FINA304 - 2022 - T2
Tutorials
Yiğit Sağlam
Tutorial 5
This tutorial is about volatility models, which are covered on Chapter 5. Please work on
the following problems, using the lecture notes.
Question 1. Market Returns
Suppose that we aim to forecast the market returns. To perform an econometric analysis,
we collect the value-weighted return (without dividends) data of NYSE, NASDAQ and
S&P500 from 1973M 1 to 2011M 12. The dataset is titled “StockReturns vwretd.csv” and
available under “Tutorials” on Blackboard.
(a) Determine the order of integration for the three variables at 5% significance level.
(b) Estimate an ARMA(1,0) model for the NASDAQ returns. Test the residuals for
heteroskedasticity.
(c) Estimate the ARCH-M(1) model for the NASDAQ returns using an ARMA(1,0)
model for the mean equation. Explain your findings.
(d) Propose a final model for the NASDAQ returns. Would you suggest to keep the
variance term in the mean equation?
(e) Predict the two years using your final model. Comment on how the variance forecast
is changing over time.
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FINA304 - 2022
Tutorials
Yiğit Sağlam
Question 2. High-Tech Companies
Suppose that we aim to investigate the distribution of returns of some high-tech companies to see how the industry worked out over time. To perform an econometric analysis,
we collect the monthly price and return (without dividends) data of IBM, Dell, and Microsoft from 1989M 1 to 2011M 12. The dataset is titled “StockPrices.csv” and available
under “Tutorials” on Blackboard.
(a) Determine the order of integration for the three price variables at the 5% significance
level.
(b) Propose a linear regression or an ARMA model for the MSFT prices.
(c) Estimate the ARCH(1) model for the MSFT returns using an ARMA model for the
mean equation. Explain your findings.
(d) Propose a final model for the MSFT returns. Would you suggest to keep the variance
term in the mean equation? How do your results change if you consider more lags
for the ARMA model?
(e) Predict the next 12 months using your final model. Comment on how the variance
forecast is changing over time.
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