FreeStatistics.org

Free Statistics

of Irreproducible Research!

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, 03 Dec 2013 14:07:23 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/03/t1386097663ms719gagdtxte3a.htm/, Retrieved Thu, 25 Apr 2024 20:46:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230381, Retrieved Thu, 25 Apr 2024 20:46:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69

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] [acf] [2013-12-03 19:07:23] [b86744663ec671173a5f381479557f00] [Current]
- RMP     [ARIMA Backward Selection] [d=1 D=1] [2013-12-04 13:47:49] [5a8f9e51417d210288970393391733f7]
- RMP     [ARIMA Backward Selection] [d=1] [2013-12-04 13:56:34] [5a8f9e51417d210288970393391733f7]
- RMP     [ARIMA Forecasting] [d=1 p=3] [2013-12-04 13:59:04] [5a8f9e51417d210288970393391733f7]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4
5
7
5
6
5
3
7
7
11
13
13
9
7
6
3
5
1
5
2
9
4
4
10
8
6
7
0
7
4
5
11
2
4
5
12
10
6
6
8
3
10
2
5
4
3
8
5
7
1
7
4
8
7
10
2
6
6
11
8
8
6
11
15
9
5
10
4
9
3
7
7
9
15
11
10
6
5
6
6
14
11
1
9
13
10
11
7
6
4
6
8
6
7
12
20
10
14
11
13
7
9
8
7
9
10
12
13
11
11
14
10
9
12
8
13
14
15
14
14
15
14
21
10
8
12
13
6
12
12

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ yule.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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230381&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230381&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230381&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 time4 seconds
R Server'George Udny Yule' @ yule.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.4388185.00331e-06
20.386974.41211.1e-05
30.2888223.29310.000638
40.2668263.04230.001421
50.2206282.51550.006551
60.1900412.16680.016037
70.1639921.86980.031881
80.1470761.67690.047981
90.1637111.86660.032105
100.3285983.74660.000134
110.3670374.18492.6e-05
120.3379163.85289.1e-05
130.2868013.270.000688
140.171341.95360.026449
150.2679323.05490.001366
160.1347861.53680.063387
170.1056261.20430.115327
180.1206061.37510.08573
190.0559430.63790.262346
200.1149111.31020.096221
210.2453892.79790.002964

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.438818 & 5.0033 & 1e-06 \tabularnewline
2 & 0.38697 & 4.4121 & 1.1e-05 \tabularnewline
3 & 0.288822 & 3.2931 & 0.000638 \tabularnewline
4 & 0.266826 & 3.0423 & 0.001421 \tabularnewline
5 & 0.220628 & 2.5155 & 0.006551 \tabularnewline
6 & 0.190041 & 2.1668 & 0.016037 \tabularnewline
7 & 0.163992 & 1.8698 & 0.031881 \tabularnewline
8 & 0.147076 & 1.6769 & 0.047981 \tabularnewline
9 & 0.163711 & 1.8666 & 0.032105 \tabularnewline
10 & 0.328598 & 3.7466 & 0.000134 \tabularnewline
11 & 0.367037 & 4.1849 & 2.6e-05 \tabularnewline
12 & 0.337916 & 3.8528 & 9.1e-05 \tabularnewline
13 & 0.286801 & 3.27 & 0.000688 \tabularnewline
14 & 0.17134 & 1.9536 & 0.026449 \tabularnewline
15 & 0.267932 & 3.0549 & 0.001366 \tabularnewline
16 & 0.134786 & 1.5368 & 0.063387 \tabularnewline
17 & 0.105626 & 1.2043 & 0.115327 \tabularnewline
18 & 0.120606 & 1.3751 & 0.08573 \tabularnewline
19 & 0.055943 & 0.6379 & 0.262346 \tabularnewline
20 & 0.114911 & 1.3102 & 0.096221 \tabularnewline
21 & 0.245389 & 2.7979 & 0.002964 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230381&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]0.438818[/C][C]5.0033[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.38697[/C][C]4.4121[/C][C]1.1e-05[/C][/ROW]
[ROW][C]3[/C][C]0.288822[/C][C]3.2931[/C][C]0.000638[/C][/ROW]
[ROW][C]4[/C][C]0.266826[/C][C]3.0423[/C][C]0.001421[/C][/ROW]
[ROW][C]5[/C][C]0.220628[/C][C]2.5155[/C][C]0.006551[/C][/ROW]
[ROW][C]6[/C][C]0.190041[/C][C]2.1668[/C][C]0.016037[/C][/ROW]
[ROW][C]7[/C][C]0.163992[/C][C]1.8698[/C][C]0.031881[/C][/ROW]
[ROW][C]8[/C][C]0.147076[/C][C]1.6769[/C][C]0.047981[/C][/ROW]
[ROW][C]9[/C][C]0.163711[/C][C]1.8666[/C][C]0.032105[/C][/ROW]
[ROW][C]10[/C][C]0.328598[/C][C]3.7466[/C][C]0.000134[/C][/ROW]
[ROW][C]11[/C][C]0.367037[/C][C]4.1849[/C][C]2.6e-05[/C][/ROW]
[ROW][C]12[/C][C]0.337916[/C][C]3.8528[/C][C]9.1e-05[/C][/ROW]
[ROW][C]13[/C][C]0.286801[/C][C]3.27[/C][C]0.000688[/C][/ROW]
[ROW][C]14[/C][C]0.17134[/C][C]1.9536[/C][C]0.026449[/C][/ROW]
[ROW][C]15[/C][C]0.267932[/C][C]3.0549[/C][C]0.001366[/C][/ROW]
[ROW][C]16[/C][C]0.134786[/C][C]1.5368[/C][C]0.063387[/C][/ROW]
[ROW][C]17[/C][C]0.105626[/C][C]1.2043[/C][C]0.115327[/C][/ROW]
[ROW][C]18[/C][C]0.120606[/C][C]1.3751[/C][C]0.08573[/C][/ROW]
[ROW][C]19[/C][C]0.055943[/C][C]0.6379[/C][C]0.262346[/C][/ROW]
[ROW][C]20[/C][C]0.114911[/C][C]1.3102[/C][C]0.096221[/C][/ROW]
[ROW][C]21[/C][C]0.245389[/C][C]2.7979[/C][C]0.002964[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230381&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230381&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
10.4388185.00331e-06
20.386974.41211.1e-05
30.2888223.29310.000638
40.2668263.04230.001421
50.2206282.51550.006551
60.1900412.16680.016037
70.1639921.86980.031881
80.1470761.67690.047981
90.1637111.86660.032105
100.3285983.74660.000134
110.3670374.18492.6e-05
120.3379163.85289.1e-05
130.2868013.270.000688
140.171341.95360.026449
150.2679323.05490.001366
160.1347861.53680.063387
170.1056261.20430.115327
180.1206061.37510.08573
190.0559430.63790.262346
200.1149111.31020.096221
210.2453892.79790.002964






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.4388185.00331e-06
20.2407722.74520.003452
30.0713130.81310.208826
40.0796670.90830.18269
50.0363460.41440.33963
60.0209460.23880.405812
70.0171330.19530.422713
80.0175910.20060.420675
90.0575420.65610.256466
100.2668213.04220.001421
110.191462.1830.015417
120.0588530.6710.251696
13-0.005855-0.06680.473437
14-0.142173-1.6210.053718
150.1074941.22560.111278
16-0.093163-1.06220.145051
17-0.066559-0.75890.224646
180.0718270.81890.207157
19-0.040469-0.46140.322635
200.0403660.46020.323056
210.16341.86310.032356

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.438818 & 5.0033 & 1e-06 \tabularnewline
2 & 0.240772 & 2.7452 & 0.003452 \tabularnewline
3 & 0.071313 & 0.8131 & 0.208826 \tabularnewline
4 & 0.079667 & 0.9083 & 0.18269 \tabularnewline
5 & 0.036346 & 0.4144 & 0.33963 \tabularnewline
6 & 0.020946 & 0.2388 & 0.405812 \tabularnewline
7 & 0.017133 & 0.1953 & 0.422713 \tabularnewline
8 & 0.017591 & 0.2006 & 0.420675 \tabularnewline
9 & 0.057542 & 0.6561 & 0.256466 \tabularnewline
10 & 0.266821 & 3.0422 & 0.001421 \tabularnewline
11 & 0.19146 & 2.183 & 0.015417 \tabularnewline
12 & 0.058853 & 0.671 & 0.251696 \tabularnewline
13 & -0.005855 & -0.0668 & 0.473437 \tabularnewline
14 & -0.142173 & -1.621 & 0.053718 \tabularnewline
15 & 0.107494 & 1.2256 & 0.111278 \tabularnewline
16 & -0.093163 & -1.0622 & 0.145051 \tabularnewline
17 & -0.066559 & -0.7589 & 0.224646 \tabularnewline
18 & 0.071827 & 0.8189 & 0.207157 \tabularnewline
19 & -0.040469 & -0.4614 & 0.322635 \tabularnewline
20 & 0.040366 & 0.4602 & 0.323056 \tabularnewline
21 & 0.1634 & 1.8631 & 0.032356 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230381&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]0.438818[/C][C]5.0033[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.240772[/C][C]2.7452[/C][C]0.003452[/C][/ROW]
[ROW][C]3[/C][C]0.071313[/C][C]0.8131[/C][C]0.208826[/C][/ROW]
[ROW][C]4[/C][C]0.079667[/C][C]0.9083[/C][C]0.18269[/C][/ROW]
[ROW][C]5[/C][C]0.036346[/C][C]0.4144[/C][C]0.33963[/C][/ROW]
[ROW][C]6[/C][C]0.020946[/C][C]0.2388[/C][C]0.405812[/C][/ROW]
[ROW][C]7[/C][C]0.017133[/C][C]0.1953[/C][C]0.422713[/C][/ROW]
[ROW][C]8[/C][C]0.017591[/C][C]0.2006[/C][C]0.420675[/C][/ROW]
[ROW][C]9[/C][C]0.057542[/C][C]0.6561[/C][C]0.256466[/C][/ROW]
[ROW][C]10[/C][C]0.266821[/C][C]3.0422[/C][C]0.001421[/C][/ROW]
[ROW][C]11[/C][C]0.19146[/C][C]2.183[/C][C]0.015417[/C][/ROW]
[ROW][C]12[/C][C]0.058853[/C][C]0.671[/C][C]0.251696[/C][/ROW]
[ROW][C]13[/C][C]-0.005855[/C][C]-0.0668[/C][C]0.473437[/C][/ROW]
[ROW][C]14[/C][C]-0.142173[/C][C]-1.621[/C][C]0.053718[/C][/ROW]
[ROW][C]15[/C][C]0.107494[/C][C]1.2256[/C][C]0.111278[/C][/ROW]
[ROW][C]16[/C][C]-0.093163[/C][C]-1.0622[/C][C]0.145051[/C][/ROW]
[ROW][C]17[/C][C]-0.066559[/C][C]-0.7589[/C][C]0.224646[/C][/ROW]
[ROW][C]18[/C][C]0.071827[/C][C]0.8189[/C][C]0.207157[/C][/ROW]
[ROW][C]19[/C][C]-0.040469[/C][C]-0.4614[/C][C]0.322635[/C][/ROW]
[ROW][C]20[/C][C]0.040366[/C][C]0.4602[/C][C]0.323056[/C][/ROW]
[ROW][C]21[/C][C]0.1634[/C][C]1.8631[/C][C]0.032356[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230381&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230381&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
10.4388185.00331e-06
20.2407722.74520.003452
30.0713130.81310.208826
40.0796670.90830.18269
50.0363460.41440.33963
60.0209460.23880.405812
70.0171330.19530.422713
80.0175910.20060.420675
90.0575420.65610.256466
100.2668213.04220.001421
110.191462.1830.015417
120.0588530.6710.251696
13-0.005855-0.06680.473437
14-0.142173-1.6210.053718
150.1074941.22560.111278
16-0.093163-1.06220.145051
17-0.066559-0.75890.224646
180.0718270.81890.207157
19-0.040469-0.46140.322635
200.0403660.46020.323056
210.16341.86310.032356


Figures (Output of Computation)

Input Parameters & R Code

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