Second Order Filter Distribution Approximations for Financial Time Series with Extreme Outlier



J.Q. Smith and Antonio Santos

to t. This corresponds to sampling from

f ( αt,kDt ) a f ( yt αt ) f ( at |at_ ɪ) k, k =1 ,...,m              (7)

where π k represents the weight given to each particle. The aim is then to sample first
from
f (kDt) and then from f (αtk, Dt), obtaining the sample {(αt,j, kj) ; j = 1, . . . , m}.
The marginal density
f (αtDt) is obtained by dropping the index k.

This resolves the problem of too many states with negligible weight being carried
forward. However, the problem of defining a good approximation to the target
distribution still remains. One of the simplest approaches is to define

g (αι,k Dt) a f yytμu) f (at\at_ɪ) k

(8)


where μt,k is the mean, mode or a highly probable value associated to f (at|at_ɪ).
It can easily be seen that

g (k|Dt)


a f f (ytμt,k) f (at\a_ɪ) πk dαt

= f {ytμt,k)


(9)

(10)


This density is used to define the first stage weights. These are the ones used to
sample the index that tell us which particles at
t - 1 are used to define the posterior
distribution at
t. Given a set of indexes, the states are drawn from f (at\at_ɪ,k) and
the second stage weights are defined as

f = f (ytαtj)
wj f (ytμtj)

(11)


The information contained in yt is carried forward through first stage weights. After
the particles
at_ɪ,k, k = 1,... ,m are chosen, the densities used, f (at\at_ɪ,k), k =
1
, . . . , m do not depend any further on yt .

G.E.M.F - F.E.U.C.



More intriguing information

1. Altruism and fairness in a public pension system
2. Wettbewerbs- und Industriepolitik - EU-Integration als Dritter Weg?
3. Do the Largest Firms Grow the Fastest? The Case of U.S. Dairies
4. The name is absent
5. The name is absent
6. Strategic monetary policy in a monetary union with non-atomistic wage setters
7. Multimedia as a Cognitive Tool
8. Julkinen T&K-rahoitus ja sen vaikutus yrityksiin - Analyysi metalli- ja elektroniikkateollisuudesta
9. The name is absent
10. The Variable-Rate Decision for Multiple Inputs with Multiple Management Zones