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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 computationFri, 22 Dec 2017 13:22:42 +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/22/t1513945394eo6offaketlvq4n.htm/, Retrieved Wed, 15 May 2024 16:35:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310770, Retrieved Wed, 15 May 2024 16:35:12 +0000
QR Codes:

Original text written by user:Stap 3 van voorbeeld 1 (Time Series)
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80

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] [Voorbeeld 1 (PAF)] [2017-12-22 12:22:42] [84a8d6985c1bda8999f49f22468687ba] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
74.2
91.7
100.7
82.7
95.1
93.3
57.5
76.7
99.2
101.5
96.1
85.9
84.4
90.8
101.9
88.7
94
101.2
61.2
80.1
98.3
100.6
90.6
83.1
82.4
87.8
94.1
89.8
84.9
91.7
63.2
70.4
97
98.5
79.2
78.7
78.7
85.7
86.4
82.7
76.1
89.7
64.4
67.9
93.1
95.7
81.3
78.6
76.1
85.8
101.5
88.5
75.8
99.1
57.8
75.8
98.8
93
93.4
88.2
80.3
92.3
98.5
92.9
85.8
100.7
60.9
80.1
106.8
93.7
98.2
91.7
86.9
93.3
106.2
86.5
91.8
107.8
60.4
84
108.3
105.6
102
93.7
91.5
101.6
109.9
96.8
100.3
116.3
71.3
96.8
112.9
117.8
104.4
95.4
92.2
103.3
103.4
112
102.2
114.9
80.2
81.4
122.1
121.6
98.4
98.2
90.2
100.8
108.8
95.9
87.7
103.9
73.2
86.6
116.1
111.4
99.5
96.5
90.7
98.9
112
100.4
94.4
111.2
71
86.8
119.5
106.3
101.5
107.3
89.2
102.6
112.3
94.3
102.2
103.4
72.2
95.9
118.8
105.1
97.2
101.9
93.4
108.4
110.7
90.8
99.6
111.6
72.4
88.1
111.6
101.6
95.2
83.8
80.2
88.2
92.6
87.7
91.8
94.2
68.8
73.7
99.3
96.8
89.1
87.9
82.8
92.6
94.7
87.8
83.3
90.3
70.6
69.9
95.6
102.3
81.1
84.2
83.8
87.6
98.8
90
80.3
104
70.5
73.2
105.9
100.1
87.5
86
79
94.4
98.6
90.2
89.7
105.7
66.9
79.5
100.2
94.6
92.1
90.4
81
89.4
103.5
79.8
89
100
68
73.7

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=310770&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=310770&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310770&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
1-0.537398-7.58090
2-0.051357-0.72450.234811
30.3296764.65073e-06
4-0.406764-5.73810
50.2023632.85470.002382
60.1271971.79430.037138
7-0.305302-4.30681.3e-05
80.1979652.79260.002869
90.0803141.1330.129296
10-0.17018-2.40070.008643
110.1570932.21610.01391
12-0.174069-2.45550.007463
130.0137770.19430.423052
140.0895781.26370.103916
15-0.012362-0.17440.430869
16-0.034235-0.48290.314834
17-0.00213-0.030.48803
180.1031971.45580.073516
19-0.153629-2.16720.015703
200.0648620.9150.180652
210.0984451.38870.083232
22-0.245453-3.46250.000327
230.3073524.33571.2e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.537398 & -7.5809 & 0 \tabularnewline
2 & -0.051357 & -0.7245 & 0.234811 \tabularnewline
3 & 0.329676 & 4.6507 & 3e-06 \tabularnewline
4 & -0.406764 & -5.7381 & 0 \tabularnewline
5 & 0.202363 & 2.8547 & 0.002382 \tabularnewline
6 & 0.127197 & 1.7943 & 0.037138 \tabularnewline
7 & -0.305302 & -4.3068 & 1.3e-05 \tabularnewline
8 & 0.197965 & 2.7926 & 0.002869 \tabularnewline
9 & 0.080314 & 1.133 & 0.129296 \tabularnewline
10 & -0.17018 & -2.4007 & 0.008643 \tabularnewline
11 & 0.157093 & 2.2161 & 0.01391 \tabularnewline
12 & -0.174069 & -2.4555 & 0.007463 \tabularnewline
13 & 0.013777 & 0.1943 & 0.423052 \tabularnewline
14 & 0.089578 & 1.2637 & 0.103916 \tabularnewline
15 & -0.012362 & -0.1744 & 0.430869 \tabularnewline
16 & -0.034235 & -0.4829 & 0.314834 \tabularnewline
17 & -0.00213 & -0.03 & 0.48803 \tabularnewline
18 & 0.103197 & 1.4558 & 0.073516 \tabularnewline
19 & -0.153629 & -2.1672 & 0.015703 \tabularnewline
20 & 0.064862 & 0.915 & 0.180652 \tabularnewline
21 & 0.098445 & 1.3887 & 0.083232 \tabularnewline
22 & -0.245453 & -3.4625 & 0.000327 \tabularnewline
23 & 0.307352 & 4.3357 & 1.2e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310770&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]-0.537398[/C][C]-7.5809[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.051357[/C][C]-0.7245[/C][C]0.234811[/C][/ROW]
[ROW][C]3[/C][C]0.329676[/C][C]4.6507[/C][C]3e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.406764[/C][C]-5.7381[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.202363[/C][C]2.8547[/C][C]0.002382[/C][/ROW]
[ROW][C]6[/C][C]0.127197[/C][C]1.7943[/C][C]0.037138[/C][/ROW]
[ROW][C]7[/C][C]-0.305302[/C][C]-4.3068[/C][C]1.3e-05[/C][/ROW]
[ROW][C]8[/C][C]0.197965[/C][C]2.7926[/C][C]0.002869[/C][/ROW]
[ROW][C]9[/C][C]0.080314[/C][C]1.133[/C][C]0.129296[/C][/ROW]
[ROW][C]10[/C][C]-0.17018[/C][C]-2.4007[/C][C]0.008643[/C][/ROW]
[ROW][C]11[/C][C]0.157093[/C][C]2.2161[/C][C]0.01391[/C][/ROW]
[ROW][C]12[/C][C]-0.174069[/C][C]-2.4555[/C][C]0.007463[/C][/ROW]
[ROW][C]13[/C][C]0.013777[/C][C]0.1943[/C][C]0.423052[/C][/ROW]
[ROW][C]14[/C][C]0.089578[/C][C]1.2637[/C][C]0.103916[/C][/ROW]
[ROW][C]15[/C][C]-0.012362[/C][C]-0.1744[/C][C]0.430869[/C][/ROW]
[ROW][C]16[/C][C]-0.034235[/C][C]-0.4829[/C][C]0.314834[/C][/ROW]
[ROW][C]17[/C][C]-0.00213[/C][C]-0.03[/C][C]0.48803[/C][/ROW]
[ROW][C]18[/C][C]0.103197[/C][C]1.4558[/C][C]0.073516[/C][/ROW]
[ROW][C]19[/C][C]-0.153629[/C][C]-2.1672[/C][C]0.015703[/C][/ROW]
[ROW][C]20[/C][C]0.064862[/C][C]0.915[/C][C]0.180652[/C][/ROW]
[ROW][C]21[/C][C]0.098445[/C][C]1.3887[/C][C]0.083232[/C][/ROW]
[ROW][C]22[/C][C]-0.245453[/C][C]-3.4625[/C][C]0.000327[/C][/ROW]
[ROW][C]23[/C][C]0.307352[/C][C]4.3357[/C][C]1.2e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310770&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310770&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
1-0.537398-7.58090
2-0.051357-0.72450.234811
30.3296764.65073e-06
4-0.406764-5.73810
50.2023632.85470.002382
60.1271971.79430.037138
7-0.305302-4.30681.3e-05
80.1979652.79260.002869
90.0803141.1330.129296
10-0.17018-2.40070.008643
110.1570932.21610.01391
12-0.174069-2.45550.007463
130.0137770.19430.423052
140.0895781.26370.103916
15-0.012362-0.17440.430869
16-0.034235-0.48290.314834
17-0.00213-0.030.48803
180.1031971.45580.073516
19-0.153629-2.16720.015703
200.0648620.9150.180652
210.0984451.38870.083232
22-0.245453-3.46250.000327
230.3073524.33571.2e-05






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.537398-7.58090
2-0.478278-6.74690
30.0580670.81910.206843
4-0.265256-3.74190.000119
5-0.143582-2.02550.022077
60.067290.94920.171826
7-0.079352-1.11940.132159
8-0.126373-1.78270.038079
90.1194271.68470.046805
100.1639392.31260.010882
110.1225361.72860.042718
12-0.154447-2.17870.015263
13-0.092944-1.31110.095662
14-0.136346-1.92340.027929
150.0409910.57830.281874
16-0.012875-0.18160.428032
17-0.068401-0.96490.16788
180.140741.98540.024237
19-0.045669-0.64420.26008
20-0.089397-1.26110.104375
210.1772082.49980.006617
22-0.015607-0.22020.412985
230.1861082.62540.004664

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.537398 & -7.5809 & 0 \tabularnewline
2 & -0.478278 & -6.7469 & 0 \tabularnewline
3 & 0.058067 & 0.8191 & 0.206843 \tabularnewline
4 & -0.265256 & -3.7419 & 0.000119 \tabularnewline
5 & -0.143582 & -2.0255 & 0.022077 \tabularnewline
6 & 0.06729 & 0.9492 & 0.171826 \tabularnewline
7 & -0.079352 & -1.1194 & 0.132159 \tabularnewline
8 & -0.126373 & -1.7827 & 0.038079 \tabularnewline
9 & 0.119427 & 1.6847 & 0.046805 \tabularnewline
10 & 0.163939 & 2.3126 & 0.010882 \tabularnewline
11 & 0.122536 & 1.7286 & 0.042718 \tabularnewline
12 & -0.154447 & -2.1787 & 0.015263 \tabularnewline
13 & -0.092944 & -1.3111 & 0.095662 \tabularnewline
14 & -0.136346 & -1.9234 & 0.027929 \tabularnewline
15 & 0.040991 & 0.5783 & 0.281874 \tabularnewline
16 & -0.012875 & -0.1816 & 0.428032 \tabularnewline
17 & -0.068401 & -0.9649 & 0.16788 \tabularnewline
18 & 0.14074 & 1.9854 & 0.024237 \tabularnewline
19 & -0.045669 & -0.6442 & 0.26008 \tabularnewline
20 & -0.089397 & -1.2611 & 0.104375 \tabularnewline
21 & 0.177208 & 2.4998 & 0.006617 \tabularnewline
22 & -0.015607 & -0.2202 & 0.412985 \tabularnewline
23 & 0.186108 & 2.6254 & 0.004664 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310770&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]-0.537398[/C][C]-7.5809[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.478278[/C][C]-6.7469[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.058067[/C][C]0.8191[/C][C]0.206843[/C][/ROW]
[ROW][C]4[/C][C]-0.265256[/C][C]-3.7419[/C][C]0.000119[/C][/ROW]
[ROW][C]5[/C][C]-0.143582[/C][C]-2.0255[/C][C]0.022077[/C][/ROW]
[ROW][C]6[/C][C]0.06729[/C][C]0.9492[/C][C]0.171826[/C][/ROW]
[ROW][C]7[/C][C]-0.079352[/C][C]-1.1194[/C][C]0.132159[/C][/ROW]
[ROW][C]8[/C][C]-0.126373[/C][C]-1.7827[/C][C]0.038079[/C][/ROW]
[ROW][C]9[/C][C]0.119427[/C][C]1.6847[/C][C]0.046805[/C][/ROW]
[ROW][C]10[/C][C]0.163939[/C][C]2.3126[/C][C]0.010882[/C][/ROW]
[ROW][C]11[/C][C]0.122536[/C][C]1.7286[/C][C]0.042718[/C][/ROW]
[ROW][C]12[/C][C]-0.154447[/C][C]-2.1787[/C][C]0.015263[/C][/ROW]
[ROW][C]13[/C][C]-0.092944[/C][C]-1.3111[/C][C]0.095662[/C][/ROW]
[ROW][C]14[/C][C]-0.136346[/C][C]-1.9234[/C][C]0.027929[/C][/ROW]
[ROW][C]15[/C][C]0.040991[/C][C]0.5783[/C][C]0.281874[/C][/ROW]
[ROW][C]16[/C][C]-0.012875[/C][C]-0.1816[/C][C]0.428032[/C][/ROW]
[ROW][C]17[/C][C]-0.068401[/C][C]-0.9649[/C][C]0.16788[/C][/ROW]
[ROW][C]18[/C][C]0.14074[/C][C]1.9854[/C][C]0.024237[/C][/ROW]
[ROW][C]19[/C][C]-0.045669[/C][C]-0.6442[/C][C]0.26008[/C][/ROW]
[ROW][C]20[/C][C]-0.089397[/C][C]-1.2611[/C][C]0.104375[/C][/ROW]
[ROW][C]21[/C][C]0.177208[/C][C]2.4998[/C][C]0.006617[/C][/ROW]
[ROW][C]22[/C][C]-0.015607[/C][C]-0.2202[/C][C]0.412985[/C][/ROW]
[ROW][C]23[/C][C]0.186108[/C][C]2.6254[/C][C]0.004664[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310770&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310770&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
1-0.537398-7.58090
2-0.478278-6.74690
30.0580670.81910.206843
4-0.265256-3.74190.000119
5-0.143582-2.02550.022077
60.067290.94920.171826
7-0.079352-1.11940.132159
8-0.126373-1.78270.038079
90.1194271.68470.046805
100.1639392.31260.010882
110.1225361.72860.042718
12-0.154447-2.17870.015263
13-0.092944-1.31110.095662
14-0.136346-1.92340.027929
150.0409910.57830.281874
16-0.012875-0.18160.428032
17-0.068401-0.96490.16788
180.140741.98540.024237
19-0.045669-0.64420.26008
20-0.089397-1.26110.104375
210.1772082.49980.006617
22-0.015607-0.22020.412985
230.1861082.62540.004664


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = -0.2 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = -0.2 ; par3 = 1 ; par4 = 1 ; 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 <- '1'
par2 <- '-0.2'
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')