Constructing a calendar-conditioned trend filter

The sleeve as a worked trend filter

A trend filter is a rule that maps ordered price, volume, or breadth observations into a directional forecast over a defined sampling interval and lookback. In this construction the observations are those ordered sector readings, the update dates are the last trading day of April and the last trading day of October, and the forecast the rule may emit is which seasonal sleeve to hold.

Equity prices are described as typically leading the economy by six to nine months, so a sector choice that begins from the present economic stage is treated as following the market rather than leading it.

Momentum, seasonality, and correlation are the named ingredients used to assemble the sector-rotation forecast.

Update dates for the two seasonal windows

A seasonal-window is a fixed calendar interval that determines which sector sleeve the forecast is allowed to hold.

From the last trading day of April through the last trading day of October, the seasonal construction assigns equal weight to healthcare and consumer staples. That window is described as traditionally defensive from May through October.

On the last trading day of October that pair is replaced with equal one-quarter weights in consumer discretionary, industrials, materials, and technology, held for the next six months. That window is described as traditionally cyclical from November through April.

January market and sector results are treated as an early-year signal for which groups may lead or lag for the remainder of the year.

A two-gain smoother and a state-space updater

As an editorial placement, an alpha-beta filter sits beside the seasonal-window. It is a two-gain recursive smoother that updates a level and a slope from each new ordered observation and emits a forecast over a stated sampling interval. The level and slope update remains a separate choice from the April and October sleeve change.

As an editorial placement, a Kalman filter sits beside the same switch. It is a state-space updater that revises a prior estimate when a new ordered observation arrives and emits a forecast over a stated sampling interval. The revision of the prior stays distinct from the date on which the allowed sleeve changes.

Noise, the correction band, and historical rhyme

On short bars, extra filters or rules are required to reduce noise-driven signals, and transaction costs are to be included before a construction is accepted.

A correction is defined as a decline of 10 percent up to 20 percent, and several 19 percent-plus drops are listed as near-bear episodes without a single agreed trigger that a bear market has begun. The correction-band labels that range as a pullback that is not treated as a settled bear market.

Historical rhyme is offered as a guide for building a forecast, not as a guarantee that the same construction will keep working.