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Since a major source of income for many countries comes from exporting commodities, price discovery and information transmission between commodity futures markets are key issues for continued economic development. Commodities: Fundamental Theory of Futures, Forwards, and Derivatives Pricing, Second Edition covers the fundamental theory of and derivatives pricing for major commodity markets, as well as the interaction between commodity prices, the real economy, and other financial markets. After a thoroughly updated and extensive theoretical and practical introduction, this new edition of the book is divided into five parts - the fifth of which is entirely new material covering cutting-edge developments. Oil Products considers the structural changes in the demand and supply for hedging services that are increasingly determining the price of oil Other Commodities examines markets related to agricultural commodities, including natural gas, wine, soybeans, corn, gold, silver, copper, and other metals Commodity Prices and Financial Markets investigates the contemporary aspects of the financialization of commodities, including stocks, bonds, futures, currency markets, index products, and exchange traded funds Electricity Markets supplies an overview of the current and future modelling of electricity markets Contemporary Topics discuss rough volatility, order book trading, cryptocurrencies, text mining for price dynamics and flash crashes

In this article we identify incrementalism in budgetary processes with regularity in the annual change in the appropriation, and non-incrementalism with irregularity in the annual appropriation change. This definition focusses interest on structural changes in the underlying budget processes. These changes may be isolated using a combination of statistical and more conventional techniques. Other meanings of incremental, we argue, are appropriate to different objectives in studying budgeting. We attempt to clarify the confusion surrounding the meaning of incremental and to answer some of the critics of our previous work.

1 The optimization problem -- 1.1 Introduction -- 1.2 Problem definition -- 1.3 Optimization in one dimension -- 1.4 Optimization in n dimensions -- 2 Single variable optimization -- 2.1 Review of methods -- 2.2 The Fibonacci search -- 2.3 The Golden Section search -- 2.4 The Algorithm of Davies, Swann, and Campey -- 3 Multi-variable optimization -- 3.1 Introduction -- 3.2 Search methods -- 3.3 Gradient methods -- 4 Advanced methods -- 4.1 Introduction -- 4.2 General considerations -- 4.3 Advanced search methods -- 4.4 Advanced gradient methods -- 4.5 Minimax methods -- 5 Constrained optimization -- 5.1 Introduction -- 5.2 The Kuhn-Tucker conditions -- 5.3 Constrained optimization techniques -- 5.4 Direct search methods with constraints -- 5.5 Small step gradient methods -- 5.6 Sequential unconstrained methods -- 5.7 Large step gradient methods -- 5.8 Lagrangian methods -- 5.9 General considerations -- 5.10 Conclusion -- References -- Further reading.

The project on which this paper reports is aimed not only at increased understanding of the United States federal budget process, but also at predicting government expenditures in total and by bureau with a view to their determination within United States national econometric models. Estimates of likely expenditures using standard econometric techniques are poor, both in absolute terms and in comparison with our own work. Management of the economy should be improved by the use of predictors based on considering budgeting as a political process that is responsive to economic and social conditions. Use of mathematical models in the social sciences should be furthered, not by arguing their hypothetical utility, but by demonstrating that they work. The proof is in the prediction.

There are striking regularities in the budgetary process. The evidence from over half of the non-defense agencies indicates that the behavior of the budgetary process of the United States government results in aggregate decisions similar to those produced by a set of simple decision rules that are linear and temporally stable. For the agencies considered, certain equations are specified and compared with data composed of agency requests (through the Bureau of the Budget) and Congressional appropriations from 1947 through 1963. The comparison indicates that these equations summarize accurately aggregate outcomes of the budgetary process for each agency.In the first section of the paper we present an analytic summary of the federal budgetary process, and we explain why basic features of the process lead us to believe that it can be represented by simple models which are stable over periods of time, linear, and stochastic. In the second section we propose and discuss the alternative specifications for the agency-Budget Bureau and Congressional decision equations. The empirical results are presented in section three. In section four we provide evidence on deviant cases, discuss predictions, and future work to explore some of the problems indicated by this kind of analysis. An appendix contains informal definitions and a discussion of the statistical terminology used in the paper.