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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 computationThu, 22 Dec 2011 17:47:38 -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/2011/Dec/22/t1324594085sw7i6mrgvw3s5tn.htm/, Retrieved Fri, 03 May 2024 06:19:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160048, Retrieved Fri, 03 May 2024 06:19:40 +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] [] [2011-12-22 22:47:38] [c7041fab4904771a5085f5eb0f28763f] [Current]
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Dataseries X:
4581945
3874038
4086290
4364364
3793586
4533914
4823043
3981535
4746356
5284534
4264830
3924674
3734753
3762290
3609739
3877594
3636415
3578195
3604342
3459513
3366571
3371277
3724848
3350830
3305159
3390736
3349758
3253655
3734250
3455433
2966726
2993716
3009320
3169713
3170061
3368934
3292638
3337344
3208306
3359130
3223078
3437159
3400156
3657576
3765613
3481921
3604800
3981340
3734078
4018173
3887417
3919880
4014466
4197758
3896531
3964742
4201847
4050512
3997402
4314479
4925744
5130631
4444855
3967319
3931250
4235952
4169219
3779064
3558810
3699466
3650693
3525633
3470276
3859094
3661155
3356365
3344440
3338684
3404294
3289319
3469252
3571850
3639914
3091730
3078149
3188115
3246082
3486992
3378187
3282306
3288345
3325749
3352262
3531954
3722622
3809365
3750617
3615286
3696556
4123959
4136163
3933392
4035576
4551202
4032195
3970893
4489016
5426127
4578224
4126390
4892100
4128697
4408721
4199465
4074767
4161758
3891319
4470302
4283111
3845962
3911471
3798478
3644313
3784029
3647134
3994662
3607836
3566008
3511412
3258665
3486573
3369443
3465544
3905224
3733881
3220642
3225812
3354461
3352261
3450652




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160048&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160048&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160048&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.7579478.96810
20.626557.41340
30.6501637.69280
40.5771846.82930
50.5225356.18270
60.4819145.70210
70.4349795.14670
80.3730834.41441e-05
90.2861873.38620.00046
100.1917692.2690.012397
110.1060971.25540.10572
120.0554620.65620.256374
130.02380.28160.389329
14-0.076582-0.90610.183211
15-0.145124-1.71710.044084
16-0.202086-2.39110.009063
17-0.260513-3.08240.001237
18-0.311756-3.68880.000161
19-0.357402-4.22882.1e-05
20-0.394787-4.67123e-06
21-0.452679-5.35620

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.757947 & 8.9681 & 0 \tabularnewline
2 & 0.62655 & 7.4134 & 0 \tabularnewline
3 & 0.650163 & 7.6928 & 0 \tabularnewline
4 & 0.577184 & 6.8293 & 0 \tabularnewline
5 & 0.522535 & 6.1827 & 0 \tabularnewline
6 & 0.481914 & 5.7021 & 0 \tabularnewline
7 & 0.434979 & 5.1467 & 0 \tabularnewline
8 & 0.373083 & 4.4144 & 1e-05 \tabularnewline
9 & 0.286187 & 3.3862 & 0.00046 \tabularnewline
10 & 0.191769 & 2.269 & 0.012397 \tabularnewline
11 & 0.106097 & 1.2554 & 0.10572 \tabularnewline
12 & 0.055462 & 0.6562 & 0.256374 \tabularnewline
13 & 0.0238 & 0.2816 & 0.389329 \tabularnewline
14 & -0.076582 & -0.9061 & 0.183211 \tabularnewline
15 & -0.145124 & -1.7171 & 0.044084 \tabularnewline
16 & -0.202086 & -2.3911 & 0.009063 \tabularnewline
17 & -0.260513 & -3.0824 & 0.001237 \tabularnewline
18 & -0.311756 & -3.6888 & 0.000161 \tabularnewline
19 & -0.357402 & -4.2288 & 2.1e-05 \tabularnewline
20 & -0.394787 & -4.6712 & 3e-06 \tabularnewline
21 & -0.452679 & -5.3562 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160048&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]0.757947[/C][C]8.9681[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.62655[/C][C]7.4134[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.650163[/C][C]7.6928[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.577184[/C][C]6.8293[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.522535[/C][C]6.1827[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.481914[/C][C]5.7021[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.434979[/C][C]5.1467[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.373083[/C][C]4.4144[/C][C]1e-05[/C][/ROW]
[ROW][C]9[/C][C]0.286187[/C][C]3.3862[/C][C]0.00046[/C][/ROW]
[ROW][C]10[/C][C]0.191769[/C][C]2.269[/C][C]0.012397[/C][/ROW]
[ROW][C]11[/C][C]0.106097[/C][C]1.2554[/C][C]0.10572[/C][/ROW]
[ROW][C]12[/C][C]0.055462[/C][C]0.6562[/C][C]0.256374[/C][/ROW]
[ROW][C]13[/C][C]0.0238[/C][C]0.2816[/C][C]0.389329[/C][/ROW]
[ROW][C]14[/C][C]-0.076582[/C][C]-0.9061[/C][C]0.183211[/C][/ROW]
[ROW][C]15[/C][C]-0.145124[/C][C]-1.7171[/C][C]0.044084[/C][/ROW]
[ROW][C]16[/C][C]-0.202086[/C][C]-2.3911[/C][C]0.009063[/C][/ROW]
[ROW][C]17[/C][C]-0.260513[/C][C]-3.0824[/C][C]0.001237[/C][/ROW]
[ROW][C]18[/C][C]-0.311756[/C][C]-3.6888[/C][C]0.000161[/C][/ROW]
[ROW][C]19[/C][C]-0.357402[/C][C]-4.2288[/C][C]2.1e-05[/C][/ROW]
[ROW][C]20[/C][C]-0.394787[/C][C]-4.6712[/C][C]3e-06[/C][/ROW]
[ROW][C]21[/C][C]-0.452679[/C][C]-5.3562[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160048&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160048&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
10.7579478.96810
20.626557.41340
30.6501637.69280
40.5771846.82930
50.5225356.18270
60.4819145.70210
70.4349795.14670
80.3730834.41441e-05
90.2861873.38620.00046
100.1917692.2690.012397
110.1060971.25540.10572
120.0554620.65620.256374
130.02380.28160.389329
14-0.076582-0.90610.183211
15-0.145124-1.71710.044084
16-0.202086-2.39110.009063
17-0.260513-3.08240.001237
18-0.311756-3.68880.000161
19-0.357402-4.22882.1e-05
20-0.394787-4.67123e-06
21-0.452679-5.35620







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.7579478.96810
20.1223611.44780.074955
30.3355333.97015.7e-05
4-0.053098-0.62830.265426
50.0816860.96650.167725
6-0.049545-0.58620.279333
70.0170070.20120.420405
8-0.083521-0.98820.162373
9-0.115615-1.3680.086756
10-0.160743-1.90190.029617
11-0.1323-1.56540.059874
12-0.033886-0.40090.344537
130.0210870.24950.401668
14-0.150548-1.78130.038516
15-0.034017-0.40250.343969
16-0.12012-1.42130.078729
176.7e-058e-040.499687
18-0.07047-0.83380.202902
19-0.021976-0.260.397613
20-0.073941-0.87490.19157
21-0.116363-1.37680.085381

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.757947 & 8.9681 & 0 \tabularnewline
2 & 0.122361 & 1.4478 & 0.074955 \tabularnewline
3 & 0.335533 & 3.9701 & 5.7e-05 \tabularnewline
4 & -0.053098 & -0.6283 & 0.265426 \tabularnewline
5 & 0.081686 & 0.9665 & 0.167725 \tabularnewline
6 & -0.049545 & -0.5862 & 0.279333 \tabularnewline
7 & 0.017007 & 0.2012 & 0.420405 \tabularnewline
8 & -0.083521 & -0.9882 & 0.162373 \tabularnewline
9 & -0.115615 & -1.368 & 0.086756 \tabularnewline
10 & -0.160743 & -1.9019 & 0.029617 \tabularnewline
11 & -0.1323 & -1.5654 & 0.059874 \tabularnewline
12 & -0.033886 & -0.4009 & 0.344537 \tabularnewline
13 & 0.021087 & 0.2495 & 0.401668 \tabularnewline
14 & -0.150548 & -1.7813 & 0.038516 \tabularnewline
15 & -0.034017 & -0.4025 & 0.343969 \tabularnewline
16 & -0.12012 & -1.4213 & 0.078729 \tabularnewline
17 & 6.7e-05 & 8e-04 & 0.499687 \tabularnewline
18 & -0.07047 & -0.8338 & 0.202902 \tabularnewline
19 & -0.021976 & -0.26 & 0.397613 \tabularnewline
20 & -0.073941 & -0.8749 & 0.19157 \tabularnewline
21 & -0.116363 & -1.3768 & 0.085381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160048&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]0.757947[/C][C]8.9681[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.122361[/C][C]1.4478[/C][C]0.074955[/C][/ROW]
[ROW][C]3[/C][C]0.335533[/C][C]3.9701[/C][C]5.7e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.053098[/C][C]-0.6283[/C][C]0.265426[/C][/ROW]
[ROW][C]5[/C][C]0.081686[/C][C]0.9665[/C][C]0.167725[/C][/ROW]
[ROW][C]6[/C][C]-0.049545[/C][C]-0.5862[/C][C]0.279333[/C][/ROW]
[ROW][C]7[/C][C]0.017007[/C][C]0.2012[/C][C]0.420405[/C][/ROW]
[ROW][C]8[/C][C]-0.083521[/C][C]-0.9882[/C][C]0.162373[/C][/ROW]
[ROW][C]9[/C][C]-0.115615[/C][C]-1.368[/C][C]0.086756[/C][/ROW]
[ROW][C]10[/C][C]-0.160743[/C][C]-1.9019[/C][C]0.029617[/C][/ROW]
[ROW][C]11[/C][C]-0.1323[/C][C]-1.5654[/C][C]0.059874[/C][/ROW]
[ROW][C]12[/C][C]-0.033886[/C][C]-0.4009[/C][C]0.344537[/C][/ROW]
[ROW][C]13[/C][C]0.021087[/C][C]0.2495[/C][C]0.401668[/C][/ROW]
[ROW][C]14[/C][C]-0.150548[/C][C]-1.7813[/C][C]0.038516[/C][/ROW]
[ROW][C]15[/C][C]-0.034017[/C][C]-0.4025[/C][C]0.343969[/C][/ROW]
[ROW][C]16[/C][C]-0.12012[/C][C]-1.4213[/C][C]0.078729[/C][/ROW]
[ROW][C]17[/C][C]6.7e-05[/C][C]8e-04[/C][C]0.499687[/C][/ROW]
[ROW][C]18[/C][C]-0.07047[/C][C]-0.8338[/C][C]0.202902[/C][/ROW]
[ROW][C]19[/C][C]-0.021976[/C][C]-0.26[/C][C]0.397613[/C][/ROW]
[ROW][C]20[/C][C]-0.073941[/C][C]-0.8749[/C][C]0.19157[/C][/ROW]
[ROW][C]21[/C][C]-0.116363[/C][C]-1.3768[/C][C]0.085381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160048&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160048&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
10.7579478.96810
20.1223611.44780.074955
30.3355333.97015.7e-05
4-0.053098-0.62830.265426
50.0816860.96650.167725
6-0.049545-0.58620.279333
70.0170070.20120.420405
8-0.083521-0.98820.162373
9-0.115615-1.3680.086756
10-0.160743-1.90190.029617
11-0.1323-1.56540.059874
12-0.033886-0.40090.344537
130.0210870.24950.401668
14-0.150548-1.78130.038516
15-0.034017-0.40250.343969
16-0.12012-1.42130.078729
176.7e-058e-040.499687
18-0.07047-0.83380.202902
19-0.021976-0.260.397613
20-0.073941-0.87490.19157
21-0.116363-1.37680.085381



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ; 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')