Stochastic Modelling and Time Series Analysis Finance

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Stochastic Modelling and Time series Analysis in Finance
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Generalities: Definitions, classification, finite-dimensional distributions, mean, autocorrelation and auto covariance functions,Important class of stochastic processes: stationary stochastic processes, stochastic processes with independent increments, Markovian stochastic processes, Gaussian stochastic processes.Examples of Gaussian processes: Wiener process, Brownian bridge, Ornstein-Uhlenbeck process, fractional Brownian motion.

Introduction and examples of economic and financial time series, asset returns. Basic models: white noise, random walk, AR(1), MA(1)

Stationary time series. Autocovariance and autocorrelation functions. Linear Prediction. Yule-Walker equations. Estimation of autocorrelation and partial autocorrelation function

Models for stationary time series - autoregressive (AR) models, moving average (MA) models, autoregressive moving average (ARMA) models. Seasonal ARMA models. Properties, estimation and model building. Diagnostic checking.Non-stationary time series. Non-stationarity in variance - logarithmic and power transformations. Non-stationarity in mean. Deterministic trends. Integrated time series. ARIMA and seasonal ARIMA models. Modelling seasonality and trend with ARIMA models