Improving the predictability of time series by chaotic parameter estimation

Limited literature regarding parameter estimation of dynamic systems has been identified as the central-most reason for not having parametric bounds in chaotic time series. However, literature suggests that a chaotic system displays a sensitive dependence on initial conditions, and our study reveals that the behavior of chaotic system: is also sensitive to changes in parameter values. Therefore, parameter estimation technique could make it possible to establish parametric bounds on a nonlinear dynamic system underlying a given time series, which in turn can improve predictability. By extracting the relationship between parametric bounds and predictability, we implemented chaos-based models for improving prediction in time series. ^ This study describes work done to establish bounds on a set of unknown parameters. Our research results reveal that by establishing parametric bounds, it is possible to improve the predictability of any time series, although the dynamics or the mathematical model of that series is not known apriori. In our attempt to improve the predictability of various time series, we have established the bounds for a set of unknown parameters. These are: (i) the embedding dimension to unfold a set of observation in the phase space, (ii) the time delay to use for a series, (iii) the number of neighborhood points to use for avoiding detection of false neighborhood and, (iv) the local polynomial to build numerical interpolation functions from one region to another. Using these bounds, we are able to get better predictability in chaotic time series than previously reported. In addition, the developments of this dissertation can establish a theoretical framework to investigate predictability in time series from the system-dynamics point of view. ^ In closing, our procedure significantly reduces the computer resource usage, as the search method is refined and efficient. Finally, the uniqueness of our method lies in its ability to extract chaotic dynamics inherent in non-linear time series by observing its values. ^

Essays on financial crises

This dissertation analyzes recent financial crises in developed and developing countries. The research emphasizes the effects of institutional factors on the international banking and currency crises and their output losses. ^ Chapter two examines the roles of regulation, supervision, and countries' institutional environment in determining the probability of banking crises for a panel of fifteen developed countries from 1975 to 1998. The results from a multivariate logit model indicated that countries with greater government involvement, less capital standard requirements, and lower lending limits on a single borrower are associated with a higher probability of banking crises. ^ Chapter three studies whether output loss in banking crisis differs in market-based or bank-based financial systems. Using existing banking crisis data for sixty-nine countries during 1970–1999, we investigate whether the underlying financial system affects the output loss. The results show that output losses are more serious in market-based economies than those in bank-based economies. Longer crisis duration tends to increase the output losses in banking crises. Finally, countries with deposit insurance and strict law enforcement have less output losses. ^ Chapter four uses macroeconomic and institutional measures to explain the extent of exchange rate depreciation and the decline in stock prices for emerging countries affected by the Mexican currency crisis of 1994–95. The results show that countries with more government budget deficits, and worse reserve adequacies tend to experience large exchange rate depreciation. The institutional measures do not explain much the extent of both the exchange rate depreciation and the decline in stock prices. ^

Three essays on trade and investment

From H. G. Johnson's work (Review of Economic Studies, 1953–54) on tariff retaliation, the questions of whether a country can win a “tariff war” and how or even the broader question of what will affect a country's strategic position in setting bilateral tariff have been tackled in various situations. Although it is widely accepted that a country will have strategic advantages in winning the tariff war if its relative monopoly power is sufficiently large, it is unclear what are the forces behind such power formation. The goal of this research is to provide a unified framework and discuss various forces such as relative country size, absolute advantages and relative advantages simultaneously. In a two-country continuum-of-commodity neoclassical trade model, it is shown that sufficiently large relative country size is a sufficient condition for a country to choose a non-cooperative tariff Nash equilibrium over free trade. It is also shown that technology disparities such as absolute advantage, rate of technology disparity and the distribution of the technology disparity all contribute to a country's strategic position and interact with country size. ^ Leverage effect is usually used to explain the phenomenon of asymmetric volatility in equity returns. However, leverage itself can only account for parts of the asymmetry. In this research, it is shown that stock return volatility is related to firms’ financial status. Financially constrained firms tend to be more sensitive to the return changes. Financial constraint factor explains why some firms tend to be more volatile than others. I found that the financial constraint factor explains the stock return volatility independent of other factors such as firm size, industry affiliation and leverage. Firms’ industry affiliations are shown to be very weak in differentiating volatility. Firm size is proven to be a good factor in distinguishing the different levels of volatility and volatility-return sensitivity. Leverage hypothesis is also partly corroborated and the situation where leverage effect is not applicable is discussed. Finally, I examined the macroeconomic policy's effects on overall market volatility. ^

Principal component and second generation wavelet analysis of Treasury yield curve evolution

Prices of U.S. Treasury securities vary over time and across maturities. When the market in Treasurys is sufficiently complete and frictionless, these prices may be modeled by a function time and maturity. A cross-section of this function for time held fixed is called the yield curve; the aggregate of these sections is the evolution of the yield curve. This dissertation studies aspects of this evolution. ^ There are two complementary approaches to the study of yield curve evolution here. The first is principal components analysis; the second is wavelet analysis. In both approaches both the time and maturity variables are discretized. In principal components analysis the vectors of yield curve shifts are viewed as observations of a multivariate normal distribution. The resulting covariance matrix is diagonalized; the resulting eigenvalues and eigenvectors (the principal components) are used to draw inferences about the yield curve evolution. ^ In wavelet analysis, the vectors of shifts are resolved into hierarchies of localized fundamental shifts (wavelets) that leave specified global properties invariant (average change and duration change). The hierarchies relate to the degree of localization with movements restricted to a single maturity at the base and general movements at the apex. Second generation wavelet techniques allow better adaptation of the model to economic observables. Statistically, the wavelet approach is inherently nonparametric while the wavelets themselves are better adapted to describing a complete market. ^ Principal components analysis provides information on the dimension of the yield curve process. While there is no clear demarkation between operative factors and noise, the top six principal components pick up 99% of total interest rate variation 95% of the time. An economically justified basis of this process is hard to find; for example a simple linear model will not suffice for the first principal component and the shape of this component is nonstationary. ^ Wavelet analysis works more directly with yield curve observations than principal components analysis. In fact the complete process from bond data to multiresolution is presented, including the dedicated Perl programs and the details of the portfolio metrics and specially adapted wavelet construction. The result is more robust statistics which provide balance to the more fragile principal components analysis. ^

Liquidity and asset pricing: A comparison between three-factor and three-moment capital asset pricing models

Liquidity is an important attribute of an asset that investors would like to take into consideration when making investment decisions. However, the previous empirical evidence whether liquidity is a determinant of stock return is not unanimous. This dissertation provides a very comprehensive study about the role of liquidity in asset pricing using the Fama-French (1993) three-factor and Kraus and Litzenberger (1976) three-moment CAPM as models for risk adjustment. The relationship between liquidity and well-known determinants of stock returns such as size and book-to-market are also investigated. This study examines the liquidity and asset pricing issues for both intertemporal as well as cross-sectional data. ^ The results indicate an existence of a liquidity premium, i.e., less liquid stocks would demand higher rate of return than more liquid stocks. More specifically, a drop of 1 percent in liquidity is associated with a higher rate of return of about 2 to 3 basis points per month. Further investigation reveals that neither the Fama-French three-factor model nor the three-moment CAPM captures the liquidity premium. Finally, the results show that well-known determinants of stock return such as size and book-to-market do not serve as proxy for liquidity. ^ Overall, this dissertation shows that a liquidity premium exists in the stock market and that liquidity is a distinct effect, and is not influenced by the presence of non-market factors, market factors and other stock characteristics.^

Essays on the selection of securities: Decision on acquisition and issuance perspectives and decision rules

This dissertation is a discourse on the capital market and its interactive framework of acquisition and issuance of financial assets that drive the economy from both sides—investors/lenders and issuers/users of capital assets. My work consists of four essays in financial economics that offer a spectrum of revisions to this significant area of study. The first essay is a delineation of the capital market over the past half a century and major developments on capital markets on issues that pertain to the investor's opportunity set and the corporation's capital-raising availability set. This chapter should have merits on two counts: (i) a comprehensive account of capital markets and return-generating assets and (ii) a backdrop against which I present my findings in Chapters 2 through 4. ^ In Chapter 2, I rework on the Markowitz-Roy-Tobin structure of the efficient frontier and of the Separation Theorem. Starting off with a 2-asset portfolio and extending the paradigm to an n-asset portfolio, I bring out the optimal choice of assets for an investor under constrained utility maximization. In this chapter, I analyze the selection and revision-theoretic construct and bring out optimum choices. The effect of a change in perceived risk or return in the mind of an investor is ascertained on the portfolio composition. ^ Chapter 3 takes a look into corporations that issue market securities. The question of how a corporation decides what kinds of securities it should issue in the marketplace to raise funds brings out the classic value invariance proposition of Modigliani and Miller and fills the gap that existed in the literature for almost half a century. I question the general validity in the classic results of Modigliani and Miller and modify the existing literature on the celebrated value invariance proposition. ^ Chapter 4 takes the Modigliani-Miller regime to its correct prescription in the presence of corporate and personal taxes. I show that Modigliani-Miller's age-old proposition needs corrections and extensions, which I derive. ^ My dissertation overall brings all of these corrections and extensions to the existing literature as my findings, showing that capital markets are in an ever-changing state of necessary revision. ^

The role of overseas Chinese investment in the emerging countries of Southeast and East Asia: A Confucian model of the foreign direct investment decision-making process using factors unconsidered in the West

The purpose of this study was to gain a better understanding of the foreign direct investment location decision making process through the examination of non-Western investors and their investment strategies in non-traditional markets. This was accomplished through in-depth personal interviews with 50 Overseas Chinese business owners and executives in several different industries from Hong Kong, Singapore, Taiwan, Malaysia, and Thailand about 97 separate investment projects in Southeast and East Asia, including The Philippines, Malaysia, Hong Kong, Singapore, Vietnam, India, Pakistan, South Korea, Australia, Indonesia, Cambodia, Thailand, Burma, Taiwan, and Mainland China.^ Traditional factors utilized in Western models of the foreign direct investment decision making process are reviewed, as well as literature on Asian management systems and the current state of business practices in emerging countries of Southeast and East Asia. Because of the lack of institutionalization in these markets and the strong influences of Confucian and patriarchal value systems on the Overseas Chinese, it was suspected that while some aspects of Western rational economic models of foreign direct investment are utilized, these models are insufficient in this context, and thus are not fully generalizable to the unique conditions of the Overseas Chinese business network in the region without further modification.^ Thus, other factors based on a Confucian value system need to be integrated into these models. Results from the analysis of structured interviews suggest Overseas Chinese businesses rely more heavily on their network and traditional Confucian values than rational economic factors when making their foreign direct investment location decisions in emerging countries in Asia. This effect is moderated by the firm's industry and the age of the firm's owners. ^

Three Essays on Asset Pricing

In this dissertation, I investigate three related topics on asset pricing: the consumption-based asset pricing under long-run risks and fat tails, the pricing of VIX (CBOE Volatility Index) options and the market price of risk embedded in stock returns and stock options. These three topics are fully explored in Chapter II through IV. Chapter V summarizes the main conclusions. In Chapter II, I explore the effects of fat tails on the equilibrium implications of the long run risks model of asset pricing by introducing innovations with dampened power law to consumption and dividends growth processes. I estimate the structural parameters of the proposed model by maximum likelihood. I find that the stochastic volatility model with fat tails can, without resorting to high risk aversion, generate implied risk premium, expected risk free rate and their volatilities comparable to the magnitudes observed in data. In Chapter III, I examine the pricing performance of VIX option models. The contention that simpler-is-better is supported by the empirical evidence using actual VIX option market data. I find that no model has small pricing errors over the entire range of strike prices and times to expiration. In general, Whaley’s Black-like option model produces the best overall results, supporting the simpler-is-better contention. However, the Whaley model does under/overprice out-of-the-money call/put VIX options, which is contrary to the behavior of stock index option pricing models. In Chapter IV, I explore risk pricing through a model of time-changed Lévy processes based on the joint evidence from individual stock options and underlying stocks. I specify a pricing kernel that prices idiosyncratic and systematic risks. This approach to examining risk premia on stocks deviates from existing studies. The empirical results show that the market pays positive premia for idiosyncratic and market jump-diffusion risk, and idiosyncratic volatility risk. However, there is no consensus on the premium for market volatility risk. It can be positive or negative. The positive premium on idiosyncratic risk runs contrary to the implications of traditional capital asset pricing theory.

Essays on competition in the pharmaceutical industry

Chapter 1: Patents and Entry Competition in the Pharmaceutical Industry: The Role of Marketing Exclusivity. Effective patent length for innovation drugs is severely curtailed because of extensive efficacy and safety tests required for FDA approval, raising concern over adequacy of incentives for new drug development. The Hatch-Waxman Act extends patent length for new drugs by five years, but also promotes generic entry by simplifying approval procedures and granting 180-day marketing exclusivity to a first generic entrant before the patent expires. In this paper we present a dynamic model to examine the effect of marketing exclusivity. We find that marketing exclusivity may be redundant and its removal may increase generic firms' profits and social welfare. ^ Chapter 2: Why Authorized Generics?: Theoretical and Empirical Investigations Facing generic competition, the brand-name companies some-times launch generic versions themselves called authorized generics. This practice is puzzling. If it is cannibalization, it cannot be profitable. If it is divisionalization, it should be practiced always instead of sometimes. I explain this phenomenon in terms of switching costs in a model in which the incumbent first develops a customer base to ready itself against generic competition later. I show that only sufficiently low switching costs or large market size justifies launch of AGs. I then use prescription drug data to test those results and find support. ^ Chapter 3: The Merger Paradox and R&D Oligopoly theory says that merger is unprofitable, unless a majority of firms in industry merge. Here, we introduce R&D opportunities to resolve this so-called merger paradox. We have three results. First, when there is one R&D firm, that firm can profitably merge with any number of non-R&D firms. Second, with multiple R&D firms and multiple non-R&D firms, all R&D firms can profitably merge. Third, with two R&D firms and two non-R&D firms, each R&D firms prefer to merge with a non-R&D firm. With three or more than non-R&D firms, however, the R&D firms prefer to merge with each other.^

Financial constraints on research and development

This dissertation examines whether-there exists financial constraints and, if so, their implications for investment in research and development expenditures. It develops a theoretical model of credit rationing and research and development in which both are determined simultaneously and endogenously. The model provides a useful tool to examine different policies that may help alleviate the negative the effect of financial constraints faced by firms.^ The empirical evidence presented deals with two different cases, namely, the motor vehicle industry in Germany (1970-1990) and the electrical machinery industry In Spain (1975-1990).^ The innovation in the empirical analysis is that it follows a novel approach to identify events that allow us to isolate the effect of financial constraints in the determination of research and development.^ Further, empirical evidence is presented to show that in the above two cases financial constraints affect investment in physical capital as well.^ The empirical evidence presented supports the results of the theoretical model developed in this dissertation, showing that financial constraints negatively affect the rate of growth of innovation by reducing the intensity of research and development activity. ^

Theory of foreign portfolio investment

This dissertation examines one category of international capital flows, private portfolio investments (private refers to the source of capital). There is an overall lack of a coherent and consistent definition of foreign portfolio investment. We clarify these definitional issues.^ Two main questions that pertain to private foreign portfolio investments (FPI) are explored. The first problem is the phenomenon of home preference, often referred to as home bias. Related to this are the observed cross-investment flows between countries that seem to contradict the textbook rendition of private FPI. A description of the theories purporting to resolve the home preference puzzle (and the cross-investment one) are summarized and evaluated. Most of this literature considers investors from major developed countries. I consider--as well--whether investors in less developed countries have home preference.^ The dissertation shows that home preference is indeed pervasive and profound across countries, in both developed and emerging markets. For the U.S., I examine home bias in both equity and bond holdings as well. I find that home bias is greater when we look at equity and bond holdings than equity holdings solely.^ In this dissertation a model is developed to explain home bias. This model is original and fills a gap in the literature as there have been no satisfactory models that handle at the same time both home preference and cross-border holdings in the context of information asymmetries. This model reflects what we see in the data and permits us to reach certain results by the use of comparative statics methods. The model suggests, counter-intuitively, that as the rate of return in a country relative to the world rate of return increases, home preference decreases. In the context of our relatively simple model we ascribe this result to the higher variance of the now higher return for home assets. We also find, this time as intended, that as risk aversion increases, investors diversify further so that home preference decreases.^ The second question that the dissertation deals with is the volatility of private foreign portfolio investment. Countries that are recipients of these flows have been wary of such flows because of their perceived volatility. Often the contrast is made with the perceived absence of volatility in foreign direct investment flows. I analyze the validity of these concerns using first net flow data and then gross flow data. The results show that FPI is not, in relative terms, more volatile than other flows in our sample of eight countries (half were developed countries and the rest were emerging markets).^ The implication therefore is that restricting FPI flows may be harmful in the sense that private capital may not be allocated efficiently worldwide to the detriment of capital poor economies. More to the point, any such restrictions would in fact be misguided. ^

Using extreme value theory to value stock market returns

Extreme stock price movements are of great concern to both investors and the entire economy. For investors, a single negative return, or a combination of several smaller returns, can possible wipe out so much capital that the firm or portfolio becomes illiquid or insolvent. If enough investors experience this loss, it could shock the entire economy. An example of such a case is the stock market crash of 1987. Furthermore, there has been a lot of recent interest regarding the increasing volatility of stock prices. ^ This study presents an analysis of extreme stock price movements. The data utilized was the daily returns for the Standard and Poor's 500 index from January 3, 1978 to May 31, 2001. Research questions were analyzed using the statistical models provided by extreme value theory. One of the difficulties in examining stock price data is that there is no consensus regarding the correct shape of the distribution function generating the data. An advantage with extreme value theory is that no detailed knowledge of this distribution function is required to apply the asymptotic theory. We focus on the tail of the distribution. ^ Extreme value theory allows us to estimate a tail index, which we use to derive bounds on the returns for very low probabilities on an excess. Such information is useful in evaluating the volatility of stock prices. There are three possible limit laws for the maximum: Gumbel (thick-tailed), Fréchet (thin-tailed) or Weibull (no tail). Results indicated that extreme returns during the time period studied follow a Fréchet distribution. Thus, this study finds that extreme value analysis is a valuable tool for examining stock price movements and can be more efficient than the usual variance in measuring risk. ^

Research on the influence of behavioral forces that motivate trader behavior and sentiment: A prospect theory exegesis

This study focuses on empirical investigations and seeks implications by utilizing three different methodologies to test various aspects of trader behavior. The first methodology utilizes Prospect Theory to determine trader behavior during periods of extreme wealth contracting periods. Secondly, a threshold model to examine the sentiment variable is formulated and thirdly a study is made of the contagion effect and trader behavior. ^ The connection between consumers' sense of financial well-being or sentiment and stock market performance has been studied at length. However, without data on actual versus experimental performance, implications based on this relationship are meaningless. The empirical agenda included examining a proprietary file of daily trader activities over a five-year period. Overall, during periods of extreme wealth altering conditions, traders "satisfice" rather than choose the "best" alternative. A trader's degree of loss aversion depends on his/her prior investment performance. A model that explains the behavior of traders during periods of turmoil is developed. Prospect Theory and the data file influenced the design of the model. ^ Additional research included testing a model that permitted the data to signal the crisis through a threshold model. The third empirical study sought to investigate the existence of contagion caused by declining global wealth effects using evidence from the mining industry in Canada. Contagion, where a financial crisis begins locally and subsequently spreads elsewhere, has been studied in terms of correlations among similar regions. The results provide support for Prospect Theory in two out of the three empirical studies. ^ The dissertation emphasizes the need for specifying precise, testable models of investors' expectations by providing tools to identify paradoxical behavior patterns. True enhancements in this field must include empirical research utilizing reliable data sources to mitigate data mining problems and allow researchers to distinguish between expectations-based and risk-based explanations of behavior. Through this type of research, it may be possible to systematically exploit "irrational" market behavior. ^

Estimation of global beta and tests of capital asset pricing models

With the rapid globalization and integration of world capital markets, more and more stocks are listed in multiple markets. With multi-listed stocks, the traditional measurement of systematic risk, the domestic beta, is not appropriate since it only contain information from one market. ^ Prakash et al. (1993) developed a technique, the global beta, to capture information from multiple markets wherein the stocks are listed. In this study, the global betas are obtained as well as domestic betas for 704 multi-listed stocks from 59 world equity markets. Welch tests show that domestic betas are not equal across markets, therefore, global beta is more appropriate in a global investment setting. ^ The traditional Capital Asset Pricing Models (CAPM) is also tested with regards to both domestic beta and global beta. The results generally support the positive relationship between stocks returns and global beta while tend to reject this relationship between stocks returns and domestic beta. Further tests of International CAPM with domestic beta and global beta strengthen the conclusion.^

A comprehensive portfolio construction under stochastic environment

Prior research has established that idiosyncratic volatility of the securities prices exhibits a positive trend. This trend and other factors have made the merits of investment diversification and portfolio construction more compelling. ^ A new optimization technique, a greedy algorithm, is proposed to optimize the weights of assets in a portfolio. The main benefits of using this algorithm are to: (a) increase the efficiency of the portfolio optimization process, (b) implement large-scale optimizations, and (c) improve the resulting optimal weights. In addition, the technique utilizes a novel approach in the construction of a time-varying covariance matrix. This involves the application of a modified integrated dynamic conditional correlation GARCH (IDCC - GARCH) model to account for the dynamics of the conditional covariance matrices that are employed. ^ The stochastic aspects of the expected return of the securities are integrated into the technique through Monte Carlo simulations. Instead of representing the expected returns as deterministic values, they are assigned simulated values based on their historical measures. The time-series of the securities are fitted into a probability distribution that matches the time-series characteristics using the Anderson-Darling goodness-of-fit criterion. Simulated and actual data sets are used to further generalize the results. Employing the S&P500 securities as the base, 2000 simulated data sets are created using Monte Carlo simulation. In addition, the Russell 1000 securities are used to generate 50 sample data sets. ^ The results indicate an increase in risk-return performance. Choosing the Value-at-Risk (VaR) as the criterion and the Crystal Ball portfolio optimizer, a commercial product currently available on the market, as the comparison for benchmarking, the new greedy technique clearly outperforms others using a sample of the S&P500 and the Russell 1000 securities. The resulting improvements in performance are consistent among five securities selection methods (maximum, minimum, random, absolute minimum, and absolute maximum) and three covariance structures (unconditional, orthogonal GARCH, and integrated dynamic conditional GARCH). ^