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6) Explain the difference between a simple moving average (SMA) and Exponential Smoothing (EWMA). Consider a series x, that has x,0 for all i30 but for i> 0, cycles through 1,0,-1 ,0, 1 ,0,-1 0.1 ,0,-1 , Let y SMA(x,4) represent the simple moving average y,-- x/4 i-j-3 and for EWMA, a +(1-α)a.! a) b) Find y, forj- 0 to 9 With α-0.5, calculate the EWMA forecast, a, of Spi for J-0 to 4 ANS a) Can set up a table of values to illustrate process Index X1 is0 0 0 1/4 0 0 (3 marks) b) In this case aj = 0.5% + 0.5a,1. Again can set up a table as below, noting ao= 0 Index X1 aj 1JS0 0 0 1/2 1/43/8 3/16 13/32 13/64 51/128 51/256 205 /512 (5 matks)

CAN YOU PLEASE EXPLAIN HOW THEY GOT THESE NUMBERS?

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