Forecasting the future is one of the fundamental tasks of time series analysis. Although linear methods, such as those introduced in §3.7, are useful, a prediction from a nonlinear point of view is one-step closer to reality. Anybody who has first-hand experience of the stock-market knows that we can forecast the future better at the right moment than at another time. Such common sense can be naturally reflected in nonlinear forecasting only! In this chapter, we first discuss the general properties of nonlinear prediction, paying particular attention to those features that distinguish nonlinear prediction from linear prediction. The sensitivity to initial condition, a key concept in deterministic chaos, plays an important role in understanding nonlinearity. Three types of predictors-namely point predictors, predictive intervals, and predictive distributions-constructed based on local regression will be presented.
KeywordsConditional Distribution Conditional Variance Coverage Probability Predictive Distribution Local Linear Regression
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