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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 11:46:43 +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/t1513853242hqpmomzailp46ea.htm/, Retrieved Tue, 14 May 2024 20:39:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310612, Retrieved Tue, 14 May 2024 20:39:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact86

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] [2017-12-21 10:46:43] [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=310612&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=310612&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310612&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
1-0.39757-5.7750
2-0.123218-1.78980.037456
30.2705743.93035.7e-05
4-0.44646-6.48520
50.1184791.7210.043358
60.2608333.78889.9e-05
7-0.1179-1.71260.044128
8-0.185453-2.69390.003816
90.2020262.93460.001855
10-0.275792-4.00614.3e-05
11-0.041192-0.59840.275123
120.5960618.65830
13-0.334172-4.85411e-06
140.109241.58680.057027
150.0510950.74220.229397
16-0.429248-6.23520
170.2614843.79839.5e-05
180.1267911.84180.033457
19-0.140519-2.04120.02124
200.001030.0150.494041
21-0.009673-0.14050.444198
22-0.247151-3.59010.000206
230.2032572.95250.001755

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.39757 & -5.775 & 0 \tabularnewline
2 & -0.123218 & -1.7898 & 0.037456 \tabularnewline
3 & 0.270574 & 3.9303 & 5.7e-05 \tabularnewline
4 & -0.44646 & -6.4852 & 0 \tabularnewline
5 & 0.118479 & 1.721 & 0.043358 \tabularnewline
6 & 0.260833 & 3.7888 & 9.9e-05 \tabularnewline
7 & -0.1179 & -1.7126 & 0.044128 \tabularnewline
8 & -0.185453 & -2.6939 & 0.003816 \tabularnewline
9 & 0.202026 & 2.9346 & 0.001855 \tabularnewline
10 & -0.275792 & -4.0061 & 4.3e-05 \tabularnewline
11 & -0.041192 & -0.5984 & 0.275123 \tabularnewline
12 & 0.596061 & 8.6583 & 0 \tabularnewline
13 & -0.334172 & -4.8541 & 1e-06 \tabularnewline
14 & 0.10924 & 1.5868 & 0.057027 \tabularnewline
15 & 0.051095 & 0.7422 & 0.229397 \tabularnewline
16 & -0.429248 & -6.2352 & 0 \tabularnewline
17 & 0.261484 & 3.7983 & 9.5e-05 \tabularnewline
18 & 0.126791 & 1.8418 & 0.033457 \tabularnewline
19 & -0.140519 & -2.0412 & 0.02124 \tabularnewline
20 & 0.00103 & 0.015 & 0.494041 \tabularnewline
21 & -0.009673 & -0.1405 & 0.444198 \tabularnewline
22 & -0.247151 & -3.5901 & 0.000206 \tabularnewline
23 & 0.203257 & 2.9525 & 0.001755 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310612&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]-0.39757[/C][C]-5.775[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.123218[/C][C]-1.7898[/C][C]0.037456[/C][/ROW]
[ROW][C]3[/C][C]0.270574[/C][C]3.9303[/C][C]5.7e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.44646[/C][C]-6.4852[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.118479[/C][C]1.721[/C][C]0.043358[/C][/ROW]
[ROW][C]6[/C][C]0.260833[/C][C]3.7888[/C][C]9.9e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.1179[/C][C]-1.7126[/C][C]0.044128[/C][/ROW]
[ROW][C]8[/C][C]-0.185453[/C][C]-2.6939[/C][C]0.003816[/C][/ROW]
[ROW][C]9[/C][C]0.202026[/C][C]2.9346[/C][C]0.001855[/C][/ROW]
[ROW][C]10[/C][C]-0.275792[/C][C]-4.0061[/C][C]4.3e-05[/C][/ROW]
[ROW][C]11[/C][C]-0.041192[/C][C]-0.5984[/C][C]0.275123[/C][/ROW]
[ROW][C]12[/C][C]0.596061[/C][C]8.6583[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.334172[/C][C]-4.8541[/C][C]1e-06[/C][/ROW]
[ROW][C]14[/C][C]0.10924[/C][C]1.5868[/C][C]0.057027[/C][/ROW]
[ROW][C]15[/C][C]0.051095[/C][C]0.7422[/C][C]0.229397[/C][/ROW]
[ROW][C]16[/C][C]-0.429248[/C][C]-6.2352[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.261484[/C][C]3.7983[/C][C]9.5e-05[/C][/ROW]
[ROW][C]18[/C][C]0.126791[/C][C]1.8418[/C][C]0.033457[/C][/ROW]
[ROW][C]19[/C][C]-0.140519[/C][C]-2.0412[/C][C]0.02124[/C][/ROW]
[ROW][C]20[/C][C]0.00103[/C][C]0.015[/C][C]0.494041[/C][/ROW]
[ROW][C]21[/C][C]-0.009673[/C][C]-0.1405[/C][C]0.444198[/C][/ROW]
[ROW][C]22[/C][C]-0.247151[/C][C]-3.5901[/C][C]0.000206[/C][/ROW]
[ROW][C]23[/C][C]0.203257[/C][C]2.9525[/C][C]0.001755[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310612&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310612&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
1-0.39757-5.7750
2-0.123218-1.78980.037456
30.2705743.93035.7e-05
4-0.44646-6.48520
50.1184791.7210.043358
60.2608333.78889.9e-05
7-0.1179-1.71260.044128
8-0.185453-2.69390.003816
90.2020262.93460.001855
10-0.275792-4.00614.3e-05
11-0.041192-0.59840.275123
120.5960618.65830
13-0.334172-4.85411e-06
140.109241.58680.057027
150.0510950.74220.229397
16-0.429248-6.23520
170.2614843.79839.5e-05
180.1267911.84180.033457
19-0.140519-2.04120.02124
200.001030.0150.494041
21-0.009673-0.14050.444198
22-0.247151-3.59010.000206
230.2032572.95250.001755






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.39757-5.7750
2-0.334086-4.85291e-06
30.0967931.4060.080598
4-0.415754-6.03920
5-0.255325-3.70880.000133
60.0466250.67730.249487
70.1967972.85860.002341
8-0.399043-5.79640
9-0.11297-1.6410.051145
10-0.26563-3.85857.6e-05
11-0.359613-5.22370
120.2317713.36670.000452
130.2274493.30390.00056
140.322014.67753e-06
150.0844621.22690.110618
16-0.061441-0.89250.186574
17-0.020218-0.29370.384643
180.0357770.51970.301911
190.0036820.05350.478699
20-0.049356-0.71690.237102
21-0.124269-1.80510.036241
22-0.16381-2.37950.009114
23-0.001788-0.0260.489654

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.39757 & -5.775 & 0 \tabularnewline
2 & -0.334086 & -4.8529 & 1e-06 \tabularnewline
3 & 0.096793 & 1.406 & 0.080598 \tabularnewline
4 & -0.415754 & -6.0392 & 0 \tabularnewline
5 & -0.255325 & -3.7088 & 0.000133 \tabularnewline
6 & 0.046625 & 0.6773 & 0.249487 \tabularnewline
7 & 0.196797 & 2.8586 & 0.002341 \tabularnewline
8 & -0.399043 & -5.7964 & 0 \tabularnewline
9 & -0.11297 & -1.641 & 0.051145 \tabularnewline
10 & -0.26563 & -3.8585 & 7.6e-05 \tabularnewline
11 & -0.359613 & -5.2237 & 0 \tabularnewline
12 & 0.231771 & 3.3667 & 0.000452 \tabularnewline
13 & 0.227449 & 3.3039 & 0.00056 \tabularnewline
14 & 0.32201 & 4.6775 & 3e-06 \tabularnewline
15 & 0.084462 & 1.2269 & 0.110618 \tabularnewline
16 & -0.061441 & -0.8925 & 0.186574 \tabularnewline
17 & -0.020218 & -0.2937 & 0.384643 \tabularnewline
18 & 0.035777 & 0.5197 & 0.301911 \tabularnewline
19 & 0.003682 & 0.0535 & 0.478699 \tabularnewline
20 & -0.049356 & -0.7169 & 0.237102 \tabularnewline
21 & -0.124269 & -1.8051 & 0.036241 \tabularnewline
22 & -0.16381 & -2.3795 & 0.009114 \tabularnewline
23 & -0.001788 & -0.026 & 0.489654 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310612&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]-0.39757[/C][C]-5.775[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.334086[/C][C]-4.8529[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.096793[/C][C]1.406[/C][C]0.080598[/C][/ROW]
[ROW][C]4[/C][C]-0.415754[/C][C]-6.0392[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]-0.255325[/C][C]-3.7088[/C][C]0.000133[/C][/ROW]
[ROW][C]6[/C][C]0.046625[/C][C]0.6773[/C][C]0.249487[/C][/ROW]
[ROW][C]7[/C][C]0.196797[/C][C]2.8586[/C][C]0.002341[/C][/ROW]
[ROW][C]8[/C][C]-0.399043[/C][C]-5.7964[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]-0.11297[/C][C]-1.641[/C][C]0.051145[/C][/ROW]
[ROW][C]10[/C][C]-0.26563[/C][C]-3.8585[/C][C]7.6e-05[/C][/ROW]
[ROW][C]11[/C][C]-0.359613[/C][C]-5.2237[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.231771[/C][C]3.3667[/C][C]0.000452[/C][/ROW]
[ROW][C]13[/C][C]0.227449[/C][C]3.3039[/C][C]0.00056[/C][/ROW]
[ROW][C]14[/C][C]0.32201[/C][C]4.6775[/C][C]3e-06[/C][/ROW]
[ROW][C]15[/C][C]0.084462[/C][C]1.2269[/C][C]0.110618[/C][/ROW]
[ROW][C]16[/C][C]-0.061441[/C][C]-0.8925[/C][C]0.186574[/C][/ROW]
[ROW][C]17[/C][C]-0.020218[/C][C]-0.2937[/C][C]0.384643[/C][/ROW]
[ROW][C]18[/C][C]0.035777[/C][C]0.5197[/C][C]0.301911[/C][/ROW]
[ROW][C]19[/C][C]0.003682[/C][C]0.0535[/C][C]0.478699[/C][/ROW]
[ROW][C]20[/C][C]-0.049356[/C][C]-0.7169[/C][C]0.237102[/C][/ROW]
[ROW][C]21[/C][C]-0.124269[/C][C]-1.8051[/C][C]0.036241[/C][/ROW]
[ROW][C]22[/C][C]-0.16381[/C][C]-2.3795[/C][C]0.009114[/C][/ROW]
[ROW][C]23[/C][C]-0.001788[/C][C]-0.026[/C][C]0.489654[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310612&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310612&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
1-0.39757-5.7750
2-0.334086-4.85291e-06
30.0967931.4060.080598
4-0.415754-6.03920
5-0.255325-3.70880.000133
60.0466250.67730.249487
70.1967972.85860.002341
8-0.399043-5.79640
9-0.11297-1.6410.051145
10-0.26563-3.85857.6e-05
11-0.359613-5.22370
120.2317713.36670.000452
130.2274493.30390.00056
140.322014.67753e-06
150.0844621.22690.110618
16-0.061441-0.89250.186574
17-0.020218-0.29370.384643
180.0357770.51970.301911
190.0036820.05350.478699
20-0.049356-0.71690.237102
21-0.124269-1.80510.036241
22-0.16381-2.37950.009114
23-0.001788-0.0260.489654


Figures (Output of Computation)

Input Parameters & R Code

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