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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 computationTue, 12 Dec 2017 22:54:18 +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/12/t1513115667bg1zr6inopnh5vp.htm/, Retrieved Wed, 15 May 2024 13:43:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309193, Retrieved Wed, 15 May 2024 13:43:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact37

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] [] [2017-12-12 21:54:18] [8829069b4432872c842806a35f4fa8df] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
122.2
136.1
145.5
116.7
137.1
125.5
112.4
106.3
145.7
151.5
144.6
116.4
137.7
138.8
149.5
125
133.4
134.4
124.8
110.6
142.4
149.6
134.6
103.3
136.5
137.1
140.7
131.4
126.2
125.3
126.6
107.7
144.5
154.2
131.4
105.7
136.2
133.3
130
129.3
113.1
117.7
116.3
97.3
140.6
141.2
120.8
106.2
121.5
122.6
137.2
118.9
107.2
127.4
111.8
100
138.3
128
121.2
105.9
112.5
123.1
129
115.5
105.7
122.3
106.4
101.1
131.6
119.5
127
106.9
115.9
122.7
137.2
108.5
115.2
129.4
112.3
104.3
140
139.9
134.9
105.1
127
135.5
143.9
115.8
117.5
129.3
117.9
108.1
131.7
143.7
126.2
96.9
125.8
129.6
124.9
136.8
107.5
114.3
110.3
85.5
116.8
115.1
95.2
83.4
95.4
96.3
100.5
90.9
80.6
94.8
93.9
75.9
101.6
103.3
91.8
83.5
92
101.2
109.1
99.8
90.8
110.6
97.8
81.9
114.4
108.8
103.1
90.4
94.4
100.5
115.1
93.9
102.5
97.1
91.2
82.3
107.1
99.2
94.8
81.1
92.5
97.7
98.5
81.2
86.2
92
86.3
74.8
90
101.1
87.8
66.3
88.6
90
92
85.1
85.9
88.5
92.3
68
93.6
97.7
85.1
69.9
96.1
97
95.9
91.3
83.5
91.4
96.8
71
106.9
102.7
84.9
75.8
93.6
100.7
100.5
95.9
85.7
104.1
93.5
81.5
102.1
98.2
88.4
77.8
90.1
101
98.6
91.5
86.4
98.9
85.2
77.3
93
86.8
91.3
74.9
93.9
95
103.1
81.4
93.1
97.2
86.4
75.5

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=309193&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=309193&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309193&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
1-0.284775-4.13662.5e-05
2-0.351665-5.10820
3-0.033978-0.49360.311064
40.2828734.1092.8e-05
5-0.075249-1.0930.137809
6-0.024769-0.35980.359682
7-0.14604-2.12140.017529
80.3560055.17130
9-0.055795-0.81050.209291
10-0.398938-5.79490
11-0.117791-1.7110.044274
120.76791511.15460
13-0.226701-3.2930.000581
14-0.282561-4.10442.9e-05
15-0.08398-1.21990.111935
160.2536473.68440.000146
170.0140740.20440.419103
18-0.110682-1.60770.054693
19-0.11226-1.63070.052226
200.3674425.33740
21-0.12643-1.83650.033845
22-0.344082-4.99811e-06
23-0.035182-0.51110.304924
240.5915058.59210

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.284775 & -4.1366 & 2.5e-05 \tabularnewline
2 & -0.351665 & -5.1082 & 0 \tabularnewline
3 & -0.033978 & -0.4936 & 0.311064 \tabularnewline
4 & 0.282873 & 4.109 & 2.8e-05 \tabularnewline
5 & -0.075249 & -1.093 & 0.137809 \tabularnewline
6 & -0.024769 & -0.3598 & 0.359682 \tabularnewline
7 & -0.14604 & -2.1214 & 0.017529 \tabularnewline
8 & 0.356005 & 5.1713 & 0 \tabularnewline
9 & -0.055795 & -0.8105 & 0.209291 \tabularnewline
10 & -0.398938 & -5.7949 & 0 \tabularnewline
11 & -0.117791 & -1.711 & 0.044274 \tabularnewline
12 & 0.767915 & 11.1546 & 0 \tabularnewline
13 & -0.226701 & -3.293 & 0.000581 \tabularnewline
14 & -0.282561 & -4.1044 & 2.9e-05 \tabularnewline
15 & -0.08398 & -1.2199 & 0.111935 \tabularnewline
16 & 0.253647 & 3.6844 & 0.000146 \tabularnewline
17 & 0.014074 & 0.2044 & 0.419103 \tabularnewline
18 & -0.110682 & -1.6077 & 0.054693 \tabularnewline
19 & -0.11226 & -1.6307 & 0.052226 \tabularnewline
20 & 0.367442 & 5.3374 & 0 \tabularnewline
21 & -0.12643 & -1.8365 & 0.033845 \tabularnewline
22 & -0.344082 & -4.9981 & 1e-06 \tabularnewline
23 & -0.035182 & -0.5111 & 0.304924 \tabularnewline
24 & 0.591505 & 8.5921 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309193&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]-0.284775[/C][C]-4.1366[/C][C]2.5e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.351665[/C][C]-5.1082[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.033978[/C][C]-0.4936[/C][C]0.311064[/C][/ROW]
[ROW][C]4[/C][C]0.282873[/C][C]4.109[/C][C]2.8e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.075249[/C][C]-1.093[/C][C]0.137809[/C][/ROW]
[ROW][C]6[/C][C]-0.024769[/C][C]-0.3598[/C][C]0.359682[/C][/ROW]
[ROW][C]7[/C][C]-0.14604[/C][C]-2.1214[/C][C]0.017529[/C][/ROW]
[ROW][C]8[/C][C]0.356005[/C][C]5.1713[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]-0.055795[/C][C]-0.8105[/C][C]0.209291[/C][/ROW]
[ROW][C]10[/C][C]-0.398938[/C][C]-5.7949[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]-0.117791[/C][C]-1.711[/C][C]0.044274[/C][/ROW]
[ROW][C]12[/C][C]0.767915[/C][C]11.1546[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.226701[/C][C]-3.293[/C][C]0.000581[/C][/ROW]
[ROW][C]14[/C][C]-0.282561[/C][C]-4.1044[/C][C]2.9e-05[/C][/ROW]
[ROW][C]15[/C][C]-0.08398[/C][C]-1.2199[/C][C]0.111935[/C][/ROW]
[ROW][C]16[/C][C]0.253647[/C][C]3.6844[/C][C]0.000146[/C][/ROW]
[ROW][C]17[/C][C]0.014074[/C][C]0.2044[/C][C]0.419103[/C][/ROW]
[ROW][C]18[/C][C]-0.110682[/C][C]-1.6077[/C][C]0.054693[/C][/ROW]
[ROW][C]19[/C][C]-0.11226[/C][C]-1.6307[/C][C]0.052226[/C][/ROW]
[ROW][C]20[/C][C]0.367442[/C][C]5.3374[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]-0.12643[/C][C]-1.8365[/C][C]0.033845[/C][/ROW]
[ROW][C]22[/C][C]-0.344082[/C][C]-4.9981[/C][C]1e-06[/C][/ROW]
[ROW][C]23[/C][C]-0.035182[/C][C]-0.5111[/C][C]0.304924[/C][/ROW]
[ROW][C]24[/C][C]0.591505[/C][C]8.5921[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309193&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309193&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
1-0.284775-4.13662.5e-05
2-0.351665-5.10820
3-0.033978-0.49360.311064
40.2828734.1092.8e-05
5-0.075249-1.0930.137809
6-0.024769-0.35980.359682
7-0.14604-2.12140.017529
80.3560055.17130
9-0.055795-0.81050.209291
10-0.398938-5.79490
11-0.117791-1.7110.044274
120.76791511.15460
13-0.226701-3.2930.000581
14-0.282561-4.10442.9e-05
15-0.08398-1.21990.111935
160.2536473.68440.000146
170.0140740.20440.419103
18-0.110682-1.60770.054693
19-0.11226-1.63070.052226
200.3674425.33740
21-0.12643-1.83650.033845
22-0.344082-4.99811e-06
23-0.035182-0.51110.304924
240.5915058.59210






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.284775-4.13662.5e-05
2-0.470955-6.8410
3-0.441068-6.40690
4-0.164269-2.38620.008955
5-0.252531-3.66820.000155
6-0.08096-1.1760.120457
7-0.300164-4.36011e-05
80.2467243.58390.00021
90.3074644.46626e-06
10-0.117756-1.71050.044322
11-0.563672-8.18780
120.2980234.3291.2e-05
130.1895182.75290.003211
140.1611222.34040.010098
15-0.017808-0.25870.398068
16-0.06166-0.89570.185726
170.0295880.42980.333895
18-0.095193-1.38280.0841
190.0139420.20250.419856
20-0.002382-0.03460.486213
21-0.159332-2.31440.010803
22-0.080188-1.16480.122709
23-0.09555-1.38790.083308
24-0.038843-0.56420.286597

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.284775 & -4.1366 & 2.5e-05 \tabularnewline
2 & -0.470955 & -6.841 & 0 \tabularnewline
3 & -0.441068 & -6.4069 & 0 \tabularnewline
4 & -0.164269 & -2.3862 & 0.008955 \tabularnewline
5 & -0.252531 & -3.6682 & 0.000155 \tabularnewline
6 & -0.08096 & -1.176 & 0.120457 \tabularnewline
7 & -0.300164 & -4.3601 & 1e-05 \tabularnewline
8 & 0.246724 & 3.5839 & 0.00021 \tabularnewline
9 & 0.307464 & 4.4662 & 6e-06 \tabularnewline
10 & -0.117756 & -1.7105 & 0.044322 \tabularnewline
11 & -0.563672 & -8.1878 & 0 \tabularnewline
12 & 0.298023 & 4.329 & 1.2e-05 \tabularnewline
13 & 0.189518 & 2.7529 & 0.003211 \tabularnewline
14 & 0.161122 & 2.3404 & 0.010098 \tabularnewline
15 & -0.017808 & -0.2587 & 0.398068 \tabularnewline
16 & -0.06166 & -0.8957 & 0.185726 \tabularnewline
17 & 0.029588 & 0.4298 & 0.333895 \tabularnewline
18 & -0.095193 & -1.3828 & 0.0841 \tabularnewline
19 & 0.013942 & 0.2025 & 0.419856 \tabularnewline
20 & -0.002382 & -0.0346 & 0.486213 \tabularnewline
21 & -0.159332 & -2.3144 & 0.010803 \tabularnewline
22 & -0.080188 & -1.1648 & 0.122709 \tabularnewline
23 & -0.09555 & -1.3879 & 0.083308 \tabularnewline
24 & -0.038843 & -0.5642 & 0.286597 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309193&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]-0.284775[/C][C]-4.1366[/C][C]2.5e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.470955[/C][C]-6.841[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.441068[/C][C]-6.4069[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.164269[/C][C]-2.3862[/C][C]0.008955[/C][/ROW]
[ROW][C]5[/C][C]-0.252531[/C][C]-3.6682[/C][C]0.000155[/C][/ROW]
[ROW][C]6[/C][C]-0.08096[/C][C]-1.176[/C][C]0.120457[/C][/ROW]
[ROW][C]7[/C][C]-0.300164[/C][C]-4.3601[/C][C]1e-05[/C][/ROW]
[ROW][C]8[/C][C]0.246724[/C][C]3.5839[/C][C]0.00021[/C][/ROW]
[ROW][C]9[/C][C]0.307464[/C][C]4.4662[/C][C]6e-06[/C][/ROW]
[ROW][C]10[/C][C]-0.117756[/C][C]-1.7105[/C][C]0.044322[/C][/ROW]
[ROW][C]11[/C][C]-0.563672[/C][C]-8.1878[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.298023[/C][C]4.329[/C][C]1.2e-05[/C][/ROW]
[ROW][C]13[/C][C]0.189518[/C][C]2.7529[/C][C]0.003211[/C][/ROW]
[ROW][C]14[/C][C]0.161122[/C][C]2.3404[/C][C]0.010098[/C][/ROW]
[ROW][C]15[/C][C]-0.017808[/C][C]-0.2587[/C][C]0.398068[/C][/ROW]
[ROW][C]16[/C][C]-0.06166[/C][C]-0.8957[/C][C]0.185726[/C][/ROW]
[ROW][C]17[/C][C]0.029588[/C][C]0.4298[/C][C]0.333895[/C][/ROW]
[ROW][C]18[/C][C]-0.095193[/C][C]-1.3828[/C][C]0.0841[/C][/ROW]
[ROW][C]19[/C][C]0.013942[/C][C]0.2025[/C][C]0.419856[/C][/ROW]
[ROW][C]20[/C][C]-0.002382[/C][C]-0.0346[/C][C]0.486213[/C][/ROW]
[ROW][C]21[/C][C]-0.159332[/C][C]-2.3144[/C][C]0.010803[/C][/ROW]
[ROW][C]22[/C][C]-0.080188[/C][C]-1.1648[/C][C]0.122709[/C][/ROW]
[ROW][C]23[/C][C]-0.09555[/C][C]-1.3879[/C][C]0.083308[/C][/ROW]
[ROW][C]24[/C][C]-0.038843[/C][C]-0.5642[/C][C]0.286597[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309193&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309193&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
1-0.284775-4.13662.5e-05
2-0.470955-6.8410
3-0.441068-6.40690
4-0.164269-2.38620.008955
5-0.252531-3.66820.000155
6-0.08096-1.1760.120457
7-0.300164-4.36011e-05
80.2467243.58390.00021
90.3074644.46626e-06
10-0.117756-1.71050.044322
11-0.563672-8.18780
120.2980234.3291.2e-05
130.1895182.75290.003211
140.1611222.34040.010098
15-0.017808-0.25870.398068
16-0.06166-0.89570.185726
170.0295880.42980.333895
18-0.095193-1.38280.0841
190.0139420.20250.419856
20-0.002382-0.03460.486213
21-0.159332-2.31440.010803
22-0.080188-1.16480.122709
23-0.09555-1.38790.083308
24-0.038843-0.56420.286597


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 24 ; 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')