A Course on Statistics for Finance

Chapter 9

Regime Switching Models

9.1 Introduction

(Parts of this chapter are more advanced than most of the rest of the book.) This chapter discusses states or phases of the market and the economy. The states of the market are conventionally called Bull and Bear. The states of the economy are referred to as recession, recovery, expansion, contraction. Questions arise as to how many such states to use, and whether the nature of the states detected by statistical methods corresponds to conventional notions about the phases of the market or the economy.

The models considered involve a series {Yt, St}, where Y is observed and S is the state, or label. For example, Yt may be the rate of return of the S&P500 index in month t, and St may be 1 or 0, ...