Use the CaseShiller Data on any metropolitan area you would like. Utilize the Dickey Fuller test and determine if the variable is stationary. If it is not, solve this problem and rerun the test. Determine which model either AR

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or ARMA model is the best model and how many lags. Conduct a test for serial correlation. Forecast for the next

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months

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Utilize out

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of

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sample forecasting methods using a

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sample split to determine if your model is superior to a random walk

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model of the just the mean

$)$Date National SanFran LA Chicago SD NY Den Bos

$1987-01-0163\mathrm{.}9640000000000046\mathrm{.}95579248965900059\mathrm{.}42622437288700054\mathrm{.}20647876431400054\mathrm{.}79411150896400074\mathrm{.}6784401616080050\mathrm{.}34801697303300070\mathrm{.}266973096972000$

$1987-02-0164\mathrm{.}4220000000000047\mathrm{.}30267479920600059\mathrm{.}89486088798200055\mathrm{.}22727413532600055\mathrm{.}21511853347300076\mathrm{.}0436870031340050\mathrm{.}16046813539600070\mathrm{.}640677975989000$

$1987-03-0164\mathrm{.}7350000000000047\mathrm{.}84021292896600060\mathrm{.}40107320210700054\mathrm{.}81103409768600055\mathrm{.}48780326410500077\mathrm{.}2370753131050050\mathrm{.}38347785569900071\mathrm{.}046773504037000$

$1987-04-0165\mathrm{.}1330000000000047\mathrm{.}98405770175600061\mathrm{.}32433370166800054\mathrm{.}80194738464500056\mathrm{.}04977840656500078\mathrm{.}2815268755820050\mathrm{.}74462753759500071\mathrm{.}411571430550000$

$1987-05-0165\mathrm{.}5640000000000048\mathrm{.}30506512939100062\mathrm{.}03091455460400055\mathrm{.}47746617402800056\mathrm{.}46209863040000079\mathrm{.}6753305939570050\mathrm{.}76353788496200071\mathrm{.}882710791649000$

$1987-06-0166\mathrm{.}0710000000000048\mathrm{.}60578686117900062\mathrm{.}77656362755800056\mathrm{.}05976670425600056\mathrm{.}78755553430400080\mathrm{.}8398015902250050\mathrm{.}43233494724500072\mathrm{.}295931836365000$

$1987-07-0166\mathrm{.}5070000000000049\mathrm{.}08456577998800063\mathrm{.}45610946796300057\mathrm{.}10936652939400057\mathrm{.}07595626170600081\mathrm{.}6950669888320050\mathrm{.}20394288778700072\mathrm{.}620964407765000$

$1987-08-0166\mathrm{.}9370000000000049\mathrm{.}54259200962400064\mathrm{.}13062268170400057\mathrm{.}61220939883100057\mathrm{.}38024736617100082\mathrm{.}2200579574360050\mathrm{.}12122157841000073\mathrm{.}162915823632000$

$1987-09-0167\mathrm{.}3290000000000050\mathrm{.}24128781470000064\mathrm{.}89362701796600058\mathrm{.}27036799826100057\mathrm{.}84333097882500082\mathrm{.}3839759498800050\mathrm{.}05828124118200073\mathrm{.}748812848762000$

$1987-10-0167\mathrm{.}7370000000000050\mathrm{.}99269818003700065\mathrm{.}77160420453400059\mathrm{.}00637888011800058\mathrm{.}29568624938100083\mathrm{.}1564060951000050\mathrm{.}14607870533400074\mathrm{.}006600741264000$