[summary]Predicting bear and bull stock markets with dynamic binary time series models

Predicting bear and bull stock markets with dynamic binary time series models

H Nyberg - Journal of Banking & Finance, 2013 - Elsevier


Abstract
Despite the voluminous empirical research on the potential predictability of stock returns, much less attention has been paid to the predictability of bear and bull stock markets. In this study, the aim is to predict U.S. bear and bull stock markets with dynamic binary time series models. Based on the analysis of the monthly U.S. data set, bear and bull markets are predictable in and out of sample. In particular, substantial additional predictive power can be obtained by allowing for a dynamic structure in the binary response model. Probability forecasts of the state of the stock market can also be utilized to obtain optimal asset allocation decisions between stocks and bonds. It turns out that the dynamic probit models yield much higher portfolio returns than the buy-and-hold trading strategy in a small-scale market timing experiment.

1. Introduction

Despite the large amount of previous research on stock return predictability, much less attention has been paid to the extensive periods of time when stock returns are rising or falling. These periods are often referred to as bull and bear markets. In this study, the main goal is to predict the state of the stock market with dynamic binary time series models.

Classifying bear and bull market

- methods that are used to determine the business cycle turning point also can use to find the stock market turning point

: Maheu and McCurdy (2000), 

- Pagan and Sossounov (2003) and Candelon et al. (2008) examine various turning point dating methods for the stock market.

- dynamic binary time series models is superior to forecast the state of the business cycle then the conventional static model

: Kauppi and Saikkonen (2008) and Nyberg (2010)

- Chen (2009) is the first study to consider the predictability of bear and bull stock markets with a static probit model and the main emphasis in his paper is also on Markov switching models.

2. Bear and bull stock markets
2.1. Regime switching dynamics in stock returns

2.2. Identifying bear and bull markets in real time

- no consensus in the literature on how these periods should be identified

- Identifying methods

: moving average -> if mean return is positive(negative) the market status is bull(bear)

: Markov switching models -> in which the underlying unobserved state of the stock market is assumed to follow a Markov
process

: the Bry and Boschan (1971) turning point dating rule

   a. mostly used in the business cycle literature

   b. consists of a set of filters and rules to locate the alternating turning points

   c. certain minimum and maximum durations

-real-time information lag

: the future stock returns are unknown. there will usually be a few months delay before the algorithm can identify a possible turning point in real time

: in this study, the probit model provided to predict the future state of the stock market

3. Forecasting bulls and bears with dynamic binary response models

3.1. Static and dynamic probit models

- static model

:Chen(2009)

:used in the previous literature to predict the future business cycle.

- dynamic model

: Kauppi and Saikkonen (2008)

: autoregressive model

: add a lagged value

3.2. Forecasting procedures 

- the methods proposed by Kauppi and Saikkonen (2008)

- h-month forecast

- calculate recursively

: eg. 2-period forcast

- forecast very long horizon is not proper

: increase complexity significantly

4. Results

4.1. U.S. stock market cycles and predictive variables

- variables

: the S&P500 index => to determine the U.S. bear and bull markets

: the first differences of the dividend-price

: earnings-price ratios

: the term spread between the 10-year government bond and the3-month Treasury Bill rate 

: the first differences of the Federal Funds rate

: the 3-month Treasury Bill rate 

: the 10-year government bond

: inflation

: the growth rates of industrial production

:the unemployment rate

- bull and bear market turning point chronology

4.2. In-sample results

- sample period from January 1957 to December 2010

- Predictive variables are first examined one by one
- most predictable variable => the lagged stock return

- the vector of predictive variables

- coefficients for the predictive variables

4.3. Out-of-sample forecasts

- the quadratic probability score(QPS)

:  see Diebold and Rudebusch, 1989

:  measure of forecast accuracy

: value 0 to 2, when value is 0 it means perfect accuracy measures

4.4. Market timing experiment

4.5. Additional robustness checks


5. Conclusions


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