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We consider the system identification problem using a time-varying quadratic Volterra model. To enable identification a set of known basis sequences are used in the model to approximate the time-variation of the true system To reduce the number of parameters in the model we wish to determine which individual sequences are signifiant in this approximation. Multiple hypothesis testing procedures are employed to select significant sequences. The tests include the Bonfermni test 131, Holm's sequentially rejective Bonferroni test [41, and Hommel's extension to Simes' pmcedure 151.

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To enable identification of a time-varying Volterra model using a single input/output realisation, sequences from an orthonormal basis are used to approximate the timevariation. Our work concerns the choice of sequencesfrom a library which comprises several bases. Using a library of wavelet packets allows-the use of the Best Basis algorithm. We apply the Best Basis algorithm in order to select the wavelet packets for approximating the true system's time-variation in the model. The minimum entropy criterion determines the most e@ient basis approximation enabling a minimum number of sequences to be used, leading to a more parsimonious model.