Chapter 2

Some Useful Time-Series

Methods

International macroeconomic and Þnance theory is typically aimed at explaining the evolution of the open economy over time. The natural way to empirically evaluate these theories are with time-series methods. This chapter summarizes some of the time-series tools that are used in later chapters to estimate and to test predictions by the theory. The material is written assuming that you have had a Þrst course in econometrics covering linear regression theory and is presented without proofs of the underlying statistical theory. There are now several accessible textbooks that contain careful treatments of the associated econometric theory.1 If you like, you may skip this chapter for now and use it as reference when the relevant material is encountered.

You will encounter the following notation and terminology. Underlined variables will denote vectors and bold faced variables will denote matrices. a = plim(XT ) indicates that the sequence of random variables {XT } converges in probability to the number a as T → ∞. This means that for su ciently large T , XT can be treated as a constant. N(µ, σ2) stands for the normal distribution with mean µ and variance σ2, U[a, b] stands for the uniform distribution over the interval [a, b],

iid N(µ, σ2) means that the random variable X				is independently
Xt		iid	t
and identically distributed as N(µ, σ2), Xt (µ, σ2) means that Xt is
1See Hamilton [66],	Hatanaka [74], and Johansen [81].

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