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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 computationTue, 19 Dec 2017 20:14:07 +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/19/t1513710867wxfht0ku8apj32q.htm/, Retrieved Wed, 15 May 2024 07:41:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310403, Retrieved Wed, 15 May 2024 07:41:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71

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] [Autocorr] [2017-12-19 19:14:07] [ec772448347bb766a411d58621b503be] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
82
96.5
104.8
87.2
98.6
98.7
75
86.8
105
109.8
108.2
99
89.6
97.8
104.8
87
87.9
93.9
84.3
84
104.3
104.4
102.3
89.4
78.7
86.9
93.7
87
83.9
95.3
73.7
76.6
94.7
97.7
90
82.4
77.4
85
90.3
82.1
79.6
86.2
73.4
66.7
96.7
98.6
83.2
84
75.8
83.2
95.7
87.3
83.8
98.7
80.8
74.2
96.1
99.4
91.8
89.7
82.9
90
98.5
93.4
89.1
103
74.7
79
101.3
96.7
99.1
92.3
90.6
95.2
107.6
97.6
104
112
90.6
84.9
112.7
115.2
110.1
95.7
104.2
103.3
116.1
106.9
105.9
120.2
96.2
91.5
108.3
121.1
111.4
95.6
98.7
117.7
124.5
114.8
108
120.7
95.6
84.3
122.2
117.1
97.2
99.5
90.1
87.3
97.4
90.1
83.6
97.8
79.7
75.1
106.1
103.5
94.5
100.9
89.7
91.4
110.2
102.8
89.8
112.8
84
86.5
107.3
120.2
105.5
99.9
100.4
99.6
118.6
96
105.3
105.8
80.1
89.3
120.4
111.3
98.1
102.9
95.4
108.7
123
107.7
97.2
127.7
100.6
89.7
108.3
110
105.2
87.7
91.4
92.8
97.5
95.7
93.5
97.3
84.1
87.8
96.2
94.6
88.7
76.5
83.9
88.1
93
81.8
84.1
89.1
75.8
71.4
93.8
88.5
78.1
83.6
78.2
76.2
92
79.5
69.5
86.4
72.3
65
86
83.4
87.2
76.4
76.3
76.9
92.7
83.3
73.8
94
73.1
69.8
86
78.8
89.4
83.8
74.1
77.2
103.6
78
80.2
88.8
72.9
73.6

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=310403&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=310403&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310403&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
1-0.444695-6.27320
2-0.133496-1.88320.030567
30.1407221.98510.024252
40.1358341.91620.028388
5-0.209685-2.9580.001736
60.0202040.2850.387966
70.2106042.97090.001667
8-0.274571-3.87337.3e-05
90.0972241.37150.085879
100.046040.64950.258392
110.1649852.32740.010475
12-0.450072-6.3490
130.2168943.05970.001261
140.0750071.05810.145647
15-0.118316-1.66910.04834
16-0.03996-0.56370.286794
170.1292621.82350.034866
180.0131150.1850.426706
19-0.19747-2.78570.002929
200.2307713.25540.000665
21-0.088148-1.24350.107578
22-0.105504-1.48830.069126
230.1605712.26510.012291

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.444695 & -6.2732 & 0 \tabularnewline
2 & -0.133496 & -1.8832 & 0.030567 \tabularnewline
3 & 0.140722 & 1.9851 & 0.024252 \tabularnewline
4 & 0.135834 & 1.9162 & 0.028388 \tabularnewline
5 & -0.209685 & -2.958 & 0.001736 \tabularnewline
6 & 0.020204 & 0.285 & 0.387966 \tabularnewline
7 & 0.210604 & 2.9709 & 0.001667 \tabularnewline
8 & -0.274571 & -3.8733 & 7.3e-05 \tabularnewline
9 & 0.097224 & 1.3715 & 0.085879 \tabularnewline
10 & 0.04604 & 0.6495 & 0.258392 \tabularnewline
11 & 0.164985 & 2.3274 & 0.010475 \tabularnewline
12 & -0.450072 & -6.349 & 0 \tabularnewline
13 & 0.216894 & 3.0597 & 0.001261 \tabularnewline
14 & 0.075007 & 1.0581 & 0.145647 \tabularnewline
15 & -0.118316 & -1.6691 & 0.04834 \tabularnewline
16 & -0.03996 & -0.5637 & 0.286794 \tabularnewline
17 & 0.129262 & 1.8235 & 0.034866 \tabularnewline
18 & 0.013115 & 0.185 & 0.426706 \tabularnewline
19 & -0.19747 & -2.7857 & 0.002929 \tabularnewline
20 & 0.230771 & 3.2554 & 0.000665 \tabularnewline
21 & -0.088148 & -1.2435 & 0.107578 \tabularnewline
22 & -0.105504 & -1.4883 & 0.069126 \tabularnewline
23 & 0.160571 & 2.2651 & 0.012291 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310403&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]-0.444695[/C][C]-6.2732[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.133496[/C][C]-1.8832[/C][C]0.030567[/C][/ROW]
[ROW][C]3[/C][C]0.140722[/C][C]1.9851[/C][C]0.024252[/C][/ROW]
[ROW][C]4[/C][C]0.135834[/C][C]1.9162[/C][C]0.028388[/C][/ROW]
[ROW][C]5[/C][C]-0.209685[/C][C]-2.958[/C][C]0.001736[/C][/ROW]
[ROW][C]6[/C][C]0.020204[/C][C]0.285[/C][C]0.387966[/C][/ROW]
[ROW][C]7[/C][C]0.210604[/C][C]2.9709[/C][C]0.001667[/C][/ROW]
[ROW][C]8[/C][C]-0.274571[/C][C]-3.8733[/C][C]7.3e-05[/C][/ROW]
[ROW][C]9[/C][C]0.097224[/C][C]1.3715[/C][C]0.085879[/C][/ROW]
[ROW][C]10[/C][C]0.04604[/C][C]0.6495[/C][C]0.258392[/C][/ROW]
[ROW][C]11[/C][C]0.164985[/C][C]2.3274[/C][C]0.010475[/C][/ROW]
[ROW][C]12[/C][C]-0.450072[/C][C]-6.349[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.216894[/C][C]3.0597[/C][C]0.001261[/C][/ROW]
[ROW][C]14[/C][C]0.075007[/C][C]1.0581[/C][C]0.145647[/C][/ROW]
[ROW][C]15[/C][C]-0.118316[/C][C]-1.6691[/C][C]0.04834[/C][/ROW]
[ROW][C]16[/C][C]-0.03996[/C][C]-0.5637[/C][C]0.286794[/C][/ROW]
[ROW][C]17[/C][C]0.129262[/C][C]1.8235[/C][C]0.034866[/C][/ROW]
[ROW][C]18[/C][C]0.013115[/C][C]0.185[/C][C]0.426706[/C][/ROW]
[ROW][C]19[/C][C]-0.19747[/C][C]-2.7857[/C][C]0.002929[/C][/ROW]
[ROW][C]20[/C][C]0.230771[/C][C]3.2554[/C][C]0.000665[/C][/ROW]
[ROW][C]21[/C][C]-0.088148[/C][C]-1.2435[/C][C]0.107578[/C][/ROW]
[ROW][C]22[/C][C]-0.105504[/C][C]-1.4883[/C][C]0.069126[/C][/ROW]
[ROW][C]23[/C][C]0.160571[/C][C]2.2651[/C][C]0.012291[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310403&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310403&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
1-0.444695-6.27320
2-0.133496-1.88320.030567
30.1407221.98510.024252
40.1358341.91620.028388
5-0.209685-2.9580.001736
60.0202040.2850.387966
70.2106042.97090.001667
8-0.274571-3.87337.3e-05
90.0972241.37150.085879
100.046040.64950.258392
110.1649852.32740.010475
12-0.450072-6.3490
130.2168943.05970.001261
140.0750071.05810.145647
15-0.118316-1.66910.04834
16-0.03996-0.56370.286794
170.1292621.82350.034866
180.0131150.1850.426706
19-0.19747-2.78570.002929
200.2307713.25540.000665
21-0.088148-1.24350.107578
22-0.105504-1.48830.069126
230.1605712.26510.012291






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.444695-6.27320
2-0.412902-5.82470
3-0.190496-2.68730.003907
40.1239751.74890.040926
5-0.015529-0.21910.413415
6-0.056021-0.79030.215153
70.1573142.21920.013802
8-0.148277-2.09170.018867
9-0.025728-0.36290.358517
10-0.041162-0.58070.281064
110.2856374.02944e-05
12-0.238066-3.35830.00047
13-0.196424-2.77090.00306
14-0.175427-2.47470.007085
15-0.068414-0.96510.167832
16-0.041953-0.59180.277322
170.0513540.72440.234825
180.0972691.37210.085782
190.0136420.19240.423795
20-0.019725-0.27830.390552
21-0.034189-0.48230.315062
22-0.148776-2.09870.018551
230.277393.91316.3e-05

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.444695 & -6.2732 & 0 \tabularnewline
2 & -0.412902 & -5.8247 & 0 \tabularnewline
3 & -0.190496 & -2.6873 & 0.003907 \tabularnewline
4 & 0.123975 & 1.7489 & 0.040926 \tabularnewline
5 & -0.015529 & -0.2191 & 0.413415 \tabularnewline
6 & -0.056021 & -0.7903 & 0.215153 \tabularnewline
7 & 0.157314 & 2.2192 & 0.013802 \tabularnewline
8 & -0.148277 & -2.0917 & 0.018867 \tabularnewline
9 & -0.025728 & -0.3629 & 0.358517 \tabularnewline
10 & -0.041162 & -0.5807 & 0.281064 \tabularnewline
11 & 0.285637 & 4.0294 & 4e-05 \tabularnewline
12 & -0.238066 & -3.3583 & 0.00047 \tabularnewline
13 & -0.196424 & -2.7709 & 0.00306 \tabularnewline
14 & -0.175427 & -2.4747 & 0.007085 \tabularnewline
15 & -0.068414 & -0.9651 & 0.167832 \tabularnewline
16 & -0.041953 & -0.5918 & 0.277322 \tabularnewline
17 & 0.051354 & 0.7244 & 0.234825 \tabularnewline
18 & 0.097269 & 1.3721 & 0.085782 \tabularnewline
19 & 0.013642 & 0.1924 & 0.423795 \tabularnewline
20 & -0.019725 & -0.2783 & 0.390552 \tabularnewline
21 & -0.034189 & -0.4823 & 0.315062 \tabularnewline
22 & -0.148776 & -2.0987 & 0.018551 \tabularnewline
23 & 0.27739 & 3.9131 & 6.3e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310403&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]-0.444695[/C][C]-6.2732[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.412902[/C][C]-5.8247[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.190496[/C][C]-2.6873[/C][C]0.003907[/C][/ROW]
[ROW][C]4[/C][C]0.123975[/C][C]1.7489[/C][C]0.040926[/C][/ROW]
[ROW][C]5[/C][C]-0.015529[/C][C]-0.2191[/C][C]0.413415[/C][/ROW]
[ROW][C]6[/C][C]-0.056021[/C][C]-0.7903[/C][C]0.215153[/C][/ROW]
[ROW][C]7[/C][C]0.157314[/C][C]2.2192[/C][C]0.013802[/C][/ROW]
[ROW][C]8[/C][C]-0.148277[/C][C]-2.0917[/C][C]0.018867[/C][/ROW]
[ROW][C]9[/C][C]-0.025728[/C][C]-0.3629[/C][C]0.358517[/C][/ROW]
[ROW][C]10[/C][C]-0.041162[/C][C]-0.5807[/C][C]0.281064[/C][/ROW]
[ROW][C]11[/C][C]0.285637[/C][C]4.0294[/C][C]4e-05[/C][/ROW]
[ROW][C]12[/C][C]-0.238066[/C][C]-3.3583[/C][C]0.00047[/C][/ROW]
[ROW][C]13[/C][C]-0.196424[/C][C]-2.7709[/C][C]0.00306[/C][/ROW]
[ROW][C]14[/C][C]-0.175427[/C][C]-2.4747[/C][C]0.007085[/C][/ROW]
[ROW][C]15[/C][C]-0.068414[/C][C]-0.9651[/C][C]0.167832[/C][/ROW]
[ROW][C]16[/C][C]-0.041953[/C][C]-0.5918[/C][C]0.277322[/C][/ROW]
[ROW][C]17[/C][C]0.051354[/C][C]0.7244[/C][C]0.234825[/C][/ROW]
[ROW][C]18[/C][C]0.097269[/C][C]1.3721[/C][C]0.085782[/C][/ROW]
[ROW][C]19[/C][C]0.013642[/C][C]0.1924[/C][C]0.423795[/C][/ROW]
[ROW][C]20[/C][C]-0.019725[/C][C]-0.2783[/C][C]0.390552[/C][/ROW]
[ROW][C]21[/C][C]-0.034189[/C][C]-0.4823[/C][C]0.315062[/C][/ROW]
[ROW][C]22[/C][C]-0.148776[/C][C]-2.0987[/C][C]0.018551[/C][/ROW]
[ROW][C]23[/C][C]0.27739[/C][C]3.9131[/C][C]6.3e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310403&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310403&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
1-0.444695-6.27320
2-0.412902-5.82470
3-0.190496-2.68730.003907
40.1239751.74890.040926
5-0.015529-0.21910.413415
6-0.056021-0.79030.215153
70.1573142.21920.013802
8-0.148277-2.09170.018867
9-0.025728-0.36290.358517
10-0.041162-0.58070.281064
110.2856374.02944e-05
12-0.238066-3.35830.00047
13-0.196424-2.77090.00306
14-0.175427-2.47470.007085
15-0.068414-0.96510.167832
16-0.041953-0.59180.277322
170.0513540.72440.234825
180.0972691.37210.085782
190.0136420.19240.423795
20-0.019725-0.27830.390552
21-0.034189-0.48230.315062
22-0.148776-2.09870.018551
230.277393.91316.3e-05


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = FALSE ; par2 = 0.1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; 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 <- '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')