Processos Estocásticos e Modelação

Apply the concepts and properties of: stationary, integrated, univariate time series, stationary random series, filter applied to a stationary random series, backwards shift operator, backwards difference operator, roots of the characteristic equation of time series, multivariate autoregressive model.

Outline the processes of identification, estimation and diagnosis of a time series, the criteria for choosing between models and the diagnostic tests that might be applied to the residuals Develop deterministic forecasts from time series data.

Formulate the Chapman-Kolmogorov equations, calculate the stationary distribution and apply Markov chains as a tool for modeling and in simulation.

Apply the main concepts of Wiener Process. Show working understanding of stochastic differential equations, Ito integral, diffusions and mean reverting processes. Ito’s Lemma and proof, apply it to write down the stochastic differential equations for important processes and solve it.