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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 computationTue, 20 Jan 2015 10:37:19 +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/20/t142175026544vd02n52cc4k0z.htm/, Retrieved Thu, 31 Oct 2024 23:49:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=275039, Retrieved Thu, 31 Oct 2024 23:49:38 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [] [2015-01-20 10:37:19] [dc060611fd89d91eb1d5c55ae338991b] [Current]
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Dataseries X:
1775
2197
2920
4240
5415
6136
6719
6234
7152
3646
2165
2803
1615
2350
3350
3536
5834
6767
5993
7276
5641
3477
2247
2466
1567
2237
2598
3729
5715
5776
5852
6878
5488
3583
2054
2282
1552
2261
2446
3519
5161
5085
5711
6057
5224
3363
1899
2115
1491
2061
2419
3430
4778
4862
6176
5664
5529
3418
1941
2402
1579
2146
2462
3695
4831
5134
6250
5760
6249
2917
1741
2359
1511
2059
2635
2867
4403
5720
4502
5749
5627
2846
1762
2429
1169
2154
2249
2687
4359
5382
4459
6398
4596
3024
1887
2070
1351
2218
2461
3028
4784
4975
4607
6249
4809
3157
1910
2228
1594
2467
2222
3607
4685
4962
5770
5480
5000
3228
1993
2288
1588
2105
2191
3591
4668
4885
5822
5599
5340
3082
2010
2301




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=275039&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=275039&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=275039&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
1-0.098066-1.07430.142431
20.1368791.49940.068194
30.4265794.67294e-06
4-0.093564-1.02490.153727
50.2040932.23570.013609
60.3541073.8798.6e-05
7-0.251376-2.75370.003405
80.2509332.74880.003453
90.2376832.60370.005193
10-0.19912-2.18130.015557
110.2314442.53530.00626
12-0.092355-1.01170.15686
13-0.180754-1.98010.024993
140.1497981.6410.051712
150.0087440.09580.461927
16-0.223117-2.44410.007987
170.166461.82350.03536
18-0.091117-0.99810.160112
19-0.159771-1.75020.04132
200.1074711.17730.120706
21-0.196621-2.15390.016625

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.098066 & -1.0743 & 0.142431 \tabularnewline
2 & 0.136879 & 1.4994 & 0.068194 \tabularnewline
3 & 0.426579 & 4.6729 & 4e-06 \tabularnewline
4 & -0.093564 & -1.0249 & 0.153727 \tabularnewline
5 & 0.204093 & 2.2357 & 0.013609 \tabularnewline
6 & 0.354107 & 3.879 & 8.6e-05 \tabularnewline
7 & -0.251376 & -2.7537 & 0.003405 \tabularnewline
8 & 0.250933 & 2.7488 & 0.003453 \tabularnewline
9 & 0.237683 & 2.6037 & 0.005193 \tabularnewline
10 & -0.19912 & -2.1813 & 0.015557 \tabularnewline
11 & 0.231444 & 2.5353 & 0.00626 \tabularnewline
12 & -0.092355 & -1.0117 & 0.15686 \tabularnewline
13 & -0.180754 & -1.9801 & 0.024993 \tabularnewline
14 & 0.149798 & 1.641 & 0.051712 \tabularnewline
15 & 0.008744 & 0.0958 & 0.461927 \tabularnewline
16 & -0.223117 & -2.4441 & 0.007987 \tabularnewline
17 & 0.16646 & 1.8235 & 0.03536 \tabularnewline
18 & -0.091117 & -0.9981 & 0.160112 \tabularnewline
19 & -0.159771 & -1.7502 & 0.04132 \tabularnewline
20 & 0.107471 & 1.1773 & 0.120706 \tabularnewline
21 & -0.196621 & -2.1539 & 0.016625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=275039&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]-0.098066[/C][C]-1.0743[/C][C]0.142431[/C][/ROW]
[ROW][C]2[/C][C]0.136879[/C][C]1.4994[/C][C]0.068194[/C][/ROW]
[ROW][C]3[/C][C]0.426579[/C][C]4.6729[/C][C]4e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.093564[/C][C]-1.0249[/C][C]0.153727[/C][/ROW]
[ROW][C]5[/C][C]0.204093[/C][C]2.2357[/C][C]0.013609[/C][/ROW]
[ROW][C]6[/C][C]0.354107[/C][C]3.879[/C][C]8.6e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.251376[/C][C]-2.7537[/C][C]0.003405[/C][/ROW]
[ROW][C]8[/C][C]0.250933[/C][C]2.7488[/C][C]0.003453[/C][/ROW]
[ROW][C]9[/C][C]0.237683[/C][C]2.6037[/C][C]0.005193[/C][/ROW]
[ROW][C]10[/C][C]-0.19912[/C][C]-2.1813[/C][C]0.015557[/C][/ROW]
[ROW][C]11[/C][C]0.231444[/C][C]2.5353[/C][C]0.00626[/C][/ROW]
[ROW][C]12[/C][C]-0.092355[/C][C]-1.0117[/C][C]0.15686[/C][/ROW]
[ROW][C]13[/C][C]-0.180754[/C][C]-1.9801[/C][C]0.024993[/C][/ROW]
[ROW][C]14[/C][C]0.149798[/C][C]1.641[/C][C]0.051712[/C][/ROW]
[ROW][C]15[/C][C]0.008744[/C][C]0.0958[/C][C]0.461927[/C][/ROW]
[ROW][C]16[/C][C]-0.223117[/C][C]-2.4441[/C][C]0.007987[/C][/ROW]
[ROW][C]17[/C][C]0.16646[/C][C]1.8235[/C][C]0.03536[/C][/ROW]
[ROW][C]18[/C][C]-0.091117[/C][C]-0.9981[/C][C]0.160112[/C][/ROW]
[ROW][C]19[/C][C]-0.159771[/C][C]-1.7502[/C][C]0.04132[/C][/ROW]
[ROW][C]20[/C][C]0.107471[/C][C]1.1773[/C][C]0.120706[/C][/ROW]
[ROW][C]21[/C][C]-0.196621[/C][C]-2.1539[/C][C]0.016625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=275039&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=275039&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
1-0.098066-1.07430.142431
20.1368791.49940.068194
30.4265794.67294e-06
4-0.093564-1.02490.153727
50.2040932.23570.013609
60.3541073.8798.6e-05
7-0.251376-2.75370.003405
80.2509332.74880.003453
90.2376832.60370.005193
10-0.19912-2.18130.015557
110.2314442.53530.00626
12-0.092355-1.01170.15686
13-0.180754-1.98010.024993
140.1497981.6410.051712
150.0087440.09580.461927
16-0.223117-2.44410.007987
170.166461.82350.03536
18-0.091117-0.99810.160112
19-0.159771-1.75020.04132
200.1074711.17730.120706
21-0.196621-2.15390.016625







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.098066-1.07430.142431
20.1284971.40760.080915
30.46295.07081e-06
4-0.012206-0.13370.446927
50.0708020.77560.219755
60.2770213.03460.001477
7-0.232951-2.55180.005986
8-0.011344-0.12430.450657
90.1885822.06580.020499
10-0.069737-0.76390.223205
11-0.072968-0.79930.212842
12-0.227535-2.49250.007024
13-0.096247-1.05430.146924
14-0.098806-1.08240.140631
150.2024662.21790.014222
16-0.039816-0.43620.331751
170.0021540.02360.490607
180.0936521.02590.153499
19-0.136876-1.49940.068198
20-0.067187-0.7360.231583
21-0.031735-0.34760.364361

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.098066 & -1.0743 & 0.142431 \tabularnewline
2 & 0.128497 & 1.4076 & 0.080915 \tabularnewline
3 & 0.4629 & 5.0708 & 1e-06 \tabularnewline
4 & -0.012206 & -0.1337 & 0.446927 \tabularnewline
5 & 0.070802 & 0.7756 & 0.219755 \tabularnewline
6 & 0.277021 & 3.0346 & 0.001477 \tabularnewline
7 & -0.232951 & -2.5518 & 0.005986 \tabularnewline
8 & -0.011344 & -0.1243 & 0.450657 \tabularnewline
9 & 0.188582 & 2.0658 & 0.020499 \tabularnewline
10 & -0.069737 & -0.7639 & 0.223205 \tabularnewline
11 & -0.072968 & -0.7993 & 0.212842 \tabularnewline
12 & -0.227535 & -2.4925 & 0.007024 \tabularnewline
13 & -0.096247 & -1.0543 & 0.146924 \tabularnewline
14 & -0.098806 & -1.0824 & 0.140631 \tabularnewline
15 & 0.202466 & 2.2179 & 0.014222 \tabularnewline
16 & -0.039816 & -0.4362 & 0.331751 \tabularnewline
17 & 0.002154 & 0.0236 & 0.490607 \tabularnewline
18 & 0.093652 & 1.0259 & 0.153499 \tabularnewline
19 & -0.136876 & -1.4994 & 0.068198 \tabularnewline
20 & -0.067187 & -0.736 & 0.231583 \tabularnewline
21 & -0.031735 & -0.3476 & 0.364361 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=275039&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]-0.098066[/C][C]-1.0743[/C][C]0.142431[/C][/ROW]
[ROW][C]2[/C][C]0.128497[/C][C]1.4076[/C][C]0.080915[/C][/ROW]
[ROW][C]3[/C][C]0.4629[/C][C]5.0708[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.012206[/C][C]-0.1337[/C][C]0.446927[/C][/ROW]
[ROW][C]5[/C][C]0.070802[/C][C]0.7756[/C][C]0.219755[/C][/ROW]
[ROW][C]6[/C][C]0.277021[/C][C]3.0346[/C][C]0.001477[/C][/ROW]
[ROW][C]7[/C][C]-0.232951[/C][C]-2.5518[/C][C]0.005986[/C][/ROW]
[ROW][C]8[/C][C]-0.011344[/C][C]-0.1243[/C][C]0.450657[/C][/ROW]
[ROW][C]9[/C][C]0.188582[/C][C]2.0658[/C][C]0.020499[/C][/ROW]
[ROW][C]10[/C][C]-0.069737[/C][C]-0.7639[/C][C]0.223205[/C][/ROW]
[ROW][C]11[/C][C]-0.072968[/C][C]-0.7993[/C][C]0.212842[/C][/ROW]
[ROW][C]12[/C][C]-0.227535[/C][C]-2.4925[/C][C]0.007024[/C][/ROW]
[ROW][C]13[/C][C]-0.096247[/C][C]-1.0543[/C][C]0.146924[/C][/ROW]
[ROW][C]14[/C][C]-0.098806[/C][C]-1.0824[/C][C]0.140631[/C][/ROW]
[ROW][C]15[/C][C]0.202466[/C][C]2.2179[/C][C]0.014222[/C][/ROW]
[ROW][C]16[/C][C]-0.039816[/C][C]-0.4362[/C][C]0.331751[/C][/ROW]
[ROW][C]17[/C][C]0.002154[/C][C]0.0236[/C][C]0.490607[/C][/ROW]
[ROW][C]18[/C][C]0.093652[/C][C]1.0259[/C][C]0.153499[/C][/ROW]
[ROW][C]19[/C][C]-0.136876[/C][C]-1.4994[/C][C]0.068198[/C][/ROW]
[ROW][C]20[/C][C]-0.067187[/C][C]-0.736[/C][C]0.231583[/C][/ROW]
[ROW][C]21[/C][C]-0.031735[/C][C]-0.3476[/C][C]0.364361[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=275039&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=275039&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
1-0.098066-1.07430.142431
20.1284971.40760.080915
30.46295.07081e-06
4-0.012206-0.13370.446927
50.0708020.77560.219755
60.2770213.03460.001477
7-0.232951-2.55180.005986
8-0.011344-0.12430.450657
90.1885822.06580.020499
10-0.069737-0.76390.223205
11-0.072968-0.79930.212842
12-0.227535-2.49250.007024
13-0.096247-1.05430.146924
14-0.098806-1.08240.140631
150.2024662.21790.014222
16-0.039816-0.43620.331751
170.0021540.02360.490607
180.0936521.02590.153499
19-0.136876-1.49940.068198
20-0.067187-0.7360.231583
21-0.031735-0.34760.364361



Parameters (Session):
par1 = Default ; par2 = -0.3 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = -0.3 ; par3 = 0 ; 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)
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')