A2.1) Suppose we model the data (not necessarily any of the series in Question A1) as an MA(1) and get the following estimated equation: = 0.51+ What is this MA(1) process theoretical ACF at lag 1? At lag 2? Discuss the ACF and PACF of general MA, AR, and ARMA processes. Why are we interested in measures like ACF? In univariate time series modelling, how can measures like ACF and PACF be used? Discuss in practice how to select the optimal lag length in time series modelling. (4 marks) (A2.2) Univariate time series models are especially useful when it comes to forecasting. Consider the following MA(1) process: = 0.51+ What is your forecast for +1 if you observe 1 = 0.2 and = -0.8? What is your forecast for +2? What is the forecast for 10-step ahead? How does the forecast for the distant future compare to the unconditional expectation of this MA(1) process? How is the forecasting exercise related to the expectation of the stochastic process {}? (4 marks) (A2.3) Distinguish between in-sample forecasts and out-of-sample forecasts. Which one is closer to the true forecasting, where we make forecast of tomorrow based on the information available until today? (6 marks) (A2.4) Suppose you are interested in forecasting the WTI spot price, how would you construct the model? Please report your results (in maximum 1000 words), including (not restricted to) the following: Discussion of the data (length, frequency, source, etc). Discussion of what you expect and why? Explain the pre-treatment(s) of the data, if necessary. Construct a model for the WTI spot price. How is the model forecasting precision? Please include all equations, figures, and tables necessary with your explanation in your report.. (