# Quant- Autoregressive problem from SS exam on q-bank

Vignette: Winston Collier, CFA, has been asked by his supervisor to develop a model for predicting the warranty expense incurred by Premier Snowplow Manufacturing Company in servicing its plows. Three years ago, major design changes were made on newly manufactured plows in an effort to reduce warranty expense. Premier warrants its snowplows for 4 years or 18,000 miles, whichever comes first. Warranty expense is higher in winter months, but some of Premier’s customers defer maintenance issues that are not essential to keeping the machines functioning to spring or summer seasons. The data that Collier will analyze is in the following table (in \$ millions): Qrt Wrtny Exp*Chng Warranty Exp(yt)*Lagged Chng Wrtny Exp(yt-1)*Seasonal Lagged Chng in Wrtny Exp(yt-4) 2002.1 103 2002.2 52*************-51 2002.3 32*************-20 ********************-51 2002.4 68*************+36********************-20 2003.1 91*************+23********************+36 2003.2 44*************-47********************+23****************-51 2003.3 30*************-14********************-47*****************-20 2003.4 60*************+30*******************-14*****************+36 2004.1 77*************+17*******************+30****************+23 2004.2 38*************-39*******************+17*****************-47 2004.3 29*************-9********************-39*****************-14 2004.4 53*************+24*******************-9******************+30 Winston submits the following results to his supervisor. The first is the estimation of a trend model for the period 2002:1 to 2004:4. The model is below. The standard errors are in parentheses. (Warranty expense)t = 74.1 - 2.7*t + et R-squared = 16.2% (14.37) (1.97) Winston also submits the following results for an autoregressive model on the differences in the expense over the period 2004:2 to 2004:4. The model is below where “y” represents the change in expense as defined in the table above. The standard errors are in parentheses. yt = -0.7 - 0.07* yt-1 + 0.83* yt-4 + et R-squared = 99.98% (0.643) (0.0222) (0.0186) After receiving the output, Collier’s supervisor asks him to compute moving averages of the sales data. Question: Based on the autoregressive model, expected warranty expense in the first quarter of 2005 will be closest to: A) \$60 million. B) \$71 million. C) \$78 million. D) \$65 million. Your answer: A was incorrect. The correct answer was D) \$65 million. Substituting the 1-period lagged data from 2004.4 and the 4-period lagged data from 2004.1 into the model formula, change in warranty expense is predicted to be higher than 2004.4. 11.73 =-0.7 - 0.07*24+ 0.83*17. The expected warranty expense is (53 + 11.73) = \$64.73 million. ******************************************************************* This took me forever to get the formatting right. Can someone explain this to me? Why are we using the change in warranty exp vs. the absolute warranty exp. Really I am looking for someone to break this whole thing down for me. Talk to me like I am in first grade. I took the SS exam for quant on the qbank today and scored an 81%, but I missed two questions like this and I really don’t get the logic at all. Thanks.

I wouldn’t stress too much about this, mv. Maximum you’ll miss one question on the exam because you don’t entirely get this. But the short and sweet answer is that the trend model has a really low R^2 compared to the lag AR model. The lagged model probably used Change in expense rather than actual expense to resolve a unit root problem (but that doesn’t matter here). Anyone else?

THIS IS WHAT YOU MISSED mwvt9!! —GIVEN ----- [“y” represents the change in expense] The dependent variable is not a simple one, it’s a change in the expense.

Wow. I am an idiot. I was making this much harder than it actually was…