A1288
Title: Identification of autoregressive models for matrix valued time series with multiple terms
Authors: Dietmar Bauer - Bielefeld University (Germany)
Kurtulus Kidik - Bielefeld University (Germany) [presenting]
Abstract: Matrix-valued time series arise, for example, for the observation of the same set of variables for numerous regions by arranging the observations for one-time points into a matrix. Autoregressive models for such data typically involve only one term per time lag, obtained by pre- and post-multiplying the matrix observations at lag $j$ with square matrices. The corresponding vectorized time series then possesses lag matrices, which are Kronecker products between the two square matrices. Clearly, this restricts the flexibility. Adding terms for each lag leads to more flexibility in modelling but, at the same time, to identifiability issues. A novel identification procedure is proposed, and its properties are investigated. In particular, information on the choice of the number of terms needed and their effects on the implied impulse response sequence is investigated. The identification scheme is used in an alternating optimization method, leading to consistent estimates and specification of the integer-valued parameters such as lag length and the number of terms. Besides the stationary case, the integrated case of particular interest for economic applications is investigated.
