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I. Simulation of an Autoregressive Process of Order One, AR(1)
Open Eviews
Object Menu: New
Workfile Object: “Autoregressive”
Frequency: • undated
observations: 1 1000
Workfile Menu: GENR
“WN=NRND”
Workfile Menu: GENR
“ARONE=WN”
sample 1 1
Workfile Menu: GENR
“ARONE= 0.2*ARONE(-1)+WN”
sample 2 1000
Reset the sample to 1 1000
Workfile Window: Select ARONE WN
Workfile Menu: VIEW: • open selection; you will see the spreadsheet view
Group Window: VIEW: • graph
Workfile Window: Select ARONE
Workfile Menu: VIEW: • open selection
Group Window: VIEW: • histogram and stats
Group Window: VIEW: • correlogram: level, 36 lags
EXERCISE: Fit a model to ARONE and show that the residuals from the model are
white noise. Due in one week.
II. Identifying and Modeling Autoregressive Time Series: The Change in Business Inventories
Lab #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
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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 Eviews
Open TSP file: change in bus. inventories
Workfile Window: Select cbusin87
Workfile Menu: VIEW: • open selection
Group Window: VIEW: • line graph
Group Window: VIEW: • histogram and stats
Group Window: VIEW: • correlogram: level, 36 lags
Object Menu/New/Equation
cbusin87 c ar(1)
sample 1954.1 1997.4
Equation Object Window Menu: VIEW: • actual, fitted, residuals: graph
Equation Object Window Menu: VIEW: • residual tests: correlogram, 36 lags
Equation Object Window Menu: VIEW: • residual tests: histogram: normality
test
Note 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
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E1997.4 [cbusin87(1998.1) - 36.58319] = 0.636816 [cbusin87(1997.4) - 36.58319]
= 0.636816 [74.0- 36.58319] = 23.8288
so 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: FORECAST
forecast series name: cbusin8f
standard error name: se
sample period: 1998.1 1998.1
Note that the series cbusin87 and se are now in the workfile window:
Workfile Window: sample 1954.1 1998.1
Workfile 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 recent
months in Business cycles Indicators.
This 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?
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(5) Are you satisfied with these models? Why or why not?