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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, 07 Dec 2017 10:54:01 +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/07/t15126406249dhlbpby1esacup.htm/, Retrieved Wed, 15 May 2024 03:08:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308661, Retrieved Wed, 15 May 2024 03:08:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123

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] [Autocorrelation] [2017-12-07 09:54:01] [6ed64e8c4e855e992fbbfd41bce49003] [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 time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308661&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308661&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308661&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 time2 seconds
R ServerBig Analytics Cloud Computing Center






Autocorrelation Function
Time lag kACF(k)T-STATP-value
1-0.642751-8.7660
20.0171510.23390.407658
30.3350254.56914e-06
4-0.381388-5.20140
50.2279423.10870.001087
60.0310730.42380.336107
7-0.224961-3.06810.001238
80.2612333.56270.000233
9-0.199067-2.71490.003627
100.0283810.38710.349576
110.2877473.92446.1e-05
12-0.495966-6.76410
130.3433784.68313e-06
14-0.043066-0.58730.278843
15-0.11491-1.56720.059388
160.1194611.62920.052478
17-0.075235-1.02610.153097
180.0422060.57560.282787
19-0.015569-0.21230.41604
20-0.041745-0.56930.284913
210.1468032.00210.023362
22-0.240404-3.27870.000622
230.1899892.59110.005163

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.642751 & -8.766 & 0 \tabularnewline
2 & 0.017151 & 0.2339 & 0.407658 \tabularnewline
3 & 0.335025 & 4.5691 & 4e-06 \tabularnewline
4 & -0.381388 & -5.2014 & 0 \tabularnewline
5 & 0.227942 & 3.1087 & 0.001087 \tabularnewline
6 & 0.031073 & 0.4238 & 0.336107 \tabularnewline
7 & -0.224961 & -3.0681 & 0.001238 \tabularnewline
8 & 0.261233 & 3.5627 & 0.000233 \tabularnewline
9 & -0.199067 & -2.7149 & 0.003627 \tabularnewline
10 & 0.028381 & 0.3871 & 0.349576 \tabularnewline
11 & 0.287747 & 3.9244 & 6.1e-05 \tabularnewline
12 & -0.495966 & -6.7641 & 0 \tabularnewline
13 & 0.343378 & 4.6831 & 3e-06 \tabularnewline
14 & -0.043066 & -0.5873 & 0.278843 \tabularnewline
15 & -0.11491 & -1.5672 & 0.059388 \tabularnewline
16 & 0.119461 & 1.6292 & 0.052478 \tabularnewline
17 & -0.075235 & -1.0261 & 0.153097 \tabularnewline
18 & 0.042206 & 0.5756 & 0.282787 \tabularnewline
19 & -0.015569 & -0.2123 & 0.41604 \tabularnewline
20 & -0.041745 & -0.5693 & 0.284913 \tabularnewline
21 & 0.146803 & 2.0021 & 0.023362 \tabularnewline
22 & -0.240404 & -3.2787 & 0.000622 \tabularnewline
23 & 0.189989 & 2.5911 & 0.005163 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308661&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]-0.642751[/C][C]-8.766[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.017151[/C][C]0.2339[/C][C]0.407658[/C][/ROW]
[ROW][C]3[/C][C]0.335025[/C][C]4.5691[/C][C]4e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.381388[/C][C]-5.2014[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.227942[/C][C]3.1087[/C][C]0.001087[/C][/ROW]
[ROW][C]6[/C][C]0.031073[/C][C]0.4238[/C][C]0.336107[/C][/ROW]
[ROW][C]7[/C][C]-0.224961[/C][C]-3.0681[/C][C]0.001238[/C][/ROW]
[ROW][C]8[/C][C]0.261233[/C][C]3.5627[/C][C]0.000233[/C][/ROW]
[ROW][C]9[/C][C]-0.199067[/C][C]-2.7149[/C][C]0.003627[/C][/ROW]
[ROW][C]10[/C][C]0.028381[/C][C]0.3871[/C][C]0.349576[/C][/ROW]
[ROW][C]11[/C][C]0.287747[/C][C]3.9244[/C][C]6.1e-05[/C][/ROW]
[ROW][C]12[/C][C]-0.495966[/C][C]-6.7641[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.343378[/C][C]4.6831[/C][C]3e-06[/C][/ROW]
[ROW][C]14[/C][C]-0.043066[/C][C]-0.5873[/C][C]0.278843[/C][/ROW]
[ROW][C]15[/C][C]-0.11491[/C][C]-1.5672[/C][C]0.059388[/C][/ROW]
[ROW][C]16[/C][C]0.119461[/C][C]1.6292[/C][C]0.052478[/C][/ROW]
[ROW][C]17[/C][C]-0.075235[/C][C]-1.0261[/C][C]0.153097[/C][/ROW]
[ROW][C]18[/C][C]0.042206[/C][C]0.5756[/C][C]0.282787[/C][/ROW]
[ROW][C]19[/C][C]-0.015569[/C][C]-0.2123[/C][C]0.41604[/C][/ROW]
[ROW][C]20[/C][C]-0.041745[/C][C]-0.5693[/C][C]0.284913[/C][/ROW]
[ROW][C]21[/C][C]0.146803[/C][C]2.0021[/C][C]0.023362[/C][/ROW]
[ROW][C]22[/C][C]-0.240404[/C][C]-3.2787[/C][C]0.000622[/C][/ROW]
[ROW][C]23[/C][C]0.189989[/C][C]2.5911[/C][C]0.005163[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308661&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308661&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
1-0.642751-8.7660
20.0171510.23390.407658
30.3350254.56914e-06
4-0.381388-5.20140
50.2279423.10870.001087
60.0310730.42380.336107
7-0.224961-3.06810.001238
80.2612333.56270.000233
9-0.199067-2.71490.003627
100.0283810.38710.349576
110.2877473.92446.1e-05
12-0.495966-6.76410
130.3433784.68313e-06
14-0.043066-0.58730.278843
15-0.11491-1.56720.059388
160.1194611.62920.052478
17-0.075235-1.02610.153097
180.0422060.57560.282787
19-0.015569-0.21230.41604
20-0.041745-0.56930.284913
210.1468032.00210.023362
22-0.240404-3.27870.000622
230.1899892.59110.005163






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.642751-8.7660
2-0.674728-9.20210
3-0.250852-3.42120.000383
4-0.364123-4.9661e-06
5-0.27776-3.78810.000102
6-0.071865-0.98010.164152
7-0.088246-1.20350.115154
80.0736651.00470.158184
9-0.086196-1.17560.120638
10-0.277113-3.77930.000106
110.2844423.87937.3e-05
120.1141461.55670.060616
130.0208270.2840.388345
14-0.244299-3.33180.00052
150.0046420.06330.474794
16-0.1414-1.92840.027662
17-0.226917-3.09470.001137
180.0148830.2030.419685
190.0629810.85890.195739
20-0.04034-0.55020.291431
210.0870191.18680.118414
22-0.265016-3.61430.000194
230.0503530.68670.246555

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.642751 & -8.766 & 0 \tabularnewline
2 & -0.674728 & -9.2021 & 0 \tabularnewline
3 & -0.250852 & -3.4212 & 0.000383 \tabularnewline
4 & -0.364123 & -4.966 & 1e-06 \tabularnewline
5 & -0.27776 & -3.7881 & 0.000102 \tabularnewline
6 & -0.071865 & -0.9801 & 0.164152 \tabularnewline
7 & -0.088246 & -1.2035 & 0.115154 \tabularnewline
8 & 0.073665 & 1.0047 & 0.158184 \tabularnewline
9 & -0.086196 & -1.1756 & 0.120638 \tabularnewline
10 & -0.277113 & -3.7793 & 0.000106 \tabularnewline
11 & 0.284442 & 3.8793 & 7.3e-05 \tabularnewline
12 & 0.114146 & 1.5567 & 0.060616 \tabularnewline
13 & 0.020827 & 0.284 & 0.388345 \tabularnewline
14 & -0.244299 & -3.3318 & 0.00052 \tabularnewline
15 & 0.004642 & 0.0633 & 0.474794 \tabularnewline
16 & -0.1414 & -1.9284 & 0.027662 \tabularnewline
17 & -0.226917 & -3.0947 & 0.001137 \tabularnewline
18 & 0.014883 & 0.203 & 0.419685 \tabularnewline
19 & 0.062981 & 0.8589 & 0.195739 \tabularnewline
20 & -0.04034 & -0.5502 & 0.291431 \tabularnewline
21 & 0.087019 & 1.1868 & 0.118414 \tabularnewline
22 & -0.265016 & -3.6143 & 0.000194 \tabularnewline
23 & 0.050353 & 0.6867 & 0.246555 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308661&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]-0.642751[/C][C]-8.766[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.674728[/C][C]-9.2021[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.250852[/C][C]-3.4212[/C][C]0.000383[/C][/ROW]
[ROW][C]4[/C][C]-0.364123[/C][C]-4.966[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]-0.27776[/C][C]-3.7881[/C][C]0.000102[/C][/ROW]
[ROW][C]6[/C][C]-0.071865[/C][C]-0.9801[/C][C]0.164152[/C][/ROW]
[ROW][C]7[/C][C]-0.088246[/C][C]-1.2035[/C][C]0.115154[/C][/ROW]
[ROW][C]8[/C][C]0.073665[/C][C]1.0047[/C][C]0.158184[/C][/ROW]
[ROW][C]9[/C][C]-0.086196[/C][C]-1.1756[/C][C]0.120638[/C][/ROW]
[ROW][C]10[/C][C]-0.277113[/C][C]-3.7793[/C][C]0.000106[/C][/ROW]
[ROW][C]11[/C][C]0.284442[/C][C]3.8793[/C][C]7.3e-05[/C][/ROW]
[ROW][C]12[/C][C]0.114146[/C][C]1.5567[/C][C]0.060616[/C][/ROW]
[ROW][C]13[/C][C]0.020827[/C][C]0.284[/C][C]0.388345[/C][/ROW]
[ROW][C]14[/C][C]-0.244299[/C][C]-3.3318[/C][C]0.00052[/C][/ROW]
[ROW][C]15[/C][C]0.004642[/C][C]0.0633[/C][C]0.474794[/C][/ROW]
[ROW][C]16[/C][C]-0.1414[/C][C]-1.9284[/C][C]0.027662[/C][/ROW]
[ROW][C]17[/C][C]-0.226917[/C][C]-3.0947[/C][C]0.001137[/C][/ROW]
[ROW][C]18[/C][C]0.014883[/C][C]0.203[/C][C]0.419685[/C][/ROW]
[ROW][C]19[/C][C]0.062981[/C][C]0.8589[/C][C]0.195739[/C][/ROW]
[ROW][C]20[/C][C]-0.04034[/C][C]-0.5502[/C][C]0.291431[/C][/ROW]
[ROW][C]21[/C][C]0.087019[/C][C]1.1868[/C][C]0.118414[/C][/ROW]
[ROW][C]22[/C][C]-0.265016[/C][C]-3.6143[/C][C]0.000194[/C][/ROW]
[ROW][C]23[/C][C]0.050353[/C][C]0.6867[/C][C]0.246555[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308661&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308661&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
1-0.642751-8.7660
2-0.674728-9.20210
3-0.250852-3.42120.000383
4-0.364123-4.9661e-06
5-0.27776-3.78810.000102
6-0.071865-0.98010.164152
7-0.088246-1.20350.115154
80.0736651.00470.158184
9-0.086196-1.17560.120638
10-0.277113-3.77930.000106
110.2844423.87937.3e-05
120.1141461.55670.060616
130.0208270.2840.388345
14-0.244299-3.33180.00052
150.0046420.06330.474794
16-0.1414-1.92840.027662
17-0.226917-3.09470.001137
180.0148830.2030.419685
190.0629810.85890.195739
20-0.04034-0.55020.291431
210.0870191.18680.118414
22-0.265016-3.61430.000194
230.0503530.68670.246555


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 0.3 ; par3 = 2 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 0.3 ; par3 = 2 ; par4 = 2 ; 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')