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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, 17 Dec 2017 16:42:06 +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/17/t1513525356si5yiif4615ez3b.htm/, Retrieved Wed, 15 May 2024 07:20:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310002, Retrieved Wed, 15 May 2024 07:20:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93

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] [] [2017-12-17 15:42:06] [ca8d18f187365d46258cefbf7e3ea6e7] [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=310002&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=310002&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310002&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
1-0.335726-4.87671e-06
2-0.259529-3.76990.000106
30.1631112.36930.009361
4-0.036823-0.53490.296648
5-0.044825-0.65110.25784
60.1066111.54860.061487
7-0.061786-0.89750.185238
8-0.037911-0.55070.291213
90.1394022.02490.022067
10-0.219326-3.18590.000831
11-0.150638-2.18810.014879
120.5030167.30670
13-0.208077-3.02250.001409
14-0.153938-2.23610.013197
150.1782392.58910.005147
16-0.074486-1.0820.140249
17-0.006123-0.08890.464604
180.1157341.68110.047109
19-0.090399-1.31310.095285
200.0427090.62040.267838
210.0606340.88080.189726
22-0.220642-3.2050.00078
23-0.079865-1.16010.123659

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.335726 & -4.8767 & 1e-06 \tabularnewline
2 & -0.259529 & -3.7699 & 0.000106 \tabularnewline
3 & 0.163111 & 2.3693 & 0.009361 \tabularnewline
4 & -0.036823 & -0.5349 & 0.296648 \tabularnewline
5 & -0.044825 & -0.6511 & 0.25784 \tabularnewline
6 & 0.106611 & 1.5486 & 0.061487 \tabularnewline
7 & -0.061786 & -0.8975 & 0.185238 \tabularnewline
8 & -0.037911 & -0.5507 & 0.291213 \tabularnewline
9 & 0.139402 & 2.0249 & 0.022067 \tabularnewline
10 & -0.219326 & -3.1859 & 0.000831 \tabularnewline
11 & -0.150638 & -2.1881 & 0.014879 \tabularnewline
12 & 0.503016 & 7.3067 & 0 \tabularnewline
13 & -0.208077 & -3.0225 & 0.001409 \tabularnewline
14 & -0.153938 & -2.2361 & 0.013197 \tabularnewline
15 & 0.178239 & 2.5891 & 0.005147 \tabularnewline
16 & -0.074486 & -1.082 & 0.140249 \tabularnewline
17 & -0.006123 & -0.0889 & 0.464604 \tabularnewline
18 & 0.115734 & 1.6811 & 0.047109 \tabularnewline
19 & -0.090399 & -1.3131 & 0.095285 \tabularnewline
20 & 0.042709 & 0.6204 & 0.267838 \tabularnewline
21 & 0.060634 & 0.8808 & 0.189726 \tabularnewline
22 & -0.220642 & -3.205 & 0.00078 \tabularnewline
23 & -0.079865 & -1.1601 & 0.123659 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310002&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]-0.335726[/C][C]-4.8767[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.259529[/C][C]-3.7699[/C][C]0.000106[/C][/ROW]
[ROW][C]3[/C][C]0.163111[/C][C]2.3693[/C][C]0.009361[/C][/ROW]
[ROW][C]4[/C][C]-0.036823[/C][C]-0.5349[/C][C]0.296648[/C][/ROW]
[ROW][C]5[/C][C]-0.044825[/C][C]-0.6511[/C][C]0.25784[/C][/ROW]
[ROW][C]6[/C][C]0.106611[/C][C]1.5486[/C][C]0.061487[/C][/ROW]
[ROW][C]7[/C][C]-0.061786[/C][C]-0.8975[/C][C]0.185238[/C][/ROW]
[ROW][C]8[/C][C]-0.037911[/C][C]-0.5507[/C][C]0.291213[/C][/ROW]
[ROW][C]9[/C][C]0.139402[/C][C]2.0249[/C][C]0.022067[/C][/ROW]
[ROW][C]10[/C][C]-0.219326[/C][C]-3.1859[/C][C]0.000831[/C][/ROW]
[ROW][C]11[/C][C]-0.150638[/C][C]-2.1881[/C][C]0.014879[/C][/ROW]
[ROW][C]12[/C][C]0.503016[/C][C]7.3067[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.208077[/C][C]-3.0225[/C][C]0.001409[/C][/ROW]
[ROW][C]14[/C][C]-0.153938[/C][C]-2.2361[/C][C]0.013197[/C][/ROW]
[ROW][C]15[/C][C]0.178239[/C][C]2.5891[/C][C]0.005147[/C][/ROW]
[ROW][C]16[/C][C]-0.074486[/C][C]-1.082[/C][C]0.140249[/C][/ROW]
[ROW][C]17[/C][C]-0.006123[/C][C]-0.0889[/C][C]0.464604[/C][/ROW]
[ROW][C]18[/C][C]0.115734[/C][C]1.6811[/C][C]0.047109[/C][/ROW]
[ROW][C]19[/C][C]-0.090399[/C][C]-1.3131[/C][C]0.095285[/C][/ROW]
[ROW][C]20[/C][C]0.042709[/C][C]0.6204[/C][C]0.267838[/C][/ROW]
[ROW][C]21[/C][C]0.060634[/C][C]0.8808[/C][C]0.189726[/C][/ROW]
[ROW][C]22[/C][C]-0.220642[/C][C]-3.205[/C][C]0.00078[/C][/ROW]
[ROW][C]23[/C][C]-0.079865[/C][C]-1.1601[/C][C]0.123659[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310002&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310002&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
1-0.335726-4.87671e-06
2-0.259529-3.76990.000106
30.1631112.36930.009361
4-0.036823-0.53490.296648
5-0.044825-0.65110.25784
60.1066111.54860.061487
7-0.061786-0.89750.185238
8-0.037911-0.55070.291213
90.1394022.02490.022067
10-0.219326-3.18590.000831
11-0.150638-2.18810.014879
120.5030167.30670
13-0.208077-3.02250.001409
14-0.153938-2.23610.013197
150.1782392.58910.005147
16-0.074486-1.0820.140249
17-0.006123-0.08890.464604
180.1157341.68110.047109
19-0.090399-1.31310.095285
200.0427090.62040.267838
210.0606340.88080.189726
22-0.220642-3.2050.00078
23-0.079865-1.16010.123659






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.335726-4.87671e-06
2-0.419527-6.0940
3-0.138718-2.0150.022587
4-0.170425-2.47560.007045
5-0.128614-1.86820.031558
60.0028430.04130.483551
7-0.044712-0.64950.258369
8-0.042106-0.61160.270722
90.1054021.5310.063628
10-0.177965-2.58510.005205
11-0.382958-5.56280
120.1974632.86830.002273
13-0.019806-0.28770.386931
14-0.016611-0.24130.404781
150.0469680.68220.247917
16-0.014558-0.21150.416362
170.044130.6410.261103
180.0764951.11120.133882
190.0304990.4430.329101
200.1409772.04780.020909
210.0375420.54530.293054
22-0.076755-1.11490.133074
23-0.167269-2.42970.007974

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.335726 & -4.8767 & 1e-06 \tabularnewline
2 & -0.419527 & -6.094 & 0 \tabularnewline
3 & -0.138718 & -2.015 & 0.022587 \tabularnewline
4 & -0.170425 & -2.4756 & 0.007045 \tabularnewline
5 & -0.128614 & -1.8682 & 0.031558 \tabularnewline
6 & 0.002843 & 0.0413 & 0.483551 \tabularnewline
7 & -0.044712 & -0.6495 & 0.258369 \tabularnewline
8 & -0.042106 & -0.6116 & 0.270722 \tabularnewline
9 & 0.105402 & 1.531 & 0.063628 \tabularnewline
10 & -0.177965 & -2.5851 & 0.005205 \tabularnewline
11 & -0.382958 & -5.5628 & 0 \tabularnewline
12 & 0.197463 & 2.8683 & 0.002273 \tabularnewline
13 & -0.019806 & -0.2877 & 0.386931 \tabularnewline
14 & -0.016611 & -0.2413 & 0.404781 \tabularnewline
15 & 0.046968 & 0.6822 & 0.247917 \tabularnewline
16 & -0.014558 & -0.2115 & 0.416362 \tabularnewline
17 & 0.04413 & 0.641 & 0.261103 \tabularnewline
18 & 0.076495 & 1.1112 & 0.133882 \tabularnewline
19 & 0.030499 & 0.443 & 0.329101 \tabularnewline
20 & 0.140977 & 2.0478 & 0.020909 \tabularnewline
21 & 0.037542 & 0.5453 & 0.293054 \tabularnewline
22 & -0.076755 & -1.1149 & 0.133074 \tabularnewline
23 & -0.167269 & -2.4297 & 0.007974 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310002&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]-0.335726[/C][C]-4.8767[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.419527[/C][C]-6.094[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.138718[/C][C]-2.015[/C][C]0.022587[/C][/ROW]
[ROW][C]4[/C][C]-0.170425[/C][C]-2.4756[/C][C]0.007045[/C][/ROW]
[ROW][C]5[/C][C]-0.128614[/C][C]-1.8682[/C][C]0.031558[/C][/ROW]
[ROW][C]6[/C][C]0.002843[/C][C]0.0413[/C][C]0.483551[/C][/ROW]
[ROW][C]7[/C][C]-0.044712[/C][C]-0.6495[/C][C]0.258369[/C][/ROW]
[ROW][C]8[/C][C]-0.042106[/C][C]-0.6116[/C][C]0.270722[/C][/ROW]
[ROW][C]9[/C][C]0.105402[/C][C]1.531[/C][C]0.063628[/C][/ROW]
[ROW][C]10[/C][C]-0.177965[/C][C]-2.5851[/C][C]0.005205[/C][/ROW]
[ROW][C]11[/C][C]-0.382958[/C][C]-5.5628[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.197463[/C][C]2.8683[/C][C]0.002273[/C][/ROW]
[ROW][C]13[/C][C]-0.019806[/C][C]-0.2877[/C][C]0.386931[/C][/ROW]
[ROW][C]14[/C][C]-0.016611[/C][C]-0.2413[/C][C]0.404781[/C][/ROW]
[ROW][C]15[/C][C]0.046968[/C][C]0.6822[/C][C]0.247917[/C][/ROW]
[ROW][C]16[/C][C]-0.014558[/C][C]-0.2115[/C][C]0.416362[/C][/ROW]
[ROW][C]17[/C][C]0.04413[/C][C]0.641[/C][C]0.261103[/C][/ROW]
[ROW][C]18[/C][C]0.076495[/C][C]1.1112[/C][C]0.133882[/C][/ROW]
[ROW][C]19[/C][C]0.030499[/C][C]0.443[/C][C]0.329101[/C][/ROW]
[ROW][C]20[/C][C]0.140977[/C][C]2.0478[/C][C]0.020909[/C][/ROW]
[ROW][C]21[/C][C]0.037542[/C][C]0.5453[/C][C]0.293054[/C][/ROW]
[ROW][C]22[/C][C]-0.076755[/C][C]-1.1149[/C][C]0.133074[/C][/ROW]
[ROW][C]23[/C][C]-0.167269[/C][C]-2.4297[/C][C]0.007974[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310002&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310002&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
1-0.335726-4.87671e-06
2-0.419527-6.0940
3-0.138718-2.0150.022587
4-0.170425-2.47560.007045
5-0.128614-1.86820.031558
60.0028430.04130.483551
7-0.044712-0.64950.258369
8-0.042106-0.61160.270722
90.1054021.5310.063628
10-0.177965-2.58510.005205
11-0.382958-5.56280
120.1974632.86830.002273
13-0.019806-0.28770.386931
14-0.016611-0.24130.404781
150.0469680.68220.247917
16-0.014558-0.21150.416362
170.044130.6410.261103
180.0764951.11120.133882
190.0304990.4430.329101
200.1409772.04780.020909
210.0375420.54530.293054
22-0.076755-1.11490.133074
23-0.167269-2.42970.007974


Figures (Output of Computation)

Input Parameters & R Code

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