ECON3206/ECON5206 Financial Econometrics
Sample Answers/Hints to Tutorial 1
1. The Taylor expansion of () = ln(1 + ) around 0 = 0 is simply () (0) +
(0)( 0) = . Then = ln 1 +
1
1
1
1
= .
2. The return from the end of day 1 to the end of day 3 is ln 3 =
Financial Econometrics
ECON3206/5206
2016, S2
Course review
School of Economics, UNSW
Review, Financial Econometrics
1
Summary & review
Course coverage
Topics 1
Data of interest: financial time series and their
features, mainly return series
Descript
University of New South Wales, School of Economics
Financial Econometrics
Tutorial 5 solutions
1. Estimating MA
Consider an invertible MA(1) model: = + + 1 1, WN(0, 2 ).
Using the MA(1) equation for = 1,2,3, we find
1 = 1 1 0 ,
2 = 2 1 1 = 2 1 (1 1 0 ),
3
Sample Answers/Hints to Tutorial 8
1. (ARCH model characteristics)
(a)
The specification |1 (0, 2 ) implies that the conditional mean of is 0. The
conditional mean of is + 1 1 . The unconditional mean of is 0, by iterated expectations.
The unconditional m
Sample Answers/Hints to Tutorial 9
1. (GARCH model characteristics)
(a-b)
From |1 (0, 2 ), it is clear that ( |1) = 0 and Var( |1 ) = 2 . It
follows that ( |1) = + 1 1 and Var( |1) = 2 . The unconditional means are
obtained by iterated expectations:
( ) =
ECON3206/ECON5206 Financial Econometrics
Sample Answers/Hints to Tutorial 2
1. Linear regression models are linear in parameters. With a log transformation, (1) becomes
ln( ) = + ln( ) + , a linear regression model. Hence both (1) and (3) are linear
regre
Sample Answers/Hints to Tutorial 6
1. (Error correction and common trend)
The first VEC equation is directly obtained from the assumption that = 1 + with 1 = 0,
11 = and 1 = . The second VEC equation can be found from = +
= 1
= 1 + +
= (1 1 ) + 1 +
= (
University of New South Wales, School of Economics
Financial Econometrics
Tutorial 4 solutions
Question 1. Consider the AR(1) model
yt =+
b1yt 1 + t where t 0 WN (0, 2 ) .
(a)
Calculate unconditional E (yt ), var(yt ) and corr(yt , yt i ) for i = 1,2 .
E
Sample Answers/Hints to Tutorial 3
1. Durbin-Watson statistics is given by as
=
=2( 1 )2
=1 2
=
= 2(1 )
=2 2
=1 2
+
=2 1 2
=1 2
2 =2 1
1 + 1 2
=1 2
As 1 1, 0 4, when is small is close to 2.
2. Show that in the linear regression sum of squares total
=
SS
Financial Econometrics
ECON3206/5206
2014, S2
Slides-05
Lecturer:Chris Strickland
School of Economics, UNSW
Slides-05, Financial Econometrics
1
Topic 4. Modelling Long-run Relationships
Plan
Long-run relationship:
co-movement in trending time series
Co
Financial Econometrics
ECON3206/5206
2014, S2
Slides-03
Lecturer: Chris Strickland
School of Economics, UNSW
Slides-03, Financial Econometrics
1
Topic 3. Time Series Models
Plan
Time series models (mainly theoretical aspects)
View time series as stocha
Financial Econometrics
ECON3206/5206
2014, S2
Slides-04
Lecturer: Chris Strickland
School of Economics, UNSW
Slides-04, Financial Econometrics
1
Topic 3. Time Series Models
Plan
AR & MA mix - ARMA models:
features, and estimation
Maximum likelihood
l
Financial Econometrics
ECON3206/5206
2013, S2
Slides-02
Lecturer: Chris Strickland
School of Economics, UNSW
Slides-02, Financial Econometrics
1
Topic 2. Linear Regression & Applications in Finance
Plan
A review of linear regression
General form and bas
Sample Answers/Hints to Tutorial 10
1. (GARCH-in-mean model)
(a)
The rationale for including the conditional variance 2 (or its square-root) in the
mean equation is that a risky investment must be compensated by an expected return that is
higher than the
TOPIC 3
INTRODUCTION TO TIME SERIES ANALYSIS
1. Introduction
We now cover the basic concepts of time series analysis. As we will see, understanding
these concepts is crucial to an understanding of the time series models that capture timevarying volatility
Introductory Econometrics
[ECON 2206/3209]
Session 1 2012
Dr Gigi Foster
School of Economics, ASB
University of New South Wales
Teaching staff and resources
Lecturer-in-charge: Dr Gigi Foster, ASB 430B
My office hours: Tuesdays/Thursdays/Fridays 11 to 12
Lecture 2
The simple cross-sectional
OLS model
Introductory Econometrics
UNSW Session 1, 2012
Outline of today
Some tales from an econometrician friend
Understanding and working with random
variables (including a few statistical proofs for
you to do at ho
Lecture 3
Multiple Cross-sectional OLS
and
Preview of Inference
Introductory Econometrics
UNSW Session 1, 2012
Motivation 1: Omitted variables
wage = 0 + 1educ + error,
where error represents (or contains) exper.
exper is likely to be related to educ.
T
Lecture 4
Inference I
Introductory Econometrics
UNSW Session 1, 2012
Motivation
y = 0 + 1x1 +.+ kxk + u
Our objective is to gain knowledge about the population
parameters (s) in the model.
OLS provides point estimates for these parameters, and we
can deri
Lecture 5
Inference II
Introductory Econometrics
UNSW Session 1, 2012
Topics for today
y = 0 + 1x1 +.+ kxk + u
How to construct prediction intervals for E(Y|X) and
for Y
A note on goodness of fit comparisons across models
Re-cap of omitted variables bias
Financial Econometrics
ECON3206/5206
2016, S2
Slides-04
Lecturer: Rachida Ouysse
School of Economics, UNSW
Slides-04, Financial Econometrics
1
Topic 3. Time Series Models
Plan
Time series models (mainly theoretical aspects)
View time series as stochast
Financial Econometrics
ECON3206/5206
2016, S2
Slides-02
Lecturer: Rachida Ouysse
School of Economics, UNSW
Slides-02, Financial Econometrics
1
Topic 2. Linear Regression & Applications in Finance
Plan
A review of linear regression
General form and basic
Financial Econometrics
ECON3206/5206
2016, S2
Slides-03
Lecturer: Rachida Ouysse
School of Economics, UNSW
Slides-02, Financial Econometrics
1
Topic 2. Linear Regression & Applications in Finance
Linear regression
Diagnostic statistics
SSR and the esti
ECON3206/5206 Financial Econometrics
Tutorial 3
1. Recall the Durbin-Watson statistics is given by as
=2( 1 )2
=1 2
Show it is approximately equal to 2(1 ) , where is sample correlation coefficient. Based
on this find the maximum and the minimum values of
ECON3206/5206 Financial Econometrics
Tutorial 1
1. Let be the price of BHP share at the end of day , adjusted for dividends. The daily
return may be calculated either as the simple = ( 1 )/1 or the log return
= ln( /1 ). Show that when |( 1 )/1 | is smal
TOPIC 1
UNDERSTANDING FINANCIAL DATA
1.
Introduction
Before building financial models, it is important to understand the empirical
characteristics of financial data. Some key empirical properties investigated here are:
(i)
(ii)
(iii)
The shape of the empi