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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 computationFri, 22 Dec 2017 14:06:35 +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/22/t1513948038ck2raxioshh84cm.htm/, Retrieved Wed, 15 May 2024 14:54:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310776, Retrieved Wed, 15 May 2024 14:54:33 +0000
QR Codes:

Original text written by user:Stap 3 voorbeeld 2 (Time Series)
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72

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] [Voorbeeld 2 (PAF)] [2017-12-22 13:06:35] [84a8d6985c1bda8999f49f22468687ba] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
55.5
63
77.2
71.1
90.1
91.5
76.1
87.8
81
77.2
73.8
68.9
68.4
65.2
78.7
77
97.6
88.1
98.7
93.4
68
87.9
75.8
66.3
68.4
71.3
77.4
87.1
88.5
85.9
92.7
88.5
80.2
81.8
70.4
82.2
72.8
69
83
92.4
92.3
100.5
106.9
99.5
85.9
92.6
77.4
84.1
75.3
73.8
100.1
90.7
96.5
111.8
97.4
100.8
93.7
82
86
84.3
73.1
75.4
97.9
97.5
106
112.8
99.5
100.8
102.9
88.8
91.3
88.3
77.4
80.5
96.7
93.8
105
117.1
111.1
105.8
95.7
97.1
91
90.9
83.5
82.3
101.7
108.3
114
118.2
103.4
106.8
95.4
101.8
95.6
94.8
94
82.4
95.8
106.7
114.1
103.9
117.4
105.9
101.7
98.7
91.3
102.3
80.5
86.7
102.6
107.3
108
124.3
117.1
103.9
104.7
95.9
94.2
102.7
70.3
90.2
107.3
104.6
102.7
124.5
117.8
104.2
99.9
91.5
95.7
91.4
86.2
91.5
115.5
113.9
131.9
121.2
105.2
107.5
113.8
100.5
104.8
103.8
93.1
106.2
117.5
109.9
123.6
131.7
111
122
110.9
108
103.6
107.3
94.4
85.2
113.2
111.7
124.3
124
133.4
112.6
115.8
112.3
103.6
111.4
95.1
93.4
117.3
121.5
123.1
139.3
125.8
108.6
121
111.6
99.7
116.7
90.3
90.4
117.3
121.6
114.6
133.3
127.4
115
112.6
108.3
107.6
109
89
102.5
124.5
124.2
130.8
138.7
127.6
130.9
136.9
125.2
131.3
124.1
103.2
118.1
136.5
117.8
145.1
158.8
136.9
132.7

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=310776&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=310776&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310776&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
10.0563410.79680.213262
20.056790.80310.211425
30.2650593.74850.000116
40.1055561.49280.068534
5-0.006099-0.08620.465678
60.1659732.34720.009946
70.0525330.74290.229199
80.0660930.93470.175536
90.1917752.71210.003634
100.018370.25980.397646
110.040110.56720.285595
12-0.296031-4.18652.1e-05
13-0.096169-1.360.087674
14-0.014566-0.2060.418504
15-0.100085-1.41540.079251
16-0.193726-2.73970.003353
170.0300160.42450.335833
18-0.068019-0.96190.168622
19-0.038632-0.54630.292719
20-0.015385-0.21760.413993
21-0.125023-1.76810.039285
22-0.146283-2.06880.019928
230.1416862.00370.023224

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.056341 & 0.7968 & 0.213262 \tabularnewline
2 & 0.05679 & 0.8031 & 0.211425 \tabularnewline
3 & 0.265059 & 3.7485 & 0.000116 \tabularnewline
4 & 0.105556 & 1.4928 & 0.068534 \tabularnewline
5 & -0.006099 & -0.0862 & 0.465678 \tabularnewline
6 & 0.165973 & 2.3472 & 0.009946 \tabularnewline
7 & 0.052533 & 0.7429 & 0.229199 \tabularnewline
8 & 0.066093 & 0.9347 & 0.175536 \tabularnewline
9 & 0.191775 & 2.7121 & 0.003634 \tabularnewline
10 & 0.01837 & 0.2598 & 0.397646 \tabularnewline
11 & 0.04011 & 0.5672 & 0.285595 \tabularnewline
12 & -0.296031 & -4.1865 & 2.1e-05 \tabularnewline
13 & -0.096169 & -1.36 & 0.087674 \tabularnewline
14 & -0.014566 & -0.206 & 0.418504 \tabularnewline
15 & -0.100085 & -1.4154 & 0.079251 \tabularnewline
16 & -0.193726 & -2.7397 & 0.003353 \tabularnewline
17 & 0.030016 & 0.4245 & 0.335833 \tabularnewline
18 & -0.068019 & -0.9619 & 0.168622 \tabularnewline
19 & -0.038632 & -0.5463 & 0.292719 \tabularnewline
20 & -0.015385 & -0.2176 & 0.413993 \tabularnewline
21 & -0.125023 & -1.7681 & 0.039285 \tabularnewline
22 & -0.146283 & -2.0688 & 0.019928 \tabularnewline
23 & 0.141686 & 2.0037 & 0.023224 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310776&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]0.056341[/C][C]0.7968[/C][C]0.213262[/C][/ROW]
[ROW][C]2[/C][C]0.05679[/C][C]0.8031[/C][C]0.211425[/C][/ROW]
[ROW][C]3[/C][C]0.265059[/C][C]3.7485[/C][C]0.000116[/C][/ROW]
[ROW][C]4[/C][C]0.105556[/C][C]1.4928[/C][C]0.068534[/C][/ROW]
[ROW][C]5[/C][C]-0.006099[/C][C]-0.0862[/C][C]0.465678[/C][/ROW]
[ROW][C]6[/C][C]0.165973[/C][C]2.3472[/C][C]0.009946[/C][/ROW]
[ROW][C]7[/C][C]0.052533[/C][C]0.7429[/C][C]0.229199[/C][/ROW]
[ROW][C]8[/C][C]0.066093[/C][C]0.9347[/C][C]0.175536[/C][/ROW]
[ROW][C]9[/C][C]0.191775[/C][C]2.7121[/C][C]0.003634[/C][/ROW]
[ROW][C]10[/C][C]0.01837[/C][C]0.2598[/C][C]0.397646[/C][/ROW]
[ROW][C]11[/C][C]0.04011[/C][C]0.5672[/C][C]0.285595[/C][/ROW]
[ROW][C]12[/C][C]-0.296031[/C][C]-4.1865[/C][C]2.1e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.096169[/C][C]-1.36[/C][C]0.087674[/C][/ROW]
[ROW][C]14[/C][C]-0.014566[/C][C]-0.206[/C][C]0.418504[/C][/ROW]
[ROW][C]15[/C][C]-0.100085[/C][C]-1.4154[/C][C]0.079251[/C][/ROW]
[ROW][C]16[/C][C]-0.193726[/C][C]-2.7397[/C][C]0.003353[/C][/ROW]
[ROW][C]17[/C][C]0.030016[/C][C]0.4245[/C][C]0.335833[/C][/ROW]
[ROW][C]18[/C][C]-0.068019[/C][C]-0.9619[/C][C]0.168622[/C][/ROW]
[ROW][C]19[/C][C]-0.038632[/C][C]-0.5463[/C][C]0.292719[/C][/ROW]
[ROW][C]20[/C][C]-0.015385[/C][C]-0.2176[/C][C]0.413993[/C][/ROW]
[ROW][C]21[/C][C]-0.125023[/C][C]-1.7681[/C][C]0.039285[/C][/ROW]
[ROW][C]22[/C][C]-0.146283[/C][C]-2.0688[/C][C]0.019928[/C][/ROW]
[ROW][C]23[/C][C]0.141686[/C][C]2.0037[/C][C]0.023224[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310776&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310776&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
10.0563410.79680.213262
20.056790.80310.211425
30.2650593.74850.000116
40.1055561.49280.068534
5-0.006099-0.08620.465678
60.1659732.34720.009946
70.0525330.74290.229199
80.0660930.93470.175536
90.1917752.71210.003634
100.018370.25980.397646
110.040110.56720.285595
12-0.296031-4.18652.1e-05
13-0.096169-1.360.087674
14-0.014566-0.2060.418504
15-0.100085-1.41540.079251
16-0.193726-2.73970.003353
170.0300160.42450.335833
18-0.068019-0.96190.168622
19-0.038632-0.54630.292719
20-0.015385-0.21760.413993
21-0.125023-1.76810.039285
22-0.146283-2.06880.019928
230.1416862.00370.023224






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.0563410.79680.213262
20.0537870.76070.223878
30.260583.68520.000147
40.0844011.19360.117021
5-0.040194-0.56840.285192
60.0980051.3860.083645
7-0.000458-0.00650.497418
80.0626310.88570.188411
90.1401431.98190.024429
10-0.032579-0.46070.322746
110.0041280.05840.47675
12-0.445025-6.29360
13-0.151756-2.14620.016532
14-0.010601-0.14990.440491
150.0580640.82120.206269
16-0.083264-1.17750.120191
17-0.00493-0.06970.472245
18-0.001195-0.01690.493268
190.1127791.59490.056153
200.0882461.2480.106747
210.0848041.19930.115914
22-0.085028-1.20250.115301
230.230173.25510.000666

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.056341 & 0.7968 & 0.213262 \tabularnewline
2 & 0.053787 & 0.7607 & 0.223878 \tabularnewline
3 & 0.26058 & 3.6852 & 0.000147 \tabularnewline
4 & 0.084401 & 1.1936 & 0.117021 \tabularnewline
5 & -0.040194 & -0.5684 & 0.285192 \tabularnewline
6 & 0.098005 & 1.386 & 0.083645 \tabularnewline
7 & -0.000458 & -0.0065 & 0.497418 \tabularnewline
8 & 0.062631 & 0.8857 & 0.188411 \tabularnewline
9 & 0.140143 & 1.9819 & 0.024429 \tabularnewline
10 & -0.032579 & -0.4607 & 0.322746 \tabularnewline
11 & 0.004128 & 0.0584 & 0.47675 \tabularnewline
12 & -0.445025 & -6.2936 & 0 \tabularnewline
13 & -0.151756 & -2.1462 & 0.016532 \tabularnewline
14 & -0.010601 & -0.1499 & 0.440491 \tabularnewline
15 & 0.058064 & 0.8212 & 0.206269 \tabularnewline
16 & -0.083264 & -1.1775 & 0.120191 \tabularnewline
17 & -0.00493 & -0.0697 & 0.472245 \tabularnewline
18 & -0.001195 & -0.0169 & 0.493268 \tabularnewline
19 & 0.112779 & 1.5949 & 0.056153 \tabularnewline
20 & 0.088246 & 1.248 & 0.106747 \tabularnewline
21 & 0.084804 & 1.1993 & 0.115914 \tabularnewline
22 & -0.085028 & -1.2025 & 0.115301 \tabularnewline
23 & 0.23017 & 3.2551 & 0.000666 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310776&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]0.056341[/C][C]0.7968[/C][C]0.213262[/C][/ROW]
[ROW][C]2[/C][C]0.053787[/C][C]0.7607[/C][C]0.223878[/C][/ROW]
[ROW][C]3[/C][C]0.26058[/C][C]3.6852[/C][C]0.000147[/C][/ROW]
[ROW][C]4[/C][C]0.084401[/C][C]1.1936[/C][C]0.117021[/C][/ROW]
[ROW][C]5[/C][C]-0.040194[/C][C]-0.5684[/C][C]0.285192[/C][/ROW]
[ROW][C]6[/C][C]0.098005[/C][C]1.386[/C][C]0.083645[/C][/ROW]
[ROW][C]7[/C][C]-0.000458[/C][C]-0.0065[/C][C]0.497418[/C][/ROW]
[ROW][C]8[/C][C]0.062631[/C][C]0.8857[/C][C]0.188411[/C][/ROW]
[ROW][C]9[/C][C]0.140143[/C][C]1.9819[/C][C]0.024429[/C][/ROW]
[ROW][C]10[/C][C]-0.032579[/C][C]-0.4607[/C][C]0.322746[/C][/ROW]
[ROW][C]11[/C][C]0.004128[/C][C]0.0584[/C][C]0.47675[/C][/ROW]
[ROW][C]12[/C][C]-0.445025[/C][C]-6.2936[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.151756[/C][C]-2.1462[/C][C]0.016532[/C][/ROW]
[ROW][C]14[/C][C]-0.010601[/C][C]-0.1499[/C][C]0.440491[/C][/ROW]
[ROW][C]15[/C][C]0.058064[/C][C]0.8212[/C][C]0.206269[/C][/ROW]
[ROW][C]16[/C][C]-0.083264[/C][C]-1.1775[/C][C]0.120191[/C][/ROW]
[ROW][C]17[/C][C]-0.00493[/C][C]-0.0697[/C][C]0.472245[/C][/ROW]
[ROW][C]18[/C][C]-0.001195[/C][C]-0.0169[/C][C]0.493268[/C][/ROW]
[ROW][C]19[/C][C]0.112779[/C][C]1.5949[/C][C]0.056153[/C][/ROW]
[ROW][C]20[/C][C]0.088246[/C][C]1.248[/C][C]0.106747[/C][/ROW]
[ROW][C]21[/C][C]0.084804[/C][C]1.1993[/C][C]0.115914[/C][/ROW]
[ROW][C]22[/C][C]-0.085028[/C][C]-1.2025[/C][C]0.115301[/C][/ROW]
[ROW][C]23[/C][C]0.23017[/C][C]3.2551[/C][C]0.000666[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310776&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310776&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
10.0563410.79680.213262
20.0537870.76070.223878
30.260583.68520.000147
40.0844011.19360.117021
5-0.040194-0.56840.285192
60.0980051.3860.083645
7-0.000458-0.00650.497418
80.0626310.88570.188411
90.1401431.98190.024429
10-0.032579-0.46070.322746
110.0041280.05840.47675
12-0.445025-6.29360
13-0.151756-2.14620.016532
14-0.010601-0.14990.440491
150.0580640.82120.206269
16-0.083264-1.17750.120191
17-0.00493-0.06970.472245
18-0.001195-0.01690.493268
190.1127791.59490.056153
200.0882461.2480.106747
210.0848041.19930.115914
22-0.085028-1.20250.115301
230.230173.25510.000666


Figures (Output of Computation)

Input Parameters & R Code

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