# quant question

where are they getting the 32, 33, and 35 numbers from in the answer explanation? thanks Troy Dillard, CFA, has estimated the following equation using semiannual data: xt = 44 + 0.1×xt–1 – 0.25×xt–2 - 0.15×xt–3 + et. Given the data in the table below, what is Dillard’s best forecast of the second half of 2007? Time Value 2003: I 31 2003: II 31 2004: I 33 2004: II 33 2005: I 36 2005: II 35 2006: I 32 2006: II 33 A) 34.05. B) 60.55. C) 34.36. D) 35.00. Your answer: A was incorrect. The correct answer was C) 34.36. To get the answer, Daily must first make the forecast for 2007:I E[x2007:I]= 44 + 0.1 × xt–1 - 0.25 × xt–2 - 0.15 × xt–3 E[x2007:I] = 44 + 0.1×33 - 0.25×32 - 0.15×35 E[x2007:I] = 34.05 Then, use this forecast in the equation for the first lag: E[x2007:II] = 44 + 0.1×34.05 - 0.25×33 - 0.15×32 E[x2007:II] = 34.36

nm i got it. boy reading 13 is kinda a pain isn’t it

It seems simple to find out. This is something like arch framework wherein you need to depend on No.1) previous semiannual data, No.2) one period prior to that, 3) one more period prior to No.2. which means 3 previous semiannual data points. Becuase this is how the equation is built. x(t-1), x(t-2), x(t-3). to find out 2007 second half, you need, 1) 2007 1st half * 2) 2006 2nd half 3) 2006 1st half. But 2007 1st half is not given. so to find out that you need previous 3 SA data points. go from bottom. 2005: II 35 2006: I 32 2006: II 33 use these three in your equation to find 2007 1st half. you got ===> 34.05 now use this and previous 2 Semi annual 2006: I 32 2006: II 33 2007: I 34.05 E[x2007:II] = 44 + 0.1×34.05 - 0.25×33 - 0.15×32 E[x2007:II] = 34.36 Isn’t it simple !

Except it isn’t anything like the ARCH framework because the ARCH framework is all about the error term which isn’t even mentioned here.