Testing non-linearity using a modified Q test

A new version of the Q test, based on generalized residual correlations (i.e. auto-correlations and cross-correlations), is developed in this paper. The Q test fixes two main shortcomings of the Mcleod and Li Q (MLQ) test often used in the literature: (i) the test is capable to capture some interesting non-linear models, for which the original MLQ test completely fails (e.g. a non-linear moving average model). Additionally, the Q test also significantly improves the power for some other non-linear models (e.g. a threshold moving average model), for which the original MLQ test does not work very well; (ii) the new Q test can be used for discrimination between simple and more complicated (non-linear/asymmetric) GARCH models as well

Consistent algorithms for clustering time series

The problem of clustering is considered for the case where every point is a time series. The time series are either given in one batch (offline setting), or they are allowed to grow with time and new time series can be added along the way (online setting). We propose a natural notion of consistency for this problem, and show that there are simple, computationally efficient algorithms that are asymptotically consistent under extremely weak assumptions on the distributions that generate the data. The notion of consistency is as follows. A clustering algorithm is called consistent if it places two time series into the same cluster if and only if the distribution that generates them is the same. In the considered framework the time series are allowed to be highly dependent, and the dependence can have arbitrary form. If the number of clusters is known, the only assumption we make is that the (marginal) distribution of each time series is stationary ergodic. No parametric, memory or mixing assumptions are made. When the number of clusters is unknown, stronger assumptions are provably necessary, but it is still possible to devise nonparametric algorithms that are consistent under very general conditions. The theoretical findings of this work are illustrated with experiments on both synthetic and real data

The Structure of US Food Demand

An exactly aggregable system of Gorman Engel curves for U.S. food consumption is developed and implemented. Box-Cox transformations on prices and income nest functional form. The model nests rank up to rank three. The model is estimated by nonlinear three-stage least squares with annual time series data on 21 foods, 17 nutrients, age and race demographics, and the distribution of income for 1919-1941 and 1947-2000. Results are consistent with full rank three. Point estimates for the Box-Cox parameters on income and prices are 0.86 and 1.09, respectively, strongly rejecting zero and one in both cases. No statistical evidence of serial correlation, specification errors, or parameter instability is found.Aggregation, food demand, functional form, parameter stability, rank, specification errors