[2019] STAT 153 Introduction to Time Series - Midterm Exam - Q1 Stationary
1. Consider the following model for time series data Xt = Xt−1 + Zt + δ, where δ is some non-zero constant and Zt is white noise with variance σ .
(a) Give the definition of weak and strong stationarity. (4 Points)
(b) Show that there exist no stationary solution for Xt in the above model. s(2 Points)
(c) From now on suppose that X0 = 0. Compute the mean and the variance of Xt for all t > 0. (3 Points)
(d) Is Xt homoscedastic? Explain. s (1 Points)
(e) Propose an invertible function f(·) such that the transformed data f(Xt) has approximately constant variance. Explain.Hint: You may assume that all your observations are positive.
(f) Propose an invertible transformation of Xt such that it is stationary. Explain. s (3 Points)
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