In a sailboat race, the navigator’s attempts to plot the fastest possible course are hindered by shifty winds. We present mathematical models appropriate for this situation, which use statistical analysis of wind fluctuations and are amenable to stochastic optimization methods. We describe the...

Whether doing parametric or nonparametric regression with shrinkage, thresholding, penalized likelihood, Bayesian posterior estimators (e.g., "ridge regression, lasso, principal component regression, waveshrink" or "Markov random field"), it is common practice to rescale covariates by dividing...

Time series of financial asset values exhibit well known statistical features such as heavy tails and volatility clustering. Strongly present in some series, nonstationarity is a feature that has been somewhat overlooked. This may however be a highly relevant feature when estimating extreme...

We consider the problem of estimating the volatility of a financial asset from a time series record of length T. We believe the underlying volatility process is smooth, possibly stationary, and with potential abrupt changes due to market news. By drawing parallels between time series and...

We consider Taylor's stochastic volatility model when the innovations of the hidden log-volatility process have a Laplace distribution (l1 exponential density), rather than the standard Gaussian distribution (l2) usually employed. Using a distribution with heavier tails allows better modeling of...