Lecture 11

# Lecture 11 - Introduction to time series analysis In many...

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1 Introduction to time series analysis In many cases (especially in macroeconomics) a sample consists of a set of observations measured over time Such data cannot be treated as a random sample - in fact we need new concept of population and sample In time series data the order (not the ‘label’) of the observations matters Means, variances, covariances do not depend on order: since summary statistics and regression do not use order information, this suggest that they need to be supplemented by other information Univariate time series analysis A single time series is explained by its own past history, and not by exogenous variables (as in linear regression) Such explanations are limited, but they • provide a framework for analysing the statistical properties of time series regressions • provide a benchmark against which we can evaluate regression models • can often suggest how a regression model of time series data should be designed Characteristics of time series - 1 Deterministic time series Are perfectly predictable from past data Constant: x t = μ Linear trend: x t = α + β t Cycles: x t = γ cos( ω t+ θ ) Stochastic time series Each observation is (wholly or partly) generated by a probabilistic mechanism and not predictable Constant + shock: x t = μ + u t The probability distribution of u t is knowable, but not the individual shocks

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2 Characteristics of time series - 2 Stationary time series The nature of the process does not depend on when it is observed Mean daily outside temperature in Cambridge
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## This note was uploaded on 03/07/2012 for the course ECON 201 taught by Professor Cowell during the Spring '10 term at LSE.

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Lecture 11 - Introduction to time series analysis In many...

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