# Implementing a Kernel Adaptive Filtering model explained in a paper

In this paper, Stock price prediction using kernel adaptive filtering within a stock market interdependence approach, the authors propose a method for predicting stock prices by combining the predictions of Kernel Adaptive Filter (KAF) models trained on different stocks in different international stock markets. In their results, they compare this model against individual KAF models trained and inferred on individual stocks. The refer to these individual models as 'KAF-based methods' and refer to their model as 'Proposal'.

I am quite new to KAFs, so excuse any ignorance I may have in my questions.

The KAF-based models use various different variants of KAFs - KLMS, QKLMS, NICE, etc. However, when they are explaining their proposed method, they never seem to mention which KAF variant is used internally in their models.

On page 9 where they outline the pseudocode of their individual models using some KAF, line 7 says "compute the filter output" where the filter is defined simply as Kσ. Prior to this, on the bottom of page 5 and top of page 6 they give the initial definition of Kσ(·, ·) just as "a Mercer Kernel".

I am attempting to reproduce their results, and am trying to implement their method in Python, potentially using the KAF implementations from here. Which KAF should I be using as Kσ? KLMS? KRLS? Have I got the wrong understanding of what Kσ in the paper is?