Signal Versus Noise in Consumer Trends

What we mean by signal and noise

A monthly consumer number is a measurement, not a fact about the world. It contains the thing we want, a real change in what households buy or pay, and things we do not want: sampling error, seasonal patterns, one-off shocks and later revisions. We call the first part signal and the rest noise. Many poor readings of consumer data come from treating one month as if it were all signal.

The NIST Engineering Statistics Handbook states the idea plainly. Data collected over time carry some random variation, and smoothing removes random variation and shows trends and cyclic components more clearly.

Two current releases

The Census Bureau advance estimate for September 2026, released on 15 October 2026, put retail and food services sales at 745.0 billion dollars. That was up 0.8 percent from August, with a stated margin of plus or minus 0.4 percent, and up 6.3 percent from September 2025, plus or minus 0.5 percent. The same release revised the July to August change from up 1.1 percent to up 1.3 percent. Census says the figures are adjusted for seasonal variation and holiday and trading-day differences, but not for price changes.

Prices tell a similar story. The BLS Consumer Price Index release for September 2026, published on 14 October 2026, shows all items up 0.6 percent on a seasonally adjusted basis, after a fall of 0.4 percent in June and rises of 0.1 percent in July and 0.4 percent in August. The 12-month change was 3.7 percent. Energy rose 5.2 percent in September and gasoline 9.1 percent, while food was unchanged and the index excluding food and energy rose 0.3 percent. One component drove the headline.

The Cleveland Fed publishes a median CPI and a trimmed-mean CPI to look through such moves. Updated on 14 October 2026, it shows median CPI up 0.2 percent in the month and 2.6 percent over 12 months, and the 16 percent trimmed mean up 0.3 percent and 2.7 percent. The gap between the 3.7 percent headline and the 2.6 percent median is 1.1 percentage points, which we read as the footprint of the energy move.

The arithmetic of uncertainty

A published change is a point estimate. The NIST handbook gives the standard form of an interval: estimate plus or minus a critical value times the standard error. Census prints the result for us. A 0.8 percent rise with a margin of 0.4 gives an interval of 0.4 to 1.2 percent. Because the interval excludes zero, sales very likely rose. Because it is wide, a true change of 0.5 percent or 1.1 percent would look much the same.

Revisions add a second layer. The August change moved by 0.2 percentage points, half the size of the printed margin. We read that as a reminder that the first print is an estimate that later data refine, not a final record.

A worked example shows what smoothing does. The numbers below are illustrative, not real data. Suppose six monthly changes are +0.9, -0.3, +0.6, +0.2, +0.7 and +0.5 percent. The raw series swings across a range of 1.2 points. Three-month averages are (0.9 - 0.3 + 0.6) / 3 = 0.40, then (-0.3 + 0.6 + 0.2) / 3 = 0.17, then (0.6 + 0.2 + 0.7) / 3 = 0.50, then (0.2 + 0.7 + 0.5) / 3 = 0.47. Their range is about 0.33 points. The six-month mean is 2.6 / 6, or 0.43 percent. The smoothed line is calmer and points to a steady gain of around 0.4 percent a month. The cost is delay: each month carries a weight of one third, so a real turn appears slowly.

What the evidence does not show

None of this proves that headline figures are wrong. Energy prices are real prices. BLS notes that unadjusted data are of primary interest to consumers concerned about the prices they actually pay. A median is a different question, not a better one.

Nor is there one best filter. Meyer and Venkatu, in a Cleveland Fed working paper from 2014, found that many trimmed-mean measures perform about the same statistically, with no single one clearly dominating. We do not know which filter will work best in the next shock.

The common mistakes follow from this. We see readers treat a change smaller than its margin as a direction. They compare a first print with a revised figure. They set a seasonally adjusted monthly change beside an unadjusted 12-month change. And they subtract one headline from another, such as 6.3 percent sales growth and 3.7 percent price growth, to infer real growth, when the two series cover different baskets and are measured differently.

Going deeper

Three formulas cover most of this topic.

• Interval = Estimate +/- Critical value x Standard error
• Simple average of n months = (x1 + x2 + ... + xn) / n, which gives each month a weight of 1/n
• Annualised rate = (1 + monthly rate)^12 - 1

On the annualised rate, an illustration only: a 0.6 percent monthly rise, repeated for twelve months, compounds to 1.006^12 - 1, or about 7.4 percent. The actual 12-month change reported for September 2026 was 3.7 percent. One month is not a trend, and annualising a single month is among the most common ways to mislead.

To read the primary releases yourself, start with the Census table, where each change sits beside its margin and the prior month's revision. In the BLS release, read Table A for the monthly path and the energy section for the driver. BLS recalculates seasonal factors each year with the January release, which may revise seasonally adjusted indexes for the previous five years. The Cleveland Fed defines median CPI as the one-month inflation rate of the component whose expenditure weight is at the 50th percentile of price changes, and the 16 percent trimmed mean as excluding the top and bottom 8 percent.

Leopard Intel is designed to serve outside customers as well as our own portfolio, which we treat as a worked example, not the limit. Every figure above links to the page we read. If any number fails to match its source, tell us and we will correct it.