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Quantitative Finance · Glossaire

Qu'est-ce que « State-space model, local level model » ?

Aussi appelé : state-space model · local level model

Definition 19.1 Quantitative Methods · Chapitre 19 — State-Space Models and the Kalman Filter

A linear Gaussian state-space model has an observation equation yt=Ztαt+εty_t = Z_t\alpha_t + \varepsilon_t, εt∼N(0,H)\varepsilon_t \sim \mathcal N(0, H), and a state equation αt+1=Tαt+ηt\alpha_{t+1} = T\alpha_t + \eta_t, ηt∼N(0,Q)\eta_t \sim \mathcal N(0, Q), with independent noises and α1∼N(a1,P1)\alpha_1 \sim \mathcal N(a_1, P_1). The local level model is the scalar case Z=T=1Z = T = 1: an observed series equals a random-walk level plus noise.

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