Walk-forward evaluation of monthly yield and real-rate forecasts

Two forecast problems, two scoreboards

The historical workflow specified two forecast problems in advance. One target was the next month-end bond yield. The other was the real yield ten months ahead. Real yield means the interest rate for a stated period minus the inflation rate for that same period.

Editorial reading: treat these as two evaluation designs rather than one fitted story. The first design is a one-month linear-style map from ordered yields and macro series into the next month-end level, then converted into a walk-forward always-in rule. The second design is a ten-month real-yield map judged only as a trend check.

The one-month map

The one-month map used ordered recent yields, the deficit-to-output ratio, and consumer-price inflation as inputs. The deficit-to-output ratio is the combined government budget balance, deficit or surplus, scaled by total output and used as a lagged macro input to the yield maps. The target was the following month-end yield.

As defined for this article, linear regression is an explicit quantitative baseline that maps ordered yield, inflation, or breadth-style observations over a stated lookback and sampling interval onto a next-period forecast, then is compared with a result computed outside the fitting sample. The sampling interval is monthly. The prediction is a month-end forecast: a one-step prediction of the next month-end yield, or of the signed change implied by that prediction, evaluated at month-end marks only.

Fitting, local minima, and holdout grading

Fitting searched for connection weights that reduced forecast error. The bond-prediction error surface was described as having many local minima that a run can settle into depending on its starting weights. If a fit cannot reduce error through repeatable input-output relationships, it tends to memorize sample quirks that fail on new observations.

Holdout grading was used to limit that memorization. Holdout grading means scoring forecast error on a user-defined test window whose inputs are withheld from training passes. The final 17 months were excluded from both fitting and internal testing and then scored separately as unseen cases.

A uniform 30-year yield series was available only from 1978, which shortened the monthly sample relative to a preferred window of two to three hundred months for a one-month forecast.

From month-end forecast to an always-in rule

The one-month forecast was turned into an always-in walk-forward signal at month-end prices. An always-in rule is long or short at every month-end decision point and never stands aside. A higher predicted yield implied a short. A lower predicted yield implied a long.

As defined for this article, walk-forward analysis turns rule inputs, market state, and execution constraints into a single testable sequence of entry, exit, and remaining-in-market decisions over the system holding period, scored on windows the fitting step did not use. Transaction costs were omitted from the score. Interest income was omitted from the score. Long and short legs were reported apart against a predominantly rising price path in a volatile training window.

The ten-month real-yield check

The budget-balance-to-output ratio was treated as leading real bond yields by about ten months. The longer-horizon map used inflation together with that ratio as inputs. The ten-month real-yield outlook was presented as a general-trend evaluation over a long horizon and was explicitly not framed as a trading signal.