Multidimensional parameter estimation of heavy‐tailed moving averages

Moving Averages

More generally, weighted averages may also be used. Moving averages are also called running means or rolling averages. They are a special case of “filtering”, which is a general process that takes one time series and transforms it into another time series. The term “moving average” is used to describe this procedure because each average is computed by dropping the oldest observation and includi...

Brownian Moving Averages

1.1. Overview. It is well known (see Soner, Shreve and Cvitanić [8], Levental and Skorokhod [6], Cherny [2]) that in the Black–Scholes–Merton model with proportional transaction costs the superreplication price of a European call option is equal to its trivial upper bound. The same is true for any European type contingent claim in this model (see Cvitanić, Pham and Touzi [3]). In the recent pap...

Gaussian Moving Averages and Semimartingales

In the present paper we study moving averages (also known as stochastic convolutions) driven by a Wiener process and with a deterministic kernel. Necessary and sufficient conditions on the kernel are provided for the moving average to be a semimartingale in its natural filtration. Our results are constructive meaning that they provide a simple method to obtain kernels for which the moving avera...

Moving averages of solutions of ODEs

Moving averages of the solution of an initial value problem for a system of ordinary differential equations are used to extract the general behavior of the solution without following it in detail. They can be computed directly by solving delay differential equations. Because they vary much less rapidly and are smoother, they are easier to compute.

Extremes of Moving Averages of Stable Processes