SP500 Stock Price Index

Linear model of SP500 Stock Price Index at period t from the other tracked series and the LN_ / squared transforms described on the Regression Models index: Y(t) = Σ a_i X_i(t−6).

Integrated series (S&P 500, Dow, Home Price Index, Commercial RE) are fit as ΔY. Quarterly series use one row per quarter.

Terms are added one at a time to minimize training AIC, at most min(5, n/8) predictors, one transform per driver, and only when the term’s p-value is at most 0.1 and |coefficient| is greater than 1.0e-10. A candidate correlated above 0.8 with Y or with an already selected X is skipped.

LN_ and squared predictors are clamped to their training range. Coefficients smaller than 0.001 are shown in scientific notation.

Each section is labeled by the month after its 12-month test window; the fit uses the prior 48 months of Y. Independents are dated six months earlier than Y.

Charts start in January 2020 and plot published prints only (not carried-forward extra samples). Fitted (train), fitted (test), and forecast are joined at the window boundaries so the line is continuous through the label month. The OLS test/forecast is shown when its test MAE beats or matches a last-print (or zero-change) baseline.

An intercept-only heading (for example “Δ SP500 = 40.657”) means no lagged series improved training AIC by at least 2 after the intercept, so the model is the training-mean change (a random walk with drift).

Test MAE is omitted when every print in the test window is a CCAR extra sample rather than a published observation.