Forecasting Assignment 1

Assignment 1 Forecasting  ________________________________________________________  ____________________________ ________________________________________________________ __________________________________  ______  Q1. The weekly deliveries of a car to an automobile dealer are as shown below. Fit Fit the straight line model xt = a + bt + € t Estimate the error variance !eek 6ales

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Q !e !eekly ekly sales for the "ot #i$$a are as follows% Weeks Demand ($) & &'(  && , &&( & *  &&*

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Weeks ) ( * &' && &

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Table & a/ Estimate Estimate demand demand for the next four four weeks using using the -0week sim1le sim1le moving moving average as well well as the sim1le sim1le ex1onential smoothing with ='.&.  b/ Evaluate the 2345 23#E5 26E5 bias and T6 in each case. c/ !hich !hich of the the two two method methodss do you you 1refer7 1refer7 !hy7 !hy7 Q,. 8onsider the time series series data shown in Table Table . a/ 2ake 2ake a tim timee series series 1lot 1lot of the data. data.  b/ 9se sim1le ex1onential smoothing with ='. to smooth first -' time 1eriods of this data. "ow well does this smoothing 1rocedure work7 c/ 2ake one0ste10ah one0ste10ahead ead forecasts forecasts of the the last &' observation observations. s. 4etermine 4etermine the forecast forecast errors. errors. Period Period Period Period Period & -(.) && -*.& & -., ,&  ' .( -&  -.( & -.)  -,., , -  .- , -.&, -).( , --. ,,   ., -, -. &-.( -).& , ' . - -& -.  ,.,  , .-  ,.( & -*.  --.* ,  , .* - ) -). &) -.( ) '. ,)   ., -) ( -) &( --.) ( -(.& ,( , -( * -). &* &.& * -.,* - ( . -* &' &.& ' -)., ,' &. -'   .' Table  Q-. :econsider the time series data given in Table . a/ 9se sim1le sim1le ex1onent ex1onential ial smoothing smoothing with o1timum o1timum value value of

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to smoot smooth h the first first -' time 1eriods 1eriods of of this this

data. "ow well does this smoothing 1rocedure work7 8om1are the results with those obtained in the  1revious 1roblem.  b/ 2ake one0ste10ahead forecasts of the last &' observations. 4etermine 4etermine the forecast errors. 8om1are these forecast errors with those from the 1revious 1roblem. Q. The data in the Table , exhibits a linear trend.

a/ ;erify that there is a trend by 1lotting the data.  b/ 9sing the first & observations5 develo1 an a11ro1riate 1rocedure for forecasting. c/ Forecast the last & observations and calculate the forecast errors. 4oes the forecast 1rocedure seem to  be working satisfactorily7 Period Period Period Period & ,& ) ,&( &, -' &* '  &* ( , &,* ' -'' , ,&' * -' & ,*' & -' ,& &' -&' & -'  ('  , && -( &) -( , -)  ,, & -' &( )' ' Table , Q. :econsider the linear trend data in Table ,. Take the first difference of this data and 1lot the time series of the first differences. "as differencing removed the trend7 9se ex1onential smoothing on the first && differences.