[2019] STAT 153 Introduction to Time Series - Midterm Exam - Q3 ARMA
3. For zero mean time series data {Xt} consider the model (1 − 0.2B)(Xt − 0.5Xt−1) = (Zt − 0.6Zt−1 + 0.05Zt−2), where {Zt} is white noise with variance σ2 = 4.
(a) Identify {Xt} as an ARMA(p,q) model and give its MA and AR polynomials. s (4 Points)
(b) Is the model invertible and causal? (2 Points)
(c) Find its unique stationary solution. (4 Points)
(d) Compute its ACVF. (4 Points)
(e) Assume someone wants to use this model to predict weekly car sales. On average the company sells 100 cars per week. Two weeks ago they sold 95 cars and last week they sold 101 cars. Based on this, what is the best linear predictor of car sales next week?
Hint: You do not have to compute the actual value, it is enough to write down a linear system of equations that needs to be solved. (3 Points)
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