COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 487

"A Note on the Saddlepoint Approximation
in the First Order Non-Circular Autoregression"

Peter C.B. Phillips

1978

In approximating the small sample distribution of the least squares estimator of the coefficient in a non-circular autoregression the saddlepoint method is complicated by the presence of a branch point of the integrand within the natural contour of integration. Some new approximations are given based on a contour looping around the branch point; and a uniform approximation which is valid as the saddlepoint crosses branch point is also developed.