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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, 21 Jan 2015 08:30:49 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Jan/21/t1421829060yrbe4ysruf4e37i.htm/, Retrieved Tue, 14 May 2024 12:15:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=275824, Retrieved Tue, 14 May 2024 12:15:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61

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] [] [2015-01-21 08:30:49] [a3de03a8fa2b95b1b988206b9ba33408] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
67
72
74
62
56
66
65
59
61
69
74
69
66
68
58
64
66
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73
61
61
57
58
57
67
81
79
76
78
74
67
84
85
79
82
87
90
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82
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79
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72
65
73
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73
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74
81
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90
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82
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87
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71
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67
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82
64
71
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68

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=275824&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=275824&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=275824&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.80903510.00720
20.7220118.93080
30.6850618.47370
40.6219817.69350
50.5502756.80650
60.4868416.02190
70.4543525.620
80.3915574.84332e-06
90.3546074.38621.1e-05
100.3042833.76380.000119
110.2715313.35860.000494
120.2030342.51140.006532
130.1746622.16040.016147
140.1375381.70130.045463
150.1217021.50540.067145
160.1380381.70740.044885
170.1126461.39340.082767
180.1333961.650.050495
190.1476711.82660.034855
200.1319211.63180.052392
210.1361661.68430.047083

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.809035 & 10.0072 & 0 \tabularnewline
2 & 0.722011 & 8.9308 & 0 \tabularnewline
3 & 0.685061 & 8.4737 & 0 \tabularnewline
4 & 0.621981 & 7.6935 & 0 \tabularnewline
5 & 0.550275 & 6.8065 & 0 \tabularnewline
6 & 0.486841 & 6.0219 & 0 \tabularnewline
7 & 0.454352 & 5.62 & 0 \tabularnewline
8 & 0.391557 & 4.8433 & 2e-06 \tabularnewline
9 & 0.354607 & 4.3862 & 1.1e-05 \tabularnewline
10 & 0.304283 & 3.7638 & 0.000119 \tabularnewline
11 & 0.271531 & 3.3586 & 0.000494 \tabularnewline
12 & 0.203034 & 2.5114 & 0.006532 \tabularnewline
13 & 0.174662 & 2.1604 & 0.016147 \tabularnewline
14 & 0.137538 & 1.7013 & 0.045463 \tabularnewline
15 & 0.121702 & 1.5054 & 0.067145 \tabularnewline
16 & 0.138038 & 1.7074 & 0.044885 \tabularnewline
17 & 0.112646 & 1.3934 & 0.082767 \tabularnewline
18 & 0.133396 & 1.65 & 0.050495 \tabularnewline
19 & 0.147671 & 1.8266 & 0.034855 \tabularnewline
20 & 0.131921 & 1.6318 & 0.052392 \tabularnewline
21 & 0.136166 & 1.6843 & 0.047083 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=275824&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]0.809035[/C][C]10.0072[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.722011[/C][C]8.9308[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.685061[/C][C]8.4737[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.621981[/C][C]7.6935[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.550275[/C][C]6.8065[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.486841[/C][C]6.0219[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.454352[/C][C]5.62[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.391557[/C][C]4.8433[/C][C]2e-06[/C][/ROW]
[ROW][C]9[/C][C]0.354607[/C][C]4.3862[/C][C]1.1e-05[/C][/ROW]
[ROW][C]10[/C][C]0.304283[/C][C]3.7638[/C][C]0.000119[/C][/ROW]
[ROW][C]11[/C][C]0.271531[/C][C]3.3586[/C][C]0.000494[/C][/ROW]
[ROW][C]12[/C][C]0.203034[/C][C]2.5114[/C][C]0.006532[/C][/ROW]
[ROW][C]13[/C][C]0.174662[/C][C]2.1604[/C][C]0.016147[/C][/ROW]
[ROW][C]14[/C][C]0.137538[/C][C]1.7013[/C][C]0.045463[/C][/ROW]
[ROW][C]15[/C][C]0.121702[/C][C]1.5054[/C][C]0.067145[/C][/ROW]
[ROW][C]16[/C][C]0.138038[/C][C]1.7074[/C][C]0.044885[/C][/ROW]
[ROW][C]17[/C][C]0.112646[/C][C]1.3934[/C][C]0.082767[/C][/ROW]
[ROW][C]18[/C][C]0.133396[/C][C]1.65[/C][C]0.050495[/C][/ROW]
[ROW][C]19[/C][C]0.147671[/C][C]1.8266[/C][C]0.034855[/C][/ROW]
[ROW][C]20[/C][C]0.131921[/C][C]1.6318[/C][C]0.052392[/C][/ROW]
[ROW][C]21[/C][C]0.136166[/C][C]1.6843[/C][C]0.047083[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=275824&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=275824&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
10.80903510.00720
20.7220118.93080
30.6850618.47370
40.6219817.69350
50.5502756.80650
60.4868416.02190
70.4543525.620
80.3915574.84332e-06
90.3546074.38621.1e-05
100.3042833.76380.000119
110.2715313.35860.000494
120.2030342.51140.006532
130.1746622.16040.016147
140.1375381.70130.045463
150.1217021.50540.067145
160.1380381.70740.044885
170.1126461.39340.082767
180.1333961.650.050495
190.1476711.82660.034855
200.1319211.63180.052392
210.1361661.68430.047083






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.80903510.00720
20.1953162.41590.008437
30.1715442.12190.017729
4-0.000697-0.00860.496564
5-0.045955-0.56840.285289
6-0.041141-0.50890.305783
70.0506820.62690.26583
8-0.062144-0.76870.221636
90.0331670.41020.341098
10-0.05569-0.68880.245982
110.0203570.25180.400765
12-0.121826-1.50690.066948
130.0426690.52780.299206
14-0.044896-0.55530.289739
150.0761030.94130.174007
160.106281.31460.095304
17-0.029971-0.37070.355679
180.092171.14010.128017
190.0434720.53770.295778
20-0.068189-0.84340.200147
210.0420060.51960.30205

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.809035 & 10.0072 & 0 \tabularnewline
2 & 0.195316 & 2.4159 & 0.008437 \tabularnewline
3 & 0.171544 & 2.1219 & 0.017729 \tabularnewline
4 & -0.000697 & -0.0086 & 0.496564 \tabularnewline
5 & -0.045955 & -0.5684 & 0.285289 \tabularnewline
6 & -0.041141 & -0.5089 & 0.305783 \tabularnewline
7 & 0.050682 & 0.6269 & 0.26583 \tabularnewline
8 & -0.062144 & -0.7687 & 0.221636 \tabularnewline
9 & 0.033167 & 0.4102 & 0.341098 \tabularnewline
10 & -0.05569 & -0.6888 & 0.245982 \tabularnewline
11 & 0.020357 & 0.2518 & 0.400765 \tabularnewline
12 & -0.121826 & -1.5069 & 0.066948 \tabularnewline
13 & 0.042669 & 0.5278 & 0.299206 \tabularnewline
14 & -0.044896 & -0.5553 & 0.289739 \tabularnewline
15 & 0.076103 & 0.9413 & 0.174007 \tabularnewline
16 & 0.10628 & 1.3146 & 0.095304 \tabularnewline
17 & -0.029971 & -0.3707 & 0.355679 \tabularnewline
18 & 0.09217 & 1.1401 & 0.128017 \tabularnewline
19 & 0.043472 & 0.5377 & 0.295778 \tabularnewline
20 & -0.068189 & -0.8434 & 0.200147 \tabularnewline
21 & 0.042006 & 0.5196 & 0.30205 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=275824&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]0.809035[/C][C]10.0072[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.195316[/C][C]2.4159[/C][C]0.008437[/C][/ROW]
[ROW][C]3[/C][C]0.171544[/C][C]2.1219[/C][C]0.017729[/C][/ROW]
[ROW][C]4[/C][C]-0.000697[/C][C]-0.0086[/C][C]0.496564[/C][/ROW]
[ROW][C]5[/C][C]-0.045955[/C][C]-0.5684[/C][C]0.285289[/C][/ROW]
[ROW][C]6[/C][C]-0.041141[/C][C]-0.5089[/C][C]0.305783[/C][/ROW]
[ROW][C]7[/C][C]0.050682[/C][C]0.6269[/C][C]0.26583[/C][/ROW]
[ROW][C]8[/C][C]-0.062144[/C][C]-0.7687[/C][C]0.221636[/C][/ROW]
[ROW][C]9[/C][C]0.033167[/C][C]0.4102[/C][C]0.341098[/C][/ROW]
[ROW][C]10[/C][C]-0.05569[/C][C]-0.6888[/C][C]0.245982[/C][/ROW]
[ROW][C]11[/C][C]0.020357[/C][C]0.2518[/C][C]0.400765[/C][/ROW]
[ROW][C]12[/C][C]-0.121826[/C][C]-1.5069[/C][C]0.066948[/C][/ROW]
[ROW][C]13[/C][C]0.042669[/C][C]0.5278[/C][C]0.299206[/C][/ROW]
[ROW][C]14[/C][C]-0.044896[/C][C]-0.5553[/C][C]0.289739[/C][/ROW]
[ROW][C]15[/C][C]0.076103[/C][C]0.9413[/C][C]0.174007[/C][/ROW]
[ROW][C]16[/C][C]0.10628[/C][C]1.3146[/C][C]0.095304[/C][/ROW]
[ROW][C]17[/C][C]-0.029971[/C][C]-0.3707[/C][C]0.355679[/C][/ROW]
[ROW][C]18[/C][C]0.09217[/C][C]1.1401[/C][C]0.128017[/C][/ROW]
[ROW][C]19[/C][C]0.043472[/C][C]0.5377[/C][C]0.295778[/C][/ROW]
[ROW][C]20[/C][C]-0.068189[/C][C]-0.8434[/C][C]0.200147[/C][/ROW]
[ROW][C]21[/C][C]0.042006[/C][C]0.5196[/C][C]0.30205[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=275824&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=275824&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
10.80903510.00720
20.1953162.41590.008437
30.1715442.12190.017729
4-0.000697-0.00860.496564
5-0.045955-0.56840.285289
6-0.041141-0.50890.305783
70.0506820.62690.26583
8-0.062144-0.76870.221636
90.0331670.41020.341098
10-0.05569-0.68880.245982
110.0203570.25180.400765
12-0.121826-1.50690.066948
130.0426690.52780.299206
14-0.044896-0.55530.289739
150.0761030.94130.174007
160.106281.31460.095304
17-0.029971-0.37070.355679
180.092171.14010.128017
190.0434720.53770.295778
20-0.068189-0.84340.200147
210.0420060.51960.30205


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 0 ; 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)
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,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),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,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),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')