Housing Lead

Abstract

Housing Lead blends forward indicators of residential activity (building permits and housing starts) with the financing constraint captured by the 30‑year mortgage rate. Because housing series are volatile and frequently revised (including seasonal factors), v1.1 introduces explicit smoothing (moving averages and percentile ranks) and an Early Warning band designed to flag rapid deterioration before the main regime threshold is crossed.

1. Data (FRED)

Calendar alignment: All inputs are aligned to a month‑end index. Weekly mortgage data are resampled using the last observed weekly value in each month (i.e., “month‑end last”).

2. Data Quality, Revisions, and Seasonal Adjustment

• Revisions are expected: Permits and starts are frequently revised in subsequent releases, so the most recent 1–3 months should be treated as “preliminary.”
• Seasonal adjustment can be unstable: Turning points (rapid slowdowns/rebounds) can amplify seasonal‑factor error and raise flip risk in threshold models.
• Practical implication: Use smoothing and rank‑based transforms; publish a “freshness / revision risk” note for the latest months when used in live monitoring.

3. Transformations (v1.1)

v1.1 keeps the original growth definitions but introduces smoothing and percentile ranks to reduce noise from revisions and seasonal adjustment.

1. Level smoothing (3‑month moving average):
   PERMIT^{MA3}_t = \frac{1}{3}(PERMIT_t + PERMIT_{t-1} + PERMIT_{t-2})

   HOUST^{MA3}_t = \frac{1}{3}(HOUST_t + HOUST_{t-1} + HOUST_{t-2})
2. Permits momentum: six‑month annualised growth (computed on smoothed levels)
   PERMIT_{6mAnn,t} = (PERMIT^{MA3}_t / PERMIT^{MA3}_{t−6})^2 − 1
3. Starts momentum: three‑month annualised growth (computed on smoothed levels)
   HOUST_{3mAnn,t} = (HOUST^{MA3}_t / HOUST^{MA3}_{t−3})^4 − 1
4. Mortgage headwind: month‑end level of MORTGAGE30US (higher is worse).
5. Percentile ranks (optional companion series): For interpretability and robustness, compute rolling percentile ranks for each transformed input.
   pct(X)_t = \mathrm{PercentileRank}(X_t; X_{t-w..t})

   Typical window: w = 60 months (minimum 24). Use percentiles as a cross‑check, not as the sole trigger.

4. Normalisation

Robust z‑scores are used to standardise components while limiting the influence of outliers and level shifts.

5. Composite Construction

Weighting emphasises permits (most forward‑looking), then starts, with a smaller penalty from mortgage rates.

Monitoring outputs (recommended): publish the component z‑scores, the composite C_t, and the companion percentile ranks. This makes it easier to distinguish “broad housing deterioration” from “rate‑only headwinds.”

6. Regime Mapping (with Early Warning)

Early Warning band (v1.1): flag rapid deterioration even if C_t is still above the contracting threshold. Use one of the two equivalent rules below (pick one for implementation consistency):

• Momentum rule: if \Delta_3 C_t = C_t − C_{t-3} < −0.60, set Early Warning.
• Rank rule: if pct(C_t) < 25 and \Delta_3 C_t < 0, set Early Warning.

Early Warning is a risk flag, not a separate regime. It indicates that the signal is deteriorating quickly and revisions/noise risk is elevated.

7. Interpretation Guide

8. Implementation (Python, reference)

import pandas as pd
import numpy as np

def robust_z(s, win=48, min_win=18):
    x = pd.to_numeric(s, errors="coerce").astype(float)
    med = x.rolling(win, min_periods=min_win).median()
    mad = (x - med).abs().rolling(win, min_periods=min_win).median()
    return (x - med) / (1.4826 * mad.replace(0, np.nan))

def pct_rank(s, win=60, min_win=24):
    x = pd.to_numeric(s, errors="coerce").astype(float)
    def _rank(v):
        if v.isna().all(): return np.nan
        return v.rank(pct=True).iloc[-1]
    return x.rolling(win, min_periods=min_win).apply(_rank, raw=False)

d = df_housing.copy()

# 1) Smooth levels
d["PERMIT_MA3"] = d["PERMIT"].rolling(3, min_periods=3).mean()
d["HOUST_MA3"]  = d["HOUST"].rolling(3, min_periods=3).mean()

# 2) Annualised momentum on smoothed levels
d["PERMIT_6mAnn"] = (d["PERMIT_MA3"] / d["PERMIT_MA3"].shift(6))**2 - 1.0
d["HOUST_3mAnn"]  = (d["HOUST_MA3"] / d["HOUST_MA3"].shift(3))**4 - 1.0

# 3) Standardise
d["Z_PERMIT"] = robust_z(d["PERMIT_6mAnn"])
d["Z_HOUST"]  = robust_z(d["HOUST_3mAnn"])
d["Z_MORT"]   = robust_z(-d["MORTGAGE30US"])  # month-end aligned series

# 4) Composite + contributions
d["Housing_Lead"] = (0.45*d["Z_PERMIT"] + 0.35*d["Z_HOUST"] + 0.20*d["Z_MORT"])
d["dC_3m"] = d["Housing_Lead"] - d["Housing_Lead"].shift(3)
d["pctC"]  = pct_rank(d["Housing_Lead"])

# 5) Regime + Early Warning
hi, lo = 0.75, -0.75

def _regime(v):
    if pd.isna(v): return np.nan
    return "Expanding" if v > hi else ("Contracting" if v < lo else "Neutral")

def _early_warning(C, dC_3m, pctC):
    if pd.isna(C) or pd.isna(dC_3m): return np.nan
    # choose ONE rule-set; keep it stable in production
    return bool(dC_3m < -0.60) or (pd.notna(pctC) and (pctC < 0.25) and (dC_3m < 0))

d["Housing_Regime"] = d["Housing_Lead"].apply(_regime)
d["Early_Warning"]  = [
    _early_warning(C, dc, pc) for C, dc, pc in zip(d["Housing_Lead"], d["dC_3m"], d["pctC"])
]

df_sig_housing = d

Note: keep the Early Warning rule stable (do not switch between rule-sets without documenting a version change).

9. Academic & Institutional References (interpretation anchors)

• Permits as leading indicators: Dua & Smyth, “Using Leading Indicators to Forecast U.S. Home Sales…” (early evidence that permits improve forecast accuracy).
• Construction lags: Bahadir (2014), documents typical delays from permitting to completion (supports “permits lead starts” intuition).
• Interest rates and housing cycles: Berger‑Thomson & Ellis (RBA RDP 2004‑08) and related housing‑cycle literature linking interest rates to construction dynamics.
• Official release/revision context: U.S. Census Bureau “New Residential Construction” documentation and releases (permits/starts revisions; SAAR; sampling error bands).

These references are used to anchor interpretation (directionality and lead/lag logic). The regime thresholds and Early Warning parameters remain heuristic and should be validated against your downstream macro model requirements.

10. Limitations

• Revision risk: the latest data points can change materially; treat near-term readings as provisional.
• Seasonality & noise: even SAAR series can be noisy; smoothing reduces false flips but adds lag.
• Threshold calibration: ±0.75 is a simple heuristic; calibrate if you need a specific false-positive/false-negative trade-off.
• Rates vs activity: mortgage rates can move faster than monthly activity; consider reporting weekly rate changes separately in dashboards.