CSSM Procedure
Scoring with State Space Models
Evaluating a previously fitted model at some new predictor setting is often called scoring. For example, a bank might score a new loan application by applying a rule that is based on a previously fitted logistic regression model. Similarly, you might want to use state space models for scoring. However, because of the sequential nature of the observation process, it is important to realize that the scoring process for state space models is inherently different from the scoring process for models that are based on independent observations, such as simple linear regression or logistic regression. Think of a sequential data process as a streaming movie, which you can pause and resume playing. Watching the movie for some time and learning about the main characters and their relationships to each other is akin to fitting a model to the initial portion of a sequential data stream. After you have learned something about the movie, you can make educated guesses about the subsequent plotline. You can also imagine different ways the movie could play out, while still being consistent with the story thus far. For sequential data, this process of forecasting and what-if analysis, based on the fitted model and ever-increasing history, is called scoring. To explain the scoring features of the CSSM procedure, it is useful to define the following notation, which is based on the section State Space Model and Notation:
denote sequential observations on the response variables 
and, optionally, the predictor variables 
and 
. For time points
, let 
denote the data between 
and 
; that is, 
. With this notation, it is easy to describe a streaming data process in which data arrive sequentially in data packets, possibly of varying lengths. For example, the data packets 
denote the data that are associated with the first 100 time indices, the data between time indices 101 and 110, the data between time indices 111 and 112, and so on. When there can be multiple measurements that use the same time index, such as in the case of panel data, the ending time index of one data packet can be the same as the starting time index of the next data packet. 
denotes the state vector at time index t, 
denotes the parameter vector, 
denotes the diffuse vector in the initial condition, and 
and 
denote the regression vectors that are associated with the observation equation and state equation, respectively.
Armed with this notation, you can understand the main activities of scoring with a state space model, which are explained in the following sections.