Constructing dollar baselines from rates, inflation, and residuals

A floating dollar as an intermarket object

After fixed exchange-rate arrangements ended in the early 1970s, the dollar floated. Its swings were described as transmitting into bond, equity, and gold markets.

Editorial reading: a dollar position is already a cross-market statement. The first job is to write an explicit linear equation, not to read the index in isolation.

Fix the window before the equation

For a longer-horizon construction, monthly averages of the dollar index and of applicable inputs were preferred over month-end prints. Consumer-price series arrive monthly, and single-day closes are more volatile. Monthly-average-sampling uses those period averages so a single volatile close does not dominate a monthly observation.

The worked construction used 72 months of monthly data from April 1983 through March 1989. That choice reflected a general practice of five-to-six-year lookbacks. The lookback-compromise is a multi-year monthly window long enough to outlast a temporary dislocation but short enough that evolving cross-market kinships are not treated as fixed.

A publication-lag-offset then shifts official rate, inflation, or flow series by one or two months relative to the dollar index so the construction uses only information that would have been in hand.

Rank drivers with same-month correlation

Twenty-six candidate series were correlated with the dollar index on a same-month basis: short- and long-term rates and consumer-price inflation for seven major economies, plus five U.S. trade and investment-flow series. Same-month-correlation is that linear association with no time offset, used to rank inputs before a regression is specified.

Over that window, Japanese short-term rates showed a same-month correlation of 0.89 with the dollar index. Japanese short- and long-term rates ranked as the two closest associations, ahead of U.S. rates. The merchandise-trade-deficit series and the dollar index had a same-month correlation of 0.52 across the 72 months, with a less negative deficit tending to coincide with a higher dollar index.

Circular flows behind the ranking

Cross-market flows were described as circular. Funds leaving Japan for the United States lifted Japanese rates and bid the dollar higher, while some of those purchases pressed U.S. Treasury yields lower, and a weaker dollar then inflicted currency losses on Japanese holders.

A same-month fitted baseline

A same-month multiple regression of the dollar index on Japanese short-term rates plus eight other inflation, yield, and U.S. overseas-investment series produced a fitted path. The coefficient of multiple determination was 94.5%, and Japanese short-term rates contributed almost 80% of the explanation.

The fitted-baseline is the monthly dollar level implied by plugging those selected cross-market inputs into a linear regression. Explained-variance-share is the portion of dollar-index variation attributed to the full regression, or to one dominant input inside that regression.

Editorial reading: a high same-month fit only shows how tightly the chosen inputs can track the index when they are allowed to sit in the same month. It is not the destination of the construction.

Offset the inputs when the baseline needs to lead

After a one-month offset to mimic data lag, a specification using U.S. rates plus inflation from seven major economies produced fitted values that led the dollar index at the early-1985 and early-1988 turns. U.S. Treasury-bond yields and Japanese inflation entered positively, and U.S. and Canadian inflation entered negatively. Rates-only inputs tracked least well as a leading baseline.

Read the residual, not a tighter fit

A five-year regression ending at the 1985 dollar peak produced fitted values whose upward slope slackened and whose gap versus the actual index widened. Residual-divergence is that flattening of the fitted baseline, or a widening gap versus the actual dollar index, treated as a falsifiable trend-change condition.

Residual-autocorrelation, the serial dependence left in regression errors, was treated as expected in market data because interventions and speculative episodes sit outside a linear specification.