4-16-2003 Lab Three 1I. Simulation of an Autoregressive Process of Order One, AR(1)Open EviewsObject Menu: NewWorkfile Object: “Autoregressive”Frequency: • undatedobservations: 1 1000Workfile Menu: GENR“WN=NRND”Workfile Menu: GENR“ARONE=WN”sample 1 1Workfile Menu: GENR“ARONE= 0.2*ARONE(-1)+WN”sample 2 1000Reset the sample to 1 1000Workfile Window: Select ARONE WNWorkfile Menu: VIEW: • open selection; you will see the spreadsheet viewGroup Window: VIEW: • graphWorkfile Window: Select ARONEWorkfile Menu: VIEW: • open selectionGroup Window: VIEW: • histogram and statsGroup Window: VIEW: • correlogram: level, 36 lagsEXERCISE: Fit a model to ARONE and show that the residuals from the model are white noise. Due in one week.4-16-2003 Lab Three 2II. Identifying and Modeling Autoregressive Time Series: The Change in Business InventoriesLab #3 includes modeling “the change in business inventories”, CBUSIN87. This is the old quarterly series in billions of 1987 dollars. Your series begins in the first quarter of 1954 and ends in the fourth quarter of 1997. Plot, identify and model the series. Use the model to forecast the change in business inventories for the first quarter of 1998. What is the standard error for your forecast?This series was obtained from Business Conditions Digest and the Survey of Current Business. The series in billions of 1982 dollars for 1954 though 1985 was obtained from the October 1988 issue of BCD. The values for 1986 through 1988 are from the August 1989 issue. The 1989 and 1990 values, through the third quarter, are from various months in 1990 and 1991 of SCB, ending with the October 1991 issue. The third quarter of 1990 provided an overlap value and the series in 1982 dollars was multiplied by 2.32 to convert to 1987 dollars. The series in 1987 dollars for the third quarter of 1990 though the second quarter of 1992 were obtained from the August 1993 issue of SCB. The remaining values are from various issues of Business Cycle Indicators published by the Conference Board..Open EviewsOpen TSP file: change in bus. inventories Workfile Window: Select cbusin87Workfile Menu: VIEW: • open selectionGroup Window: VIEW: • line graphGroup Window: VIEW: • histogram and statsGroup Window: VIEW: • correlogram: level, 36 lagsObject Menu/New/Equationcbusin87 c ar(1) sample 1954.1 1997.4Equation Object Window Menu: VIEW: • actual, fitted, residuals: graph4-16-2003 Lab Three 3Equation Object Window Menu: VIEW: • residual tests: correlogram, 36 lagsEquation Object Window Menu: VIEW: • residual tests: histogram: normalitytestNote that the estimated model is: cbusin87(t) = 36.58319 + Res(t),where Res(t) = 0.635386 Res(t-1) + WN*(t), and WN* is orthogonal but not normally distributed.We have [cbusin87(t) - 36.58319] = Res(t), so[cbusin87(t) - 36.58319] = 0.636816 [cbusin87(t-1) - 36.58319] + WN*(t)and the expected value of [cbusin87(t) - 36.58319] at time t-1 is E1997.4 [cbusin87(1998.1) - 36.58319] = 0.636816 [cbusin87(1997.4) - 36.58319]= 0.636816 [74.0- 36.58319] = 23.8288so the one period ahead forecast, E1997.4 cbusin87(1998.1) =36.58319 + 23.8288 =60.412 with a standard error of 33.50 .Rather than calculating this by hand, Eviews will calculate it:Equation Object Window Menu: FORECASTforecast series name: cbusin8fstandard error name: sesample period: 1998.1 1998.1Note that the series cbusin87 and se are now in the workfile window:Workfile Window: sample 1954.1 1998.1Workfile Window: Select cbusin87, cbusin8f, se III. Exercise: Due in One Week:Sales of retail stores in the US, in 1987 dollars, is available monthly from January 1948 through December 1994 in the Survey of Current Business , V. 76, Jan./Feb. 1996 on p.C-15, and for more recentmonths in Business cycles Indicators.4-16-2003 Lab Three 4This data is available as the series, retail, on the Eviews file US Retail Sales.wf1(1) Fit a linear trend to this series and then a linear and quadratic trend to this series for the period 1955:01-1993:12. This is the same period used by Diebold in Ch.4, although his series was not deflated.(2) Which of these two models do you think is best? Why?(3) Calculate by hand the one period ahead forecast for 1994:01 for both of these models and report the standard error of the regression.(4) Use Eviews to forecast retail sales from each model for the period 1994:01-1996:02, and plot your forecasts and the observed series. How does the Eviews forecast compare to your hand calculation? Why is Eviews standard error of the forecast larger than the standard error of the regression?(5) Are you satisfied with these models? Why or why
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