Graduation Year

2023

Document Type

Dissertation

Degree

Ph.D.

Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Mathematics and Statistics

Major Professor

Chris P. Tsokos, Ph.D.

Committee Member

Kandethody M. Ramachandran, Ph.D.

Committee Member

Lu Lu, Ph.D.

Committee Member

Yicheng Tu, Ph.D.

Keywords

Desirability Function, Financial Indicator, Kumaraswamy Laplace, Stochastic–Index–Return-Indicator, Variance–Gamma Distribution

Abstract

Data contain important information and data driven decision making process is the most for any type of businesses to succeed. It is the fact that businesses which follow data driven decision making process will have competitive edge over their counterparts which contributes in value creation for any firm or individual. Statistical procedure and methodology is the heart of data science which helps to extract crucial information from the data scientifically. It is common technique to use algorithm on historical data to see the outcome for the future which we defined as “prediction”, and predictive modeling is one of major statistical analysis applications in a real world. More specifically, predictive modeling is the algorithm based mathematical/statistical process used to predict future outcomes by analyzing patterns on the historical data. A real data-driven predictive models in any field may it be finance, economics, healthcare or any industry assist individual and institutions to make informed decisions. In this dissertation, we proposed an advanced real data-driven analytical predictive models to predict weekly closing price of the Information Technology Sector Index of S&P 500 and one of the leading companies of the index–Microsoft Corporation (MSFT stock) to predict the weekly closing price with at least 98% of predictive accuracy. We identified statistically significant attributable indicators and their interactions that influence the weekly closing price of the index/stock. The rank of the indicators and their interactions based on the percentage of their contribution to the weekly closing prices provides significant information for the beneficiaries of proposed model. In addition, we developed mathematical driven optimization model to maximize the response (weekly closing price) of the stock by controlling the statistically significant attributable indicators using response surface desirability function method. The optimization method using desirability function well executed to set the target value of our response. We strongly believe that the proposed model has significant contribution in investment analysis decision making process.

Monitoring returns through stock price prediction is a real world complicated problem because the market is affected by many non-numerical factors and there is a high level of noisiness. We have introduced and defined stochastic–index–return–intensity-function and stochastic–index–return–indicator to monitor returns using non-homogeneous Poison process. The stochastic–index–return–indicator generates trading signals which assists investors in investment decision making process for setting trading rules in buy–sell-hold decisions. This research aims to contribute highly in strategic investment planning process for optimal return.

Further, identification of the right kind of probability distribution for stock returns modeling is the key in investment analysis and we conducted an empirical study with Laplace family of probability distributions using real market data from the S&P 500 and its eleven constituents business segments. Novel statistical methodologies are used to examine the goodness–of–fit of the distributions and identified that Kumaraswamy Laplace probability distribution outperforms the selected other four distributions from the Laplace family. This finding about the best fit probability distribution–‘Kumaraswamy Laplace’ over four other similar distribution from Laplace family, especially, the most popular Variance-Gamma dis- tribution will definitely brings lots of discussions and applications in the area of applied finance and economics for stock returns modeling and predictions.

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