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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, 13 Dec 2017 14:31:10 +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/13/t1513171911dcavw2m34qfer4m.htm/, Retrieved Wed, 15 May 2024 20:44:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309301, Retrieved Wed, 15 May 2024 20:44:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62

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] [(Partial) Autocor...] [2017-12-13 13:31:10] [bd83e7d2022b632a928e3cc7dd68d98c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
58.5
59.8
64.6
62.2
68
64.3
58.9
64.8
67.5
76.2
73.7
70.4
67.7
63.7
72.4
66
70.1
70.4
66.6
72.6
74
79
76.1
72.3
71.6
67.2
73.8
70.8
71.4
70.4
70.7
70.6
75.5
82.1
74.3
76.3
74.5
71.1
73.3
73.8
69
71.1
71.9
69
77.3
82.8
74
77.6
72.3
70.7
81
76.4
72.3
79.5
73.3
74.5
82.7
83.8
81.6
85.5
76.7
71.8
80.2
76.8
76.1
80.7
71.3
80.9
85
84.5
87.7
87.7
80.2
74.4
85.8
77
84.5
83.6
77.7
85.7
87.9
93.7
92.3
87
89.1
81.3
92.7
83.9
87.3
89.1
86.9
91.7
93
105.3
101.6
94.2
100.5
95.8
95.8
102.1
96
96.8
98.9
93.4
105.5
110.9
98.6
102.6
93.5
90.8
99.7
97.8
91.1
98.1
96
93.5
101.2
105.2
98.9
101.3
92.1
90.6
105.4
98.4
92.7
101.2
93.4
98.3
104.3
107
107.7
108.9
99.6
96.1
109
99.5
104.6
99.9
94.1
105.3
110.4
110.5
110
108.5
104.3
101.2
109.2
99.6
105.6
106.2
102.2
107.5
105.8
120.5
113.2
104.3
107.7
99.2
105.1
104.3
106.1
100.8
106.7
101.6
104.4
114.8
105.4
104
102
96.5
102.3
105.3
101.9
102.2
102.8
100.4
110.7
116.4
106
109.2
103
99.8
109.8
107.3
101.2
111.8
106.9
103.5
113.1
119.4
113.3
115
104.7
107.2
116.6
111.3
111.4
115
102.4
111.4
113.2
112.9
114.2
115.6
107.1
102.3
117.9
105.8
114.3
113.1
102.9
112.2

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 time4 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309301&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]4 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309301&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309301&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 time4 seconds
R ServerBig Analytics Cloud Computing Center






Autocorrelation Function
Time lag kACF(k)T-STATP-value
1-0.544989-7.6880
2-0.114899-1.62090.053316
30.3954225.57810
4-0.31232-4.40589e-06
50.0728021.0270.152835
60.2017532.84610.002445
7-0.311067-4.38819e-06
80.1037981.46430.072351
90.201532.84290.002468
10-0.257498-3.63250.000179
110.1478842.08620.01912
12-0.008376-0.11820.45303
13-0.209848-2.96030.001724
140.2643243.72870.000125
15-0.019317-0.27250.392761
16-0.293431-4.13942.6e-05
170.2460043.47030.000319
180.0787051.11030.13411
19-0.291321-4.10962.9e-05
200.2605033.67490.000153
21-0.045179-0.63730.26232
22-0.281563-3.97195e-05
230.4736656.68190

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.544989 & -7.688 & 0 \tabularnewline
2 & -0.114899 & -1.6209 & 0.053316 \tabularnewline
3 & 0.395422 & 5.5781 & 0 \tabularnewline
4 & -0.31232 & -4.4058 & 9e-06 \tabularnewline
5 & 0.072802 & 1.027 & 0.152835 \tabularnewline
6 & 0.201753 & 2.8461 & 0.002445 \tabularnewline
7 & -0.311067 & -4.3881 & 9e-06 \tabularnewline
8 & 0.103798 & 1.4643 & 0.072351 \tabularnewline
9 & 0.20153 & 2.8429 & 0.002468 \tabularnewline
10 & -0.257498 & -3.6325 & 0.000179 \tabularnewline
11 & 0.147884 & 2.0862 & 0.01912 \tabularnewline
12 & -0.008376 & -0.1182 & 0.45303 \tabularnewline
13 & -0.209848 & -2.9603 & 0.001724 \tabularnewline
14 & 0.264324 & 3.7287 & 0.000125 \tabularnewline
15 & -0.019317 & -0.2725 & 0.392761 \tabularnewline
16 & -0.293431 & -4.1394 & 2.6e-05 \tabularnewline
17 & 0.246004 & 3.4703 & 0.000319 \tabularnewline
18 & 0.078705 & 1.1103 & 0.13411 \tabularnewline
19 & -0.291321 & -4.1096 & 2.9e-05 \tabularnewline
20 & 0.260503 & 3.6749 & 0.000153 \tabularnewline
21 & -0.045179 & -0.6373 & 0.26232 \tabularnewline
22 & -0.281563 & -3.9719 & 5e-05 \tabularnewline
23 & 0.473665 & 6.6819 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309301&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]-0.544989[/C][C]-7.688[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.114899[/C][C]-1.6209[/C][C]0.053316[/C][/ROW]
[ROW][C]3[/C][C]0.395422[/C][C]5.5781[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.31232[/C][C]-4.4058[/C][C]9e-06[/C][/ROW]
[ROW][C]5[/C][C]0.072802[/C][C]1.027[/C][C]0.152835[/C][/ROW]
[ROW][C]6[/C][C]0.201753[/C][C]2.8461[/C][C]0.002445[/C][/ROW]
[ROW][C]7[/C][C]-0.311067[/C][C]-4.3881[/C][C]9e-06[/C][/ROW]
[ROW][C]8[/C][C]0.103798[/C][C]1.4643[/C][C]0.072351[/C][/ROW]
[ROW][C]9[/C][C]0.20153[/C][C]2.8429[/C][C]0.002468[/C][/ROW]
[ROW][C]10[/C][C]-0.257498[/C][C]-3.6325[/C][C]0.000179[/C][/ROW]
[ROW][C]11[/C][C]0.147884[/C][C]2.0862[/C][C]0.01912[/C][/ROW]
[ROW][C]12[/C][C]-0.008376[/C][C]-0.1182[/C][C]0.45303[/C][/ROW]
[ROW][C]13[/C][C]-0.209848[/C][C]-2.9603[/C][C]0.001724[/C][/ROW]
[ROW][C]14[/C][C]0.264324[/C][C]3.7287[/C][C]0.000125[/C][/ROW]
[ROW][C]15[/C][C]-0.019317[/C][C]-0.2725[/C][C]0.392761[/C][/ROW]
[ROW][C]16[/C][C]-0.293431[/C][C]-4.1394[/C][C]2.6e-05[/C][/ROW]
[ROW][C]17[/C][C]0.246004[/C][C]3.4703[/C][C]0.000319[/C][/ROW]
[ROW][C]18[/C][C]0.078705[/C][C]1.1103[/C][C]0.13411[/C][/ROW]
[ROW][C]19[/C][C]-0.291321[/C][C]-4.1096[/C][C]2.9e-05[/C][/ROW]
[ROW][C]20[/C][C]0.260503[/C][C]3.6749[/C][C]0.000153[/C][/ROW]
[ROW][C]21[/C][C]-0.045179[/C][C]-0.6373[/C][C]0.26232[/C][/ROW]
[ROW][C]22[/C][C]-0.281563[/C][C]-3.9719[/C][C]5e-05[/C][/ROW]
[ROW][C]23[/C][C]0.473665[/C][C]6.6819[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309301&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309301&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
1-0.544989-7.6880
2-0.114899-1.62090.053316
30.3954225.57810
4-0.31232-4.40589e-06
50.0728021.0270.152835
60.2017532.84610.002445
7-0.311067-4.38819e-06
80.1037981.46430.072351
90.201532.84290.002468
10-0.257498-3.63250.000179
110.1478842.08620.01912
12-0.008376-0.11820.45303
13-0.209848-2.96030.001724
140.2643243.72870.000125
15-0.019317-0.27250.392761
16-0.293431-4.13942.6e-05
170.2460043.47030.000319
180.0787051.11030.13411
19-0.291321-4.10962.9e-05
200.2605033.67490.000153
21-0.045179-0.63730.26232
22-0.281563-3.97195e-05
230.4736656.68190






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.544989-7.6880
2-0.585945-8.26580
3-0.050304-0.70960.239384
4-0.127326-1.79610.036994
5-0.035362-0.49880.309219
60.180022.53950.005933
7-0.008023-0.11320.454999
8-0.155743-2.1970.014586
90.0529010.74630.228196
100.0726771.02520.153249
110.1588622.2410.013064
120.0344740.48630.313642
13-0.234869-3.31320.000548
14-0.172526-2.43380.007913
150.081151.14480.126842
16-0.101415-1.43060.077051
17-0.20657-2.9140.001988
180.0988841.39490.082296
19-0.022597-0.31880.37512
20-0.034204-0.48250.314988
210.1295541.82760.034555
22-0.142916-2.01610.022568
230.1478662.08590.019131

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.544989 & -7.688 & 0 \tabularnewline
2 & -0.585945 & -8.2658 & 0 \tabularnewline
3 & -0.050304 & -0.7096 & 0.239384 \tabularnewline
4 & -0.127326 & -1.7961 & 0.036994 \tabularnewline
5 & -0.035362 & -0.4988 & 0.309219 \tabularnewline
6 & 0.18002 & 2.5395 & 0.005933 \tabularnewline
7 & -0.008023 & -0.1132 & 0.454999 \tabularnewline
8 & -0.155743 & -2.197 & 0.014586 \tabularnewline
9 & 0.052901 & 0.7463 & 0.228196 \tabularnewline
10 & 0.072677 & 1.0252 & 0.153249 \tabularnewline
11 & 0.158862 & 2.241 & 0.013064 \tabularnewline
12 & 0.034474 & 0.4863 & 0.313642 \tabularnewline
13 & -0.234869 & -3.3132 & 0.000548 \tabularnewline
14 & -0.172526 & -2.4338 & 0.007913 \tabularnewline
15 & 0.08115 & 1.1448 & 0.126842 \tabularnewline
16 & -0.101415 & -1.4306 & 0.077051 \tabularnewline
17 & -0.20657 & -2.914 & 0.001988 \tabularnewline
18 & 0.098884 & 1.3949 & 0.082296 \tabularnewline
19 & -0.022597 & -0.3188 & 0.37512 \tabularnewline
20 & -0.034204 & -0.4825 & 0.314988 \tabularnewline
21 & 0.129554 & 1.8276 & 0.034555 \tabularnewline
22 & -0.142916 & -2.0161 & 0.022568 \tabularnewline
23 & 0.147866 & 2.0859 & 0.019131 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309301&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]-0.544989[/C][C]-7.688[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.585945[/C][C]-8.2658[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.050304[/C][C]-0.7096[/C][C]0.239384[/C][/ROW]
[ROW][C]4[/C][C]-0.127326[/C][C]-1.7961[/C][C]0.036994[/C][/ROW]
[ROW][C]5[/C][C]-0.035362[/C][C]-0.4988[/C][C]0.309219[/C][/ROW]
[ROW][C]6[/C][C]0.18002[/C][C]2.5395[/C][C]0.005933[/C][/ROW]
[ROW][C]7[/C][C]-0.008023[/C][C]-0.1132[/C][C]0.454999[/C][/ROW]
[ROW][C]8[/C][C]-0.155743[/C][C]-2.197[/C][C]0.014586[/C][/ROW]
[ROW][C]9[/C][C]0.052901[/C][C]0.7463[/C][C]0.228196[/C][/ROW]
[ROW][C]10[/C][C]0.072677[/C][C]1.0252[/C][C]0.153249[/C][/ROW]
[ROW][C]11[/C][C]0.158862[/C][C]2.241[/C][C]0.013064[/C][/ROW]
[ROW][C]12[/C][C]0.034474[/C][C]0.4863[/C][C]0.313642[/C][/ROW]
[ROW][C]13[/C][C]-0.234869[/C][C]-3.3132[/C][C]0.000548[/C][/ROW]
[ROW][C]14[/C][C]-0.172526[/C][C]-2.4338[/C][C]0.007913[/C][/ROW]
[ROW][C]15[/C][C]0.08115[/C][C]1.1448[/C][C]0.126842[/C][/ROW]
[ROW][C]16[/C][C]-0.101415[/C][C]-1.4306[/C][C]0.077051[/C][/ROW]
[ROW][C]17[/C][C]-0.20657[/C][C]-2.914[/C][C]0.001988[/C][/ROW]
[ROW][C]18[/C][C]0.098884[/C][C]1.3949[/C][C]0.082296[/C][/ROW]
[ROW][C]19[/C][C]-0.022597[/C][C]-0.3188[/C][C]0.37512[/C][/ROW]
[ROW][C]20[/C][C]-0.034204[/C][C]-0.4825[/C][C]0.314988[/C][/ROW]
[ROW][C]21[/C][C]0.129554[/C][C]1.8276[/C][C]0.034555[/C][/ROW]
[ROW][C]22[/C][C]-0.142916[/C][C]-2.0161[/C][C]0.022568[/C][/ROW]
[ROW][C]23[/C][C]0.147866[/C][C]2.0859[/C][C]0.019131[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309301&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309301&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
1-0.544989-7.6880
2-0.585945-8.26580
3-0.050304-0.70960.239384
4-0.127326-1.79610.036994
5-0.035362-0.49880.309219
60.180022.53950.005933
7-0.008023-0.11320.454999
8-0.155743-2.1970.014586
90.0529010.74630.228196
100.0726771.02520.153249
110.1588622.2410.013064
120.0344740.48630.313642
13-0.234869-3.31320.000548
14-0.172526-2.43380.007913
150.081151.14480.126842
16-0.101415-1.43060.077051
17-0.20657-2.9140.001988
180.0988841.39490.082296
19-0.022597-0.31880.37512
20-0.034204-0.48250.314988
210.1295541.82760.034555
22-0.142916-2.01610.022568
230.1478662.08590.019131


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 1 ; 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')