CS代考 ECON3206/5206 Financial Econometrics

Microsoft Word – Tutorial 2.docx

ECON3206/5206 Financial Econometrics

Tutorial 2
1. With a suitable transformation, which of the following models can be classified as linear

regression and estimated by OLS? Comment.

(1) 𝑦! = 𝑒”𝑥!

(2) 𝑦! = 𝛼 + 𝛽𝛾𝑥! + 𝑢! ,

(3) 𝑦! = 𝛼 + 𝛽𝑥!𝑧! + 𝑢! ,

where 𝑒% is the exponential function; 𝛼, 𝛽 and 𝛾 are parameters to be estimated; 𝑦! is a

dependent variable; 𝑥! and 𝑧! are explanatory variables; 𝑢! is the error term with

𝐸(𝑢!|𝑥! , 𝑧!) = 0.

2. Derive the OLS estimator for the coefficient α for the following simple model: .

You may use matrix notation, if you want.

3. Suppose that a population equation is given by . Instead you estimated

the following linear regression model . Assume . It is well known

that the estimator of typically will suffer from the omitted variables bias. Derive the bias

and state the condition(s) under which the estimator will be still unbiased.

4. The chart below describes the evolution of the yield curve for the Australian government

bonds at different maturities. Interpret the annualized yield? What it the relation between the

yields and the bond prices? Which tendency do you observe about the yield curve? What

does it signal about the expectations of the market participants about the future yields? (Use

the law of one price to support your discussion). How these expectations relate to the

inflation expectations and the level of economic activity?

a= +t tY u

= + +Y Xβ Zγ u

= +Y Xb e =E u X Z[ | , ] 0

Source: Bloomberg

Python exercises

1. (Commodity Prices) The Excel data file commod.XLS contains daily data from the 1st

of May 1989 to the 26th of February 1993 (a total of 1000 observations) on the following

commodity prices: copper, gold, lead and silver.

(a) For the commodity price (denoted P) of Copper,

– generate the returns: 𝑟! = 100[ln(𝑃!) − ln(𝑃!&’)],

– generate squared (and absolute) returns,

– Time series plot the returns, the squared (and absolute) returns.

(b) For the returns, squared returns and absolute returns, compute

i. Summary or descriptive statistics: mean, variance, skewness and kurtosis.

ii. The empirical distribution a histogram.

iii. The Jarque-Bera test of normality.

Characterise their empirical distributions.

(d) For the three series (returns, absolute returns and squared returns, compute

i. The first twelve autocorrelation coefficients of returns.

ii. Are the returns, squared returns and absolute returns autocorrelated?

iii. Given the results, would you support the claim that the Copper market is

efficient?

(e) Repeat (a) – (d) for Gold price series (and the other two commodities if you wish).

2. Under the Fisher hypothesis, nominal interest rates fully reflect the long-run movements

in inflation. Let 𝑅! be the nominal interest rate and 𝜋! be the inflation rate. The Fisher

hypothesis (due to of the University of Chicago) is given by 𝑅! = 𝛽( +

where 𝑢! is a disturbance term. If the Fisher hypothesis is correct 𝛽’ = 1. Using the

data in the excel file fisher.XLS, which contains 108 quarterly Australian data for

the period 1969:3 to 1996:2 on R (90 day bank accepted bill rate) and P (the

Australian CPI), test the Fisher hypothesis by doing the following.

(a) Construct the inflation rate as . We multiply by 400 to

express the change in price as an annual percentage change. In EViews, generate

the series as Graph both the interest rate and

inflation.

(b) Estimate the model and interpret the parameter estimates.

(d) Compute the autocorrelations and partial autocorrelations for and . Interpret

your results

1400(log log )t t tP Pp += –

400 * (log( (1)) log( ))INF P P= –

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