notes10 - Time Series Regression Models ECON 399 Neil...

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Unformatted text preview: Time Series Regression Models ECON 399 Neil Hepburn Contents 1 Introduction 1 2 The Nature of Time Series Models 1 3 OLS Methods in Time Series Models 2 3.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.2 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4 Types of Models Static vs. Distributed Lag 5 5 Special Considerations 7 5.1 Functional Form . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.2 Dummy Variables & Index Numbers . . . . . . . . . . . . . . . . 8 5.3 Trending & Seasonality . . . . . . . . . . . . . . . . . . . . . . . 10 1 Introduction Introduction We now turn our attention to the last topic area of the course Time Series models We begin by looking at the general nature of time series models In the next (and final) set of lecture notes we will conclude with a look at the key problem that crops up in time series models - serial correlation 2 The Nature of Time Series Models Data has a temporal ordering The characteristic thing about time series models is that there is a definite ordering to the data 2000 comes before 2001, 2001 comes before 2002, and so on 1 In contrast, with cross-section data there is no such ordering The temporal ordering of the data is one of the key characteristics of time-series models The Meaning of Random We should take a moment to look at the issue of what the implications of time series data are for the concept of randomness In our earlier work, we could imagine the population being student grades at the U of A. A sample is drawn at random from that population and thus we have a random sample Time series data is somewhat different in that our data set will contain all observations between some starting point and an end point (say, 1951 to 2000) The Meaning of Random Some critics incorrectly assert that we can no longer assume randomness because of this feature. Not true We have to recognize that the actual values that arise each period (GDP, price level, unemployment, etc) are the result of stochastic processes The particular value that GDP takes on in a particular year is a function of a number of factors such as interest rates, consumer confidence, etc There is also a certain amount of randomness It is the nature of the stochastic processes inherent in time series models that creates some challenges for us 3 OLS Methods in Time Series Models OLS Methods Fortunately, much of what we have already covered is applicable to time series problems There are a couple of tweaks that we need to make to our underlying assumptions The temporal nature of time-series data also presents some particular challenges that we will address in the next set of lecture notes 2 3.1 Assumptions Assumptions The assumptions underlying OLS in time series models are largely the same as in the cross-sectional case There are a couple of exceptions These assumptions will lead us to similar conclusions about unbiasedness...
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notes10 - Time Series Regression Models ECON 399 Neil...

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