Characterizing a Relationship between Time Series

Once an analyst characterizes a time series in terms of its cycle and trend, then he or she may wish to identify a possible statistical relationship between that series and another time series of interest by asking: Do the two time series have a statistical relationship between themselves? More fundamentally, if a statistical relationship exists between the variables, why is it of interest to decision makers? As mentioned previously, there are many relationships suggested by economic and financial theory, such as the relationship between: gross domestic product (GDP) and the unemployment rate (Okun's law); inflation and the unemployment rate (Phillips curve); financial development and economic growth;1 and the money supply and inflation (money neutrality). For each theory, a decision maker will test a relationship to answer key questions, such as: If there is a link between GDP growth and employment, then how many new jobs would be associated with a certain pace of GDP growth? How much inflation do we get for a given increase in the money supply?

Many of these relationships are based on different economic theories of behavior. In practice, however, these theories must be confirmed in order to offer a real-world guideline for decision makers. For instance, one economic theory might suggest that an increase in a country's money supply may change its price level, all else being equal, yet not impact real growth. Such money ...

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