Testing for residual autocorrelation in growth curve models

Growth curve models are frequently used for technological forecasting. Despite the practical importance of these models, the time series properties of the residuals in these models are often overlooked. Neglected serial correlation in the residuals leads to suboptimal statistical inference and inaccurate out-of-sample forecasts. This paper gives a general diagnostic test for residual autocorrelation, which is based on the Lagrange multiplier principle. The test is illustrated for the logistic curve and the Gompertz curve. It is shown that the test can also be helpful for selecting between these two models. Simulation experiments indicate the usefulness of the test in terms of size and power. Next, two applications illustrate the empirical relevance of the test. Finally, it is illustrated that more appropriate error structures can lead to substantially better out-of-sample forecasts indeed.

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