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Ramos, Luís P., Pedro Mota, and João T. Mexia. "Sample Partitioning Estimation for Ergodic Diffusions." Communications in Statistics - Simulation and Computation. 44 (2015): 105-117. AbstractWebsite

In this article, we present a new technique to obtain estimators for parameters of ergodic processes. When a diffusion is ergodic its transition density converges to the invariant density Durett (1996). This convergence enabled us to introduce a sample partitioning technique that gives, in each subsample, observations that can be treated as independent and identically distributed. Within this framework, is possible the construction of estimators like maximum likelihood estimators or others.

Câmara, T., and P. Mota. "Simple Moving Average vs Buy and Hold Revisited." (Submitted). Abstract

Nowadays, there are still countless researchers defending the effectiveness of the moving average technical analysis and they are able to present evidences for certain stocks, indexes and/or markets where this technical indicator is extremely useful for defining trading strategies. But the contrary also exists, i.e. a lot of researchers show distrust of this technical indicator and also provide evidences with particular stocks, indexes and/or markets where moving averages based strategies do not work well.
Aiming to understand why is it that with some stocks the moving average is indeed an excellent indicator while with others it is not, in this paper we implement moving average based strategies to buy and/or sell stocks for more than 480 companies from the NASDAQ 100, FTSE 100 and SP 500 indexes and compare the results with the ones obtained when using the buy-and-hold strategy.

Mota, P., M. L. Esquível, and NP Krasii. "Some Double Diffusion Models For Stock Prices." Global and Stochastic Analysis. 8.2 (2021). AbstractWebsite

Regime switching diffusion processes with one or two thresholds and regime switching occurring by a change in the diffusion drift and/or volatility functions parameters of a stochastic differential equation, whose solution defines a continuous time diffusion process, were defined in previous works; the change in regime occurring whenever the trajectory of the process crosses a threshold, possibly with some delay. In this paper we generalise the previous
results by allowing the underlying diffusion process to change from one family of diffusions in one regime to an entirely different one in the other regime; these families of diffusions are characterised by specific functional forms for drift and volatility coefficients depending on parameters. We propose an estimation procedure for all the parameters, namely the thresholds, the delay and, for both regimes, diffusion’s parameters and we apply the introduced estimation procedure to both simulated and real data.