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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 computationWed, 24 Jan 2018 11:32:26 +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/2018/Jan/24/t1516789969ym42577ayya698q.htm/, Retrieved Mon, 06 May 2024 02:26:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=312694, Retrieved Mon, 06 May 2024 02:26:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact52

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] [] [2018-01-24 10:32:26] [5afcb1189196649f11ed89361ecc5748] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
62.4
67.4
76.1
67.4
74.5
72.6
60.5
66.1
76.5
76.8
77
71
74.8
73.7
80.5
71.8
76.9
79.9
65.9
69.5
75.1
79.6
75.2
68
72.8
71.5
78.5
76.8
75.3
76.7
69.7
67.8
77.5
82.5
75.3
70.9
76
73.7
79.7
77.8
73.3
78.3
71.9
67
82
83.7
74.8
80
74.3
76.8
89
81.9
76.8
88.9
75.8
75.5
89.1
88
85.9
89.3
82.9
81.2
90.5
86.4
81.8
91.3
73.4
76.6
91
87
89.7
90.7
86.5
86.6
98.8
84.4
91.4
95.7
78.5
81.7
94.3
98.5
95.4
91.7
92.8
90.5
102.2
91.8
95
102
88.9
89.6
97.9
108.6
100.8
95.1
101
100.9
102.5
105.4
98.4
105.3
96.5
88.1
107.9
107
92.5
95.7
85.2
85.5
94.7
86.2
88.8
93.4
83.4
82.9
96.7
96.2
92.8
92.8
90
95.4
108.3
96.3
95
109
92
92.3
107
105.5
105.4
103.9
99.2
102.2
121.5
102.3
110
105.9
91.9
100
111.7
104.9
103.3
101.8
100.8
104.2
116.5
97.9
100.7
107
96.3
96
104.5
107.4
102.4
94.9
98.8
96.8
108.2
103.8
102.3
107.2
102
92.6
105.2
113
105.6
101.6
101.7
102.7
109
105.5
103.3
108.6
98.2
90
112.4
111.9
102.1
102.4
101.7
98.7
114
105.1
98.3
110
96.5
92.2
112
111.4
107.5
103.4
103.5
107.4
117.6
110.2
104.3
115.9
98.9
101.9
113.5
109.5
110
114.2
106.9
109.2
124.2
104.7
111.9
119
102.9
106.3

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=312694&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=312694&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312694&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
1-0.501014-7.06770
2-0.088547-1.24910.106547
30.371945.24690
4-0.328864-4.63923e-06
50.1316941.85780.032339
60.1692712.38790.008941
7-0.259943-3.6670.000157
80.100231.41390.079474
90.0627190.88480.188677
10-0.11455-1.61590.053848
110.1634292.30550.011086
12-0.188705-2.6620.004201
13-0.02337-0.32970.370998
140.0990611.39740.081921
15-0.039998-0.56420.286612
16-0.089242-1.25890.104767
170.0775931.09460.137511
180.0396510.55930.288278
19-0.179766-2.53590.005992
200.1360051.91860.028234
210.0326170.46010.322968
22-0.275168-3.88177.1e-05
230.3552125.01091e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.501014 & -7.0677 & 0 \tabularnewline
2 & -0.088547 & -1.2491 & 0.106547 \tabularnewline
3 & 0.37194 & 5.2469 & 0 \tabularnewline
4 & -0.328864 & -4.6392 & 3e-06 \tabularnewline
5 & 0.131694 & 1.8578 & 0.032339 \tabularnewline
6 & 0.169271 & 2.3879 & 0.008941 \tabularnewline
7 & -0.259943 & -3.667 & 0.000157 \tabularnewline
8 & 0.10023 & 1.4139 & 0.079474 \tabularnewline
9 & 0.062719 & 0.8848 & 0.188677 \tabularnewline
10 & -0.11455 & -1.6159 & 0.053848 \tabularnewline
11 & 0.163429 & 2.3055 & 0.011086 \tabularnewline
12 & -0.188705 & -2.662 & 0.004201 \tabularnewline
13 & -0.02337 & -0.3297 & 0.370998 \tabularnewline
14 & 0.099061 & 1.3974 & 0.081921 \tabularnewline
15 & -0.039998 & -0.5642 & 0.286612 \tabularnewline
16 & -0.089242 & -1.2589 & 0.104767 \tabularnewline
17 & 0.077593 & 1.0946 & 0.137511 \tabularnewline
18 & 0.039651 & 0.5593 & 0.288278 \tabularnewline
19 & -0.179766 & -2.5359 & 0.005992 \tabularnewline
20 & 0.136005 & 1.9186 & 0.028234 \tabularnewline
21 & 0.032617 & 0.4601 & 0.322968 \tabularnewline
22 & -0.275168 & -3.8817 & 7.1e-05 \tabularnewline
23 & 0.355212 & 5.0109 & 1e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=312694&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]-0.501014[/C][C]-7.0677[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.088547[/C][C]-1.2491[/C][C]0.106547[/C][/ROW]
[ROW][C]3[/C][C]0.37194[/C][C]5.2469[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.328864[/C][C]-4.6392[/C][C]3e-06[/C][/ROW]
[ROW][C]5[/C][C]0.131694[/C][C]1.8578[/C][C]0.032339[/C][/ROW]
[ROW][C]6[/C][C]0.169271[/C][C]2.3879[/C][C]0.008941[/C][/ROW]
[ROW][C]7[/C][C]-0.259943[/C][C]-3.667[/C][C]0.000157[/C][/ROW]
[ROW][C]8[/C][C]0.10023[/C][C]1.4139[/C][C]0.079474[/C][/ROW]
[ROW][C]9[/C][C]0.062719[/C][C]0.8848[/C][C]0.188677[/C][/ROW]
[ROW][C]10[/C][C]-0.11455[/C][C]-1.6159[/C][C]0.053848[/C][/ROW]
[ROW][C]11[/C][C]0.163429[/C][C]2.3055[/C][C]0.011086[/C][/ROW]
[ROW][C]12[/C][C]-0.188705[/C][C]-2.662[/C][C]0.004201[/C][/ROW]
[ROW][C]13[/C][C]-0.02337[/C][C]-0.3297[/C][C]0.370998[/C][/ROW]
[ROW][C]14[/C][C]0.099061[/C][C]1.3974[/C][C]0.081921[/C][/ROW]
[ROW][C]15[/C][C]-0.039998[/C][C]-0.5642[/C][C]0.286612[/C][/ROW]
[ROW][C]16[/C][C]-0.089242[/C][C]-1.2589[/C][C]0.104767[/C][/ROW]
[ROW][C]17[/C][C]0.077593[/C][C]1.0946[/C][C]0.137511[/C][/ROW]
[ROW][C]18[/C][C]0.039651[/C][C]0.5593[/C][C]0.288278[/C][/ROW]
[ROW][C]19[/C][C]-0.179766[/C][C]-2.5359[/C][C]0.005992[/C][/ROW]
[ROW][C]20[/C][C]0.136005[/C][C]1.9186[/C][C]0.028234[/C][/ROW]
[ROW][C]21[/C][C]0.032617[/C][C]0.4601[/C][C]0.322968[/C][/ROW]
[ROW][C]22[/C][C]-0.275168[/C][C]-3.8817[/C][C]7.1e-05[/C][/ROW]
[ROW][C]23[/C][C]0.355212[/C][C]5.0109[/C][C]1e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=312694&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312694&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
1-0.501014-7.06770
2-0.088547-1.24910.106547
30.371945.24690
4-0.328864-4.63923e-06
50.1316941.85780.032339
60.1692712.38790.008941
7-0.259943-3.6670.000157
80.100231.41390.079474
90.0627190.88480.188677
10-0.11455-1.61590.053848
110.1634292.30550.011086
12-0.188705-2.6620.004201
13-0.02337-0.32970.370998
140.0990611.39740.081921
15-0.039998-0.56420.286612
16-0.089242-1.25890.104767
170.0775931.09460.137511
180.0396510.55930.288278
19-0.179766-2.53590.005992
200.1360051.91860.028234
210.0326170.46010.322968
22-0.275168-3.88177.1e-05
230.3552125.01091e-06






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.501014-7.06770
2-0.453363-6.39550
30.1349871.90420.029162
4-0.076355-1.07710.141367
50.0466310.65780.255711
60.189332.67080.004096
70.051410.72520.234583
8-0.066563-0.9390.174438
9-0.050592-0.71370.238127
10-0.00567-0.080.468163
110.1359261.91750.028305
12-0.140821-1.98650.024173
13-0.194504-2.74380.003314
14-0.19084-2.69210.003852
150.0217910.30740.37943
16-0.139068-1.96180.02559
17-0.074214-1.04690.148203
180.1875252.64540.004406
19-0.034018-0.47990.31592
20-0.119521-1.68610.046676
210.0317090.44730.32757
22-0.191465-2.70090.003755
230.1612212.27430.012007

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.501014 & -7.0677 & 0 \tabularnewline
2 & -0.453363 & -6.3955 & 0 \tabularnewline
3 & 0.134987 & 1.9042 & 0.029162 \tabularnewline
4 & -0.076355 & -1.0771 & 0.141367 \tabularnewline
5 & 0.046631 & 0.6578 & 0.255711 \tabularnewline
6 & 0.18933 & 2.6708 & 0.004096 \tabularnewline
7 & 0.05141 & 0.7252 & 0.234583 \tabularnewline
8 & -0.066563 & -0.939 & 0.174438 \tabularnewline
9 & -0.050592 & -0.7137 & 0.238127 \tabularnewline
10 & -0.00567 & -0.08 & 0.468163 \tabularnewline
11 & 0.135926 & 1.9175 & 0.028305 \tabularnewline
12 & -0.140821 & -1.9865 & 0.024173 \tabularnewline
13 & -0.194504 & -2.7438 & 0.003314 \tabularnewline
14 & -0.19084 & -2.6921 & 0.003852 \tabularnewline
15 & 0.021791 & 0.3074 & 0.37943 \tabularnewline
16 & -0.139068 & -1.9618 & 0.02559 \tabularnewline
17 & -0.074214 & -1.0469 & 0.148203 \tabularnewline
18 & 0.187525 & 2.6454 & 0.004406 \tabularnewline
19 & -0.034018 & -0.4799 & 0.31592 \tabularnewline
20 & -0.119521 & -1.6861 & 0.046676 \tabularnewline
21 & 0.031709 & 0.4473 & 0.32757 \tabularnewline
22 & -0.191465 & -2.7009 & 0.003755 \tabularnewline
23 & 0.161221 & 2.2743 & 0.012007 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=312694&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]-0.501014[/C][C]-7.0677[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.453363[/C][C]-6.3955[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.134987[/C][C]1.9042[/C][C]0.029162[/C][/ROW]
[ROW][C]4[/C][C]-0.076355[/C][C]-1.0771[/C][C]0.141367[/C][/ROW]
[ROW][C]5[/C][C]0.046631[/C][C]0.6578[/C][C]0.255711[/C][/ROW]
[ROW][C]6[/C][C]0.18933[/C][C]2.6708[/C][C]0.004096[/C][/ROW]
[ROW][C]7[/C][C]0.05141[/C][C]0.7252[/C][C]0.234583[/C][/ROW]
[ROW][C]8[/C][C]-0.066563[/C][C]-0.939[/C][C]0.174438[/C][/ROW]
[ROW][C]9[/C][C]-0.050592[/C][C]-0.7137[/C][C]0.238127[/C][/ROW]
[ROW][C]10[/C][C]-0.00567[/C][C]-0.08[/C][C]0.468163[/C][/ROW]
[ROW][C]11[/C][C]0.135926[/C][C]1.9175[/C][C]0.028305[/C][/ROW]
[ROW][C]12[/C][C]-0.140821[/C][C]-1.9865[/C][C]0.024173[/C][/ROW]
[ROW][C]13[/C][C]-0.194504[/C][C]-2.7438[/C][C]0.003314[/C][/ROW]
[ROW][C]14[/C][C]-0.19084[/C][C]-2.6921[/C][C]0.003852[/C][/ROW]
[ROW][C]15[/C][C]0.021791[/C][C]0.3074[/C][C]0.37943[/C][/ROW]
[ROW][C]16[/C][C]-0.139068[/C][C]-1.9618[/C][C]0.02559[/C][/ROW]
[ROW][C]17[/C][C]-0.074214[/C][C]-1.0469[/C][C]0.148203[/C][/ROW]
[ROW][C]18[/C][C]0.187525[/C][C]2.6454[/C][C]0.004406[/C][/ROW]
[ROW][C]19[/C][C]-0.034018[/C][C]-0.4799[/C][C]0.31592[/C][/ROW]
[ROW][C]20[/C][C]-0.119521[/C][C]-1.6861[/C][C]0.046676[/C][/ROW]
[ROW][C]21[/C][C]0.031709[/C][C]0.4473[/C][C]0.32757[/C][/ROW]
[ROW][C]22[/C][C]-0.191465[/C][C]-2.7009[/C][C]0.003755[/C][/ROW]
[ROW][C]23[/C][C]0.161221[/C][C]2.2743[/C][C]0.012007[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=312694&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312694&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
1-0.501014-7.06770
2-0.453363-6.39550
30.1349871.90420.029162
4-0.076355-1.07710.141367
50.0466310.65780.255711
60.189332.67080.004096
70.051410.72520.234583
8-0.066563-0.9390.174438
9-0.050592-0.71370.238127
10-0.00567-0.080.468163
110.1359261.91750.028305
12-0.140821-1.98650.024173
13-0.194504-2.74380.003314
14-0.19084-2.69210.003852
150.0217910.30740.37943
16-0.139068-1.96180.02559
17-0.074214-1.04690.148203
180.1875252.64540.004406
19-0.034018-0.47990.31592
20-0.119521-1.68610.046676
210.0317090.44730.32757
22-0.191465-2.70090.003755
230.1612212.27430.012007


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 0.3 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.99 ;
Parameters (R input):
par1 = Default ; par2 = 0.3 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.99 ; 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')