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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 computationSun, 10 Dec 2017 14:43:54 +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/10/t1512913619kwmvml8fco1ylyp.htm/, Retrieved Wed, 15 May 2024 15:08:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308922, Retrieved Wed, 15 May 2024 15:08:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130

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 f...] [2017-12-10 13:43:54] [a8eb7d5a2159f1476456749db34f2e15] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
46.8
52.8
58.3
54.5
64.7
58.3
57.5
56.7
56
66.2
58.2
53.9
53.1
54.4
59.2
57.8
61.5
60.1
60.1
58.4
56.8
63.8
53.9
63.1
55.7
54.9
64.6
60.2
63.9
69.9
58.5
52
66.7
72
68.4
70.8
56.5
62.6
66.5
69.2
63.7
73.6
64.1
53.8
72.2
80.2
69.1
72
66.3
72.5
88.9
88.6
73.7
86
70
71.6
90.5
85.7
84.8
81.1
70.8
65.7
86.2
76.1
79.8
85.2
75.8
69.4
85
75
77.7
68.5
68.4
65
73.2
67.9
76.5
85.5
71.7
57.9
75.5
78.2
75.7
67.1
74.6
66.2
74.9
69.5
76.1
82.3
82.1
60.5
71.2
81.4
74.5
61.4
83.8
85.4
91.6
91.9
86.3
96.8
81
70.8
98.8
94.5
84.5
92.8
81.2
75.7
86.7
87.5
87.8
103.1
96.4
77.1
106.5
95.7
95.3
86.6
89.6
81.9
98.4
92.9
83.9
121.8
103.9
87.5
118.9
109
112.2
100.1
111.3
102.7
122.6
124.8
120.3
118.3
108.7
100.7
124
103.1
115
112.7
101.7
111.5
114.4
112.5
107.2
136.7
107.8
94.6
110.7
126.6
127.9
109.2
87.1
90.8
94.5
103.3
103.2
105.4
103.9
79.8
105.6
113
87.7
110
90.3
108.9
105.1
113
100.4
110.1
114.7
88.6
117.2
127.7
107.8
102.8
100.2
108.4
114.2
94.4
92.2
115.3
102
86.3
112
112.5
109.5
105.9
115.3
126.2
112.2
112.5
106.9
90.6
75.6
78.8
101.8
93.9
100
89.2
97.7
121.1
108.8
92.9
113.6
112.6
98.8
78

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=308922&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=308922&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308922&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
1-0.332878-4.83531e-06
2-0.25058-3.63990.000172
30.1463892.12640.017315
4-0.041328-0.60030.274469
5-0.067594-0.98190.163647
60.1669182.42460.008083
7-0.079674-1.15730.124223
8-0.033988-0.49370.311017
90.1310351.90340.029175
10-0.226302-3.28720.000593
11-0.165561-2.40490.00852
120.5464747.9380
13-0.219522-3.18870.000823
14-0.14342-2.08330.019214
150.1295061.88120.030662
16-0.042076-0.61120.270867
17-0.04111-0.59720.27552
180.1597172.320.010648
19-0.088375-1.28370.100323
200.0099870.14510.442399
210.0770081.11860.13229
22-0.226396-3.28860.00059
23-0.082475-1.1980.116128

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.332878 & -4.8353 & 1e-06 \tabularnewline
2 & -0.25058 & -3.6399 & 0.000172 \tabularnewline
3 & 0.146389 & 2.1264 & 0.017315 \tabularnewline
4 & -0.041328 & -0.6003 & 0.274469 \tabularnewline
5 & -0.067594 & -0.9819 & 0.163647 \tabularnewline
6 & 0.166918 & 2.4246 & 0.008083 \tabularnewline
7 & -0.079674 & -1.1573 & 0.124223 \tabularnewline
8 & -0.033988 & -0.4937 & 0.311017 \tabularnewline
9 & 0.131035 & 1.9034 & 0.029175 \tabularnewline
10 & -0.226302 & -3.2872 & 0.000593 \tabularnewline
11 & -0.165561 & -2.4049 & 0.00852 \tabularnewline
12 & 0.546474 & 7.938 & 0 \tabularnewline
13 & -0.219522 & -3.1887 & 0.000823 \tabularnewline
14 & -0.14342 & -2.0833 & 0.019214 \tabularnewline
15 & 0.129506 & 1.8812 & 0.030662 \tabularnewline
16 & -0.042076 & -0.6112 & 0.270867 \tabularnewline
17 & -0.04111 & -0.5972 & 0.27552 \tabularnewline
18 & 0.159717 & 2.32 & 0.010648 \tabularnewline
19 & -0.088375 & -1.2837 & 0.100323 \tabularnewline
20 & 0.009987 & 0.1451 & 0.442399 \tabularnewline
21 & 0.077008 & 1.1186 & 0.13229 \tabularnewline
22 & -0.226396 & -3.2886 & 0.00059 \tabularnewline
23 & -0.082475 & -1.198 & 0.116128 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308922&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]-0.332878[/C][C]-4.8353[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.25058[/C][C]-3.6399[/C][C]0.000172[/C][/ROW]
[ROW][C]3[/C][C]0.146389[/C][C]2.1264[/C][C]0.017315[/C][/ROW]
[ROW][C]4[/C][C]-0.041328[/C][C]-0.6003[/C][C]0.274469[/C][/ROW]
[ROW][C]5[/C][C]-0.067594[/C][C]-0.9819[/C][C]0.163647[/C][/ROW]
[ROW][C]6[/C][C]0.166918[/C][C]2.4246[/C][C]0.008083[/C][/ROW]
[ROW][C]7[/C][C]-0.079674[/C][C]-1.1573[/C][C]0.124223[/C][/ROW]
[ROW][C]8[/C][C]-0.033988[/C][C]-0.4937[/C][C]0.311017[/C][/ROW]
[ROW][C]9[/C][C]0.131035[/C][C]1.9034[/C][C]0.029175[/C][/ROW]
[ROW][C]10[/C][C]-0.226302[/C][C]-3.2872[/C][C]0.000593[/C][/ROW]
[ROW][C]11[/C][C]-0.165561[/C][C]-2.4049[/C][C]0.00852[/C][/ROW]
[ROW][C]12[/C][C]0.546474[/C][C]7.938[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.219522[/C][C]-3.1887[/C][C]0.000823[/C][/ROW]
[ROW][C]14[/C][C]-0.14342[/C][C]-2.0833[/C][C]0.019214[/C][/ROW]
[ROW][C]15[/C][C]0.129506[/C][C]1.8812[/C][C]0.030662[/C][/ROW]
[ROW][C]16[/C][C]-0.042076[/C][C]-0.6112[/C][C]0.270867[/C][/ROW]
[ROW][C]17[/C][C]-0.04111[/C][C]-0.5972[/C][C]0.27552[/C][/ROW]
[ROW][C]18[/C][C]0.159717[/C][C]2.32[/C][C]0.010648[/C][/ROW]
[ROW][C]19[/C][C]-0.088375[/C][C]-1.2837[/C][C]0.100323[/C][/ROW]
[ROW][C]20[/C][C]0.009987[/C][C]0.1451[/C][C]0.442399[/C][/ROW]
[ROW][C]21[/C][C]0.077008[/C][C]1.1186[/C][C]0.13229[/C][/ROW]
[ROW][C]22[/C][C]-0.226396[/C][C]-3.2886[/C][C]0.00059[/C][/ROW]
[ROW][C]23[/C][C]-0.082475[/C][C]-1.198[/C][C]0.116128[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308922&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308922&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
1-0.332878-4.83531e-06
2-0.25058-3.63990.000172
30.1463892.12640.017315
4-0.041328-0.60030.274469
5-0.067594-0.98190.163647
60.1669182.42460.008083
7-0.079674-1.15730.124223
8-0.033988-0.49370.311017
90.1310351.90340.029175
10-0.226302-3.28720.000593
11-0.165561-2.40490.00852
120.5464747.9380
13-0.219522-3.18870.000823
14-0.14342-2.08330.019214
150.1295061.88120.030662
16-0.042076-0.61120.270867
17-0.04111-0.59720.27552
180.1597172.320.010648
19-0.088375-1.28370.100323
200.0099870.14510.442399
210.0770081.11860.13229
22-0.226396-3.28860.00059
23-0.082475-1.1980.116128






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.332878-4.83531e-06
2-0.406422-5.90360
3-0.143083-2.07840.019441
4-0.179525-2.60780.004882
5-0.181834-2.64130.004439
60.0316170.45930.323257
7-0.042516-0.61760.268758
80.0014670.02130.49151
90.1220571.7730.038837
10-0.16503-2.39720.008696
11-0.401396-5.83060
120.2410233.50110.000283
13-0.005617-0.08160.467523
140.018710.27180.393028
15-0.000346-0.0050.498
160.0167620.24350.403935
170.0282130.40980.341179
180.0797981.15910.123855
190.0518310.75290.226176
200.1031361.49810.067795
210.0285580.41480.339344
22-0.089071-1.29380.098568
23-0.144055-2.09250.018794

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.332878 & -4.8353 & 1e-06 \tabularnewline
2 & -0.406422 & -5.9036 & 0 \tabularnewline
3 & -0.143083 & -2.0784 & 0.019441 \tabularnewline
4 & -0.179525 & -2.6078 & 0.004882 \tabularnewline
5 & -0.181834 & -2.6413 & 0.004439 \tabularnewline
6 & 0.031617 & 0.4593 & 0.323257 \tabularnewline
7 & -0.042516 & -0.6176 & 0.268758 \tabularnewline
8 & 0.001467 & 0.0213 & 0.49151 \tabularnewline
9 & 0.122057 & 1.773 & 0.038837 \tabularnewline
10 & -0.16503 & -2.3972 & 0.008696 \tabularnewline
11 & -0.401396 & -5.8306 & 0 \tabularnewline
12 & 0.241023 & 3.5011 & 0.000283 \tabularnewline
13 & -0.005617 & -0.0816 & 0.467523 \tabularnewline
14 & 0.01871 & 0.2718 & 0.393028 \tabularnewline
15 & -0.000346 & -0.005 & 0.498 \tabularnewline
16 & 0.016762 & 0.2435 & 0.403935 \tabularnewline
17 & 0.028213 & 0.4098 & 0.341179 \tabularnewline
18 & 0.079798 & 1.1591 & 0.123855 \tabularnewline
19 & 0.051831 & 0.7529 & 0.226176 \tabularnewline
20 & 0.103136 & 1.4981 & 0.067795 \tabularnewline
21 & 0.028558 & 0.4148 & 0.339344 \tabularnewline
22 & -0.089071 & -1.2938 & 0.098568 \tabularnewline
23 & -0.144055 & -2.0925 & 0.018794 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308922&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]-0.332878[/C][C]-4.8353[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.406422[/C][C]-5.9036[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.143083[/C][C]-2.0784[/C][C]0.019441[/C][/ROW]
[ROW][C]4[/C][C]-0.179525[/C][C]-2.6078[/C][C]0.004882[/C][/ROW]
[ROW][C]5[/C][C]-0.181834[/C][C]-2.6413[/C][C]0.004439[/C][/ROW]
[ROW][C]6[/C][C]0.031617[/C][C]0.4593[/C][C]0.323257[/C][/ROW]
[ROW][C]7[/C][C]-0.042516[/C][C]-0.6176[/C][C]0.268758[/C][/ROW]
[ROW][C]8[/C][C]0.001467[/C][C]0.0213[/C][C]0.49151[/C][/ROW]
[ROW][C]9[/C][C]0.122057[/C][C]1.773[/C][C]0.038837[/C][/ROW]
[ROW][C]10[/C][C]-0.16503[/C][C]-2.3972[/C][C]0.008696[/C][/ROW]
[ROW][C]11[/C][C]-0.401396[/C][C]-5.8306[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.241023[/C][C]3.5011[/C][C]0.000283[/C][/ROW]
[ROW][C]13[/C][C]-0.005617[/C][C]-0.0816[/C][C]0.467523[/C][/ROW]
[ROW][C]14[/C][C]0.01871[/C][C]0.2718[/C][C]0.393028[/C][/ROW]
[ROW][C]15[/C][C]-0.000346[/C][C]-0.005[/C][C]0.498[/C][/ROW]
[ROW][C]16[/C][C]0.016762[/C][C]0.2435[/C][C]0.403935[/C][/ROW]
[ROW][C]17[/C][C]0.028213[/C][C]0.4098[/C][C]0.341179[/C][/ROW]
[ROW][C]18[/C][C]0.079798[/C][C]1.1591[/C][C]0.123855[/C][/ROW]
[ROW][C]19[/C][C]0.051831[/C][C]0.7529[/C][C]0.226176[/C][/ROW]
[ROW][C]20[/C][C]0.103136[/C][C]1.4981[/C][C]0.067795[/C][/ROW]
[ROW][C]21[/C][C]0.028558[/C][C]0.4148[/C][C]0.339344[/C][/ROW]
[ROW][C]22[/C][C]-0.089071[/C][C]-1.2938[/C][C]0.098568[/C][/ROW]
[ROW][C]23[/C][C]-0.144055[/C][C]-2.0925[/C][C]0.018794[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308922&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308922&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
1-0.332878-4.83531e-06
2-0.406422-5.90360
3-0.143083-2.07840.019441
4-0.179525-2.60780.004882
5-0.181834-2.64130.004439
60.0316170.45930.323257
7-0.042516-0.61760.268758
80.0014670.02130.49151
90.1220571.7730.038837
10-0.16503-2.39720.008696
11-0.401396-5.83060
120.2410233.50110.000283
13-0.005617-0.08160.467523
140.018710.27180.393028
15-0.000346-0.0050.498
160.0167620.24350.403935
170.0282130.40980.341179
180.0797981.15910.123855
190.0518310.75290.226176
200.1031361.49810.067795
210.0285580.41480.339344
22-0.089071-1.29380.098568
23-0.144055-2.09250.018794


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = -0.3 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = -0.3 ; par3 = 1 ; par4 = 0 ; 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 <- '1'
par2 <- '-0.3'
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')