Assignment: Volatility modelling of exchange rate

In the wake of recent financial news of
i the rising bad debts of Australian banks, and consumers,
ii the 25 basis cut of interest rate by RBA to its historically low level of 1.5%,
iii the BHP Billiton’s first annual loss of USD6.385 since the BHP and Billiton merged 15 years
ago,
iv the UK decided to leave Europe, and
v a stubbornly high AUD (making Australian products less competitive internationally)
have had impacted local equity and the currency markets. One of the ways to analyze these impact
on the AU-US dollar exchange rate can be to look at the volatility movements of the exchange rate.
Crises period tend to increase volatility and the tranquil period tend to calm the market volatility.
The aim of this assignment is to analyze the same while building up the crucial concepts of ARCH
modeling along the way.
Download the data of Australian-US dollar exchange rate from the source mentioned below and
answer the followings:
i whether the Aus-US dollar exchange rate is a stationary process. Use both the graphical
approach and the statistical test.
ii draw the histogram of the exchange rate returns and compare it with the histogram of a
normally distributed random variable. Explain in few lines the differences you observe between
the two histogram. You can simulate data from the normal distribution with the mean and
the standard deviation obtained from the exchange rate returns data. The length of this
simulated/artificial data should match with the length of the exchange rate returns data.
iii set-up a statistical/econometric model for the exchange rate returns data with ARCH(2) process. Explain in a few lines what are known and unknown in this model and

how can we get
to know about the unknown?
iv determine whether there are ARCH effects in the model. Use both the graph and the statistical
test to justify your answer.
v redo the above with the artificial data you created in part (ii) above. Is there an ARCH effect
and why not?
vi set-up a likelihood function in Microsoft Excel and estimate unknown part of the model. You
will need to know the mean and variance equations and the likelihood function of the ARCH
model. Estimate the same model in EViews and compare the estimates of the model from two
software. At this point, you would appreciate yourself that you have unraveled (the black-box
of) what EViews has done it for you in one click.
vii obtain the forecast of the conditional variance of the return for the one week and comment on
2
the forecast.
Data: The price of the Australian dollar in terms of US dollar or the US dollar exchange rate per
Australian dollar. The sample period is from 04/01/2010 to date.
Data source: DATA
Notes: You will see a few observations are missing (ND: No data for this date) in the data. This is a
common problem when we deal with the real-life data. You can fix this problem in a few ways. Either replace the missing value with the value of the Aus-US dollar

exchange rate prior to the missing
value or replace it by the average value of the exchange rates of prior and post missing values. Since
the data size is huge, we perhaps do not need to worry about missing observations. Simply delete
the rows of your data set where missing observation appears. From part ii onwards, you would be
dealing with the continuously compounded daily returns of the Australian-US dollar price.
You are to submit a document in the CloudDeakin folder that lists the number and part of each
question (e.g. (b)I ) followed by your answer and the files containing all working on Excel/Eviews.
Do not replicate the question. Verbose and overly long assignments are not appreciated.
Please note that the word document file is to be marked. Any information you need
from Excel and/EViews output, please make it a part of the word document.