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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 06 Sep 2018 13:45:36 +0200

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2018/Sep/06/t1536234377qbgm8b5bfn66gpn.htm/, Retrieved Thu, 02 May 2024 01:25:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=315392, Retrieved Thu, 02 May 2024 01:25:55 +0000

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [] [2018-09-06 11:45:36] [a0c5ecdf8f2a1a070f47cb7d81822904] [Current]

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0.0976999042077651
0.0888998338005906
0.0964998334679063
0.0894998341831167
0.0853998438657789
0.0842998482610295
0.0836998497391663
0.0861998477733592
0.0906998413388313
0.0956998327961495
0.095599828849401
0.0969998524271482
-0.357053321260274
-1.64125592174998
-5.65398562941077
-3.57369093017378
3.08909186160842
-1.14294096349874
0.602499286559887
0.166822064597347
-2.02531351834469
-1.51546107389643
0.0724805852747878
-2.12205929540466
2.19628766173121
-0.0605079650571812
3.64463341109045
4.3312299372585
2.20072805798757
2.74253723998927
2.80660340500022
2.42310540764882
-1.664502969128
1.80722045286534
-0.0879161686365307
-0.790544927696883
3.70734995450548
2.45145951417313
0.471526918886696
3.41122052361345
0.187591405261646
1.87810105953099
4.50494118727212
1.9031677843587
1.52467514737968
1.72575668554543
-3.58861424781686
6.96148170420439
1.69928770794081
3.04405183004109
2.48606121085736
-0.807396900146041
1.53657589478381
-1.38161897704946
2.77598793097358
-5.93296184347235
-0.263889052860067
-3.02535674547065
4.0012575934818
4.32801939555623
-2.04085540667922
6.68357991579588
-2.06004642382633
3.522754668406
-3.36850476440946
-0.711479229976281
-1.61039660855169
-1.94921198196442
-1.21319020567838
-2.44756150052018
-1.41356427888564
5.47243063881544
1.89600852094512
3.88035094112904
0.922325836564759
-3.08706584611076
1.06860614455855
0.881413679492219
-1.57557832654175
0.527939913027753
-3.86831652628551
1.40765149496435
-1.40354501070749
-1.55576677799834
0.914900847927305
2.99711419297897
1.32395378714095
2.39203609300244
-0.726259896583282
2.29567767446795
-2.53527156152751
3.74269940625232
-1.86879168954026
4.51712030941218
4.45668746161051
1.59689203792215
3.26315868802412
-0.543077103435425
-3.46548932688626
0.0598501475597718
-3.52257936759703
0.879330630495331
0.808267955488759
-0.891900331296483
0.443994317595385
0.141298011897711
-2.80826062918138
5.52761466380316
2.17891836739269
0.581613942878553
2.24179847901961
-2.07361858024247
4.4969886566

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	Big 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 time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315392&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]

3 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=315392&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315392&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 Output	view raw output of R engine
Computing time	3 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.095085	-0.9556	0.170779
2	0.234353	2.3552	0.010222
3	0.053786	0.5405	0.295008
4	-0.145984	-1.4671	0.072724
5	0.178012	1.789	0.038307
6	-0.100236	-1.0074	0.158086
7	-0.037844	-0.3803	0.352251
8	0.018186	0.1828	0.427675
9	0.025347	0.2547	0.399722
10	-0.086482	-0.8691	0.193417
11	0.030311	0.3046	0.380642
12	-0.401688	-4.0369	5.3e-05
13	0.021959	0.2207	0.412891
14	-0.019437	-0.1953	0.422762
15	0.056661	0.5694	0.285161
16	0.057921	0.5821	0.280899
17	-0.040302	-0.405	0.343156
18	0.141562	1.4227	0.078955
19	-0.107459	-1.0799	0.141369
20	0.086938	0.8737	0.192173

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.095085 & -0.9556 & 0.170779 \tabularnewline
2 & 0.234353 & 2.3552 & 0.010222 \tabularnewline
3 & 0.053786 & 0.5405 & 0.295008 \tabularnewline
4 & -0.145984 & -1.4671 & 0.072724 \tabularnewline
5 & 0.178012 & 1.789 & 0.038307 \tabularnewline
6 & -0.100236 & -1.0074 & 0.158086 \tabularnewline
7 & -0.037844 & -0.3803 & 0.352251 \tabularnewline
8 & 0.018186 & 0.1828 & 0.427675 \tabularnewline
9 & 0.025347 & 0.2547 & 0.399722 \tabularnewline
10 & -0.086482 & -0.8691 & 0.193417 \tabularnewline
11 & 0.030311 & 0.3046 & 0.380642 \tabularnewline
12 & -0.401688 & -4.0369 & 5.3e-05 \tabularnewline
13 & 0.021959 & 0.2207 & 0.412891 \tabularnewline
14 & -0.019437 & -0.1953 & 0.422762 \tabularnewline
15 & 0.056661 & 0.5694 & 0.285161 \tabularnewline
16 & 0.057921 & 0.5821 & 0.280899 \tabularnewline
17 & -0.040302 & -0.405 & 0.343156 \tabularnewline
18 & 0.141562 & 1.4227 & 0.078955 \tabularnewline
19 & -0.107459 & -1.0799 & 0.141369 \tabularnewline
20 & 0.086938 & 0.8737 & 0.192173 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315392&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]-0.095085[/C][C]-0.9556[/C][C]0.170779[/C][/ROW]
[ROW][C]2[/C][C]0.234353[/C][C]2.3552[/C][C]0.010222[/C][/ROW]
[ROW][C]3[/C][C]0.053786[/C][C]0.5405[/C][C]0.295008[/C][/ROW]
[ROW][C]4[/C][C]-0.145984[/C][C]-1.4671[/C][C]0.072724[/C][/ROW]
[ROW][C]5[/C][C]0.178012[/C][C]1.789[/C][C]0.038307[/C][/ROW]
[ROW][C]6[/C][C]-0.100236[/C][C]-1.0074[/C][C]0.158086[/C][/ROW]
[ROW][C]7[/C][C]-0.037844[/C][C]-0.3803[/C][C]0.352251[/C][/ROW]
[ROW][C]8[/C][C]0.018186[/C][C]0.1828[/C][C]0.427675[/C][/ROW]
[ROW][C]9[/C][C]0.025347[/C][C]0.2547[/C][C]0.399722[/C][/ROW]
[ROW][C]10[/C][C]-0.086482[/C][C]-0.8691[/C][C]0.193417[/C][/ROW]
[ROW][C]11[/C][C]0.030311[/C][C]0.3046[/C][C]0.380642[/C][/ROW]
[ROW][C]12[/C][C]-0.401688[/C][C]-4.0369[/C][C]5.3e-05[/C][/ROW]
[ROW][C]13[/C][C]0.021959[/C][C]0.2207[/C][C]0.412891[/C][/ROW]
[ROW][C]14[/C][C]-0.019437[/C][C]-0.1953[/C][C]0.422762[/C][/ROW]
[ROW][C]15[/C][C]0.056661[/C][C]0.5694[/C][C]0.285161[/C][/ROW]
[ROW][C]16[/C][C]0.057921[/C][C]0.5821[/C][C]0.280899[/C][/ROW]
[ROW][C]17[/C][C]-0.040302[/C][C]-0.405[/C][C]0.343156[/C][/ROW]
[ROW][C]18[/C][C]0.141562[/C][C]1.4227[/C][C]0.078955[/C][/ROW]
[ROW][C]19[/C][C]-0.107459[/C][C]-1.0799[/C][C]0.141369[/C][/ROW]
[ROW][C]20[/C][C]0.086938[/C][C]0.8737[/C][C]0.192173[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315392&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315392&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 k	ACF(k)	T-STAT	P-value
1	-0.095085	-0.9556	0.170779
2	0.234353	2.3552	0.010222
3	0.053786	0.5405	0.295008
4	-0.145984	-1.4671	0.072724
5	0.178012	1.789	0.038307
6	-0.100236	-1.0074	0.158086
7	-0.037844	-0.3803	0.352251
8	0.018186	0.1828	0.427675
9	0.025347	0.2547	0.399722
10	-0.086482	-0.8691	0.193417
11	0.030311	0.3046	0.380642
12	-0.401688	-4.0369	5.3e-05
13	0.021959	0.2207	0.412891
14	-0.019437	-0.1953	0.422762
15	0.056661	0.5694	0.285161
16	0.057921	0.5821	0.280899
17	-0.040302	-0.405	0.343156
18	0.141562	1.4227	0.078955
19	-0.107459	-1.0799	0.141369
20	0.086938	0.8737	0.192173

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.095085	-0.9556	0.170779
2	0.227368	2.285	0.012201
3	0.098562	0.9905	0.162139
4	-0.200341	-2.0134	0.023367
5	0.127741	1.2838	0.101078
6	0.003273	0.0329	0.486912
7	-0.118862	-1.1945	0.117531
8	-0.00583	-0.0586	0.476697
9	0.142582	1.4329	0.077483
10	-0.145051	-1.4577	0.074007
11	-0.037497	-0.3768	0.353543
12	-0.368516	-3.7035	0.000173
13	-0.003479	-0.035	0.48609
14	0.158534	1.5932	0.057115
15	0.188239	1.8918	0.030692
16	-0.131457	-1.3211	0.094723
17	0.007223	0.0726	0.471139
18	0.140935	1.4164	0.07987
19	-0.164096	-1.6491	0.051112
20	-0.043038	-0.4325	0.333141

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.095085 & -0.9556 & 0.170779 \tabularnewline
2 & 0.227368 & 2.285 & 0.012201 \tabularnewline
3 & 0.098562 & 0.9905 & 0.162139 \tabularnewline
4 & -0.200341 & -2.0134 & 0.023367 \tabularnewline
5 & 0.127741 & 1.2838 & 0.101078 \tabularnewline
6 & 0.003273 & 0.0329 & 0.486912 \tabularnewline
7 & -0.118862 & -1.1945 & 0.117531 \tabularnewline
8 & -0.00583 & -0.0586 & 0.476697 \tabularnewline
9 & 0.142582 & 1.4329 & 0.077483 \tabularnewline
10 & -0.145051 & -1.4577 & 0.074007 \tabularnewline
11 & -0.037497 & -0.3768 & 0.353543 \tabularnewline
12 & -0.368516 & -3.7035 & 0.000173 \tabularnewline
13 & -0.003479 & -0.035 & 0.48609 \tabularnewline
14 & 0.158534 & 1.5932 & 0.057115 \tabularnewline
15 & 0.188239 & 1.8918 & 0.030692 \tabularnewline
16 & -0.131457 & -1.3211 & 0.094723 \tabularnewline
17 & 0.007223 & 0.0726 & 0.471139 \tabularnewline
18 & 0.140935 & 1.4164 & 0.07987 \tabularnewline
19 & -0.164096 & -1.6491 & 0.051112 \tabularnewline
20 & -0.043038 & -0.4325 & 0.333141 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315392&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]-0.095085[/C][C]-0.9556[/C][C]0.170779[/C][/ROW]
[ROW][C]2[/C][C]0.227368[/C][C]2.285[/C][C]0.012201[/C][/ROW]
[ROW][C]3[/C][C]0.098562[/C][C]0.9905[/C][C]0.162139[/C][/ROW]
[ROW][C]4[/C][C]-0.200341[/C][C]-2.0134[/C][C]0.023367[/C][/ROW]
[ROW][C]5[/C][C]0.127741[/C][C]1.2838[/C][C]0.101078[/C][/ROW]
[ROW][C]6[/C][C]0.003273[/C][C]0.0329[/C][C]0.486912[/C][/ROW]
[ROW][C]7[/C][C]-0.118862[/C][C]-1.1945[/C][C]0.117531[/C][/ROW]
[ROW][C]8[/C][C]-0.00583[/C][C]-0.0586[/C][C]0.476697[/C][/ROW]
[ROW][C]9[/C][C]0.142582[/C][C]1.4329[/C][C]0.077483[/C][/ROW]
[ROW][C]10[/C][C]-0.145051[/C][C]-1.4577[/C][C]0.074007[/C][/ROW]
[ROW][C]11[/C][C]-0.037497[/C][C]-0.3768[/C][C]0.353543[/C][/ROW]
[ROW][C]12[/C][C]-0.368516[/C][C]-3.7035[/C][C]0.000173[/C][/ROW]
[ROW][C]13[/C][C]-0.003479[/C][C]-0.035[/C][C]0.48609[/C][/ROW]
[ROW][C]14[/C][C]0.158534[/C][C]1.5932[/C][C]0.057115[/C][/ROW]
[ROW][C]15[/C][C]0.188239[/C][C]1.8918[/C][C]0.030692[/C][/ROW]
[ROW][C]16[/C][C]-0.131457[/C][C]-1.3211[/C][C]0.094723[/C][/ROW]
[ROW][C]17[/C][C]0.007223[/C][C]0.0726[/C][C]0.471139[/C][/ROW]
[ROW][C]18[/C][C]0.140935[/C][C]1.4164[/C][C]0.07987[/C][/ROW]
[ROW][C]19[/C][C]-0.164096[/C][C]-1.6491[/C][C]0.051112[/C][/ROW]
[ROW][C]20[/C][C]-0.043038[/C][C]-0.4325[/C][C]0.333141[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315392&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315392&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 k	PACF(k)	T-STAT	P-value
1	-0.095085	-0.9556	0.170779
2	0.227368	2.285	0.012201
3	0.098562	0.9905	0.162139
4	-0.200341	-2.0134	0.023367
5	0.127741	1.2838	0.101078
6	0.003273	0.0329	0.486912
7	-0.118862	-1.1945	0.117531
8	-0.00583	-0.0586	0.476697
9	0.142582	1.4329	0.077483
10	-0.145051	-1.4577	0.074007
11	-0.037497	-0.3768	0.353543
12	-0.368516	-3.7035	0.000173
13	-0.003479	-0.035	0.48609
14	0.158534	1.5932	0.057115
15	0.188239	1.8918	0.030692
16	-0.131457	-1.3211	0.094723
17	0.007223	0.0726	0.471139
18	0.140935	1.4164	0.07987
19	-0.164096	-1.6491	0.051112
20	-0.043038	-0.4325	0.333141

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.99 ; par8 = ;

R code (references can be found in the software module):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1'
par1 <- 'Default'
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code