Derivatives and Internal Models pp 634-655 | Cite as

# Time Series Modeling

## Abstract

*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 30.5 are examples of how *parameters* can be estimated which are subsequently used to model the stochastic process governing the time series (e.g., a random walk with drift μ and volatility σ). Building a model which “explains” and “describes” the time series data is the principal 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*, for example.

## Keywords

Time Series Random Walk Time Series Analysis Internal Model Conditional Variance## Preview

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