Empirical Economics of Production, Governance, Finance and Regu

The main theme of this chapter is that univariate time series are everywhere in empirical economics. We suggest tools for a deeper understanding of them. Certain macroeconomic time series such as GNP have been studied by univariate time series methods by many authors. Most are published as “seasonally” adjusted. In Finance, the stock returns are also widely studied by these methods for so called “technical” analysis with a view to forecasting future returns. If $1 is invested on portfolio priced at Pt at time t, if the price (adjusted for dividends) at time t+1 is higher, the net return (Pt+1−Pt)/Pt will exceed the initial investment of $1. Continuously compounded return is defined as the exponential return, exp(rt), which is always positive. Since the net return can be negative when losses are incurred, one defines gross return as: GRt= 1+ (Pt+1−Pt)/Pt =Pt+1/Pt, which is always positive, since prices are positive. It is customary to equate the exponential return to the gross return and write rt = log(Pt+1/Pt) = logPt+1−logPt. This is called the first difference of logs of prices evaluated at time t+1. The theory of stochastic difference equations discussed later deals with equations involving such differences denoted by the difference operator ∆. The following R programming snippets should be used to plot the typical time series.