Momentum and Market States:
A Regime Switching Approach
Thesis Proposal
By Jia Xu
Department of Finance and Accounting
Business School
National University of Singapore
This version:
Feb 2004
1
Abstract
By using an alternative measure of market state, I will re-examine the relationship
between market state and momentum as well as long-run reversal profits. The measure
classifies excess market returns into two regimes using a Markov-switching model. There
are at least two advantages to this approach. First, this measure of market states is more
natural as we let the data to classify market states. Second, in this study we can account
for the possibility of regime switches, the market state prior to as well as during the
holding period. I will investigate the effects of both the prior and the contemporaneous
market state on the momentum and long-run reversal profits.
I. Introduction
1.1 Objectives and Potential Contribution of the Study
Since DeBondt and Thaler (1985) and Jegadeesh and Titman (1993), extensive research
has been done on the short-run momentum and long-run reversal. The anomalies have
been found in both US and non-US markets. Attempts using risk-based models to account
for these anomalies have largely been unsuccessful. Several behavioral theories were
developed to jointly explain both the momentum and contrarian phenomena. Daniel,
Hirshleifer, and Subrahmanyam (DHS, 1998) and Hong and Stein (HS, 1999) each
constructed a behavioral model to explain these anomalies. Particularly, they link the
investor overreaction to new information with momentum profits. Moreover, the degree
2
of overreaction is believed to be higher following market gains as well as the decreasing
investor risk aversion.
Following these models, Cooper et al (2003) has tested the overreaction theories of shortrun momentum and long-run reversal in the cross section of stock returns. They find that
the momentum and long-run reversal profits depend on the state of the market prior to the
beginning of the momentum holding periods. They call attention for later research to take
regime switches into account.
Given the critical effects of market states, it is natural to pay attention to the criterion for
identifying them. In Cooper et al (2003), they define the two market states based on
whether the lagged market returns are positive (UP market) or negative (DOWN market).
The lags they used are one-year, two-year and three-year. However, in this study, I
propose an alternative measure of market states, which classifies excess market returns
into two regimes using a Markov-switching model. There are at least two advantages to
my approach. First, this measure of market states is more natural as we let the data to
classify market states. Second, in this study we can account for the possibility of regime
switches, the market state prior to as well as during the holding period. Some empirical
exploration can be conducted.
This study may have two potential contributions: Firstly, based on the two market states I
identify, I will re-examine the relationship between market states and the momentum and
long-run reversal profits. Besides, in Cooper et al (2003), there is an open question that
3
there seems no initial momentum before the long-run reversal following the DOWN
states. In my paper, it would be interesting to see if the phenomenon persists.
Secondly, since momentum profits can also be influenced by the market state during the
holding periods, the study will investigate the effects of both the prior and the
contemporaneous market state on the momentum and long-run reversal profits. I would
test which effect is more important to momentum and long-run reversal profits. The
results may lead to some interesting discussions about behavioral models.
1.2 Organization of the thesis
The thesis proposal is organized as the following: Section II reviews the literature on
momentum and contrarian studies, behavioral models and market states, and regime
switching models and its application. Section III details the research design, methodology
and data. Section IV discusses further study beyond this thesis.
II. Literature Review
2.1.1 Momentum Studies
The momentum effect, first elaborated by Jegadeesh and Titman (1993), is still a major
puzzle in finance literature up to today. They show that a simple strategy, buy high sell
low, based on previous 3 to 12 months stock returns will generate about 12% return for
the following year. It has drawn great attention thereafter. Among a lot other research,
4
Jegadeesh and Titman (2001) give further evidence on the momentum effect, which
cannot be explained by data mining. Forner and Marhuenda (2003) confirmed that
momentum is significant. Rouwenhost (1998) and Chan, Hameed and Tong (2000) tested
and confirmed the momentum anomaly in the international equity market.
Current asset pricing models have difficulty in explaining momentum. Some studies find
that it is not primarily driven by market risk. In Fama and French (1996), they show that
their unconditional three-factor model cannot explain the momentum. And Grundy and
Martin (2001) confirmed the result later on. Chordia and Shivakumar (2002) try to use a
conditional asset pricing model with lagged macroeconomic risk factors to forecast
momentum profits. But Griffin et al (2003) show that Chordia-Shivakumar model cannot
be applied internationally. Moreover, Cooper et al (2003) also find that macroeconomic
factors cannot explain momentum profits after simple methodological adjustments to take
account of microstructure concerns.
2.1.2 Contrarian Studies
DeBondt and Thaler (1985) suggest that over long period of time there are reverse
changes in stock returns: specifically, the stocks that have lowest returns (the losers)
during the previous three to five years (the formation period) will do better during the
following three to five years (the test period) than those that previously had the highest
returns (the winners). Based on the findings of Kahnem and Tversky (1982) in the field
of cognitive psychology, DeBondt and Thaler (1985) interpret their results as irrational
behavior on the part of investors. This will lead to excessive optimism toward good news
5
and excessive pessimism over bad news. Such a situation can cause the stock price
temporarily stray from its fundamental value. This potential violation of the Efficient
Market Hypothesis is called as the overreaction effect. It remains one of the most
controversial topics in finance field. Forner and Marhuenda (2003) showed contrarian is
significant and not from data mining. Supporting evidence has also come from
MacDonald and Power (1991) and Campbell and Limmack (1997) in the UK, Mai (1995)
from the French Market, Da Costa (1994) in Brazil and Alonso and Rubio (1990) in
Spain. Besides, a lot research has also found similar phenomena in financial markets that
are not based on stocks. Not surprisingly, existing asset pricing models cannot fully
explain the contrarian profits, neither.
2.2 Behavioral Models and Market States
Facing the challenges the above study has raised against rational asset pricing models,
quite a few behavioral models have been developed to explain the anomalies. De Long et
al. (1991) develops a model to examine the profits of traders who underestimate risk.
Hirshleifer, Subrahmanyam, Titman (1994) tries to see how traders who overestimate the
probability that they get information before others will increase stock selection herding.
But the above models are not unified. The following are some of the integrated models.
Daniel, Hirshleifer, and Subrahmanyam (DHS, 1998) develop a theory of security market
under- and overreaction on the bases of two psychological biases: investor
overconfidence about the precision of private information and variation in confidence
arising from biased self-attribution. A typical investor in the context is who overestimate
6
the precision of his private information rather than the public information and whose
confidence will change asymmetrically to confirming versus disconfirming pieces of
news. Thus, the arrival of confirming news tends to raise the overconfidence of the
investor, which may trigger further overreaction. Such continuing overreaction will cause
momentum in security prices. But, in the long run, with further public information
arriving, the momentum is eventually reversed towards fundamental values. Thus, the
model may account for both short-run momentum and long-run reversal.
Hong and Stein (1999) provide another unified account for under- and overreaction. In
their models, under the assumption of the gradual diffusing news about fundamentals,
there are two different groups of investors: “newswatchers” and “momentum traders”.
The authors emphasize on the interaction of heterogeneous investors. The newswatchers
base their decisions only on their private information. While the momentum traders, on
the contrary, only condition on the past price changes. They show that the newswatchers
tend to underreact to the private information at the beginning. And the momentum traders
try to exploit the underreaction and, thus, create an excessive momentum profit which
inevitably leads to overreaction.
Good theories must be potentially rejectable by empirical tests. By extending the above
theories (mainly DHS (1998) and HS (1999)) to the relationship between market states
and momentum, Cooper et al (2003) tests the short-run momentum and long-run reversal
in the cross section of stock returns conditioned on UP and DOWN markets. They find
the results are, in general, consistent with the overreaction theories: the monthly
7
momentum profit does depend on the market state, and that the up-market momentum
will reverse in the long run.
But Cooper et al (2003) leaves an open question: they find significant long-run reversal in
the DOWN states without any initial momentum. They note that, “[t]his finding indicates
that long-run reversal is not solely due to the corrections of prior momentum.” Does this
suggest the limits of overreaction theories? Or “there may be other factors causing longrun reversal in general”, as the authors mentioned? In my suspicion, it may simply
because of measurement error. By using another way of measuring and identifying the
market states, this study will examine whether the puzzle is still there.
2.3 Regime-switching Model and Market State
In Cooper et al (2003), they define two market states: “‘UP’ is when the lagged threeyear market return is non-negative, and ‘DOWN’ is when the three-year lagged market
return is negative.” Although their results are robust using one- or two- year lagged
market states and risk-adjustments, the definition of market states is still rather subjective.
Why not use six months as the window? Why not set the cutting return to be 0.5% instead
of 0%? ... Questions as these are unavoidable.
Besides, defining market states according to the sign of index returns may misclassify the
true state of the market. Suppose the index return over a given lag period, say 36 months
is positive. Thus, the market is considered to follow an UP state according to Coopers et.
al (2003). However, if the market is volatile, it is possible to have many down states
8
within the 36-month period. It is very likely that the holding period is actually following
a recent down market, instead of UP market. Consequently, it may be quite misleading to
classify that period as a bullish period. Conversely, a DOWN market according to their
classification may actually consist of many up states. Again, if this is true, then it is
misleading to consider that period as a down period.
Here, I provide a more inclusive definition of UP and DOWN market states by fitting a
Markov switching model to excess returns (over Treasury bills) on the market index.
From the literature in statistics, economics and finance, regime-switching models have
their advantages in identifying the market states.
Often, we define model instability as a switch in a regression equation from one regime
to another. However, in many cases, we may have little information on the dates at which
parameters change, and thus need to make inferences about the turning points as well as
the significance of parameter shifts. In statistics and econometrics, a lot research has been
done on switching models. In the sixties and seventies, many models have been
developed to deal with the issue, for example, Quandt (1958, 1960, 1972), Farley and
Hinich (1970), H. Kim and Siegmund (1989) and I.-M. Kim and Maddala (1991). An
interesting and important point of the above models is that the time at which a structural
change occurs is endogenous to the model.
Hamilton (1989) proposes a tractable state-dependent Markov-switching model. We can
apply it to the important case of structural changes in the parameters of an autoregressive
9
process. Compared to the traditional models, there are at least three advantages of this
model. First, the model sorts data endogenously into regimes. Second, unlike the
traditional models, in this latent variable model, we do not need to assume the
information set of the researcher, i.e., the econometrician, coincides with that of the agent
in the market. Thirdly, empirically, among other studies, Ryden et al (1998) show that the
Markov-switching model can explain the temporal and distributional properties of stock
returns.
The model has drawn a lot attention in modeling structural changes in dependent data. In
economics, it has been used to identify business fluctuations, see Hamiltion (1989); to
study the changes in real interest rates, Garcia and Perron (1996). Recently, the model
has been used extensively in finance area, esp. to model the nonlinear structure in time
series data. Turner et al (1989) use the model to explain a time-varying risk premium in
stock returns. Methodologically, they consider a Markov-switching model which allows
either the mean or the variance or both to differ between the two regimes. Hamilton and
Lin (1996) adapt the model to capture the dynamics between the stock market and
business cycle. Gordon and St-Amour (2000) use a two-state Markov process to model
risk aversion, called as preference regimes, and link this model with the cyclical pattern
of asset prices.
Specifically, some research has been conducted on identifying market states. Borrowing
the method from Turner et al (1989), Schaller and van Norden (1997) find strong
evidence for switching behavior in stock returns in the US market. By allowing for
10
switch in both means and variances, they discover two distinct states: in one state, the
excess returns are low and the variance is low; in the other state, the excess return goes to
negative and the variance is high. The results agree with Brock et al (1992) and Maheu
and McCurdy (2000). For the point of illustration, a specific description of the market
state from Nielsen and Olesen (2000) will be cited in Section III.
III. Research Design and Data
3.1 Data
The data are all NYSE and AMEX stocks listed on the CRSP monthly file. To be
consistent with Cooper et al (2003), the sample period is from January 1926 to December
1995. To identify the market states, I will collect monthly excess returns on the valueweighted market index. Excess return is the difference between the market returns on
CRSP Value-Weighted Index (adjusted for dividends) and the one-month Treasury-bill
rate.
3.2 Methodology and Research Design
3.2.1 On identifying market states
In this study, I will mainly follow Hamilton’s (1989) Markov-switching model to identify
two market states.
A normal regression model without any switching is:
11
yt  xt  et ,
et ~ i.i.d .N (0, 2 )
(1)
A model with structural breaks in the parameters is:
yt  xt St  et ,
t  1, 2, 3..., T .
(2)
et ~ N (0, St )
(3)
 S    (1  S t )   S t
(4)
2
t
 S 2   02 (1  S t )   12 S t
(5)
S t  0 or 1,
(6)
t
(Regime 0 or 1)
where under regime 1, parameters are given by  and  12 , and under regime 0,
parameters are given by   and  02 . If the dates of switching or structural breaks are
know a priori, the above will be reduced to a dummy variable model. The problem here
is we do not know when St is 0 or 1. The evolution of the discrete variable St may be
dependent upon S t 1 , S t  2 , …, S t  r , in which case the process of St is named as an r-th
order Markov switching process.
Here, I adapt the standard Hamilton’s (1989) model into the following model:
Rt  RFt   St   ( Rt 1  RFt 1   St 1 )   t
(7)
 ~ N (0,  2 )
(8)
 S   0 (1  S t )  1 S t
(9)
t
t
Pr S t  1 S t 1  1  p, Pr S t  0 S t 1  0  q
(10)
12
where St , equals to 0 or 1, follows a first order Markov switching process. Rt is
monthly return on the CRSP Value-Weighted Index (adjusted for dividends). RFt is
risk-free interest rate, here I use one-month Treasury bill rate. Please note that this
model allows for the switching in means, and that an autoregressive term is included in
each state.
The parameter estimates can be obtained by numerically maximizing the log likelihood
function. The likelihood function and the maximizing procedure are standard for
regime-switching models and described in both Hamilton (1994), section 22.4 and Kim
and Nelson (1999), chapter 4.
Given parameter estimates of the model, we can make inference on St using all the
information in the sample by using Hamilton’s (1989) filter and Kim’s (1994)
smoothing. Thus, we can get the smoothed probability of stock returns. By way of
illustration, I would like to cite one of the results from Nielsen and Olesen (2000),
which studies the Danish market.
13
In their figure 2 is the probability that observation t is in state 0 given the information on
current and past stock returns available at time t.
It is natural to use a 50% probability cutoff point to delineate between UP and DOWN
market. That is, at time t, if the smoothed probability of the UP state is say 0.7, I label
the market state then as an UP state. If the smoothed probability is 0.4, I label the
market state then as a DOWN state. States with probability bigger than 0.5 are assigned
a value of “1” to indicate a bull market. States with probability equal to or less than 0.5
are assigned a value of 0 to indicate a bear market.
Since the smoothed probability of market states can be very volatile, to decide the prior
market state, I look at the entire lagged period, say month t-6 to t-1. To decide whether
the entire lagged period is an UP or DOWN state, I use the following formula:
N
D
i 1
t i
/N
(11)
14
For example, suppose the lagged period has 10 months, and this comprises 7 months
(not necessary contiguous) where the market is in UP state (probability of UP state > 0.5)
and 3 months in which the market is in down state. Then, the probability of the market
being in the up state over the last 10 months is 0.7. Based on this, I classify the prior
market as being in an UP state. Likewise, if the same probability is say 0.4, I classify
the prior market as being in a DOWN state.
I use the similar formula to decide the contemporaneous market state. I look at the entire
holding period, say month t to t+6. The formula is:
N
D
i 1
t  i 1
/N
(12)
The rest is the same as defining prior market state above.
3.2.2 On calculating the momentum and long-run reversal profits
I will mainly follow Cooper et al (2003). Here I would just outline the major steps. For
details, please refer to Cooper et al (2003). It is a rather standard process including prior
6-months of formation-period and 6, 12, and 60 months of test-period. The momentum
portfolio is defined as long in the prior 6-month winners (highest decile) and short in the
prior 6-months losers (lowest decile). To form the Fama-French (1993) risk-adjusted
profits, for each holding-period month, I regress the time series of raw profits on three
factors and a constant. The three factors are a) the excess return of the value-weighted
market index over the one-month Treasure bill rate (MKTRF), b) the small-minus-big
return premium (SMB) and the high-book-to-market-minus-low-book-to-market return
premium (HML). Thus, the risk-adjusted profits are
15
Rktadj  Rkt  ˆ1k MKTRFt  ˆ2k SMBt  ˆ3k HMLt
(13)
where Rkt is the raw profit for the strategy in the holding-period month k, for k=1,
2,…60, in calendar month t. The ˆ s are the estimated loading of the time-series of raw
profits in holding-period-month k on their respective factors. The monthly raw or FamaFrench-adjusted profits are cumulated to form the holding-period profits (CAR).
CARt  K 2 
K2
R
k  K1
*
k ,t  k
(14)
where R* is either raw ( Rkt ) or risk-adjusted ( Rktadj ) profits and the (K1, K2) pairs are (1,
6), (1, 12), and (13, 60).
3.2.3 On analyzing the profits across market states
Cooper et al’s (2003) results may be contaminated by the contemporaneous market state.
In particular, it is not clear whether the strong momentum that they find following UP
states is due to delayed overreaction (their explanation) or simply due to the fact that
momentum happens to be strong during a holding period in which the market is also in an
UP state.
a. Contingency table
To disentangle the prior and contemporaneous market state influences, I first use a 2 x 2
contingency table to document the distribution of momentum profits by prior and
contemporaneous market states. Table 1 presents the contingency table where I document
in each cell: 1) Mean raw CAR, 2) Mean risk-adjusted CAR (using FF model), 3)
16
Proportion of holding periods where CAR is greater than 0, and 4) Proportion of holding
periods where CAR less than or equal to 0.
CON = UP
CON = DOWN
PRIOR = UP
1), 2)
3), 4)
1), 2)
3), 4)
PRIOR = DOWN
1), 2)
3), 4)
1), 2)
3), 4)
Table 1. CAR measures contingent on prior (PRIOR) and contemporaneous (CON) market states
A series of tests would be conducted to investigate (a) whether CARs differ across prior
states, and (b) whether CARs differ across contemporaneous states. In addition, I use the
Chi-square test (see Siegel and Castellan (1988)) to test whether (a) the proportion of
positive CARs differs across prior and contemporaneous states and (b) the proportion of
negative CARs differs across the two groups.
To investigate the impact of lagged and contemporaneous market states on momentum
profits, I perform CAR regressions on prior and contemporaneous market states. I first
perform regressions using dummy variables as described above to measure market states.
I then perform regressions using continuous rather than discrete measure of the state of
the market.
b. Dummy Variable Regressions
Regression 1
CARt  K2   0  1 Dlag t   t
17
Regression 2
CARt  K2   0  1 Dlag t   2 Dcont   t
Regression 3
CARt  K2   0  1 Dlag t   2 Dcont   3 ( Dlag t )( Dcont )   t
Where:
CARt  K 2 is cumulative excess returns of the momentum portfolio which is formed at the
beginning of month t and held for K2 month. K2 =6, 12 or 60.
Dlag = 1 if the market is UP prior to holding period and 0 otherwise
Dcon = 1 if the market is UP during the holding period and 0 otherwise.
Dlag t * Dcon t is an interactive variable to measure the impact on CAR of the combined
effects of an UP market in both prior and contemporaneous periods.
Here, regression 1 is similar to the tests in Cooper et al (2003) to see whether the mean
momentum profits following UP and DOWN markets are equal. The overreaction
theories predict that  1 is significantly positive, when K2 is 6 or 12. When K2 is 60,  1 is
significantly negative. In regression 2 and 3, we can ask many interesting questions. Is
 2 significant or not? If yes, what happens to the significance of  1 , when  2 is added?
What is the sign of  2 ? How about  3 ?
c. Regressions using a Continuous Measure of Market State
Following Coopers et. al.(2003), I perform CAR regressions on the lagged market returns
as well as contemporaneous holding-period market returns. Again, we can ask similar
questions about the signs and magnitudes of the  s.
Regression 4
CARt  K 2   0  1 LAGMKTt   2CONMKTt   t
18
where LAGMKTt is lagged 36-month market return at time t, and CONMKTt is
contemporaneous holding-period market return.
To summarize all the three series of tests, I want to point out four possible results that
might be interesting for discussion. a) The prior market state influences momentum
profits, but the contemporaneous one does not. b) The contemporaneous market state
influences momentum profits, but the prior one does not. c) Both have significant
influences. And d) neither of them have significant influences on momentum profits.
Result d) is less likely to happen, since the tests in this study are somewhat consistent to
the tests in Cooper et al (2003). Market state is expected to play a role on momentum
profits. Result a) will best support the overreaction models (mainly DHS (1998) and HS
(1999)), while c) cannot reject the overreaction models and needs future study. If result b)
comes out, the overreaction models will be put into greater doubt, or at least, we need to
turn to other overreaction models that can incorporate the influence of the
contemporaneous market state.
IV. Further Study
Firstly, to continue with the discussion of the results in last section, if result b) comes out,
further tests may need to check the risk of the contemporaneous market states. For
example, if UP market is associated with higher risk, then the momentum profits may
simply be the compensation for bearing the extra risk, which supports the tradition riskbased theories.
19
Besides, instead of identifying the market into two states as in Cooper et al (2003), I may
also add a medium state between UP and DOWN markets. By adding this state, we get
the chance to see whether momentum or long-run reversal profits will disappear in the
middle states. This may serve as a further test of the overreaction theories.
Reference:
Alonso, A. and Rubio, G., (1990), "Overreaction in the Spanish equity market', Journal of
Banking and Finance, Vol. 14, 1990, pp. 469-481
Brock, W., Lakonishok, J., and LeBaron, B. (1992), "Simple technical trading rules and the
stochastic properties of stock returns", Journal of Finance, 47, 1731-64
Campbell, K. and Limmack, R. (1997), "Long-term overreaction in the UK stock market and size
adjustments', Applied Financial Economics, Vol. 7, 1997, pp. 537-548.
Chan, Hameed and Tong (2000), "Profitability of Momentun Strategies in the International Equity
Markets", Journal of Financial and Quantitative Analysis, June 2000
Cooper, M., Gutierrez, R., and Hameed, A. (2003), "Market States and Momentum", Working
paper, forthcoming in Journal of Finance 2004.
Da Costa, N., (1994), "Overreaction in the Brazilian stock market", Journal of Banking and
Finance, Vol. 18, 1994, pp. 633-642
Daniel, K., Hirshleifer, D. and Subrahmanyam, A., (1998), "Investor Psychology and Security
Market Under- and Overreactions", Journal of Finance, Vol. LIII, No. 6. December 1998.
De Long, J. Bradford, Shleifer, A., Summers, L., and Waldmann, R., (1991), "The survival of
noise traders in financial markets", Journal of Business 64, pp. 1-20
DeBondt, W.F.M., and Thaler, R.H., (1985), "Does the stock market overract?", Journal of
Finance 40, 793-808
Fama, E.F., and French, K.R., (1993), "Common risk factors in the returns on stocks and bonds",
Journal of Financial Economics, 33, 3-56
Farley, J.U., and Hinich, M.J., (1970), "A test for a shifting slope coefficient in a linear model.",
Journal of the American Statistical Association, 65, 1320-1329
Forner, C. and Marhuenda, J., (2003), "Contrarian and Momentum Strategies in the Spanish
Stock Market", European Financial Management, Vol. 9, No. 1, 2003, pp. 67-88
Garcia, R., and Perron, P., (1996), "An analysis of real interest under regime shift", Review of
Economics and Statistics, 78, 111-125
Gordon, S., and St-Amour, P., (2000), "A preference regime model of bull and bear markets",
The American Economic Review, Vol 90, No. 4 (Sep., 2000), 1019-1033
20
Hamilton, J.D. (1994), "Time series analysis", Princeton University Press, Princeton, New Jersey.
Hamilton, J.D., (1989), "A new approach to the economic analysis of nonstationary time series
and the business cycle.", Econometrica, 57(2), 357-384
Hamilton, J.D., and Lin, G. (1996), "Stock Market Volatility and the Business Cycle." Journal of
Applied Econometrics, 11, 573-593
Hirshleifer,D., Subrahmanyam, A., and Titman, S., (1994), "Security analysis and trading
patterns when some investors receive information before others", Journal of Finance 49,
pp. 1665-1698
Hong, H. and Stein, J., (1999), "A unified theory of underreaction, momentum trading and
overreaction in asset markets", Journal of Finance, Vol. LIV, No 6, Dec 1999
Jegadeesh, N., and Titman, S., (1993), "Returns to buying winners and selling losers:
Implications for stock market efficiency", Journal of Finance 48, 65-91
Kim C., and Nelson, C.R., (1999), "State-space models with regime switching", The MIT Press,
Cambridge, Massachusetts, London, England.
Kim, C., (1994), "Dynamics linear models with markov-switching", Journal of Econometrics, 60,
1-22
Kim, H. J., and Siegmund, D., (1989), "The likelihood ratio test for a change-point in simple
linear regression.", Biometrika, 76, 409-423
Kim, I.-M., and Maddala, G.S., (1991), "Multiple structural breaks and unit roots in the nominal
and real exchange rates.", Unpublished manuscript. Department of Economics, The
University of Florida.
MacDonald, R. and Power, D., (1991), "Persistence in UK stock market returns: aggregated and
disaggregated perspectives", in Taylor (ed.), Money and Financial Markets (Oxford: Basil
Blackwell, 1991), pp. 277-296
Maheu, J.M., and McCurdy, T., (2000), "Identifying bull and bear markets in stock returns",
Journal of Business & Economic Statistics, Jan 2000, 18, 1, 100-112
Mai, H., (1995), "Sur-reaction sur le marche francais des actions au Reglement Mensuel 19771990", Finance, Vol. 16, 1, 1995, pp. 113-136
Nielsen, S., and Olesen. J. O. (2000), "Regime-switching stock returns and mean reversion",
Working paper, Department of Economics, Copenhagen Business School.
Quandt, R. E. (1958), "The estimation of the parameters of a linear regression system obeying
two separate regimes.", Journal of American Statistical Association, 53, 873-880.
Quandt, R. E. (1960), "Tests of the hypothesis that a linear regression system obeys two
separate regimes.", Journal of the American Statistical Association, 55, 324-330
Quandt, R. E. (1972), "A new approach to estimating switching regressions.", Journal of the
American Statistical Association, 67, 306-310.
Rouwenhourst (1998), "International Momentum Strategies", Journal of Finance, 267-284
21
Ryden, T., Terasvirta, T., and Asbrink, S., (1998), "Stylied facts of daily return series and the
hidden markov model", Journal of Applied Econometrics, 1998, 13, 217-244
Schaller, H., and Van Norden, S., (1997), "Regime switching in stock market returns", Applied
Financial Economics, 1997, 7, 177-191
Siegel and Castellan (1988), "Nonparametric Statistics in Behavioral Science", Chapter 6
Turner, C.M., Startz, R. and Nelson, C.R. (1989), "A markov model of heteroscedasticity, risk
and learning in the stock market," Journal of Financial Economics, 25, 3-22
22