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http://dspace.cityu.edu.hk:80/handle/2031/714
2017-03-23T14:08:34ZPenalized likelihood and model averaging
http://dspace.cityu.edu.hk:80/handle/2031/8483
Title: Penalized likelihood and model averaging
Authors: Zhou, Jianhong (周建红)
Abstract: Penalized likelihood and model averaging are alternatives to model selection. The
former has the attractive feature of model selection, and its parameter estimation can be
achieved by a single minimization problem with computational cost growing polynomially
with the sample size. The latter compromises across all the competing models so
that it can incorporate model uncertainty into the estimation process. Model averaging
also can avoid selecting very poor models, which in turn holds the promise of reducing
estimation risks.
Penalized likelihood and model averaging have advantages over model selection
in some aspects, and they have been developed in parallel. This prompts the question
whether there exists any relationship between penalized likelihood and model averaging.
However, to the best of my knowledge, there is a paucity of literature focused on this
question. An creditable exception is made by Ullah et al. (2013). They propose a new
generalized ridge estimator which is one of the penalized likelihoods, and prove that
this estimator is algebraically identical to the model average estimator.
In this thesis, we choose the Tobit model and Poisson regression model to study
penalized likelihood, model averaging and the relationship between them. The Tobit
model is now a standard approach to model censored dependent variables. Based on
the seminal contribution of Tobin (1958), many extensions of the original Tobit model
have been developed, and numerous applications of these models have appeared in economics
since the 1970s. The Poisson regression model is a widely used econometric
and statistical tool for studying the relationship between a Poisson-type response variable
and a set of explanatory variables. We arrange this thesis in the following manner:
Chapter 1 presents the rationale and introduction. We also introduce the Tobit model,
the Poisson regression model, and the methodology of the performance measures.
Chapter 2 surveys the relevant literature on model selection, penalized likelihood,
and model averaging. Additionally, under the statistical framework, we discuss the
relationship between model selection and penalized likelihood, and the relationship
between pretest and the WALS (weighted-average least squares) estimator. We also
present model averaging, i.e., Bayesian model averaging and frequestist model averaging
under the same statistical framework.
Chapter 3 considers the Tobit I model. First, we propose one-step sparse estimates,
and their adjusted implication is also suggested. We conduct a simulation study to
investigate the performance of one-step sparse estimates with LASSO (least absolute
shrinkage and selection operator) and ALASSO (adaptive LASSO) penalties. For simplicity,
we call them LASSO estimator and ALASSO estimator. The results demonstrate
that, compared with LASSO estimators, ALASSO estimators usually have advantages
on getting more accurate results in terms of mean square error, and providing a more
accurate number of correct zeros. However, they have a disadvantage on producing a
more accurate number of correct nonzeros. Second, we explore the relationships among
one-step sparse estimates, model selection, and model averaging. The results by both a
simulation study and empirical example, demonstrate that none of these three methods
consistently performs better than the others. Model averaging tends to get more accurate
results when there is a high noise level to the model; otherwise, none of these three
methods has an obvious superiority.
Chapter 4 considers the Tobit II model. We propose a procedure combining the
Heckman two-step procedure with penalized regression for parameter estimation and
variable selection. We investigate the finite samples results of this procedure with
LASSO and ALASSO penalties by designing a simulation study. The conclusion is
similar with that of Chapter 3. Next, we study the relationships among this procedure,
model selection, and model averaging. From the results by both simulation study and
empirical example, it can be seen that each method has its own advantage. Especially
in cases with a high level of noise, model averaging has competitive strength over other
methods.
Chapter 5 develops a model averaging procedure based on an unbiased estimator of
the expected Kullback-Leibler distance for the Poisson regression. Simulation studies
show that, compared with other commonly used model selection and model average
estimators, the proposed model average estimator performs better in certain situations,
especially when the model is nonsparse. In all the cases we simulated, the proposed
method never produces the worst results. Our proposed method is further applied to a
real data example, demonstrating the advantage of our method.
Finally, Chapter 6 summarizes this thesis and presents possible directions for future
study.
Notes: CityU Call Number: QA276 .Z45 2015; xviii, 173 pages : illustrations 30 cm; Thesis (Ph.D.)--City University of Hong Kong, 2015.; Includes bibliographical references (pages 153-166)2015-01-01T00:00:00ZHedging parameters estimation for American options and its application in upper bound algorithms
http://dspace.cityu.edu.hk:80/handle/2031/8482
Title: Hedging parameters estimation for American options and its application in upper bound algorithms
Authors: Zhang, Bingfeng (張炳鋒)
Abstract: Upper bound algorithms for pricing American-style options (also called
American options) usually rely on the approximations of the optimal
martingale. Tightness of the estimated upper bounds highly depends on the
construction of the martingale. The nested simulation method constructs
the martingale with the aid of an estimated lower bound process. It can be
easily implemented. However, a limitation of the nested simulation method
is its requirement of large computational effort.
Several non-nested upper bound algorithms for pricing American-style
options have been proposed in recent years. They are computationally
attractive where nested simulations are not necessary. The computational cost
is linear in the number of exercise dates. To incubate non-nested upper bound
algorithms, researchers study the characteristics of the optimal martingale
from various aspects, such as stability, martingale representation theorem,
analytical representation and connection with delta hedging. For the ideas
of analytical representation and connection with delta hedging, the
construction of the martingale comes down to the estimation of delta process.
It is well known that delta is one of the most important hedging parameters
for American-style options. However, estimating hedging parameters at any
date efficiently is not an easy task.
In this thesis, based on the dynamic-programming representation of the
value process, a least-squares method (LSM) is proposed to estimate the
hedging parameters backwardly. With this method, estimation of the delta
process can be done in an efficient way. Based on the delta estimates, two
ideas are implemented to generate non-nested upper bounds. The first one
is that the delta estimates can be included into the basis functions of the
regression procedure when estimating the martingale. The other one is that
the martingale can be constructed directly with no sub-simulation and no
optimization. Through numerical experiments, it is found that the latter
one is a better choice.
Notes: CityU Call Number: HG6024.A3 Z426 2015; xiii, 87 pages : illustrations 30 cm; Thesis (Ph.D.)--City University of Hong Kong, 2015.; Includes bibliographical references (pages 84-87)2015-01-01T00:00:00ZAnalysis of currency crises and exchange rate markets : Markov-switching based and vector auto-regression based approach
http://dspace.cityu.edu.hk:80/handle/2031/8481
Title: Analysis of currency crises and exchange rate markets : Markov-switching based and vector auto-regression based approach
Authors: Yu, Runfang (喻潤方)
Abstract: With opening up and liberalization of international financial markets, the frequency of currency crises has risen and the impact of currency crises has become larger. Thus, exchange rate markets analysis has become increasingly more important. The research on currency crisis identification and exchange rate forecasting can not only reflect the inherent pattern of financial markets but can also provide beneficial information for market participants which include hedgers, speculators, arbitrageurs and regulators. On the other hand, as the RMB’s role in global markets is expanding and its internationalization has been accelerating, it has become quite necessary and interesting to investigate the relationship of different RMB markets. This thesis proposes three research topics and makes contributions as follows.
The first topic of my thesis is about investigation of ways of identifying and predicting currency crises in world-wide markets, with special focus on 1997 and 2008 currency crises. A novel Markov Switching method is proposed for identifying a crisis regime, based on different states. Compared with previous Markov switching currency crisis studies, this model is different in several ways. Firstly, the dependent variable is different. While other papers use the exchange rate directly or the estimation of devaluation probability, this thesis uses the market pressure index calculated from nominal exchange rate and foreign reserves. Secondly, we allow different volatilities in different states while other papers assume the same volatility in two states. Thirdly, our transition probabilities are constant rather than time-varying. The model shows evidence of state switching before crisis in many different currency markets. Moreover, we compare the Markov-switching method with the more usual probit model which proposed an early warning system in terms of forecasting performance and it is better significantly as the result shows.
The second topic of my thesis is about the exchange rate forecasting improvement. The thesis extends the traditional monetary model and the random walk model with Markov-switching method and proposes two new forecasting models called Markov switching monetary model (MSMM) and Markov switching random walk model (MSRW). Then we evaluate the forecasting ability of these two new mixed models, MSMM and MSRW, and compare their results with traditional pure monetary model and pure Random walk model. The research shows that the two new mixed models outperform the two usual models in most scenarios.
My third topic is about the inter-relationship between three RMB exchange rate markets, CNH (offshore Renminbi market), CNY (onshore Renminbi market) and NDF (Renminbi non-deliverable forward) exchange rate markets. We analyze the latest three years daily exchange rate data by Johansen co-integration test, vector auto-regression model and granger causality test. The results show that long run equilibrium relationship does exist between these three markets. NDF market influences both CNH and CNY severely. However, CNH and CNY exchange rate markets do not influence NDF market much. Besides, CNY can guide CNH while the opposite is not true.
To sum up, this thesis investigates three research topics, currency crisis identification, exchange rate forecasting improvement and RMB markets interrelationships. Based on Markov-switching model, some combinations of Markov-switching model with random walk and monetary model and Vector auto-regression model, some impressive results can be obtained. Of course, some future works and problems need to be pointed out. First, more complex Markov-Switching Models can be investigated in the future. For example, two regimes Markov switching model can be extended to three regimes Markov switching model or the time varying transition probability matrix can be tried in assumption settings of Markov switching model. Second, in order to make the empirical results more convincing, categories of target currencies should be augmented and not be limited to only two currencies, JPY and GBP.
Notes: CityU Call Number: HG3851.3 .Y8 2015; x, 128 pages : illustrations 30 cm; Thesis (Ph.D.)--City University of Hong Kong, 2015.; Includes bibliographical references (pages 122-128)2015-01-01T00:00:00ZDynamic trading strategies in portfolio choice problems
http://dspace.cityu.edu.hk:80/handle/2031/8480
Title: Dynamic trading strategies in portfolio choice problems
Authors: Wang, Fei (王飛)
Abstract: This thesis studies dynamic trading strategies in portfolio choice problems. Investors
seek to allocate their wealth among different investment opportunities. The
optimal strategies are determined by various aspects related to risk attitudes of investors
and dynamic conditions of financial markets. The risk-averse utility functions
are used to characterize the investors risk preference. We consider three portfolio
choice problems.
The first model studies a portfolio choice problem with budget constraints. Borrowing
and short-selling constraints are not allowed. We characterize the optimal
dynamic policy for a two-period problem using an exponential utility function. Additionally,
we compare myopic and static policies with dynamic policies for different
conditions. Furthermore, we also study the optimality of dynamic and myopic policies
for multi-period problems with HARA utility functions. Finally, we provide
numerical examples in order to compare the different strategies’ performances.
In the second model, we determine the optimal investment strategy for scenarios
with both fixed and proportional transaction costs in a multi-period setting. The
optimal decision for the single period problem can be characterized by three regions
in which the investor should buy, sell, or hold his position. The optimal policy for
the multi-period problem is, unfortunately, more complicated, but with numerical
examples, we are able to show that a heuristic based on a single period policy
performs quite well.
In the third model, we study the mean-reversion effect in the stock market.
The market efficiency theory implies that prices respond quickly and accurately to
relevant information in the stock market. However, there is a great deal of debate
over the efficient market hypothesis with a large amount of empirical evidence both
supporting and contradicting the argument. Mean reversion in stock prices would
indicate that this theory is largely incorrect, and as such, we examine the China
A-share market for this phenomenon. An analysis of 700 stocks over a 6-year period
shows that there is a significant mean reversion effect under the appropriate horizon.
Notes: CityU Call Number: HG4529.5 .W36 2015; v, 93 pages : illustrations 30 cm; Thesis (Ph.D.)--City University of Hong Kong, 2015.; Includes bibliographical references (pages 88-93)2015-01-01T00:00:00Z