Forecasting the 10-Year Treasury Yield Dashboard

The latest values

The latest month-end close, the equation's forecast twelve months ahead, and two measures of the one-month accuracy of the equation with the close, which adds the month-end close less the month's average as a regressor.

The 10-year Treasury yield and the federal funds rate

The 10-year yield and the federal funds rate, as monthly averages: the two rates of the model's long-run relation.

The model

Forecast for the next twelve months

The equation's forecast of the monthly average for each of the twelve months after the origin, with its intervals, beside the forecasts of the equation with the close and of the close carried forward.

Monthly average of the 10-year yield, percent. The bands are the 68 and 95 percent intervals of the equation's forecast, taken from the percentiles of its own out-of-sample errors at each horizon. The forecast uses only the data published by the close of its month of origin.

Forecast table

The forecasts of the chart, month by month, in percent.

Error relative to the no-change forecast

The no-change forecast is the benchmark against which the published studies of the Literature tab state their results; here it is the no-change forecast of the monthly average. Each bar is a procedure's root mean squared error divided by that of the no-change forecast of the monthly average; a value below 1 marks a forecast more accurate than no change.

Error relative to the month-end close

Each line is a procedure's root mean squared error divided by that of the close, over rolling-window forecasts. A value above 1 marks a forecast less accurate than the close.

Out-of-sample tests

Each cell gives the bootstrap p-value, with the asymptotic value in parentheses; a bootstrap value below 0.05 rejects the null hypothesis, by which the rows are labeled, at the 5 percent level. Clark-West tests are read one-sided and Diebold-Mariano tests two-sided. The four tabs give three evaluation samples and, in the fourth, the month-end target.

Published results in context

Results of published studies for long-term yields, beside this page's error ratios against no change.

Published results are stated in words, as each study or, for the first row, a later study reports them. Samples, maturities, data vintages, and designs differ across the rows; the table is a guide to the literature and not a ranking.

How to read the comparison

Regression coefficients

The model is an error correction equation for the change in the monthly average of the yield from the origin month to the next. It is reported in two forms: the equation and the equation with the month-end close.

Coefficient t-statistics

The t-statistic of each regressor in the two forms of the one-month equation.

Newey-West t-statistics of the one-month equation. The vertical lines mark ±1.96, the two-sided 5 percent critical values of the standard normal distribution. The deviation from the long-run relation is read against a bootstrap distribution, shown in the table of the deviation's bootstrap distribution below, and not against these lines.

Long-run relation

The relation between the yield and the federal funds rate whose deviation the equation corrects.

y_t = \alpha + \beta f_t + z_t

The deviation from the long-run relation against its bootstrap distribution

The t-statistic of the deviation from the long-run relation, the error correction term, in each form of the one-month equation, read against its bootstrap distribution.

The 5th percentile and the p-value are from a bootstrap under a zero coefficient, one-sided; a p-value below 0.05 rejects a zero coefficient in the direction of error correction.

Supply-side and demand-side inflation signals

The one-month equation estimated with the PPI term as the supply-side signal and, in its place, the PCE term, the change in the latest published year-over-year rate of the price index of personal consumption expenditures (PCE), as the demand-side signal.

The PPI term by regime

The PPI term in three segments of the sample, split at July 1996, when the Federal Open Market Committee agreed internally on an inflation objective, and at January 2012, when it announced one.

Newey-West t-statistic of the PPI term, one-month equation, by segment of the sample. Each segment is estimated on the origin-target pairs whose origin and target month both lie inside it, so a pair that spans a segment's first month belongs to neither segment, and the three counts sum to fewer than the sample's origins. Each t-statistic is read against ±1.96, the two-sided 5 percent critical values.