Stochastic kernel

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A stochastic kernel is the transition function of a (usually discrete-time) stochastic process. Often, it is assumed to be iid, thus a probability density function.

Formally a density can be

where y_i is the observed series, λ is the bandwidth, and K is the kernel function.

[edit] Examples

• The uniform kernel is K = 1 / 2 for − 1 < t < 1.
• The triangular kernel is K = 1 − | t | for − 1 < t < 1.
• The quartic kernel is K = (15 / 16)(1 − t²)² for − 1 < t < 1.
• The Epanechnikov kernel is K = (3 / 4)(1 − t²) for − 1 < t < 1.