Séries Temporais - Simulando Modelos AR, MA, ARMA no R

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Simulating AR, MA, and ARMA Time Series 
 
R : Copyright 2003, The R Development Core Team 
Version 1.7.1 (2003-06-16) 
 
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You are welcome to redistribute it under certain conditions. 
Type `license()' or `licence()' for distribution details. 
 
R is a collaborative project with many contributors. 
Type `contributors()' for more information. 
 
Type `demo()' for some demos, `help()' for on-line help, or 
`help.start()' for a HTML browser interface to help. 
Type `q()' to quit R. 
 
 
1. Simulate 100 observations from an AR(2) Process 
 
> ar.sim<-arima.sim(model=list(ar=c(.9,-.2)),n=100) 
> ar.sim 
 
Time Series: 
Start = 1 
End = 100 
Frequency = 1 
 [1] -1.8433144709 -0.8242793538 1.7323369494 0.6918267491 
 
 [89] -1.3957581475 -0.7982898404 -0.4325019866 -0.5814940714 
 [97] -0.9410123993 -1.6146934819 -1.8047969752 0.2062163735 
 
 
Make a time series plot of the data 
 
> ts.plot(ar.sim) 
 
Calculate the Sample Autocorrelation Function 
 
> ar.acf<-acf(ar.sim,type="correlation",plot=T) 
> ar.acf 
 
$acf 
, , 1 
 [,1] 
 [1,] 1.000000000 
 [2,] 0.748512403 
 [3,] 0.472943619 
 [4,] 0.343917588 
 [5,] 0.259486147 
 [6,] 0.144046313 
 [7,] 0.054406353 
 [8,] 0.005221371 
 [9,] -0.099083683 
[10,] -0.207233569 
[11,] -0.282578172 
[12,] -0.315600329 
[13,] -0.320707072 
[14,] -0.341260786 
[15,] -0.336039006 
[16,] -0.299153645 
[17,] -0.215101539 
[18,] -0.154908350 
[19,] -0.162841021 
[20,] -0.153521927 
[21,] -0.133979280 
 
 
$type 
[1] "correlation" 
 
$n.used 
[1] 100 
 
$lag 
, , 1 
 [,1] 
 [1,] 0 
 [2,] 1 
 [3,] 2 
 [4,] 3 
 [5,] 4 
 [6,] 5 
 [7,] 6 
 [8,] 7 
 [9,] 8 
[10,] 9 
[11,] 10 
[12,] 11 
[13,] 12 
[14,] 13 
[15,] 14 
[16,] 15 
[17,] 16 
[18,] 17 
[19,] 18 
[20,] 19 
[21,] 20 
 
 
$series 
[1] "ar.sim" 
 
$snames 
NULL 
 
attr(,"class") 
[1] "acf" 
 
 
 
 
 
Calculate the Sample Partial Autocorrelation Function 
 
> ar.pacf<-acf(ar.sim,type="partial",plot=T) 
> ar.pacf 
 
$acf 
, , 1 
 [,1] 
 [1,] 0.748512403 
 [2,] -0.198593141 
 [3,] 0.161605633 
 [4,] -0.045146522 
 [5,] -0.092461467 
 [6,] -0.001441216 
 [7,] -0.026228801 
 [8,] -0.193432432 
 [9,] -0.065314914 
[10,] -0.115355223 
[11,] -0.050063371 
[12,] -0.026196645 
[13,] -0.119366937 
[14,] -0.015351077 
[15,] -0.016780893 
[16,] 0.071314527 
[17,] -0.047199599 
[18,] -0.138808338 
[19,] -0.021273769 
[20,] -0.097357883 
 
$type 
[1] "partial" 
 
$n.used 
[1] 100 
 
 
 
$lag 
, , 1 
 [,1] 
 [1,] 1 
 [2,] 2 
 [3,] 3 
 . 
 : 
 [19,] 19 
 [20,] 20 
 
$series 
[1] "ar.sim" 
 
$snames 
NULL 
 
attr(,"class") 
[1] "acf" 
 
2. Simulate 100 observations from an MA(2) Process 
 
> ma.sim<-arima.sim(model=list(ma=c(-.7,.1)),n=100) 
> ma.sim 
 
Time Series: 
Start = 1 
End = 100 
Frequency = 1 
 [1] -0.87447285 0.63656103 -0.54056772 -0.57388832 -2.15373596 
 [7] -2.97748126 2.43923508 -0.14334954 1.03403360 -1.37024531 
 [97] -0.20538390 1.06791016 -0.94993364 -0.78650534 
 
 
Make a time series plot of the data 
 
> ts.plot(ma.sim) 
 
Calculate the Sample Autocorrelation Function 
 
> ma.acf<-acf(ma.sim,type="correlation",plot=T) 
> ma.acf 
 
$acf 
, , 1 
 [,1] 
 [1,] 1.00000000 
 [2,] -0.46805524 
 [3,] 0.04228515 
 [4,] 0.03384565 
 [5,] -0.03368293 
 [6,] -0.09589762 
 [7,] 0.06240342 
 [8,] 0.14175077 
 [9,] -0.14860861 
[10,] 0.07104588 
[11,] 0.06607164 
[12,] -0.07641769 
[13,] -0.05545542 
[14,] 0.05480033 
[15,] -0.01883246 
[16,] -0.02417799 
[17,] 0.05422257 
[18,] 0.05044019 
[19,] -0.09032521 
[20,] 0.02966781 
21,] 0.01376021 
$type 
[1] "correlation" 
 
$n.used 
[1] 100 
 
 
 
 
$lag 
, , 1 
 [,1] 
 [1,] 0 
 [2,] 1 
 [3,] 2 
 [4,] 3 
 : 
 : 
 [20,] 19 
 [21,] 20 
 
$series 
[1] "ma.sim" 
 
$snames 
NULL 
 
attr(,"class") 
[1] "acf" 
 
Calculate the Sample Partial Autocorrelation Function 
 
> ma.pacf<-acf(ma.sim,type="partial",plot=T) 
> ma.pacf 
 
$acf 
, , 1 
 
 [,1] 
 [1,] -0.468055236 
 [2,] -0.226386291 
 [3,] -0.064574413 
 [4,] -0.044515987 
 [5,] -0.167726138 
 [6,] -0.101464760 
 [7,] 0.160809025 
 [8,] 0.025753880 
 [9,] 0.016403226 
[10,] 0.113118340 
[11,] 0.070886919 
[12,] -0.046819468 
[13,] -0.055640224 
[14,] -0.038556585 
[15,] -0.022126555 
[16,] -0.017238550 
[17,] 0.055662118 
[18,] 0.003943671 
[19,] 0.002336962 
[20,] 0.012238024 
 
$type 
[1] "partial" 
 
$n.used 
[1] 100 
$lag 
, , 1 
 
 [,1] 
 [1,] 1 
 [2,] 2 
 [3,] 3 
 [4,] 4 
 [5,] 5 
 : 
 : 
 [19,] 19 
 [20,] 20 
 
$series 
[1] "ma.sim" 
 
$snames 
NULL 
 
attr(,"class") 
[1] "acf" 
 
3. Simulate 100 observations from an ARMA(2,2) Process 
 
> arma.sim<-arima.sim(model=list(ar=c(.9,-.2),ma=c(-.7,.1)),n=100) 
> arma.sim 
 
Time Series: 
Start = 1 
End = 100 
Frequency = 1 
 [1] 0.1483409916 0.0854933511 -0.0434418077 -1.2835971342 - 
 [6] -1.8957362452 0.3333418141 0.9664180374 0.9278551531 - 
 
 [96] -1.7813203295 1.1258970748 0.0996796875 -0.1425092157 
 
 
Make a time series plot of the data 
 
> ts.plot(arma.sim) 
 
Calculate the Sample Autocorrelation Function 
 
> arma.acf<-acf(arma.sim,type="correlation",plot=T) 
> arma.acf 
 
$acf 
, , 1 
 
 [,1] 
 [1,] 1.000000000 
 [2,] 0.315245096 
 [3,] -0.059896299 
 [4,] -0.237902709 
 [5,] -0.092537118 
 [6,] -0.103890952 
 [7,] -0.028736539 
 [8,] -0.002451483 
 [9,] 0.014186051 
[10,] 0.037810416 
[11,] 0.015967242 
[12,] 0.060710828 
[13,] -0.177129949 
[14,] -0.269788989 
[15,] -0.160815161 
[16,] 0.089192658 
[17,] 0.178159031 
[18,] 0.092086805 
[19,] 0.026411807 
[20,] 0.032653798 
[21,] -0.036084767 
 
 
$type 
[1] "correlation" 
 
$n.used 
[1] 100 
 
$lag 
, , 1 
 
 [,1] 
 [1,] 0 
 [2,] 1 
 [3,] 2 
 [4,] 3 
 [5,] 4 
 [6,] 5 
 [7,] 6 
 [8,] 7 
 [9,] 8 
[10,] 9 
[11,] 10 
[12,] 11 
[13,] 12 
[14,] 13 
[15,] 14 
[16,] 15 
[17,] 16 
[18,] 17 
[19,] 18 
[20,] 19 
[21,] 20 
 
$series 
[1] "arma.sim" 
 
$snames 
NULL 
 
attr(,"class") 
 Calculate the Sample Partial Autocorrelation Function 
 
[1] "acf" 
> arma.pacf<-acf(arma.sim,type="partial",plot=T) 
> arma.pacf 
$acf 
, , 1 
 [,1] 
 [1,] 0.31524510 
 [2,] -0.17685114 
 [3,] -0.18331078 
 [4,] 0.04658796 
 [5,] -0.14628277 
 [6,] -0.00399760 
 [7,] -0.01257163 
 [8,] -0.04032162 
 [9,] 0.04088976 
[10,] -0.02888498 
[11,] 0.07058412 
[12,] -0.25198075 
[13,] -0.16572419 
[14,] -0.01731102 
[15,] 0.02316375 
[16,] 0.06311867 
[17,] -0.05903080 
[18,] 0.01426275 
[19,] 0.05546888 
[20,] -0.08827248 
 
$type 
[1] "partial" 
 
$n.used 
[1] 100 
 
$lag 
, , 1 
 
 [,1] 
 [1,] 1 
 [2,] 2 
 [3,] 3 
 [4,] 4 
 [5,] 5 
 : 
 : 
 [19,] 19 
 [20,] 20 
 
$series 
[1] "arma.sim" 
 
$snames 
NULL 
 
attr(,"class")