Applied Econometric Time Series by Walter Enders

By Walter Enders

Applied Econometric Time sequence, 4th Edition demonstrates sleek ideas for constructing types able to forecasting, examining, and checking out hypotheses referring to financial information. during this textual content, Dr. Walter Enders commits to utilizing a “learn-by-doing” method of support readers grasp time-series research successfully and effectively.

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11. 5) to determine the restrictions on ???? and ???? necessary to ensure that the {yt } process is stable. tex CHAPTER 1 V3 - 09/02/2014 12:52pm Page 46 DIFFERENCE EQUATIONS 12. Consider the following two stochastic difference equations i. 125yt−2 + ????t ii. 375yt−2 + ????t a. Use the method of undetermined coefficients to find the particular solution for each equation. b. Find the homogeneous solutions for each equation. c. For each process, suppose that y0 = y1 = 8 and that all values of ????t for t = 1, 0, −1, −2, … = 0.

The key point is that the stability condition for the homogeneous equation is precisely the condition for convergence of the particular solution. If any characteristic root of the homogeneous equation is equal to unity, a polynomial time trend will appear in the particular solution. The order of the polynomial is the number of unitary characteristic roots. This result generalizes to higher order equations. If you are really clever, you can combine the discussion of the last section with the method of undetermined coefficients.

Tex V3 - 09/02/2014 12:52pm Page 25 SOLVING HOMOGENEOUS DIFFERENCE EQUATIONS 25 It should be clear that if the absolute value of either ????1 or ????2 exceeds unity, the homogeneous solution will explode. 1 examines two second-order equations showing real and distinct characteristic roots. 5. 5)t . Since both roots are less than unity in absolute value, the homogeneous solution is convergent. 5)t . 35yt−2 . The worksheet indicates how to obtain the solution for the two characteristic roots. 037, the {yt } sequence explodes.

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