How to judge a Kalman filter forecast as a Trend filter

The filter as a directional rule

The evaluation treats a Kalman filter forecast as a directional Trend filter. A fixed-size trade is taken only when the alpha indicator exceeds a threshold C. When the indicator does not exceed that threshold, the trade is skipped. The daily result is the signed relative price change.

Last-day fortune is defined as an idealized accumulation that assumes no commissions and fills at the prescribed prices. That path is used to score the filter's direction skill. It is not presented as a live-account result.

The Ford illustration

On the Ford illustration the authors report a C of 0.38. They mark a largest daily result of 0.436 when the filter called the move from 1.72 toward 2.47, even though the predicted level 1.84 missed the actual close. Last-day fortune is 1.37 on 124 trades, and the profit ratio is 0.59.

Efficiency against available profit

Filter efficiency is the ratio of accumulated fortune to available profit. Available profit is the sum of absolute daily returns. For the Ford example that ratio is 0.104 against an available-profit total of 13.15.

Choosing the threshold

An optimal C is chosen by minimizing the distance between the fortune path and the available-profit path. When that criterion and last-day-fortune maximization disagree, the larger C is preferred, because the larger C yields a smoother fortune line.

What the table does not prove

Across the tabulated symbols, reported efficiencies, profit ratios, trade counts, and dollar returns vary widely by name and by the fitted T and C. The profit ratio is described as nearly independent of the dataset.

The authors state that selecting only the top table rows would look highly profitable. They also state that the simulation cannot be implemented as shown, because optimal C and T are determined from the entire sample on day 1.

They propose that fitting T and C on a shorter recent window, such as the prior quarter or two, would be the operational way to obtain values for the next day's forecast. They leave that rolling evaluation to later work.