Time Series Analysis Assignment for Stochastic Processes

This is an assignment on time series analysis within stochastic processes, requiring MATLAB programming to implement operations such as model identification, parameter estimation, and model prediction. I have also included my complete assignment documentation, hoping it can provide valuable reference material for others. In this assignment, I investigated various time series models including AR (Autoregressive) models, MA (Moving Average) models, ARMA (Autoregressive Moving Average) models, and ARIMA (Autoregressive Integrated Moving Average) models. For model identification and parameter estimation, I implemented fundamental statistical methods such as Maximum Likelihood Estimation and Bayesian Information Criterion using MATLAB's system identification toolbox and custom optimization functions. During model forecasting implementation, I experimented with both rolling forecast methods (updating parameters with new observations) and dynamic forecast approaches (using predicted values as inputs for future steps). The code utilizes MATLAB's predict and forecast functions while incorporating error analysis through mean squared error calculations and confidence interval generation. Ultimately, this assignment requires deep understanding of various methods and models in time series analysis, reinforced through practical implementation. My complete documentation includes MATLAB code examples with detailed comments, algorithmic explanations of difference operations for stationarity, and autocorrelation function analysis for model selection. I hope my work can provide inspiration and guidance for others studying time series analysis.