Lecture 11

# Lecture 11 - Introduction to Econometrics Lecture 11...

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Introduction to Econometrics 11-1 Technical Notes Introduction to Econometrics Lecture 11: Introduction to time series analysis Introduction Much of the data analysed by economists takes the form of time series. These differ from the random samples discussed so far, and analysing them statistically requires new concepts of the population and the sample : it also requires new statistical techniques. The distinctive feature of time series is that the sequential ordering of observations matters (this ordering differs from the ‘labels’ (special events) which may matter even in random samples). Since means, variances, and covariances (and regression coefficients) do not depend on the ordering of observations, this suggests that using summary statistics and regression may not make full use of the information in the data, and that additional techniques are needed to analyse time series. The most simple application of these techniques is to a single time series (a process called ‘univariate’ time series analysis). Variables are explained by their own past history, not by exogenous variables (as in regression): this appears to ‘step back’, but in fact the techniques can be extended to multiple time series and linked to regression analysis. Key characteristics of time series The first distinction is between deterministic and stochastic series. Deterministic series are wholly predictable (given enough information) from past data: examples are Constant: x t = μ for all observations t Linear trend: x t = α + β t for all observations t Periodic cycle (waves): x t = γ cos( ω t + θ ) for all observations t Stochastic series have the property that each observation is (wholly or partly) generated by a probabilistic mechanism and not predictable: an obvious example is Constant + random shock: x t = μ + u t for all observations t The probability distribution of u t is knowable, but not the individual shocks. Most economic series will have both deterministic and stochastic concepts, and we need to analyse both.

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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 Econometrics Lecture 11...

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