## Regression analysis

Let's first review the classic stationary regression theory. Let be a time series, it can be represented in the norm of (called basis function) in the least square criteria:

 (1)

where is the regressive coefficient and denotes the squared L2 norm of a function. In the non-stationary case, the regressive coefficients become variable with time, which can be expressed as:

 (2)

The minimization of equation 2 is ill-posed for the reason that more unknown variables than given variables need to be found. In the theory of SDRNAR, Fomel (2013) used shaping regularization to constrain equation 2.

2020-03-10