Time-Series Models for Financial Data › Time-Series Models for Financial Data

Financial markets generate vast streams of sequential observations: prices, returns, interest rates, volatility measures, and economic indicators. Understanding the temporal structure of these data is essential for forecasting, risk management, and trading strategy development. Time-series models provide a principled framework for capturing the statistical dependencies that exist between observations across time.

Unlike the stochastic differential equations we explored in earlier chapters on Brownian motion and Itô calculus, the models in this chapter operate in discrete time and focus on the autocorrelation structure of observed data. While Black-Scholes assumes returns are independent and identically distributed, empirical evidence from our study of stylized facts reveals that financial returns exhibit serial correlation in their magnitudes (volatility clustering) and occasional predictable patterns in their levels. Time-series models let us analyze these patterns and build trading rules around them.

This chapter introduces the foundational autoregressive (AR) and moving average (MA) models, then combines them into the ARMA framework for stationary series. We extend to ARIMA models for handling non-stationary data like trending economic indicators or asset prices. Throughout, we develop practical skills for model identification using autocorrelation analysis, parameter estimation, and forecasting with proper uncertainty quantification.