Exampleofcointegratedseries:
Timeseriesofconsumptionand
income
1
CointegrationandError
CorrectionModels
Continued
2
TheErrorCorrectionMechanism
Consider a simple bi-variate case where yt and x1t
are cointegrated
yt = B1x1t + et
et = yt B1x1t in LR equilib
Modelling Volatility GARCH
Heteroscedasticity Revisited
An example of a structural model is
yt = 1 + 2x2t + 3x3t + 4x4t + u t
with ut N(0, u2 ).
The assumption that the variance of the errors is constant is known as
2
homoskedasticity, i.e. Var (ut) = u .
Multivariate time series
models
VARs and Causality Tests
Chapter 12&15 Asteriou (apprx 20-pages)
Chapter 6 Brooks
Chapter 5 Enders
Simultaneous Equations Models
All the models we have looked at thus far have dealt with single dependent
variables and estim
EC564FinancialEconometricsI
(TimeSeriesAnalysis)
Stephen ONeill
Department of Economics
St Anthonys
Email: [email protected]
WhatisEconometrics?
The study of methods that enables us to
quantify economic relationships using actual
data
It inclu
Lecture5:StationarityandUnitRoots
ReadingAsteriouP229239andChapter16
(orEndersChapter4)
1
Background
Up to now we have been mostly looking at
cross-section methods, today we will begin to
move towards time-series econometrics and
we will focus on this for
StationaryTimeSeriesModels
(Wellseenonstationarymodelslaterinthecourse)
Univariate Time Series Analysis
ARIMA Models
StationarySeries
Reviewfromearlierlectures:
A series is covariance stationary when
Mean:
Variance:
Covariance
E(Yt) = u
Var(Yt) = E (Yt u)
MultipleRegression
MultipleRegression
So far we have only examined the case where there
is only one explanatory variable.
Often the variable we are interested in is related to
more than one variable and their effects on Y
E.g.1 A firms share price may be
A quick note on the difference between PACF and ACF:
Consider a series like: Yt = + 1yt-1 + 2Yt-2 +t
suppose we use backward substitution:
Yt = + 1yt-1 + 2Yt-2 +t
=> Yt-1 = + 1yt-2 + 2Yt-3 +t-1
=> Yt = + 1 ( + 1yt-2 + 2Yt-3 +t-1) + 2Yt-2 +t
So here Yt-3 w
Questions on OLS
Consider the econometric model of the following form
Yt = 1 + 2X2t + 3X3t + 4X4t + t,
where Yt is the dependent variable, X2t, X2t, X4t are observations on independent
variables, i are unknown parameters and t is a random error term.
1. E
Exercises for Hypothesis testing:
1) Using the Z tables find the probability of observing a value in the following ranges:
(a) 0 < Z < 2
(b) 0 < Z < 3
(c) 0 < Z < 2.57
(d) -2 < Z < 0
(e) -1 < Z < 0
(f) -1 < Z < 1
(g) -1 < Z < 3
2) Suppose now that we have