This paper assess nonlinear structures in the time series data generating mechanism of crude oil prices. We apply well-known univariate tests for nonlinearity, with distinct power functions over alternatives, but with different null hypotheses reflecting the existence of different concepts of linearity and nonlinearity in the time series literature. We utilize daily data on crude oil spot prices for over 26 years, as well as monthly data on crude oil spot prices for 41 years. Investigating the monthly price process of crude oil distinguishes this paper from existing studies of the time series structure of energy markets. All the tests detect strong evidence of general nonlinear serial dependence, as well as nonlinearity in the mean, variance, and skewness functions in the daily spot price process of crude oil. Since evidence of nonlinear dependence is less dramatic in monthly observations, nonlinear serial dependence is moderated by time aggregation in crude oil prices.

This chapter provides a review of hydraulic fracturing fluids and its effect on fracture propagation. It also reviews the effect of hydraulic fracturing and horizontal drilling on the aggregate economy, the factors that construct the cash flow of a project over its lifetime, and finally the production curves of hydraulically fractured wells. The first section of this chapter provides an in-depth review of economics of hydraulic fracturing including the variables that impact the cash flow and net present value analysis. The second section reviews the principals of hydraulic fracture propagation and summarizes the most applied models by the industry. A review of hydraulic fracturing fluid systems followed by their rheological properties and an example schedule of a hydraulic fracturing job are reported in the fourth section of this chapter. The fifth section provides a review of the environmental aspects of hydraulic fracturing fluids with a focus on chemical characteristics and produced water issues. The last section reviews different classes of production decline curve models with details of the analysis techniques for each model and discusses an example decline curve model from Kansas.