The Rational Expectations Permanent Income Hypothesis implies that consumption follows a martingale. However, most empirical tests have rejected the hypothesis. Those empirical tests are based on linear models. If the data generating process is non-linear, conventional tests may not assess some of the randomness properly. As a result, inference based on conventional tests of linear models can be misleading. This paper tests for the presence of stochastic non- linearity in aggregate consumption of non- durable goods and services, using US and Canadian data. The two major tests applied are a test devised by Brock, Dechert, and Scheinkman, and a test based on an Artificial Neural Network model. The results support the hypothesis that there is no non- linearity in the data. The forecast results, however, suggest that even though linearity is not rejected, the non-linear ANN model tends to outperform the linear ARIMA model over three different horizons.