Supposetheq vectortimeseriesyt followsaVARq(p)modelwith yt=

p r=1 ryt r+ t t N(0V)

withindependent innovations tovertime.

(a) Showthat themodel canbewrittenasyt = Ft+ t for some regressionvectorFtandmatrixparameter .Givethede nitionsof Ft and andcommentontheirdimensions.Thisresultshowsthat theVARmodelcanbecastasamultivariateDLMwithveryspeci c structure.The followingChapter10, particularlySection10.2, dis cussestheimportantbroaderclassofexchangeabletimeseries(com moncomponents)models; thisexerciseshowsthatVARmodelsare aspecialsubsetofthisbroaderclass.

(b)Howcanyouextendthismodel to includeanonzero level for the series?Whatchangestothede nitionsofFt doesthisentail?

(c) Supposeq=400withtheytj being400dailystockprices fromthe S&P500,andamodelersuggestsaVARq(3)model-upto3dayslags mightcaptureatleastsomeaspectsofprice momentum. Assuming thebasicideaofsuchamodel isattractive,whatkindsofstatistical issuesdoyouseearising?