Applications of Information Theory to Economics and Finance

This thesis applies methods from the discipline of Information Theory to selected problems in both Economics and Finance. One concept that is central to Information Theory is Entropy. Entropy aims to measure the degree of uncertainty or randomness in a probability distribution. Rather than arbitrarily choosing a distribution as a suitable model, one could choose a distribution that possesses the maximum uncertainty while satisfying certain characteristics such as integrating to one and having specific moments (supplied by the modeller). A set of these characteristics form the constraints (or conditions) in the optimisation problem which involves maximising Shannon’s entropy. The solution to this optimisation problem is known as the Maximum Entropy Density (MED) and it is the most non-committal distribution function. As such, it is an excellent choice for modelling random phenomenon. This thesis applies this framework to four different applications across Economics and Finance. The global financial crisis led to a renewed focus on risk management along with an increased need to develop more robust methods to measure financial risks. Among these risks is liquidity i.e. an investor may find it difficult to convert some of their assets to their true market values in cash. As such, the investor may have to sell at a discount in order to maintain a certain level of liquidity. This thesis develops a model for liquidation discount rate, the discount an investor has to bear in the event of a liquidation sale of a portfolio of Australian stocks. The results indicate that the log liquidation discount rate possesses a long memory property. Hence, an ARFIMA-GARCH model is used to capture its dynamics. The resulting model is used for forecasting future discount rates as well as creating a new measure of liquidation discount-at-risk. This at-risk measure provides fund managers with a likelihood of an expected discount rate. A MED is estimated from the liquidation data and subsequently used to calculate the liquidation discount-at-risk. This process allows fund managers to budget for the future cost of liquidity for a given liquidation horizon and confidence level. vi For the second application, this thesis examines the seasonality in financial returns. This topic has been of major interest to financial investors ever since the creation of financial markets. In the existing literature, the majority of the studies focus on the seasonal behaviour of returns in terms of the mean and variance. This behaviour/periodic change for returns is not considered in terms of higher moments. Using a MED, this thesis to generalises the method for detecting seasonal behaviour in return data. The proposed method will enable the analyst to capture seasonal/periodic changes in higher moments. This method is applied to study seasonality in weekdays (day of the week effect) and also for trading hours within a given day (time of the day effect). By comparing MED densities (parameters) across each weekday or time of the day, one can test for differences between different days or for different times of the day. This methodology is applied to examine the seasonal behaviour of returns for foreign exchange rates. The results indicate that Wednesday is significantly different from the rest of the weekdays. Secondly, the 12 p.m. to 2 p.m. time slot is significantly different from the rest of the trading hours in the day. Both these results indicate changes in higher moments and these results have implications for funds management. For the third application, this thesis proposes a novel multivariate framework for MED. Unlike existing approaches, this framework is able to handle both a high number of variables as well as a high number of moment constraints with relative ease. In addition to this, the framework allows the each MED parameter to be function of one or more exogenous variables. The statistical properties (consistency and asymptotic normality) are provided for this multivariate framework. Next, this framework is used to model the distribution of Body Mass Index (BMI) for an individual given their socioeconomic attributes. From the results, it is evident that these attributes affect different moments of the estimated BMI distribution. These findings can be used to develop policies that reduce obesity levels. Finally, the thesis proposes a new method of modelling population changes. It is based on the cohort component model whereby the individuals in a given age group category transition to the next age group category over time. Based on this, the change in population for each age group is calculated and is modelled using a varying limit censoring regression model. Prior to the modelling stage, the Kullback-Leibler (KL) divergence measure is used to assess if there is difference in the population across two different time periods. These methods are applied to model indigenous populations in regional and remote Australia. The results indicate that the distributions differ significantly over time. vii Additionally, the model predicts an increase in the overall indigenous population by approximately 15% from 2011 to 2016. In the absence of population forecasts for regional and remote communities in Australia, these results bring direct benefits to researchers and planning agencies. The results also have important ramifications for services providers such as housing, health, education and infrastructure.