Stat homework help
(Questions) The time plot below displays the absolute value of Tesla’s daily returns from January 3, 2018, to November 19, 2020. Let us define: volatility = absolute value of daily return values of Tesla stock. The red line drawn on the plot simply connects the consecutive data points. The horizontal black line corresponds to the mean of the volatility values. You may assume all the volatility values are unique. The sample size (number of days) is 727.
(1) Approximately, what is the mean volatility?
A) 0.001 B) 0.04 C) Near zero D) 0.01 E) 0.03
(2) Approximately, what is the largest volatility value?
A) 0.24 B) 0.18 C) 0.50 D) 0.05 E) 0.08
(3) Only one of the plots given below could be the plot of the actual daily return values. Which one? The range of y and x axes are the same for all the plots. The dashed horizontal grey lines are just grid lines.
A) Plot A B) Plot B C) Plot C D) Plot D E) Plot E
An AR(2) model is fitted to the data. The parameter estimate values are shown below. The volatility values for the last three days are also shown. One of the standard errors shows up as 0.00 but this due to rounding.
(4) What is the predicted volatility for 2020-11-20 based on the estimated AR(2) model?
A) 0.048 B) 0.046 C) 0.018 D) 0.030 E) 0.016
(5) The approximate 95% prediction interval formula is used to obtain the interval (-0.01446, 0.10554) for 2020-11-20. What is the RMSE value?
A) 0.01 B) 0.04 C) Cannot be determined. D) 0.00 E) 0.03
(6) To get a better model, 11 AR models with orders 1, 2, 3, …, 10, and 11 are fitted. The plot below shows the AIC values of the 11 AR models versus the AR model order. Based on the plot given, what is the best model? Why?
A) AR(1) since it has the highest AIC value. B) AR(11) since this is where the AIC values are converging to. C) AR(5) since the AIC value is the lowest. D) AR(3) since this AIC value drops substantially for this model. E) AR(6) since this is the first jump in the AIC value after the AIC value has bottomed.
(7) Suppose we pick the best model implied by question 6 and fit only the first 726 days, which include the dates 2018-01-03 to 2020-11-18. Then we predict the volatility for 2020- 11-19. The residual for 2020-11-19 turns out to be -0.002. What is the predicted volatility?
A) 0.028 B) 0.026 C) 0.030 D) -0.019 E) 0.024
(8) The data (all 727 days) are smoothed with an exponentially weighted moving average (EWMA) to obtain an equation of the form: St = α(Yt-1)+ (1-α)(St-1), where St is the smoothed value at time t, Yt- 1 is the volatility value at time t-1, St-1 is the smoothed value at time t-1, and so on. Suppose when t = 2020-11-19 we have the values St = 0.070, and St-1 = 0.007. What is the value of α?
A) 0.070 B) 0.190 C) 0.700 D) 0.581 E) 0.856