[R] Simulate an AR(1) process via distributions? (without specifying a model specification)

[Matthias Kohl]

Dear Pedro,

you might be interested in the demo "StationaryRegressorDistr" of 
package "distr".

library(distr)
demo("StationaryRegressorDistr")

hth,
Matthias


Pedro.Rodriguez at sungard.com wrote:
> Thanks Prof. Ripley.
>
> My apologies for not including the code.
>
> Below I illustrate my point using the GLD package. 
>
> Thank you very much for your time.
>
> Kind Regards,
>
> Pedro N. Rodriguez 
>
>
> # Code begins
>
> # Simulate an ar(1) process  
> # x = 0.05 + 0.64*x(t-1) + e
>
> # Create the vector x
> 	x	<- vector(length=1000)
>
> #simulate the own risk
> 	e	<- rnorm(1000)
>
> #Set the coefficient
> 	beta 	<- 1.50
>
> # set an initial value
> 	x[1] 	<- 5
>
> #Fill the vector x
> 	for(i in 2:length(x))
> 	{
> 		x[i]	<- 0.05 + beta*x[i-1] + e[i] 
> 	}
>
> #Check the AR(1) 
> 	simulated_data_ar <- arima(x,order=c(1,0,0))
> 	simulated_data_ar
>
> #Using the G Lambda Distribution to fit the distribution. 
> 	library(gld)
> 	resul1		<- starship(x,optim.method="Nelder-Mead") 
> 	lambdas1	<- resul1$lambda
>
> #Plot the Distribution
> 	plotgld(lambdas1[1],lambdas1[2],lambdas1[3],lambdas1[4])
>
> #Random Deviates from GLD
> 	x_sim		<-
> rgl(1000,lambdas1[1],lambdas1[2],lambdas1[3],lambdas1[4])
>
> #Fit an AR(1)
> 	gld_simulated	<- arima(x_sim,order=c(1,0,0))
> 	gld_simulated
>
> #Code ends
>
>
> -----Original Message-----
> From: Prof Brian Ripley [mailto:ripley at stats.ox.ac.uk] 
> Sent: Wednesday, November 28, 2007 11:37 AM
> To: Rodriguez, Pedro
> Cc: r-help at stat.math.ethz.ch
> Subject: Re: [R] Simulate an AR(1) process via distributions? (without
> specifying a model specification)
>
> On Wed, 28 Nov 2007, Pedro.Rodriguez at sungard.com wrote:
>
>   
>> Is it possible to simulate an AR(1) process via a distribution?
>>     
>
> Any distribution *of errors*, yes.  Of the process values, not in
> general.
>
>   
>> I have simulated an AR(1) process the usual way (that is, using a
>>     
> model
>   
>> specification and using the random deviates in the error), and used
>>     
> the
>   
>> generated time series to estimate 3- and 4-parameter distributions
>>     
> (for
>   
>> instance, GLD). However, the random deviates generated from these
>> distributions do not follow the specified AR process.
>>     
>
> How do you know that?  Please give us the reproducible example we asked 
> for (in the posting guide, at the bottom of every message), and we
> should 
> be able to explain it to you.
>
>