0.003574 \tabularnewline
15 & -0.141845 & -2.0604 & 0.020293 \tabularnewline
16 & 0.004665 & 0.0678 & 0.473018 \tabularnewline
17 & -0.070653 & -1.0263 & 0.152964 \tabularnewline
18 & -0.091547 & -1.3298 & 0.092511 \tabularnewline
19 & -0.113542 & -1.6493 & 0.050287 \tabularnewline
20 & -0.063369 & -0.9205 & 0.179183 \tabularnewline
21 & -0.015731 & -0.2285 & 0.409737 \tabularnewline
22 & -0.097008 & -1.4091 & 0.080137 \tabularnewline
23 & -0.135672 & -1.9707 & 0.02503 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310157&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]-0.323977[/C][C]-4.706[/C][C]2e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.565996[/C][C]-8.2216[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.013671[/C][C]-0.1986[/C][C]0.421389[/C][/ROW]
[ROW][C]4[/C][C]-0.411057[/C][C]-5.9709[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]-0.241011[/C][C]-3.5009[/C][C]0.000283[/C][/ROW]
[ROW][C]6[/C][C]0.006702[/C][C]0.0974[/C][C]0.46127[/C][/ROW]
[ROW][C]7[/C][C]-0.059703[/C][C]-0.8672[/C][C]0.1934[/C][/ROW]
[ROW][C]8[/C][C]0.07692[/C][C]1.1173[/C][C]0.132562[/C][/ROW]
[ROW][C]9[/C][C]0.310917[/C][C]4.5163[/C][C]5e-06[/C][/ROW]
[ROW][C]10[/C][C]-0.247081[/C][C]-3.5891[/C][C]0.000206[/C][/ROW]
[ROW][C]11[/C][C]-0.511676[/C][C]-7.4325[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.205753[/C][C]2.9887[/C][C]0.001567[/C][/ROW]
[ROW][C]13[/C][C]0.26046[/C][C]3.7834[/C][C]0.000101[/C][/ROW]
[ROW][C]14[/C][C]0.187003[/C][C]2.7164[/C][C]0.003574[/C][/ROW]
[ROW][C]15[/C][C]-0.141845[/C][C]-2.0604[/C][C]0.020293[/C][/ROW]
[ROW][C]16[/C][C]0.004665[/C][C]0.0678[/C][C]0.473018[/C][/ROW]
[ROW][C]17[/C][C]-0.070653[/C][C]-1.0263[/C][C]0.152964[/C][/ROW]
[ROW][C]18[/C][C]-0.091547[/C][C]-1.3298[/C][C]0.092511[/C][/ROW]
[ROW][C]19[/C][C]-0.113542[/C][C]-1.6493[/C][C]0.050287[/C][/ROW]
[ROW][C]20[/C][C]-0.063369[/C][C]-0.9205[/C][C]0.179183[/C][/ROW]
[ROW][C]21[/C][C]-0.015731[/C][C]-0.2285[/C][C]0.409737[/C][/ROW]
[ROW][C]22[/C][C]-0.097008[/C][C]-1.4091[/C][C]0.080137[/C][/ROW]
[ROW][C]23[/C][C]-0.135672[/C][C]-1.9707[/C][C]0.02503[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310157&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310157&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
1-0.323977-4.7062e-06
2-0.565996-8.22160
3-0.013671-0.19860.421389
4-0.411057-5.97090
5-0.241011-3.50090.000283
60.0067020.09740.46127
7-0.059703-0.86720.1934
80.076921.11730.132562
90.3109174.51635e-06
10-0.247081-3.58910.000206
11-0.511676-7.43250
120.2057532.98870.001567
130.260463.78340.000101
140.1870032.71640.003574
15-0.141845-2.06040.020293
160.0046650.06780.473018
17-0.070653-1.02630.152964
18-0.091547-1.32980.092511
19-0.113542-1.64930.050287
20-0.063369-0.92050.179183
21-0.015731-0.22850.409737
22-0.097008-1.40910.080137
23-0.135672-1.97070.02503


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):
par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
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')