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Prepare your modelling report with related tables, figures, interpretations, and explanations based on the following tasks (please submit in PDF format):

  1. Get access to Yahoo Finance and download five-year historical daily prices of a stock or stock index.
  2. Divide the sample into two sub-samples: in sample for model estimation, and out-of-sample for forecasting. The length of the out-of-sample is two weeks (10 trading days)
  3. Calculate the logarithm returns for the stock. Analyse the stock return characteristics, including, return distribution, serial correlation, and volatility clustering for the in-sample period. (20 marks)
  4. Based on analyses in step 3, build an appropriate GARCH model for the return volatility using the in-sample period and explain why the model specification is appropriate. (Note that: you may not need to capture the serial correlation of the return level using ARMA model, but if you do so, you can earn the reward mark of 5 marks). (20 marks)
  5. Fix the model specification you found in Step 4, fix the size of the in-sample period as the window size, using 1-step (day) rolling window method to re-estimate the model, make 1-step ahead forecasts of the volatilities, and calculate the 99% Value-at-Risk for the out-of-sample period. (30 marks)
  6. Graph the calculated 99% Value-at-Risk and the observed returns in one figure, calculate the hits rate (hits =1 if a daily observed return is greater than the calculated 99% Value-at-Risk ∑𝑁 h𝑖𝑡𝑠
    and hits =0 otherwise; and h𝑖𝑡𝑠 𝑟𝑎𝑡𝑒 = 𝑡=1 ) and comment about the accuracy of the 𝑁 model. (20 marks)
  7. Provide suggestions that can improve the model (Note: you do not need to perform these suggestions. Instead, you only need to discuss about the suggestions and their rationale). (10 marks)

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