Consider a series of macroeconomic data yt = t + ct, where t is the trend, ct is the cycle, and t = 1,2,3. a) Use the HP filter to solve for 1, 2, and 3 in terms of y1, y2, y3, and . b) Using the analytical expressions you derived in the previous question, what are 1,2,3 andc1,c2,c3 if=1600,y1 =180,y2 =194,andy3 =105? c) Find analytical expressions for 1, 2, and 3 when . What is the constant growth rate?