Time Series Modeling and Forecasting

Analysis and modeling of financial time series data and forecasting future values of market variables constitute an important empirical core of quantitative finance. This chapter introduces some basic statistical models and methods of this core. Section 5.1 begins with stationary time series models that generalize the classical i.i.d. (independent and identically distributed) observations and introduces moving average (MA) and autoregressive (AR) models and their hybrid (ARMA) models. Estimation of model order and parameters and applications to forecasting are described. Section 5.2 considers nonstationary models that can be converted to stationary ones by detrending, differencing, and transformations. In particular, differencing is particularly effective for nonstationary processes with stationary increments, which generalize random walks (i.e., sums of i.i.d. random variables) to ARIMA (or integrated ARMA) models. Section 5.3 considers linear state-space models and the Kalman filter and their applications to forecasting. Volatility modeling of financial time series will be considered in the next chapter. Part II of the book will introduce more advanced topics in time series analysis. In particular, nonparametric time series modeling is introduced in Chapter 7, and time series models of high-frequency transaction data are introduced in Chapter 11. Chapter 9 considers multivariate time series, while Chapters 8 and 10 describe and strengthen the connections between empirical time series analysis and stochastic process models in the theory of option pricing and interest rate derivatives.