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POManual Maximum-Likelihood Estimation of an AR-Model in R
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copied!<p>I am trying to estimate a simple AR(1) model in R of the form <b>y[t] = alpha + beta * y[t-1] + u[t] </b> with u[t] being normally distributed with mean zero and standard deviation sigma.</p> <p>I have simulated an AR(1) model with <b>alpha = 10</b> and <b>beta = 0.1</b>:</p> <pre><code>library(stats) data<-arima.sim(n=1000,list(ar=0.1),mean=10) </code></pre> <p>First check: OLS yields the following results:</p> <pre><code>lm(data~c(NA,data[1:length(data)-1])) Call: lm(formula = data ~ c(NA, data[1:length(data) - 1])) Coefficients: (Intercept) c(NA, data[1:length(data) - 1]) 10.02253 0.09669 </code></pre> <p>But my goal is to estimate the coefficients with ML. My negative log-likelihood function is:</p> <pre><code>logl<-function(sigma,alpha,beta){ -sum(log((1/(sqrt(2*pi)*sigma)) * exp(-((data-alpha-beta*c(NA,data[1:length(data)-1]))^2)/(2*sigma^2)))) } </code></pre> <p>that is, the sum of all log-single observation normal distributions, that are transformed by u[t] = y[t] - alpha - beta*y[t-1]. The lag has been created (just like in the OLS estimation above) by c(NA,data[1:length(data)-1]).</p> <p>When I try to put it at work I get the following error:</p> <pre><code>library(stats4) mle(logl,start=list(sigma=1,alpha=5,beta=0.05),method="L-BFGS-B") Error in optim(start, f, method = method, hessian = TRUE, ...) : L-BFGS-B needs finite values of 'fn' </code></pre> <p>My log-likelihood function must be correct, when I try to estimate a linear model of the form <b>y[t] = alpha + beta * x[t] + u[t]</b> it works perfectly.</p> <p>I just do not see how my initial values lead to a non-finite result? Trying any other initial values does not solve the problem.</p> <p>Any help is highly appreciated!</p>

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