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Author*The author of this computation has been verified*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationTue, 12 Dec 2017 15:01:34 +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/12/t15130873615zmwh1jeebbaack.htm/, Retrieved Wed, 15 May 2024 12:57:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309099, Retrieved Wed, 15 May 2024 12:57:01 +0000
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Original text written by user:Unsure, TBA
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact33
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [Dataset_3_ACF] [2017-12-12 14:01:34] [453a4fcb74c301cf89bf197d0ef2c60e] [Current]
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Dataseries X:
78
100.1
113.2
93.1
115.4
103.3
45.1
104.7
111.3
111.5
100.9
82.1
85.4
97.7
106.6
92.6
109.2
110
52.5
105.3
102.3
118.5
100
74.4
89.2
91.9
107
103.6
101.8
105.1
55.5
92.1
109.8
112.7
98.5
70.3
84.5
91.1
107.6
102.2
96
107.3
59.9
90.2
116.3
115.6
92
76.5
87.9
95.8
116.9
102.9
95.8
117.3
52.8
100.1
116.3
111.8
98.5
86.2
79.9
92.3
100.5
112.5
101.1
121.5
49.6
104.8
120.4
108.3
105.2
85.7
86.8
95.1
117
100.1
112.3
119.6
51.8
105.5
119.9
115.4
112.8
85.1
96.2
103.6
119.9
103.7
109
119.6
57
109.2
112.6
126
109.7
80.1
105.8
114.1
98.3
125.3
111.6
119.7
65
99
124.5
119
98.8
81.8
90.3
102
119.3
104.3
102.8
118.8
60.9
101
122.6
122.2
95
75.6
83.1
89.8
126.1
108.6
98.9
124.3
56.8
102.7
121.7
118.2
101
69
88.6
109.6
128.2
102
122.7
110.5
54
108.1
125
114.1
112.4
87.3
95.4
96.9
125.8
102
112.5
118.9
62.7
110
114.7
124.4
111.9
77
84.1
96.5
106.8
107.9
107.5
114.3
66.6
97.9
117.8
123.8
103.3
84.2
103.6
103.6
112.2
102.7
100.8
109.4
63.5
92.3
119.2
121.5
97.6
78.3
95.6
97.9
114.4
100.9
94.4
117.2
61
95.8
116.2
118.5
94.3
74.4
94.9
102
102.9
109.5
99.7
118.3
56.2
100.3
116.9
108.7
93.9
85.3
85.3
102.4
121.6
91.4
110.2
112.7
55.7
100.1




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=309099&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=309099&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309099&T=0

As an alternative you can also use a 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
1-0.215149-3.04270.00133
2-0.00573-0.0810.467747
30.2522813.56780.000225
4-0.119608-1.69150.046148
5-0.041063-0.58070.281041
60.1476532.08810.019026
7-0.047878-0.67710.249565
80.1274651.80260.036476
9-0.015819-0.22370.411605
100.0558260.78950.215379
110.1293751.82960.034396
12-0.262409-3.7110.000134

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.215149 & -3.0427 & 0.00133 \tabularnewline
2 & -0.00573 & -0.081 & 0.467747 \tabularnewline
3 & 0.252281 & 3.5678 & 0.000225 \tabularnewline
4 & -0.119608 & -1.6915 & 0.046148 \tabularnewline
5 & -0.041063 & -0.5807 & 0.281041 \tabularnewline
6 & 0.147653 & 2.0881 & 0.019026 \tabularnewline
7 & -0.047878 & -0.6771 & 0.249565 \tabularnewline
8 & 0.127465 & 1.8026 & 0.036476 \tabularnewline
9 & -0.015819 & -0.2237 & 0.411605 \tabularnewline
10 & 0.055826 & 0.7895 & 0.215379 \tabularnewline
11 & 0.129375 & 1.8296 & 0.034396 \tabularnewline
12 & -0.262409 & -3.711 & 0.000134 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309099&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]-0.215149[/C][C]-3.0427[/C][C]0.00133[/C][/ROW]
[ROW][C]2[/C][C]-0.00573[/C][C]-0.081[/C][C]0.467747[/C][/ROW]
[ROW][C]3[/C][C]0.252281[/C][C]3.5678[/C][C]0.000225[/C][/ROW]
[ROW][C]4[/C][C]-0.119608[/C][C]-1.6915[/C][C]0.046148[/C][/ROW]
[ROW][C]5[/C][C]-0.041063[/C][C]-0.5807[/C][C]0.281041[/C][/ROW]
[ROW][C]6[/C][C]0.147653[/C][C]2.0881[/C][C]0.019026[/C][/ROW]
[ROW][C]7[/C][C]-0.047878[/C][C]-0.6771[/C][C]0.249565[/C][/ROW]
[ROW][C]8[/C][C]0.127465[/C][C]1.8026[/C][C]0.036476[/C][/ROW]
[ROW][C]9[/C][C]-0.015819[/C][C]-0.2237[/C][C]0.411605[/C][/ROW]
[ROW][C]10[/C][C]0.055826[/C][C]0.7895[/C][C]0.215379[/C][/ROW]
[ROW][C]11[/C][C]0.129375[/C][C]1.8296[/C][C]0.034396[/C][/ROW]
[ROW][C]12[/C][C]-0.262409[/C][C]-3.711[/C][C]0.000134[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309099&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309099&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag kACF(k)T-STATP-value
1-0.215149-3.04270.00133
2-0.00573-0.0810.467747
30.2522813.56780.000225
4-0.119608-1.69150.046148
5-0.041063-0.58070.281041
60.1476532.08810.019026
7-0.047878-0.67710.249565
80.1274651.80260.036476
9-0.015819-0.22370.411605
100.0558260.78950.215379
110.1293751.82960.034396
12-0.262409-3.7110.000134







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.215149-3.04270.00133
2-0.054544-0.77140.220699
30.2516073.55830.000233
4-0.013118-0.18550.426505
5-0.076596-1.08320.140006
60.0701620.99220.16114
70.0381620.53970.295005
80.1625132.29830.01129
9-0.023746-0.33580.36868
100.0589230.83330.202835
110.124331.75830.040113
12-0.233534-3.30270.000567

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.215149 & -3.0427 & 0.00133 \tabularnewline
2 & -0.054544 & -0.7714 & 0.220699 \tabularnewline
3 & 0.251607 & 3.5583 & 0.000233 \tabularnewline
4 & -0.013118 & -0.1855 & 0.426505 \tabularnewline
5 & -0.076596 & -1.0832 & 0.140006 \tabularnewline
6 & 0.070162 & 0.9922 & 0.16114 \tabularnewline
7 & 0.038162 & 0.5397 & 0.295005 \tabularnewline
8 & 0.162513 & 2.2983 & 0.01129 \tabularnewline
9 & -0.023746 & -0.3358 & 0.36868 \tabularnewline
10 & 0.058923 & 0.8333 & 0.202835 \tabularnewline
11 & 0.12433 & 1.7583 & 0.040113 \tabularnewline
12 & -0.233534 & -3.3027 & 0.000567 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309099&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]-0.215149[/C][C]-3.0427[/C][C]0.00133[/C][/ROW]
[ROW][C]2[/C][C]-0.054544[/C][C]-0.7714[/C][C]0.220699[/C][/ROW]
[ROW][C]3[/C][C]0.251607[/C][C]3.5583[/C][C]0.000233[/C][/ROW]
[ROW][C]4[/C][C]-0.013118[/C][C]-0.1855[/C][C]0.426505[/C][/ROW]
[ROW][C]5[/C][C]-0.076596[/C][C]-1.0832[/C][C]0.140006[/C][/ROW]
[ROW][C]6[/C][C]0.070162[/C][C]0.9922[/C][C]0.16114[/C][/ROW]
[ROW][C]7[/C][C]0.038162[/C][C]0.5397[/C][C]0.295005[/C][/ROW]
[ROW][C]8[/C][C]0.162513[/C][C]2.2983[/C][C]0.01129[/C][/ROW]
[ROW][C]9[/C][C]-0.023746[/C][C]-0.3358[/C][C]0.36868[/C][/ROW]
[ROW][C]10[/C][C]0.058923[/C][C]0.8333[/C][C]0.202835[/C][/ROW]
[ROW][C]11[/C][C]0.12433[/C][C]1.7583[/C][C]0.040113[/C][/ROW]
[ROW][C]12[/C][C]-0.233534[/C][C]-3.3027[/C][C]0.000567[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309099&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309099&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.215149-3.04270.00133
2-0.054544-0.77140.220699
30.2516073.55830.000233
4-0.013118-0.18550.426505
5-0.076596-1.08320.140006
60.0701620.99220.16114
70.0381620.53970.295005
80.1625132.29830.01129
9-0.023746-0.33580.36868
100.0589230.83330.202835
110.124331.75830.040113
12-0.233534-3.30270.000567



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