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Chapter 2Some Useful Time-SeriesMethodsInternational macroeconomic and Þnance theory is typically aimed atexplaining the evolution of the open economy over time. The naturalway to empirically evaluate these theories are with time-series methods.This chapter summarizes some of the time-series tools that areused in later chapters to estimate and to test predictions by the theory.The material is written assuming that you have had a Þrst course ineconometrics covering linear regression theory and is presented withoutproofs of the underlying statistical theory. There are now severalaccessible textbooks that contain careful treatments of the associatedeconometric theory. 1 If you like, you may skip this chapter for now anduse it as reference when the relevant material is encountered.You will encounter the following notation and terminology. Underlinedvariables will denote vectors and bold faced variables will denotematrices. a = plim(X T ) indicates that the sequence of random variables{X T } converges in probability to the number a as T →∞.Thismeans that for sufficiently large T , X T can be treated as a constant.N(µ, σ 2 ) stands for the normal distribution with mean µ and varianceσ 2 , U[a, b] stands for the uniform distribution over the interval [a, b],iidX t ∼ N(µ, σ 2 ) means that the random variable X t is independentlyand identically distributed as N(µ, σ 2 iid), X t ∼ (µ, σ 2 )meansthatX t is1 See Hamilton [66], Hatanaka [74], and Johansen [81].23