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Temporal Issues in Market Inefficiency in asset prices with an emphasis on commodities



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Ahmed, Muhammad Farid  ORCID logo


This summary provides an overview of the contributions made in this thesis to the literature. No references are included in the summary; these can be found in the Bibliography on page 156. This dissertation consists of 6 chapters. The first chapter acts as an introduction to the thesis and discusses the central theme of the dissertation along with providing a preview of what to expect in the following chapters. The contributions of the different chapters vary. Chapter 2 is a more introductory chapter and its contributions are perhaps less consequential than those in Chapters 3-5. Chapter 2 makes contributions to the literature on testing for explosive roots or bubbles. By modifying the Bhargava test statistic, we show in Chapter 2 that the Bhargava test can address earlier criticisms that had been cited against it; namely that it has low power when multiple bubbles are present in a particular series. Through introducing a rolling window approach, we are able to address that criticism and show that the modified Bhargava test statistic achieves better power. We compare and contrast the power of the modified test with the popular GSADF test statistic which has recently become popular in bubble testing literature. Another contribution made in this chapter is the application of these tests to a data set comprising of 25 commodities. As at the writing of the chapter this was believed to be a first attempt to perform bubble testing on a comprehensive commodity data set. Since commodities are often deemed to be targets of speculative behaviour, they are a natural universe for testing notions of market efficiency as they tend to go through different regimes through natural economic processes. Using both tests we are able to detect bubbles in similar periods with most of them being concentrated around the two oil price crises (1972-73 and 1979-80) and the financial crisis (2005-2007). Our conclusion is that the modified Bhargava statistic works better than the original statistic and can be used to complement the results of other statistics. The major contributions of Chapter 3 and 4 are the introduction of different methodologies that enable the user to assess how often asset markets are efficient. In Chapter 3 we argue that commodity prices can be estimated using switching-regression models including hidden Markov state-switching models. Instead of estimating Markov transition matrices directly from the estimation procedure, we estimate the transition matrix separately using unit root tests. By restricting the transition matrix to our estimated matrix and then estimating a Markov state-switching regression we show that we get more accurate smoothed probabilities i.e. a high probability is assigned to explosive states when the price was actually explosive and a high probability is assigned to the random walk/efficient state when the price exhibited efficient behaviour. This methodology is then extended to the three state case and it is argued that the transition matrices estimated this way will inform us of how often commodity markets are efficient. The methodology is empirically applied to non-ferrous metals with particular attention to Copper; we believe this is an additional contribution of the article. Chapter 3 also presents a partial equilibrium model which leads to an estimable reduced form expression for commodities and thereby motivates estimation by Markov switching-regressions. Three major contributions are made in Chapter 4. Firstly, we make a theoretical contribution to the literature on threshold auto-regressive models with exogenous triggers. Conditions for the existence of a mean and variance when a series follows a threshold auto-regressive (TAR) process with an exogenous trigger are derived. The second contribution is the use of TAR simulations to show that the tests which try to detect bubbles in asset prices lose a substantial amount of power when the asset price spends some time in the mean reverting state in addition to being in the explosive and random walk states. The third contribution of this article is the provision of a framework using TAR models which acts as a metric for market efficiency. By considering three states, an efficient/random walk state, a mean reverting state and an explosive state, we show that estimating asset prices as TARs with exogenous triggers can allow us to measure how often an asset market is efficient. This methodology uses a different class of models from those used in Chapter 4. The methodology is then applied to the S&P500 and FTSE100 process and it is shown that under the most general model specification, the indices primarily exhibit market efficiency. Chapter 5 looks deeper into how commodity prices are determined and thereby the main contribution is to the literature on commodity market pricing. By making three important changes to the commodity storage model of William and Wright (1991), we are able to show that our model is able to capture essential features of commodity prices that have not been captured by previous iterations. The numerical solution for the model is obtained using the Parameterized Expectations Algorithm (PEA) and simulated series based on this solution are able to reproduce some statistical features of real commodity price series including a high degree of first order auto-correlation, skewness and kurtosis. A second contribution is with regards to the application of the model; we calibrate the model to match five real commodities and show that the model’s solution is able to match real life data. The model is also able to explain why we observe spikes (bubbles) in commodity prices and cites the impact of storage as a probable contributor. Chapter 6 provides concluding remarks on the dissertation.





Satchell, Stephen


Asset Prices, Threshold Regressions, Time Series Econometrics, Commodity prices, Bubbles, Non-linear regression, Markov process, Markov regression


Doctor of Philosophy (PhD)

Awarding Institution

University of Cambridge
Higher Education Commission of Pakistan, Cambridge Commonwealth Trust