Bilinear Models (BL)

It is well known that for the adequate description of some phenomena additional non-linear terms of the time series could be of use. A simple example is to add a bilinear term (see [16,12]). Here are bilinear time series extending the ARMA model:

$$w_{t} = \sum_{i=1}^p a_i w_{t-i} +\sum_{i=1}^q b_i \epsilon_{t-i} + \sum_{i=1}^s \sum_{j=1}^r c_{ij} z_{t-i}\epsilon_{t-j}+\epsilon_t$$ (34)

For an illustrative example of the bilinear time series see [].