A researcher estimated a model for the daily percentage returns (rt) on the Australian stock market...

 

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A researcher estimated a model for the daily percentage returns (rt) on the Australian stock market index over the last 100 days of trading. The results for this model (Model 1) were: rt = 0.25 +0.39ut-1 + Ut o² = 0.28 + 0.06u²_₁ + 0.9207_1. The log-likelihood was 679.2. (i) (ii) (iii) The researcher estimated a second model for the daily percentage returns. The results for Model 2 were: rt = 0.19 + 0.25ut−1 + 0.62o? + Ut of: = 0.25 +0.07u²-1 + 0.9107_1 + 0.16u²-1lt-1 where It-1 = 1 if ut-1 < 0 and Is the conditional variance always positive in this model? Justify your answer. (1 mark) What feature of stock market returns does the conditional variance equation account for? (1 mark) Will forecasts of the conditional variance of returns converge to a finite value as the forecast horizon increases? Justify your answer. (1 mark) The log-likelihood was 681.6. (iv) (v) rt = The researcher estimated a third model for the daily percentage returns. The results for Model 3 were: 0.28 +0.37ut-1 + 0.5807 + ut In what respects does Model 2 explain features of the data which Model 1 does not. Explain your answer fully. (2 marks) Conduct a statistical test to determine whether Model 1 or Model 2 is better supported by the data. Be sure to state the null and alternative hypotheses, calculate the test statistic and report the 5% critical value, and state your conclusion. (3 marks) = 0 otherwise. ·|u₁-11 Ot-1 log(ot) = -0.22 +0.05 The log-likelihood was 678.4. +0.93 log(0²-₁) A researcher estimated a model for the daily percentage returns (rt) on the Australian stock market index over the last 100 days of trading. The results for this model (Model 1) were: rt = 0.25 +0.39ut-1 + Ut o² = 0.28 + 0.06u²_₁ + 0.9207_1. The log-likelihood was 679.2. (i) (ii) (iii) The researcher estimated a second model for the daily percentage returns. The results for Model 2 were: rt = 0.19 + 0.25ut−1 + 0.62o? + Ut of: = 0.25 +0.07u²-1 + 0.9107_1 + 0.16u²-1lt-1 where It-1 = 1 if ut-1 < 0 and Is the conditional variance always positive in this model? Justify your answer. (1 mark) What feature of stock market returns does the conditional variance equation account for? (1 mark) Will forecasts of the conditional variance of returns converge to a finite value as the forecast horizon increases? Justify your answer. (1 mark) The log-likelihood was 681.6. (iv) (v) rt = The researcher estimated a third model for the daily percentage returns. The results for Model 3 were: 0.28 +0.37ut-1 + 0.5807 + ut In what respects does Model 2 explain features of the data which Model 1 does not. Explain your answer fully. (2 marks) Conduct a statistical test to determine whether Model 1 or Model 2 is better supported by the data. Be sure to state the null and alternative hypotheses, calculate the test statistic and report the 5% critical value, and state your conclusion. (3 marks) = 0 otherwise. ·|u₁-11 Ot-1 log(ot) = -0.22 +0.05 The log-likelihood was 678.4. +0.93 log(0²-₁)

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ANSWER i Is the conditional variance always positive in this model Justify your answer To determine if the conditional variance is always positive we need to examine the equation for the conditional v... View the full answer