Hidden Markov Models (eBook)

Contents 7
Acknowledgments 11
List of Figures 13
List of Tables 17
1 INTRODUCTION 19
1. Introduction 19
2. Markov Chains 19
3. Passage Time 23
4. Markov Chains and the Term Structure of Interest Rates 24
5. State Space Methods and Kalman Filter 29
6. Hidden Markov Models and Hidden Markov Experts 31
7. HMM Estimation Algorithm 34
8. HMM Parameter Estimation 36
9. HMM Most Probable State Sequence: Viterbi Algorithm 40
10. HMM Illustrative Examples 42
2 VOLATILITY IN GROWTH RATE OF REAL GDP 47
1. Introduction 47
2. Models 49
2.1 GARCH Model 49
2.2 Markov Switching Variance Model 50
3. Data 51
4. Empirical Results 51
5. Conclusion 56
3 LINKAGES AMONG G7 STOCK MARKETS 59
1. Introduction 59
2. Empirical Technique 62
2.1 Markov Switching Stock Return Model 62
2.2 Concordance Measure 63
3. Data 64
4. Empirical Results 64
5. Conclusion 69
4 INTERPLAY BETWEEN INDUSTRIAL PRODUCTION AND STOCK MARKET 73
1. Introduction 73
2. Markov Switching Heteroscedasticity Model of Output and Equity 76
3. Data 80
4. Empirical Results 81
5. Conclusion 94
5 LINKING INFLATION AND INFLATION UNCERTAINTY 99
1. Introduction 99
1.1 Inflation and Inflation Uncertainty 99
1.2 Inflation Uncertainty and Markov Switching Model 101
2. Empirical Technique 103
2.1 Markov Switching Heteroscedasticity Model of the Inflation Rate 103
2.2 Non-Nested Model Selection using Vuong Statistic 104
3. Data 105
4. Empirical Results 109
5. Conclusion 125
6 EXPLORING PERMANENT AND TRANSITORY COMPONENTS OF STOCK RETURN 135
1. Introduction 135
2. Markov Switching Heteroscedasticity Model of Stock Return 137
3. Data 138
4. Empirical Results 139
5. Conclusion 143
7 EXPLORING THE RELATIONSHIP BETWEEN COINCIDENT FINANCIAL MARKET INDICATORS 145
1. Introduction 145
2. Markov Switching Coincidence Index Model 147
3. Data 149
4. Empirical Results 149
5. Conclusion 157
References 163
Index 171

Chapter 4 INTERPLAY BETWEEN INDUSTRIAL PRODUCTION AND STOCK MARKET  (p.55)


1. Introduction
 
Extensive studies have focused on the empirical regularity in the degree of correlations and related issues between di.erent equity markets. These studies have provided insight into the nature of comovements across markets and what might be driving this phenomenon. Baca et al. (2000) ascribe the phenomenon to the global industry factor. Brooks and Del Negro (2002) .nd that there may be only one industry factor (high technology) that might explain this notion. They also demonstrate that this might be a temporary phenomenon, as country-based diversi- .cation appears to have remained e.ective for portfolio risk since the collapse of the technology bubble.

In studies adopting a slightly di.erent focus, researchers such as Kasa (1992) and Engsted and Lund (1997) rely on the results from cointegration tests in international equity prices. They also examine whether the underlying dividend process can explain this cointegrating behavior. Although the return patterns from these markets can di.er in the short term, cointegrating behavior would suggest that they are closely linked over the long term. In a paper stressing the unlikelihood of cointegrating behavior from the perspective of economic theory, Richard (1995) proves that Kasa’s (1992) .nding may result from the inappropriate use of critical values in their statistical tests.

In this chapter we attempt to explore the phenomenon of comovement among the G7 equity markets from a di.erent perspective. We make use of a concordance measure to document whether any of these markets tend to be in phase with the equivalent volatility state of the economy. Speci.cally, our analysis focuses on the G7 markets over a 30-year period at a monthly frequency. The .rst step in our approach is to model the interaction between the state of the economy and the stock market. This stems from the work of Hamilton and Lin (1996) and Chauvet (1998/1999), who demonstrate important relationships between stock markets and business cycle variables such as industrial production. Once equipped with our model, we can develop a probabilistic picture of whether a particular month is in the state of expansion or contraction. We then utilize this information and apply the concordance measure (Harding and Pagan, 1999) to capture the likelihood that the stock markets are in the same phase. Our results show that not all the G7 economies are commoving in this respect.

In modeling stock return and return volatility, the return volatility can be forecasted though the return itself cannot. Another important point to recognize is the dynamic relationship between the stock market and business cycle observed by Chauvet (1998/1999) in his attempts to anticipate turning points in the business cycle using stock market factors in a dynamic factor framework at a monthly frequency.

As large changes in volatility may alarm investors and adversely in- .uence their investment behavior, many investigators have sought to capture the patterns of stock return volatility. Several studies have applied time-varying conditional moments to capture such stylized facts. ARCH and GARCH models have been popular for this purpose, and Nelson (1991) and Glosten, Jagannathan and Runkle (1993) have proposed a variation of the GARCH model to capture asymmetries in stock return and stock index return.