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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 computationMon, 19 Dec 2016 11:57:21 +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/2016/Dec/19/t1482145398qvgeg22mofsngm2.htm/, Retrieved Fri, 17 May 2024 18:50:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301291, Retrieved Fri, 17 May 2024 18:50:43 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact111
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [Auto correlation] [2016-12-19 10:57:21] [63af9ed1c5670c0e3049894fd77d93e0] [Current]
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Dataseries X:
5610
3530
2370
11610
4630
8760
4130
5400
5630
7050
5620
5510
4240
3620
4220
3480
3400
4830
3060
8030
8480
7270
10030
7810
6470
5150
4580
2640
2180
6250
4310
6160
8560
6250
8940
8040
6290
2630
4760
3820
2350
2420
4780
6120
4290
5540
6120
5110
4800
2670
5120
2370
3280
4090
2250
2520
3670
6440
5490
2000
2130
1210
6770
2380
2380
3760
3860
4590
4580
8030
5880
1770
5440
4090
3360
1240
1890
3390
2980
5030
3720
3530
1620
2290
2050
2070
2760
1500
1850
2760
3360
2120
3970
3760
3630
1850
3160
2700
1080
1150
1230
2180
2310
2940
4370
4750
7810
2880




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=301291&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=301291&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301291&T=0

As an alternative you can also use a 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
10.4517444.69474e-06
20.417544.33921.6e-05
30.2858192.97030.001833
40.1882611.95650.026496
50.1004751.04420.149371
6-0.019046-0.19790.421734
70.0577420.60010.274858
80.0371310.38590.350173
90.1402841.45790.073889
100.2968523.0850.001293
110.3355543.48720.000354
120.4441564.61585e-06
130.2812062.92240.002116
140.3019933.13840.001095
150.1906941.98170.025024
160.167471.74040.042319
170.0833640.86630.194112
18-0.06413-0.66650.253269
190.0579740.60250.274057
200.0304850.31680.375998

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.451744 & 4.6947 & 4e-06 \tabularnewline
2 & 0.41754 & 4.3392 & 1.6e-05 \tabularnewline
3 & 0.285819 & 2.9703 & 0.001833 \tabularnewline
4 & 0.188261 & 1.9565 & 0.026496 \tabularnewline
5 & 0.100475 & 1.0442 & 0.149371 \tabularnewline
6 & -0.019046 & -0.1979 & 0.421734 \tabularnewline
7 & 0.057742 & 0.6001 & 0.274858 \tabularnewline
8 & 0.037131 & 0.3859 & 0.350173 \tabularnewline
9 & 0.140284 & 1.4579 & 0.073889 \tabularnewline
10 & 0.296852 & 3.085 & 0.001293 \tabularnewline
11 & 0.335554 & 3.4872 & 0.000354 \tabularnewline
12 & 0.444156 & 4.6158 & 5e-06 \tabularnewline
13 & 0.281206 & 2.9224 & 0.002116 \tabularnewline
14 & 0.301993 & 3.1384 & 0.001095 \tabularnewline
15 & 0.190694 & 1.9817 & 0.025024 \tabularnewline
16 & 0.16747 & 1.7404 & 0.042319 \tabularnewline
17 & 0.083364 & 0.8663 & 0.194112 \tabularnewline
18 & -0.06413 & -0.6665 & 0.253269 \tabularnewline
19 & 0.057974 & 0.6025 & 0.274057 \tabularnewline
20 & 0.030485 & 0.3168 & 0.375998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301291&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]0.451744[/C][C]4.6947[/C][C]4e-06[/C][/ROW]
[ROW][C]2[/C][C]0.41754[/C][C]4.3392[/C][C]1.6e-05[/C][/ROW]
[ROW][C]3[/C][C]0.285819[/C][C]2.9703[/C][C]0.001833[/C][/ROW]
[ROW][C]4[/C][C]0.188261[/C][C]1.9565[/C][C]0.026496[/C][/ROW]
[ROW][C]5[/C][C]0.100475[/C][C]1.0442[/C][C]0.149371[/C][/ROW]
[ROW][C]6[/C][C]-0.019046[/C][C]-0.1979[/C][C]0.421734[/C][/ROW]
[ROW][C]7[/C][C]0.057742[/C][C]0.6001[/C][C]0.274858[/C][/ROW]
[ROW][C]8[/C][C]0.037131[/C][C]0.3859[/C][C]0.350173[/C][/ROW]
[ROW][C]9[/C][C]0.140284[/C][C]1.4579[/C][C]0.073889[/C][/ROW]
[ROW][C]10[/C][C]0.296852[/C][C]3.085[/C][C]0.001293[/C][/ROW]
[ROW][C]11[/C][C]0.335554[/C][C]3.4872[/C][C]0.000354[/C][/ROW]
[ROW][C]12[/C][C]0.444156[/C][C]4.6158[/C][C]5e-06[/C][/ROW]
[ROW][C]13[/C][C]0.281206[/C][C]2.9224[/C][C]0.002116[/C][/ROW]
[ROW][C]14[/C][C]0.301993[/C][C]3.1384[/C][C]0.001095[/C][/ROW]
[ROW][C]15[/C][C]0.190694[/C][C]1.9817[/C][C]0.025024[/C][/ROW]
[ROW][C]16[/C][C]0.16747[/C][C]1.7404[/C][C]0.042319[/C][/ROW]
[ROW][C]17[/C][C]0.083364[/C][C]0.8663[/C][C]0.194112[/C][/ROW]
[ROW][C]18[/C][C]-0.06413[/C][C]-0.6665[/C][C]0.253269[/C][/ROW]
[ROW][C]19[/C][C]0.057974[/C][C]0.6025[/C][C]0.274057[/C][/ROW]
[ROW][C]20[/C][C]0.030485[/C][C]0.3168[/C][C]0.375998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301291&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301291&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.4517444.69474e-06
20.417544.33921.6e-05
30.2858192.97030.001833
40.1882611.95650.026496
50.1004751.04420.149371
6-0.019046-0.19790.421734
70.0577420.60010.274858
80.0371310.38590.350173
90.1402841.45790.073889
100.2968523.0850.001293
110.3355543.48720.000354
120.4441564.61585e-06
130.2812062.92240.002116
140.3019933.13840.001095
150.1906941.98170.025024
160.167471.74040.042319
170.0833640.86630.194112
18-0.06413-0.66650.253269
190.0579740.60250.274057
200.0304850.31680.375998







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.4517444.69474e-06
20.2681992.78720.003141
30.0360490.37460.354333
4-0.03627-0.37690.353484
5-0.05378-0.55890.288694
6-0.118723-1.23380.109976
70.1111191.15480.125365
80.0593150.61640.269456
90.1485581.54390.062773
100.2733022.84020.002694
110.1433211.48940.069643
120.1837481.90960.029421
13-0.128474-1.33510.092319
14-0.02881-0.29940.382603
15-0.046496-0.48320.314967
160.0764970.7950.214184
170.0247740.25750.398658
18-0.123138-1.27970.101698
190.0936160.97290.166392
200.0153860.15990.436632

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.451744 & 4.6947 & 4e-06 \tabularnewline
2 & 0.268199 & 2.7872 & 0.003141 \tabularnewline
3 & 0.036049 & 0.3746 & 0.354333 \tabularnewline
4 & -0.03627 & -0.3769 & 0.353484 \tabularnewline
5 & -0.05378 & -0.5589 & 0.288694 \tabularnewline
6 & -0.118723 & -1.2338 & 0.109976 \tabularnewline
7 & 0.111119 & 1.1548 & 0.125365 \tabularnewline
8 & 0.059315 & 0.6164 & 0.269456 \tabularnewline
9 & 0.148558 & 1.5439 & 0.062773 \tabularnewline
10 & 0.273302 & 2.8402 & 0.002694 \tabularnewline
11 & 0.143321 & 1.4894 & 0.069643 \tabularnewline
12 & 0.183748 & 1.9096 & 0.029421 \tabularnewline
13 & -0.128474 & -1.3351 & 0.092319 \tabularnewline
14 & -0.02881 & -0.2994 & 0.382603 \tabularnewline
15 & -0.046496 & -0.4832 & 0.314967 \tabularnewline
16 & 0.076497 & 0.795 & 0.214184 \tabularnewline
17 & 0.024774 & 0.2575 & 0.398658 \tabularnewline
18 & -0.123138 & -1.2797 & 0.101698 \tabularnewline
19 & 0.093616 & 0.9729 & 0.166392 \tabularnewline
20 & 0.015386 & 0.1599 & 0.436632 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301291&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]0.451744[/C][C]4.6947[/C][C]4e-06[/C][/ROW]
[ROW][C]2[/C][C]0.268199[/C][C]2.7872[/C][C]0.003141[/C][/ROW]
[ROW][C]3[/C][C]0.036049[/C][C]0.3746[/C][C]0.354333[/C][/ROW]
[ROW][C]4[/C][C]-0.03627[/C][C]-0.3769[/C][C]0.353484[/C][/ROW]
[ROW][C]5[/C][C]-0.05378[/C][C]-0.5589[/C][C]0.288694[/C][/ROW]
[ROW][C]6[/C][C]-0.118723[/C][C]-1.2338[/C][C]0.109976[/C][/ROW]
[ROW][C]7[/C][C]0.111119[/C][C]1.1548[/C][C]0.125365[/C][/ROW]
[ROW][C]8[/C][C]0.059315[/C][C]0.6164[/C][C]0.269456[/C][/ROW]
[ROW][C]9[/C][C]0.148558[/C][C]1.5439[/C][C]0.062773[/C][/ROW]
[ROW][C]10[/C][C]0.273302[/C][C]2.8402[/C][C]0.002694[/C][/ROW]
[ROW][C]11[/C][C]0.143321[/C][C]1.4894[/C][C]0.069643[/C][/ROW]
[ROW][C]12[/C][C]0.183748[/C][C]1.9096[/C][C]0.029421[/C][/ROW]
[ROW][C]13[/C][C]-0.128474[/C][C]-1.3351[/C][C]0.092319[/C][/ROW]
[ROW][C]14[/C][C]-0.02881[/C][C]-0.2994[/C][C]0.382603[/C][/ROW]
[ROW][C]15[/C][C]-0.046496[/C][C]-0.4832[/C][C]0.314967[/C][/ROW]
[ROW][C]16[/C][C]0.076497[/C][C]0.795[/C][C]0.214184[/C][/ROW]
[ROW][C]17[/C][C]0.024774[/C][C]0.2575[/C][C]0.398658[/C][/ROW]
[ROW][C]18[/C][C]-0.123138[/C][C]-1.2797[/C][C]0.101698[/C][/ROW]
[ROW][C]19[/C][C]0.093616[/C][C]0.9729[/C][C]0.166392[/C][/ROW]
[ROW][C]20[/C][C]0.015386[/C][C]0.1599[/C][C]0.436632[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301291&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301291&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.4517444.69474e-06
20.2681992.78720.003141
30.0360490.37460.354333
4-0.03627-0.37690.353484
5-0.05378-0.55890.288694
6-0.118723-1.23380.109976
70.1111191.15480.125365
80.0593150.61640.269456
90.1485581.54390.062773
100.2733022.84020.002694
110.1433211.48940.069643
120.1837481.90960.029421
13-0.128474-1.33510.092319
14-0.02881-0.29940.382603
15-0.046496-0.48320.314967
160.0764970.7950.214184
170.0247740.25750.398658
18-0.123138-1.27970.101698
190.0936160.97290.166392
200.0153860.15990.436632



Parameters (Session):
par1 = 12 ;
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)
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')