Introduction to Econometrics
111
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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 Spring '10
 Cowell
 Economics, Econometrics, Autocorrelation, Stationary process, RK, autocorrelation function

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