Posted: May 7th, 2022
SMM622 Advanced Financial Modelling and Forecasting
From either https://uk.finance.yahoo.com/ or Datastream or
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html or any alternative data provider
a) fifty price series of financial asset (say 𝑟𝑟𝑖𝑖𝑖𝑖 with 𝑖𝑖 = 1, … . , 50 and 𝑡𝑡 = 1, … . , 𝑇𝑇)
b) one of the major stock indices (say 𝑟𝑟𝑀𝑀𝑀𝑀 with M being either SP500 or FTSE100 or DW or Nasdaq or
….) at daily frequency for the last ten years from 1 January 2010 to the 31 March 2021.
1. Aggregate both 𝑟𝑟𝑖𝑖𝑖𝑖 and 𝑟𝑟𝑀𝑀𝑀𝑀 at annual frequency and take the log-returns.
a. Estimate the model 𝑟𝑟𝑖𝑖𝑖𝑖 = 𝜂𝜂𝑖𝑖 𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 ∗ 𝑟𝑟𝑀𝑀𝑀𝑀 𝜃𝜃𝑡𝑡 𝜃𝜃𝐽𝐽 𝑣𝑣𝑖𝑖𝑖𝑖 using pooled, least-squares dummy
variable (LSDV) and within-groups (WG) estimators and evaluate. Explain the difference
between random and fixed effects and describe the way in which you can test whether the
individual effects (𝜂𝜂𝑖𝑖) are random or fixed
b. Estimate an AR(1) dynamic model 𝑟𝑟𝑖𝑖𝑖𝑖 = 𝜂𝜂𝑖𝑖 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 ∗ 𝑟𝑟𝑖𝑖𝑖𝑖−1 𝜃𝜃𝑡𝑡 𝜃𝜃𝐽𝐽 𝑣𝑣𝑖𝑖𝑖𝑖 considering the
last only the first 5 years (2010-2014) and implement the Anderson and Hsiao (1981, 1982) and
the Arellano and Bond (1991) estimator where the number of valid instruments to exploit are
c. Contrast the results in b. with those that you obtain considering the last 5 years (2015-2019)
2. From the data set above, consider only five the log-returns series at daily frequency:
a. Assuming that the conditional mean follows an ARMA(0,0), estimate the conditional variance
of each log returns series by identifying the appropriate univariate (G)ARCH specification by
considering alternative GARCH models and alternative distributions of the innovations as
available in G@RCH.
b. Estimate an ARMA (1,1)-GARCH representation and compare it with the case of a simple
ARMA(0,0)-GARCH model identified above.
c. Estimate and comment the results from the implementation of three MGARCH models. In
particular, focus on the time pattern of the conditional correlations you get from the DCC model
highlighting links with stylized facts you know.
3. Evaluate the forecasting capability of three alternative volatility models following guidelines provided
in Brownlees et al (2011) and Hansen and Lunde (2015).
4. Following the Shu and Zhang (2013) paper, where authors used daily S
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