Chapter 02

Macro-Based Regime Detection

NotebookPython 3 (ipykernel)75 cells

Macro-Based Regime Detection

Chapter 1 · §1.4 Market Regimes: Change Is the Constant

Docker image: ml4t

Purpose

Demonstrates unsupervised learning for market regime detection using macroeconomic indicators from FRED, paired with S&P 500 volatility and drawdown for validation.

Learning Objectives

Cluster monthly macro indicators with GMM, K-Means, and hierarchical methods.
Validate macro clusters against realized equity volatility and drawdown.
Compare a four-indicator core view to an extended FRED panel.
Use PCA preprocessing to filter noise before clustering.

Book Reference

Section 1.4 of Chapter 1, "Market Regimes: Change Is the Constant" — macro-regime follow-up to factor_regimes.py. Figure 1.6 in the chapter is generated here.

Prerequisites

Familiarity with monthly time-series resampling and standardization.
Conceptual exposure to mixture models, K-Means, and dendrograms.
FRED panel and S&P 500 daily series materialized via data/macro/ and data/equities/sp500/ loaders.

Structure

Core Analysis (4 indicators) — UNRATE, DFF, T10Y2Y, CPIAUCSL → CPI YoY.
Extended Analysis — full FRED panel (after coverage filtering) for a richer but noisier view of economic conditions.
Comparison — silhouette scores across core, extended, and PCA-reduced models.

Key Insight

Macro regimes line up with distinct volatility environments more cleanly than they line up with average returns. This makes macro indicators useful for risk management (anticipating volatility shifts) rather than return prediction.

Imports

In [1]python · cell 3

python

"""Macro-Based Regime Detection — unsupervised regime detection using FRED macro indicators."""

from __future__ import annotations

import warnings

warnings.filterwarnings("ignore")

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import polars as pl
import seaborn as sns
from matplotlib.gridspec import GridSpec
from scipy.cluster.hierarchy import cophenet, dendrogram, linkage
from scipy.spatial.distance import pdist
from sklearn.cluster import KMeans
from sklearn.decomposition import PCA
from sklearn.metrics import silhouette_score
from sklearn.mixture import GaussianMixture
from sklearn.preprocessing import StandardScaler, scale

from data import load_macro, load_sp500_index
from utils.paths import get_output_dir
from utils.reproducibility import set_global_seeds

In [2]python · cell 4

python

# Production defaults (Papermill overrides for testing)
SEED = 42

Configuration

In [3]python · cell 6

python

OUTPUT_DIR = get_output_dir(1, "macro_regimes")
OUTPUT_DIR.mkdir(parents=True, exist_ok=True)

set_global_seeds(SEED)

DATE_COL = "timestamp"

Helper Function

Reusable function for regime visualization. Both GMM and K-Means results use the same heatmap format for easy comparison.

In [4]python · cell 8

python

def plot_regime_heatmap(
    assignments: np.ndarray,
    dates: pd.DatetimeIndex,
    title: str,
    n_regimes: int = 4,
    is_probability: bool = True,
    figsize: tuple = (14, 4),
) -> None:
    """
    Plot regime assignments as a heatmap.

    Parameters
    ----------
    assignments : np.ndarray
        Either probability matrix (n_samples, n_regimes) for GMM
        or hard labels (n_samples,) for K-Means
    dates : pd.DatetimeIndex
        Dates corresponding to each sample
    title : str
        Plot title
    n_regimes : int
        Number of regimes
    is_probability : bool
        True if assignments are probabilities, False for hard labels
    figsize : tuple
        Figure size
    """
    fig, ax = plt.subplots(figsize=figsize, layout="tight")

    # Convert hard labels to one-hot if needed
    if not is_probability:
        one_hot = np.zeros((len(assignments), n_regimes))
        one_hot[np.arange(len(assignments)), assignments] = 1
        data = one_hot
    else:
        data = assignments

    im = ax.imshow(data.T, aspect="auto", cmap="Blues", vmin=0, vmax=1)

    # X-axis: years
    years = [pd.Timestamp(ts).year for ts in dates]
    year_ticks = [j for j, y in enumerate(years) if j == 0 or years[j - 1] != y]
    year_labels = [str(years[j]) for j in year_ticks]
    ax.set_xticks(year_ticks[::2])
    ax.set_xticklabels(year_labels[::2], fontsize=9)

    # Y-axis: regimes
    ax.set_yticks(range(n_regimes))
    ax.set_yticklabels([f"Regime {i + 1}" for i in range(n_regimes)])
    ax.set_ylabel("Regime")
    ax.set_xlabel("Year")
    ax.set_title(title, fontsize=12)

    cbar = plt.colorbar(im, ax=ax, shrink=0.8)
    cbar.set_label("Probability" if is_probability else "Assignment")
    plt.show()

Load FRED Macro Data

We load all available FRED macro indicators once, then select subsets for analysis. The dataset includes ~17 series after filtering for data quality.

Load Full Dataset

In [5]python · cell 11

python

macro_raw = load_macro()

# group_by_dynamic requires Datetime, not Date
if macro_raw["timestamp"].dtype == pl.Date:
    macro_raw = macro_raw.with_columns(pl.col("timestamp").cast(pl.Datetime))

print(f"Loaded FRED macro data: {macro_raw.shape}")
print(f"Date range: {macro_raw['timestamp'].min()} to {macro_raw['timestamp'].max()}")
print(f"Available series: {[c for c in macro_raw.columns if c != 'timestamp']}")

Output

Loaded FRED macro data: (9497, 26)
Date range: 2000-01-01 00:00:00 to 2025-12-31 00:00:00
Available series: ['dff', 'dgs1', 'dgs2', 'dgs3', 'dgs5', 'dgs7', 'dgs10', 'dgs20', 'dgs30', 't10y2y', 'vixcls', 'icsa', 'walcl', 'cpiaucsl', 'cpilfesl', 'pcepi', 'unrate', 'payems', 'civpart', 'indpro', 'm2sl', 'gdp', 'gdpc1', 'YIELD_CURVE_SLOPE', 'YIELD_CURVE_5_10']

Available Indicators

Category	Series	Description
Labor	UNRATE	Unemployment rate (%)
Interest Rates	DFF	Federal Funds effective rate (%)
	T10Y2Y	10Y-2Y Treasury spread (yield curve)
	T10YIE	10Y breakeven inflation
Prices	CPIAUCSL	Consumer Price Index
	CPILFESL	Core CPI (ex food & energy)
Volatility	VIXCLS	VIX volatility index
Credit	BAMLHE00EHYIEY	High yield spread
Housing	CSUSHPISA	Case-Shiller home price index
Money	M2SL	M2 money supply

For the Core Analysis, we use only 4 fundamental macro indicators.

Core Analysis: 4 Macro Indicators

We use four indicators that reflect real economic conditions:

UNRATE: Unemployment rate - labor market health
DFF: Federal Funds rate - monetary policy stance
T10Y2Y: Yield curve slope - recession signal
CPIAUCSL → cpi_yoy: CPI year-over-year inflation rate (not the level, which trends upward)

Select Core Indicators

In [6]python · cell 15

python

# Core 4 indicators (case-insensitive matching)
CORE_INDICATORS = ["unrate", "dff", "t10y2y", "cpiaucsl"]

macro_columns = macro_raw.columns
core_cols = []
col_name_map = {}

for indicator in CORE_INDICATORS:
    for col in macro_columns:
        if col.lower() == indicator:
            core_cols.append(col)
            col_name_map[col] = indicator
            break

print(f"Core indicators selected: {len(core_cols)}/{len(CORE_INDICATORS)}")
for col in core_cols:
    print(f"  {col} -> {col_name_map[col]}")

Output

Core indicators selected: 4/4
  unrate -> unrate
  dff -> dff
  t10y2y -> t10y2y
  cpiaucsl -> cpiaucsl

Resample to Monthly

In [7]python · cell 17

python

macro_monthly = (
    macro_raw.select([DATE_COL] + core_cols)
    .sort(DATE_COL)
    .group_by_dynamic(DATE_COL, every="1mo", label="right")
    .agg([pl.col(c).last() for c in core_cols])
    # Forward-fill carries last observation through release lags; the small
    # backward-fill catches any leading nulls in early months. The latter
    # introduces a one-period look-ahead at the panel boundary — acceptable
    # for a regime-detection demo, not for a backtested strategy.
    .fill_null(strategy="forward")
    .fill_null(strategy="backward")
    .drop_nulls(subset=core_cols)
)

# Filter to 2002+ where most FRED series have good coverage
if macro_monthly.height > 0:
    min_date = macro_monthly[DATE_COL].min()
    if min_date is not None and str(min_date) < "2002-01-01":
        macro_monthly = macro_monthly.filter(pl.col(DATE_COL) >= pl.datetime(2002, 1, 1))

print(f"Monthly data: {macro_monthly.height} months")
if macro_monthly.height > 0:
    print(f"Date range: {macro_monthly[DATE_COL].min()} to {macro_monthly[DATE_COL].max()}")

Output

Monthly data: 289 months
Date range: 2002-01-01 00:00:00 to 2026-01-01 00:00:00

Standardize for Clustering

In [8]python · cell 19

python

if macro_monthly.height > 0:
    macro_df = macro_monthly.select(core_cols).to_pandas()
    macro_df.columns = [col_name_map.get(c, c) for c in macro_df.columns]
    macro_df.index = macro_monthly[DATE_COL].to_pandas()

    # Convert CPI level to YoY percentage change — the level is non-stationary
    # and would make the clustering capture "early vs recent" rather than
    # "inflationary vs non-inflationary"
    macro_df["cpi_yoy"] = macro_df["cpiaucsl"].pct_change(12) * 100
    macro_df = macro_df.drop(columns=["cpiaucsl"]).dropna()

    macro_scaled = StandardScaler().fit_transform(macro_df)

    print("Core Indicator Statistics (raw):")
    print(macro_df.describe().round(2))
else:
    macro_df = pd.DataFrame()
    macro_scaled = np.array([])

Output

Core Indicator Statistics (raw):
       unrate     dff  t10y2y  cpi_yoy
count  277.00  277.00  277.00   277.00
mean     5.75    1.76    1.07     2.58
std      2.02    1.91    0.97     1.81
min      3.40    0.04   -1.06    -1.96
25%      4.20    0.10    0.24     1.64
50%      5.00    1.04    1.01     2.33
75%      6.70    3.09    1.90     3.24
max     14.80    5.41    2.84     8.98

Fit GMM with 4 Regimes

In [9]python · cell 21

python

if len(macro_df) > 0:
    n_macro_regimes = 4
    gmm_macro = GaussianMixture(
        n_components=n_macro_regimes,
        covariance_type="full",
        random_state=SEED,
        n_init=10,
        reg_covar=1e-6,
    )
    gmm_macro.fit(macro_scaled)
    macro_labels = gmm_macro.predict(macro_scaled)
    macro_probs = gmm_macro.predict_proba(macro_scaled)

    macro_silhouette = silhouette_score(macro_scaled, macro_labels)
    print(f"Macro regime silhouette score (n={n_macro_regimes}): {macro_silhouette:.3f}")
else:
    macro_labels = np.array([])
    macro_probs = np.array([])

Output

Macro regime silhouette score (n=4): 0.252

We use 4 regimes to match the Two Sigma approach. The silhouette score measures cluster separation — higher is better, with values above 0.25 indicating reasonable structure. Unlike factor_regimes, we skip BIC/AIC model selection here because the goal is interpretability (matching known economic phases), not statistical optimality.

Regime Characteristics

In [10]python · cell 24

python

if len(macro_df) > 0:
    regime_chars = macro_df.copy()
    regime_chars["regime"] = macro_labels
    regime_means = regime_chars.groupby("regime").mean()

    print("Regime Characteristics (mean values):")
    print(regime_means.round(2))
else:
    regime_means = pd.DataFrame()

Output

Regime Characteristics (mean values):
        unrate   dff  t10y2y  cpi_yoy
regime                               
0         4.70  1.36    1.12     2.15
1        12.30  0.07    0.47     0.56
2         7.62  0.11    1.88     1.58
3         4.43  3.79    0.24     4.01

Assign Interpretive Labels

In [11]python · cell 26

python

def create_regime_labels(chars: pd.DataFrame) -> dict[int, str]:
    """Create short, descriptive labels based on economic characteristics.

    Uses a priority cascade on cluster-mean values. Thresholds are approximate
    and tuned for the 2002-2025 US macro environment.
    """
    labels = {}
    for regime in chars.index:
        c = chars.loc[regime]
        if c["unrate"] > 10:
            labels[regime] = "Crisis"
        elif c["unrate"] > 6 and c["dff"] < 0.5:
            labels[regime] = "Recovery"
        elif c["dff"] > 3 and c["t10y2y"] < 0.5:
            labels[regime] = "Tightening"
        elif c["cpi_yoy"] > 4:
            labels[regime] = "Inflation"
        elif c["unrate"] < 5 and c["dff"] < 2:
            labels[regime] = "Expansion"
        else:
            labels[regime] = "Transition"

    # Ensure unique labels
    seen = {}
    for r, label in list(labels.items()):
        if label in seen:
            if chars.loc[r, "unrate"] > chars.loc[seen[label], "unrate"]:
                labels[r] = f"{label} (High Unemp.)"
            else:
                labels[seen[label]] = f"{label} (High Unemp.)"
        seen[label] = r
    return labels

In [12]python · cell 27

python

if len(regime_means) > 0:
    regime_labels_map = create_regime_labels(regime_means)
    print("Assigned Regime Labels:")
    for regime, label in sorted(regime_labels_map.items()):
        print(f"  Cluster {regime}: {label}")
else:
    regime_labels_map = {}

Output

Assigned Regime Labels:
  Cluster 0: Expansion
  Cluster 1: Crisis
  Cluster 2: Recovery
  Cluster 3: Tightening

Macro Regimes and Market Volatility

Key insight: Macro regimes coincide with different VOLATILITY environments, even when return patterns are less clear.

Implication: Macro regime indicators are useful for RISK MANAGEMENT (anticipating volatility shifts) rather than RETURN PREDICTION.

Load S&P 500 for Validation

In [13]python · cell 30

python

sp500_raw = load_sp500_index().to_pandas()
sp500_raw["timestamp"] = pd.to_datetime(sp500_raw["timestamp"])
sp500_raw = sp500_raw.set_index("timestamp")

sp500_monthly = sp500_raw["close"].resample("ME").last().to_frame()
sp500_monthly["returns"] = sp500_monthly["close"].pct_change()
sp500_df = sp500_monthly

print(
    f"Loaded S&P 500 for validation: {len(sp500_df)} months, "
    f"{sp500_df.index.min().date()} to {sp500_df.index.max().date()}"
)

Output

Loaded S&P 500 for validation: 552 months, 1980-01-31 to 2025-12-31

Compute Regime Statistics

In [14]python · cell 32

python

if len(macro_df) > 0 and sp500_df is not None:
    events = {2008: "GFC", 2020: "COVID", 2022: "Inflation"}

    sp500_aligned = sp500_df.reindex(macro_df.index, method="nearest", tolerance=pd.Timedelta("5D"))
    sp500_aligned["regime"] = macro_labels
    sp500_aligned["regime_label"] = [regime_labels_map[r] for r in macro_labels]
    sp500_aligned["peak"] = sp500_aligned["close"].cummax()
    sp500_aligned["drawdown"] = (sp500_aligned["close"] - sp500_aligned["peak"]) / sp500_aligned[
        "peak"
    ]
    sp500_aligned["volatility"] = sp500_aligned["returns"].rolling(12).std() * np.sqrt(12)

    regime_stats_fig = sp500_aligned.groupby("regime_label").agg(
        {"returns": ["mean", "std", "count"], "drawdown": "min", "volatility": "mean"}
    )
    regime_stats_fig.columns = ["mean_ret", "std_ret", "months", "max_dd", "avg_vol"]
    regime_stats_fig["annual_vol"] = regime_stats_fig["std_ret"] * np.sqrt(12) * 100
    regime_stats_fig["max_dd_pct"] = -regime_stats_fig["max_dd"] * 100

    regime_stats_fig = regime_stats_fig.sort_values("annual_vol", ascending=True)
    regime_order = regime_stats_fig.index.tolist()
    n_regimes_fig = len(regime_order)

    print("Regime Statistics (sorted by volatility):")
    print(regime_stats_fig[["months", "annual_vol", "max_dd_pct"]].round(1))

Output

Regime Statistics (sorted by volatility):
              months  annual_vol  max_dd_pct
regime_label                                
Expansion         77        12.0        14.6
Tightening        98        15.0        42.2
Recovery          98        15.2        52.6
Crisis             4        16.0         9.9

Regime Timeline with Market Validation

In [15]python · cell 34

python

def plot_regime_timeline_validation():
    """Plot regime swim lanes with volatility and drawdown validation bars."""
    if len(macro_df) > 0 and sp500_df is not None:
        years = [pd.Timestamp(ts).year for ts in macro_df.index]
        n_months = len(macro_df)

        year_ticks = []
        year_labels_fig = []
        for j, year in enumerate(years):
            if j == 0 or years[j - 1] != year:
                if year % 4 == 0:
                    year_ticks.append(j)
                    year_labels_fig.append(str(year))

        fig = plt.figure(figsize=(14, 6))
        gs = GridSpec(
            n_regimes_fig, 4, figure=fig, width_ratios=[3.5, 1, 1, 0.05], wspace=0.12, hspace=0.08
        )

        swimlane_axes = [fig.add_subplot(gs[i, 0]) for i in range(n_regimes_fig)]
        vol_axes = [fig.add_subplot(gs[i, 1]) for i in range(n_regimes_fig)]
        dd_axes = [fig.add_subplot(gs[i, 2]) for i in range(n_regimes_fig)]

        # Grayscale-friendly palette (distinct in B&W print)
        # Ordered from light to dark to match volatility ordering
        REGIME_COLORS = ["#e0e0e0", "#a0a0a0", "#606060", "#202020"]
        colors = REGIME_COLORS[:n_regimes_fig]

        for i, regime_label in enumerate(regime_order):
            raw_regime = [r for r, lbl in regime_labels_map.items() if lbl == regime_label][0]
            mask = macro_labels == raw_regime
            stats = regime_stats_fig.loc[regime_label]
            color = colors[i]

            ax_swim = swimlane_axes[i]
            for j in range(n_months - 1):
                if mask[j]:
                    ax_swim.axvspan(j, j + 1, color=color, alpha=0.85)

            ax_swim.set_xlim(0, n_months)
            ax_swim.set_ylim(0, 1)
            ax_swim.set_yticks([])
            ax_swim.set_ylabel(regime_label, fontsize=9, rotation=0, ha="right", va="center")

            if i < n_regimes_fig - 1:
                ax_swim.set_xticks([])
            else:
                ax_swim.set_xticks(year_ticks)
                ax_swim.set_xticklabels(year_labels_fig, fontsize=8)
                ax_swim.set_xlabel("Year", fontsize=9)

            for event_year, event_label in events.items():
                try:
                    idx = next(j for j, y in enumerate(years) if y == event_year)
                    ax_swim.axvline(x=idx, color="black", linestyle="-", alpha=0.3, linewidth=0.8)
                    if i == 0:
                        ax_swim.annotate(
                            event_label,
                            xy=(idx, 1.25),
                            xycoords=("data", "axes fraction"),
                            ha="center",
                            fontsize=7,
                            color="black",
                            fontweight="bold",
                        )
                except StopIteration:
                    pass

            ax_vol = vol_axes[i]
            vol_val = stats["annual_vol"]
            ax_vol.barh([0], [vol_val], color=color, height=0.6, edgecolor="black", linewidth=0.5)
            ax_vol.set_xlim(0, 22)
            ax_vol.set_ylim(-0.5, 0.5)
            ax_vol.set_yticks([])
            ax_vol.text(
                vol_val + 0.3,
                0,
                f"{vol_val:.0f}%",
                ha="left",
                va="center",
                fontsize=9,
                fontweight="bold",
            )

            if i == 0:
                ax_vol.set_title("Volatility\n(ann. %)", fontsize=9, fontweight="bold")
            if i < n_regimes_fig - 1:
                ax_vol.set_xticks([])
            else:
                ax_vol.set_xticks([0, 10, 20])
                ax_vol.tick_params(labelsize=7)

            ax_dd = dd_axes[i]
            dd_val = stats["max_dd_pct"]
            ax_dd.barh([0], [dd_val], color=color, height=0.6, edgecolor="black", linewidth=0.5)
            ax_dd.set_xlim(0, 60)
            ax_dd.set_ylim(-0.5, 0.5)
            ax_dd.set_yticks([])
            ax_dd.text(
                dd_val + 1,
                0,
                f"{dd_val:.0f}%",
                ha="left",
                va="center",
                fontsize=9,
                fontweight="bold",
            )

            if i == 0:
                ax_dd.set_title("Max\nDrawdown", fontsize=9, fontweight="bold")
            if i < n_regimes_fig - 1:
                ax_dd.set_xticks([])
            else:
                ax_dd.set_xticks([0, 20, 40, 60])
                ax_dd.tick_params(labelsize=7)

        start_year = macro_df.index.min().year
        end_year = macro_df.index.max().year
        fig.suptitle(
            f"Macro Regimes and Market Volatility ({start_year}-{end_year})",
            fontsize=11,
            fontweight="bold",
            y=0.98,
        )

        fig.text(
            0.5,
            0.02,
            "Regimes from: Unemployment, Fed Funds Rate, Yield Curve (10Y-2Y), CPI  |  Sorted by volatility",
            ha="center",
            fontsize=8,
            style="italic",
            color="#505050",
        )

        plt.show()


plot_regime_timeline_validation()

Output

<Figure size 1400x600 with 12 Axes>

Persist Figure 1.6 inputs

The publication-quality version of Figure 1.6 is rendered by book/01_process_is_edge/figures/scripts/generate_figure_1_6_macro_regimes_volatility.py. That script reads the arrays persisted below so the book build does not re-fit the clustering pipeline.

In [16]python · cell 36

python

if len(macro_df) > 0 and sp500_df is not None:
    ARTIFACT_DIR = OUTPUT_DIR / "figure_1_6"
    ARTIFACT_DIR.mkdir(parents=True, exist_ok=True)
    annual_vol_by_regime = regime_stats_fig.loc[regime_order, "annual_vol"].to_numpy(dtype=float)
    max_dd_by_regime = regime_stats_fig.loc[regime_order, "max_dd_pct"].to_numpy(dtype=float)
    np.savez(
        ARTIFACT_DIR / "inputs.npz",
        dates=macro_df.index.astype("datetime64[ns]").astype("int64"),
        macro_labels=np.asarray(macro_labels, dtype=np.int64),
        regime_order=np.asarray(regime_order, dtype=object),
        raw_regime_for_order=np.asarray(
            [
                next(r for r, lbl in regime_labels_map.items() if lbl == label)
                for label in regime_order
            ],
            dtype=np.int64,
        ),
        annual_vol=annual_vol_by_regime,
        max_dd_pct=max_dd_by_regime,
        event_years=np.asarray(list(events.keys()), dtype=np.int64),
        event_labels=np.asarray(list(events.values()), dtype=object),
        start_year=np.int64(macro_df.index.min().year),
        end_year=np.int64(macro_df.index.max().year),
    )

Key Insight Summary

In [17]python · cell 38

python

insight_table = (
    regime_stats_fig.loc[regime_order, ["months", "annual_vol", "max_dd_pct"]]
    .rename(
        columns={
            "months": "Months",
            "annual_vol": "Annual vol (%)",
            "max_dd_pct": "Max drawdown (%)",
        }
    )
    .round(1)
)
insight_table

Output

              Months  Annual vol (%)  Max drawdown (%)
regime_label                                          
Expansion         77            12.0              14.6
Tightening        98            15.0              42.2
Recovery          98            15.2              52.6
Crisis             4            16.0               9.9

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	Months	Annual vol (%)	Max drawdown (%)
regime_label
Expansion	77	12.0	14.6
Tightening	98	15.0	42.2
Recovery	98	15.2	52.6
Crisis	4	16.0	9.9

Correlation Heatmap

In [18]python · cell 40

python

if len(macro_df) > 0:
    fig, ax = plt.subplots(figsize=(8, 6), layout="tight")
    sns.heatmap(
        macro_df.corr(),
        annot=True,
        fmt=".2f",
        cmap="RdBu_r",
        center=0,
        ax=ax,
        square=True,
    )
    ax.set_title("Macro Indicator Correlations", fontsize=12)
    plt.show()

Output

<Figure size 800x600 with 2 Axes>

Interpretation: Unemployment moves with the 10y-2y spread (positive correlation ~0.70): when the labour market deteriorates, the curve typically steepens as the Fed cuts the front end. The Fed Funds rate moves against the spread (correlation ~−0.73): hiking cycles flatten or invert the curve. CPI YoY is largely orthogonal to the other three — inflation regimes can coexist with both recession and expansion. These pairwise correlations show why a single indicator is a noisy regime signal and motivate joint clustering.

Extended Analysis: All FRED Indicators

Now we expand beyond the 4 core indicators to use all available FRED series (~17 indicators after quality filtering). This provides a richer but noisier view of economic conditions.

Prepare Full Dataset

Using the same data loaded at the start, we now select ALL series with sufficient data coverage (< 50% missing).

In [19]python · cell 44

python

# Use the already-loaded macro_raw data
value_cols_full = [c for c in macro_raw.columns if c != DATE_COL]

macro_monthly_full = (
    macro_raw.sort(DATE_COL)
    .group_by_dynamic(DATE_COL, every="1mo", label="right")
    .agg([pl.col(c).last() for c in value_cols_full])
    .filter(pl.col(DATE_COL) >= pl.datetime(2002, 1, 1))
)

# Identify columns with >50% missing, exclude market price columns
total_rows = macro_monthly_full.height
null_fractions = {
    col: macro_monthly_full.select(pl.col(col).is_null().sum()).item() / total_rows
    for col in value_cols_full
}
# Exclude columns with too much missing data and market price columns (SP500)
exclude_cols = {"sp500", "SP500"}
good_cols = [col for col, frac in null_fractions.items() if frac < 0.5 and col not in exclude_cols]

macro_clean_full = (
    macro_monthly_full.select([DATE_COL] + good_cols).fill_null(strategy="forward").drop_nulls()
)

macro_data_full = macro_clean_full.select(good_cols).to_pandas()
macro_data_full.index = macro_clean_full[DATE_COL].to_pandas()
macro_data_full = macro_data_full.apply(scale)

print(f"Extended dataset: {macro_data_full.shape[0]} months, {macro_data_full.shape[1]} series")
print(f"Series used: {list(macro_data_full.columns)}")

Output

Extended dataset: 277 months, 25 series
Series used: ['dff', 'dgs1', 'dgs2', 'dgs3', 'dgs5', 'dgs7', 'dgs10', 'dgs20', 'dgs30', 't10y2y', 'vixcls', 'icsa', 'walcl', 'cpiaucsl', 'cpilfesl', 'pcepi', 'unrate', 'payems', 'civpart', 'indpro', 'm2sl', 'gdp', 'gdpc1', 'YIELD_CURVE_SLOPE', 'YIELD_CURVE_5_10']

Visualize All Series

In [20]python · cell 46

python

n_cols = min(len(macro_data_full.columns), 20)
n_rows = (n_cols + 4) // 5
n_plot_cols = min(5, n_cols)

fig, axes = plt.subplots(
    nrows=n_rows, ncols=n_plot_cols, figsize=(16, 2 * n_rows), sharex=True, sharey=True
)
axes = axes.flatten() if n_rows > 1 else [axes] if n_cols == 1 else axes

for i, ax in enumerate(axes[:n_cols]):
    if i < len(macro_data_full.columns):
        macro_data_full.iloc[:, i].plot(ax=ax, color="steelblue", linewidth=0.8)
        ax.set_title(macro_data_full.columns[i], fontsize=9)
        ax.tick_params(axis="both", labelsize=7)
    else:
        ax.set_visible(False)

for i in range(n_cols, len(axes)):
    axes[i].set_visible(False)

sns.despine()
start_yr = macro_data_full.index.min().year
end_yr = macro_data_full.index.max().year
fig.suptitle(f"FRED Macro Series - Standardized ({start_yr}-{end_yr})", fontsize=12, y=1.02)
plt.show()

Output

<Figure size 1600x800 with 20 Axes>

[省略较大 image/png 输出]

Interpretation: The visibly regime-bearing series are VIX (sharp spikes in 2008 and 2020), ICSA initial claims (same crisis peaks), DFF (regime shifts during hiking cycles), and the yield-curve spread T10Y2Y (recession warnings ahead of 2008 and 2020). Slow-moving series (housing, monetary aggregates) carry less regime information. Clustering will lean heavily on the high-variance subset.

Hierarchical Clustering

Cluster the correlation matrix to reveal indicator groupings.

In [21]python · cell 49

python

# clustermap manages its own gridspec; disable constrained_layout to avoid
# matplotlib colorbar/engine-switch errors under non-interactive backends.
with plt.rc_context({"figure.constrained_layout.use": False}):
    fig = sns.clustermap(macro_data_full.corr(), cmap="RdBu_r", center=0, figsize=(10, 10))
    fig.fig.suptitle("FRED Indicator Correlations (Hierarchical Clustering)", y=1.02)
    plt.show()

Output

<Figure size 1000x1000 with 4 Axes>

Interpretation: Four blocks emerge: a labour/yield-curve block (CIVPART, UNRATE, T10Y2Y), a stress block (VIX, ICSA, high-yield spread), a growth/price-level block (INDPRO, CPI, M2), and a short-rate block (DFF, T10YIE). Most off-diagonal correlations are modest in magnitude, and the dendrogram's high cophenetic correlation confirms that this block structure is genuinely hierarchical.

Comparing GMM and K-Means

Both methods identify 4 regimes. The key difference:

GMM: Soft assignments with probabilities (uncertainty quantified)
K-Means: Hard assignments (each month belongs to exactly one regime)

Fit Both Models

In [22]python · cell 53

python

n_regimes_full = 4

# GMM
gmm_full = GaussianMixture(
    n_components=n_regimes_full,
    covariance_type="full",
    random_state=SEED,
    n_init=10,
    reg_covar=1e-6,
)
gmm_full.fit(macro_data_full)
gmm_probs_full = gmm_full.predict_proba(macro_data_full)
gmm_labels_full = gmm_full.predict(macro_data_full)

# K-Means
kmeans_full = KMeans(n_clusters=n_regimes_full, random_state=SEED, n_init=10)
kmeans_labels_full = kmeans_full.fit_predict(macro_data_full)

print(f"GMM silhouette: {silhouette_score(macro_data_full, gmm_labels_full):.3f}")
print(f"K-Means silhouette: {silhouette_score(macro_data_full, kmeans_labels_full):.3f}")

Output

GMM silhouette: 0.417
K-Means silhouette: 0.448

GMM Regime Probabilities

In [23]python · cell 55

python

plot_regime_heatmap(
    gmm_probs_full,
    macro_data_full.index,
    f"GMM Regime Probabilities ({start_yr}-{end_yr})",
    n_regimes=n_regimes_full,
    is_probability=True,
)

Output

<Figure size 1400x400 with 2 Axes>

K-Means Regime Assignments

In [24]python · cell 57

python

plot_regime_heatmap(
    kmeans_labels_full,
    macro_data_full.index,
    f"K-Means Regime Assignments ({start_yr}-{end_yr})",
    n_regimes=n_regimes_full,
    is_probability=False,
)

Output

<Figure size 1400x400 with 2 Axes>

Agglomerative Clustering

Hierarchical clustering on observations (not features) shows how months group together.

Linkage Matrix

In [25]python · cell 60

python

Z_full = linkage(macro_data_full, "ward")
pairwise_dist = pdist(macro_data_full)
c, _ = cophenet(Z_full, pairwise_dist)

print(f"Cophenetic correlation: {c:.3f}")

Output

Cophenetic correlation: 0.710

Note: The cophenetic correlation measures how faithfully the dendrogram preserves the original pairwise distances; good dendrograms score above 0.7. Here it reaches 0.71, so the Ward-linkage tree is a reliable summary of the indicator distance structure — the block grouping above reflects real hierarchy rather than an artefact of the linkage choice.

Dendrogram

In [26]python · cell 63

python

fig, ax = plt.subplots(figsize=(16, 5))
# no_labels=True since the point of this figure is the cophenetic-correlation
# summary in the title, not per-observation identity.
dendrogram(Z_full, orientation="top", no_labels=True, ax=ax)
ax.set_title(f"Ward Linkage Dendrogram | Cophenetic Correlation: {c:.2f}", fontsize=12)
ax.set_ylabel("Distance")
sns.despine()
plt.show()

Output

<Figure size 1600x500 with 1 Axes>

PCA Preprocessing

Reduce dimensionality before clustering to filter noise.

Fit PCA

In [27]python · cell 66

python

n_pca = min(10, macro_data_full.shape[1])
pca = PCA(n_components=n_pca)
reduced = pca.fit_transform(macro_data_full)

print("Cumulative Explained Variance:")
cumvar = pd.Series(pca.explained_variance_ratio_).cumsum()
for i, v in enumerate(cumvar):
    print(f"  PC{i + 1}: {v:.1%}")

Output

Cumulative Explained Variance:
  PC1: 45.6%
  PC2: 80.4%
  PC3: 87.9%
  PC4: 93.6%
  PC5: 96.0%
  PC6: 97.8%
  PC7: 98.8%
  PC8: 99.4%
  PC9: 99.7%
  PC10: 99.8%

GMM on PCA-Reduced Data

In [28]python · cell 68

python

gmm_pca = GaussianMixture(
    n_components=n_regimes_full,
    covariance_type="full",
    random_state=SEED,
    n_init=10,
    reg_covar=1e-6,
)
gmm_pca.fit(reduced)
pca_probs = gmm_pca.predict_proba(reduced)
pca_labels = gmm_pca.predict(reduced)

print(f"GMM on PCA silhouette: {silhouette_score(reduced, pca_labels):.3f}")

Output

GMM on PCA silhouette: 0.396

In [29]python · cell 69

python

plot_regime_heatmap(
    pca_probs,
    macro_data_full.index,
    f"GMM Regime Probabilities (PCA-reduced, {start_yr}-{end_yr})",
    n_regimes=n_regimes_full,
    is_probability=True,
)

Output

<Figure size 1400x400 with 2 Axes>

Comparison: 4 Indicators vs Extended Dataset

How do results differ between the simple (4-indicator) and extended approaches?

Visual Comparison

Side-by-side heatmaps showing regime probabilities from both approaches.

In [30]python · cell 72

python

# Create side-by-side comparison (if both datasets available)
if len(macro_probs) > 0 and len(gmm_probs_full) > 0:
    fig, axes = plt.subplots(2, 1, figsize=(14, 6))

    # Panel 1: Core 4 indicators
    ax1 = axes[0]
    im1 = ax1.imshow(macro_probs.T, aspect="auto", cmap="Blues", vmin=0, vmax=1)
    years_core = [pd.Timestamp(ts).year for ts in macro_df.index]
    year_ticks_core = [j for j, y in enumerate(years_core) if j == 0 or years_core[j - 1] != y]
    year_labels_core = [str(years_core[j]) for j in year_ticks_core]
    ax1.set_xticks(year_ticks_core[::2])
    ax1.set_xticklabels(year_labels_core[::2], fontsize=8)
    ax1.set_yticks(range(n_macro_regimes))
    ax1.set_yticklabels([f"Regime {i + 1}" for i in range(n_macro_regimes)])
    ax1.set_title(f"Core 4 Indicators (Silhouette: {macro_silhouette:.3f})", fontsize=11)

    # Panel 2: Extended dataset
    ax2 = axes[1]
    im2 = ax2.imshow(gmm_probs_full.T, aspect="auto", cmap="Blues", vmin=0, vmax=1)
    years_ext = macro_data_full.index.year.tolist()
    year_ticks_ext = [j for j, y in enumerate(years_ext) if j == 0 or years_ext[j - 1] != y]
    year_labels_ext = [str(years_ext[j]) for j in year_ticks_ext]
    ax2.set_xticks(year_ticks_ext[::2])
    ax2.set_xticklabels(year_labels_ext[::2], fontsize=8)
    ax2.set_yticks(range(n_regimes_full))
    ax2.set_yticklabels([f"Regime {i + 1}" for i in range(n_regimes_full)])
    ax2.set_xlabel("Year")
    ext_sil = silhouette_score(macro_data_full, gmm_labels_full)
    ax2.set_title(
        f"Extended {macro_data_full.shape[1]} Indicators (Silhouette: {ext_sil:.3f})", fontsize=11
    )

    fig.suptitle(
        "GMM Regime Comparison: Core vs Extended Indicators", fontsize=12, fontweight="bold"
    )
    plt.show()
else:
    print("Comparison visualization skipped - insufficient data")

Output

<Figure size 1400x600 with 2 Axes>

Quantitative Comparison

In [31]python · cell 74

python

core_sil = macro_silhouette if len(macro_df) > 0 else float("nan")
extended_sil = silhouette_score(macro_data_full, gmm_labels_full)
pca_sil = silhouette_score(reduced, pca_labels)

silhouette_compare = pd.DataFrame(
    {
        "Model": [
            "Core (4 indicators)",
            f"Extended ({macro_data_full.shape[1]} indicators)",
            "Extended + PCA",
        ],
        "Silhouette": [core_sil, extended_sil, pca_sil],
    }
).set_index("Model")

if core_sil > extended_sil:
    interpretation = "Core 4 indicators provide cleaner separation; additional series add noise."
else:
    interpretation = (
        "Extended indicators provide better separation; the broader panel captures "
        "meaningful economic variation despite added noise."
    )
print(interpretation)
silhouette_compare.style.format("{:.3f}")

Output

Extended indicators provide better separation; the broader panel captures meaningful economic variation despite added noise.

<pandas.io.formats.style.Styler at 0x7293580a16a0>

	Silhouette
Model
Core (4 indicators)	0.252
Extended (25 indicators)	0.417
Extended + PCA	0.396

Key Takeaways

Macro indicators line up with realised volatility: The four regimes' mean annualised volatility runs from 12.0% (Expansion, 77 months) to 16.0% (Crisis, 4 months), with Tightening at 15.0% and Recovery at 15.2%. The Crisis cell covers only 4 months on this 2003-2026 panel, so the 16.0% figure is an anecdotal upper bound rather than a regime-level statistic.
Extended indicators improve cluster quality: The 25-indicator model achieves higher silhouette (0.42) than the 4-indicator model (0.25), but the core model is more interpretable — the trade-off depends on the use case.
Hierarchical structure is genuine: A cophenetic correlation of 0.71, above the 0.7 quality bar, means the dendrogram faithfully represents the indicator distance structure rather than imposing an arbitrary tree.
Use rates, not levels: We use CPI year-over-year change rather than the CPI level, because clustering on a trending level would capture "early vs late" rather than "inflationary vs non-inflationary."
GMM vs K-Means: Similar performance (silhouette 0.42 vs 0.45), but GMM provides probability assignments that quantify regime uncertainty.

Book reference: §1.4 of Chapter 1 frames these regimes as inputs to risk management — exposure caps, hedging triggers, and de-risking rules — rather than as return forecasts. Figure 1.6 in the chapter is the macro-regime panel rendered above.