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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 11:49:11 +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/t1513853383pyr0uw49kgmmsdt.htm/, Retrieved Tue, 14 May 2024 15:32:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310614, Retrieved Tue, 14 May 2024 15:32:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84

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 10:49:11] [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=310614&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=310614&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310614&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
10.3066254.33631.1e-05
20.3727025.27080
30.5766678.15530
40.2549763.60590.000196
50.3727965.27210
60.374465.29570
70.0991371.4020.081232
80.2455133.47210.000316
90.2484923.51420.000273
10-0.005639-0.07970.468259
110.0853611.20720.114392
12-0.014085-0.19920.421159
13-0.114495-1.61920.053489
140.0716271.0130.15615
15-0.08994-1.27190.102435
16-0.23484-3.32110.000533
170.0237540.33590.368639
18-0.05006-0.7080.239898
19-0.240454-3.40050.000406
20-0.019181-0.27130.393233
21-0.159877-2.2610.012418
22-0.246169-3.48140.000306
230.0677680.95840.169512

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.306625 & 4.3363 & 1.1e-05 \tabularnewline
2 & 0.372702 & 5.2708 & 0 \tabularnewline
3 & 0.576667 & 8.1553 & 0 \tabularnewline
4 & 0.254976 & 3.6059 & 0.000196 \tabularnewline
5 & 0.372796 & 5.2721 & 0 \tabularnewline
6 & 0.37446 & 5.2957 & 0 \tabularnewline
7 & 0.099137 & 1.402 & 0.081232 \tabularnewline
8 & 0.245513 & 3.4721 & 0.000316 \tabularnewline
9 & 0.248492 & 3.5142 & 0.000273 \tabularnewline
10 & -0.005639 & -0.0797 & 0.468259 \tabularnewline
11 & 0.085361 & 1.2072 & 0.114392 \tabularnewline
12 & -0.014085 & -0.1992 & 0.421159 \tabularnewline
13 & -0.114495 & -1.6192 & 0.053489 \tabularnewline
14 & 0.071627 & 1.013 & 0.15615 \tabularnewline
15 & -0.08994 & -1.2719 & 0.102435 \tabularnewline
16 & -0.23484 & -3.3211 & 0.000533 \tabularnewline
17 & 0.023754 & 0.3359 & 0.368639 \tabularnewline
18 & -0.05006 & -0.708 & 0.239898 \tabularnewline
19 & -0.240454 & -3.4005 & 0.000406 \tabularnewline
20 & -0.019181 & -0.2713 & 0.393233 \tabularnewline
21 & -0.159877 & -2.261 & 0.012418 \tabularnewline
22 & -0.246169 & -3.4814 & 0.000306 \tabularnewline
23 & 0.067768 & 0.9584 & 0.169512 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310614&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]0.306625[/C][C]4.3363[/C][C]1.1e-05[/C][/ROW]
[ROW][C]2[/C][C]0.372702[/C][C]5.2708[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.576667[/C][C]8.1553[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.254976[/C][C]3.6059[/C][C]0.000196[/C][/ROW]
[ROW][C]5[/C][C]0.372796[/C][C]5.2721[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.37446[/C][C]5.2957[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.099137[/C][C]1.402[/C][C]0.081232[/C][/ROW]
[ROW][C]8[/C][C]0.245513[/C][C]3.4721[/C][C]0.000316[/C][/ROW]
[ROW][C]9[/C][C]0.248492[/C][C]3.5142[/C][C]0.000273[/C][/ROW]
[ROW][C]10[/C][C]-0.005639[/C][C]-0.0797[/C][C]0.468259[/C][/ROW]
[ROW][C]11[/C][C]0.085361[/C][C]1.2072[/C][C]0.114392[/C][/ROW]
[ROW][C]12[/C][C]-0.014085[/C][C]-0.1992[/C][C]0.421159[/C][/ROW]
[ROW][C]13[/C][C]-0.114495[/C][C]-1.6192[/C][C]0.053489[/C][/ROW]
[ROW][C]14[/C][C]0.071627[/C][C]1.013[/C][C]0.15615[/C][/ROW]
[ROW][C]15[/C][C]-0.08994[/C][C]-1.2719[/C][C]0.102435[/C][/ROW]
[ROW][C]16[/C][C]-0.23484[/C][C]-3.3211[/C][C]0.000533[/C][/ROW]
[ROW][C]17[/C][C]0.023754[/C][C]0.3359[/C][C]0.368639[/C][/ROW]
[ROW][C]18[/C][C]-0.05006[/C][C]-0.708[/C][C]0.239898[/C][/ROW]
[ROW][C]19[/C][C]-0.240454[/C][C]-3.4005[/C][C]0.000406[/C][/ROW]
[ROW][C]20[/C][C]-0.019181[/C][C]-0.2713[/C][C]0.393233[/C][/ROW]
[ROW][C]21[/C][C]-0.159877[/C][C]-2.261[/C][C]0.012418[/C][/ROW]
[ROW][C]22[/C][C]-0.246169[/C][C]-3.4814[/C][C]0.000306[/C][/ROW]
[ROW][C]23[/C][C]0.067768[/C][C]0.9584[/C][C]0.169512[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310614&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310614&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
10.3066254.33631.1e-05
20.3727025.27080
30.5766678.15530
40.2549763.60590.000196
50.3727965.27210
60.374465.29570
70.0991371.4020.081232
80.2455133.47210.000316
90.2484923.51420.000273
10-0.005639-0.07970.468259
110.0853611.20720.114392
12-0.014085-0.19920.421159
13-0.114495-1.61920.053489
140.0716271.0130.15615
15-0.08994-1.27190.102435
16-0.23484-3.32110.000533
170.0237540.33590.368639
18-0.05006-0.7080.239898
19-0.240454-3.40050.000406
20-0.019181-0.27130.393233
21-0.159877-2.2610.012418
22-0.246169-3.48140.000306
230.0677680.95840.169512






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.3066254.33631.1e-05
20.3076044.35021.1e-05
30.4915796.9520
4-0.010823-0.15310.439255
50.092051.30180.097245
60.0221090.31270.37743
7-0.214018-3.02670.001399
8-0.067356-0.95260.170981
90.0713431.00890.157109
10-0.118513-1.6760.047648
11-0.121842-1.72310.043208
12-0.165978-2.34730.009944
13-0.08058-1.13960.127914
140.1504952.12830.017267
150.0801741.13380.129111
16-0.143141-2.02430.022134
170.0855071.20920.113997
180.1995032.82140.002632
19-0.148356-2.09810.018577
20-0.041826-0.59150.277423
21-0.014563-0.2060.418518
22-0.179775-2.54240.005883
230.0973341.37650.085101

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.306625 & 4.3363 & 1.1e-05 \tabularnewline
2 & 0.307604 & 4.3502 & 1.1e-05 \tabularnewline
3 & 0.491579 & 6.952 & 0 \tabularnewline
4 & -0.010823 & -0.1531 & 0.439255 \tabularnewline
5 & 0.09205 & 1.3018 & 0.097245 \tabularnewline
6 & 0.022109 & 0.3127 & 0.37743 \tabularnewline
7 & -0.214018 & -3.0267 & 0.001399 \tabularnewline
8 & -0.067356 & -0.9526 & 0.170981 \tabularnewline
9 & 0.071343 & 1.0089 & 0.157109 \tabularnewline
10 & -0.118513 & -1.676 & 0.047648 \tabularnewline
11 & -0.121842 & -1.7231 & 0.043208 \tabularnewline
12 & -0.165978 & -2.3473 & 0.009944 \tabularnewline
13 & -0.08058 & -1.1396 & 0.127914 \tabularnewline
14 & 0.150495 & 2.1283 & 0.017267 \tabularnewline
15 & 0.080174 & 1.1338 & 0.129111 \tabularnewline
16 & -0.143141 & -2.0243 & 0.022134 \tabularnewline
17 & 0.085507 & 1.2092 & 0.113997 \tabularnewline
18 & 0.199503 & 2.8214 & 0.002632 \tabularnewline
19 & -0.148356 & -2.0981 & 0.018577 \tabularnewline
20 & -0.041826 & -0.5915 & 0.277423 \tabularnewline
21 & -0.014563 & -0.206 & 0.418518 \tabularnewline
22 & -0.179775 & -2.5424 & 0.005883 \tabularnewline
23 & 0.097334 & 1.3765 & 0.085101 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310614&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]0.306625[/C][C]4.3363[/C][C]1.1e-05[/C][/ROW]
[ROW][C]2[/C][C]0.307604[/C][C]4.3502[/C][C]1.1e-05[/C][/ROW]
[ROW][C]3[/C][C]0.491579[/C][C]6.952[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.010823[/C][C]-0.1531[/C][C]0.439255[/C][/ROW]
[ROW][C]5[/C][C]0.09205[/C][C]1.3018[/C][C]0.097245[/C][/ROW]
[ROW][C]6[/C][C]0.022109[/C][C]0.3127[/C][C]0.37743[/C][/ROW]
[ROW][C]7[/C][C]-0.214018[/C][C]-3.0267[/C][C]0.001399[/C][/ROW]
[ROW][C]8[/C][C]-0.067356[/C][C]-0.9526[/C][C]0.170981[/C][/ROW]
[ROW][C]9[/C][C]0.071343[/C][C]1.0089[/C][C]0.157109[/C][/ROW]
[ROW][C]10[/C][C]-0.118513[/C][C]-1.676[/C][C]0.047648[/C][/ROW]
[ROW][C]11[/C][C]-0.121842[/C][C]-1.7231[/C][C]0.043208[/C][/ROW]
[ROW][C]12[/C][C]-0.165978[/C][C]-2.3473[/C][C]0.009944[/C][/ROW]
[ROW][C]13[/C][C]-0.08058[/C][C]-1.1396[/C][C]0.127914[/C][/ROW]
[ROW][C]14[/C][C]0.150495[/C][C]2.1283[/C][C]0.017267[/C][/ROW]
[ROW][C]15[/C][C]0.080174[/C][C]1.1338[/C][C]0.129111[/C][/ROW]
[ROW][C]16[/C][C]-0.143141[/C][C]-2.0243[/C][C]0.022134[/C][/ROW]
[ROW][C]17[/C][C]0.085507[/C][C]1.2092[/C][C]0.113997[/C][/ROW]
[ROW][C]18[/C][C]0.199503[/C][C]2.8214[/C][C]0.002632[/C][/ROW]
[ROW][C]19[/C][C]-0.148356[/C][C]-2.0981[/C][C]0.018577[/C][/ROW]
[ROW][C]20[/C][C]-0.041826[/C][C]-0.5915[/C][C]0.277423[/C][/ROW]
[ROW][C]21[/C][C]-0.014563[/C][C]-0.206[/C][C]0.418518[/C][/ROW]
[ROW][C]22[/C][C]-0.179775[/C][C]-2.5424[/C][C]0.005883[/C][/ROW]
[ROW][C]23[/C][C]0.097334[/C][C]1.3765[/C][C]0.085101[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310614&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310614&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
10.3066254.33631.1e-05
20.3076044.35021.1e-05
30.4915796.9520
4-0.010823-0.15310.439255
50.092051.30180.097245
60.0221090.31270.37743
7-0.214018-3.02670.001399
8-0.067356-0.95260.170981
90.0713431.00890.157109
10-0.118513-1.6760.047648
11-0.121842-1.72310.043208
12-0.165978-2.34730.009944
13-0.08058-1.13960.127914
140.1504952.12830.017267
150.0801741.13380.129111
16-0.143141-2.02430.022134
170.0855071.20920.113997
180.1995032.82140.002632
19-0.148356-2.09810.018577
20-0.041826-0.59150.277423
21-0.014563-0.2060.418518
22-0.179775-2.54240.005883
230.0973341.37650.085101


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 0.5 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 0.5 ; par3 = 0 ; 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')