Time Series Modeling

Time series analysis goes a significant step further than merely determining statistical parameters from observed time series data (such as the variance, correlation, etc.) as described above. Indeed, it is primarily used as a tool for deriving models describing the time series concerned. Estimators such as those appearing in Equation 29.5 are examples of how parameters can be estimated which are subsequently used to model the stochastic process governing the time series (for example, a random walk with drift μ and volatility σ). Building a model which “explains” and “describes” the time series data is the principle goal of time series analysis. The object is thus to interpret a series of observed data points {X _t }, for example a historical price or volatility evolution (in this way acquiring a fundamental understanding of the process) and to model the processes underlying the observed historical evolution. In this sense, the historical sequence of data points is interpreted as just one realization of the time series process. The parameters of the process are then estimated from the available data and can subsequently be used in making forecasts