Aggregating and Decaying Sentiment Scores

A single news article about a company gets scored as +0.6 sentiment (on a −1 to +1 scale) by a text model. On its own, that's a snapshot with a very short shelf life: is this the fifth positive article in a week, reinforcing an established trend, or an isolated positive story following three negative ones? Should an article from three weeks ago still matter as much as one from this morning? A usable sentiment signal has to answer both questions — how to combine many individual scores into one number, and how much weight to give older scores relative to newer ones — and both choices materially change what the resulting signal actually captures.

Aggregation: combining many scores into one

The simplest aggregation is a plain average of all sentiment scores in a window, but this treats a single throwaway mention the same as a detailed analyst report, and treats five separate articles about the same underlying event as five independent pieces of evidence when they're really one. Better aggregation schemes weight each score by source credibility (a wire-service headline versus a detailed research note), by article length or specificity, and — importantly — collapse duplicate coverage of the same story into one contribution rather than letting republished or lightly-rewritten articles inflate the count (see news deduplication).

Decay: how much the past should still matter

A sentiment score from this morning is more informative about the current mood than one from three weeks ago, so most aggregation schemes apply exponential decay, weighting a score from $t$ days ago by

$$w(t) = e^{-\lambda t} ,$$

where $\lambda$ controls how fast old information fades — in plain English, each additional day multiplies the article's remaining weight by the same fraction, so old news never disappears entirely but its influence shrinks geometrically. A small $\lambda$ keeps a long memory (useful for slow-moving reputational sentiment); a large $\lambda$ makes the signal react almost entirely to the last day or two (useful for short-horizon trading signals reacting to breaking news).

Worked example: decayed sentiment across a week

Suppose five articles about a stock arrived with these ages and raw sentiment scores: 0 days ago, +0.6; 1 day ago, +0.2; 3 days ago, −0.4; 5 days ago, +0.5; 7 days ago, +0.3. Using $\lambda = 0.3$ per day, the weights are $w(0)=1$, $w(1)=e^{-0.3}\approx0.741$, $w(3)=e^{-0.9}\approx0.407$, $w(5)=e^{-1.5}\approx0.223$, $w(7)=e^{-2.1}\approx0.122$. The decayed weighted average is

$$\frac{1(0.6) + 0.741(0.2) + 0.407(-0.4) + 0.223(0.5) + 0.122(0.3)}{1 + 0.741 + 0.407 + 0.223 + 0.122} \approx \frac{0.799}{2.493} \approx 0.32 .$$

Compare that to the plain unweighted average of the same five scores, $(0.6+0.2-0.4+0.5+0.3)/5 = 0.24$. The decayed version sits higher because it correctly gives today's strongly positive article far more say than the older, mildly negative one from three days ago — exactly the behavior you'd want from a signal meant to track current sentiment rather than sentiment averaged uniformly over the whole week.

What this means in practice

The decay rate $\lambda$ is itself a parameter worth tuning against the strategy's actual holding horizon: a signal meant to trade on multi-week reputational drift should decay slowly, while one meant to react to same-day news should decay fast, and using the wrong speed either drowns a genuine short-term reaction in stale history or throws away real information about a slower-moving trend.