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Tagged with brownian-motion estimation
4 questions
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Max Likelihood of GBM with 2 Markov States
Consider the stochastic process
$$dX_t = \mu_{\epsilon_t}X_tdt + \sigma_{\epsilon_t}X_tdW_t$$
where $W_t$ is a standard Brownian motion. The process $X_t$ is a geometric Brownian motion (GBM) whose ...
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Estimate parameters in Brownian Motion with drift, $dX_t = \mu dt + \sigma dW_t$
Consider a Brownian Motion with drift, $X$, on the interval $[0; T]$ given by
$$dX_t = \mu dt + \sigma dW_t.$$
Suppose that the interval is split into $n$ pieces of equal size to define $\Delta:=T/n$ ...
- 103
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Sampling distribution of GBM Maximum-Likelihood estimator
Given the geometric Brownian diffusion
$$ X_t = \mu X_t \, dt + \sigma X_t \, d W_t$$
I learnt that its maximum likelihood estimators are the following as this web article suggests
$$\hat \mu = \frac{\...
- 261
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Hurst estimation in small samples
I'm trying to estimate the Hurst exponent of a time series which I believe behaves as a fractional Brownian motion. My problem is that all the estimation methods I have found so far (r/s, Whittle, etc....
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