to prepare and allow a large number of options. The program can be run in batch mode or interactively at a computer terminal. Computer core storage is dynamically allocated so that large problems are only limited by the size of the machine. SHAZAM is designed to grow so that new algorithms and procedures can easily be added by any programmer familiar with the internal structure of the program. Features of SHAZAM include ordinary least squares, two-stage least squares, seemingly unrelated regressions and iterative estimation of seemingly unrelated regressions, threestage least squares and iterative three-stage least squares, models with first and second order autocorrelated disturbances, estimation of Box-Cox [1] type nonlinear functional forms, principal components and factor analysis, regression on principal components, ridge regression, regressions by matrix decompositions, random number generatign for Monte Carlo samples, forecasting, and plotting. Any set of linear restrictions or hypothesis tests can be used in the estimation. A wide variety of output statistics are available with each procedure. The autocorrelation section of SHAZAM is rather extensive and includes maximum likelihood or least squares estimation by a grid search or iterative Cochrane-Orcutt [2] procedure and inclusion or deletion of initial observations, exact and higher-order DurbinWatson [4] type tests, tests based on Golub's [6] uncorrelated residuals, Dhrymes [3, p. 199] corrections for lagged dependent variables, Savin-White [7] corrections for missing observations in a time series, Savin-White [8] type simultaneous testing for functional form and autocorrelation, and forecasting using Goldberger's [5] best linear unbiased predictor. A SHAZAM user's manual [9], which is also machine readable, is available from the author on request.

[This paper considers procedures for testing for autocorrelation when there are missing observations on both the dependent and explanatory variables. These procedures include Durbin-Watson type tests given the vector of residuals, tests based on a set of uncorrelated residuals, and large sample likelihood ratio and Wald tests.]

Recent studies by Durbin and Watson [5], L'Esperance and Taylor [10], Koerts and Abrahamse [8], Tillman [15], Vinod [16], Savin and White [14] and others have shown increasing interest in the test of autocorrelation based on the d statistic proposed by Durbin and Watson [3 and 4]. The focus of these papers has been the computation of the exact distribution of d and the power of the test based on d. The exact distribution of d has been developed by Imhof [7] and Pan Jie-Jian [12]. However, few of the generally available computer programs for regression analysis incorporate these methods,2 possibly because of computational costs, particularly for large samples. With the Durbin and Watson [4] tables the bounds test is restricted to time series regressions with 15 to 100 observations and a maximum of 5 regressors in addition to unity. Often regression studies do not meet these restrictions since samples with less than 15 observations commonly occur with annual time series and regressions with more than 5 regressors are often found in the context of simultaneous equations and of distributed lags.3 In this paper we present extended tables for the bounds test. Our tables can be used for samples with 6 to 200 observations and for as many as 20 regressors.

This paper shows a simple method of approximating the exact distribution of the Durbin-Watson Test Statistic for first-order autocorrelation in a nonlinear model.The proposed Approximate Nonlinear Durbin-Watson (A.N.D.) test has good size and power when compared to alternatives.