Uso de BSTS e placebos para estudar efeitos de anúncios do Fed em ETFs de títulos

# 06_fed_announcement_bsts.py


```py
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# %% [markdown]
# # Fed Announcement Event Study with BSTS
#
# **Chapter 15: Causal Machine Learning**
# **Docker image**: `ml4t-py312`
# **Section Reference**: See Section 15.5 for BSTS theory and event study methodology
#
# > **`ml4t-py312` image required.** `tfcausalimpact` (the TensorFlow-Probability
# > BSTS package) does not support the Python the main `ml4t` image runs, so this
# > notebook runs in the `py312` image instead:
# >
# > ```bash
# > docker compose --profile py312 run --rm py312 \
# >     /opt/bsts/bin/python 15_causal_estimation/06_fed_announcement_bsts.py
# > ```
#
# ## Purpose
# This notebook implements a **Bayesian Structural Time-Series (BSTS)** event study
# to measure the causal impact of Federal Reserve announcements on bond ETFs. We
# demonstrate counterfactual construction, control selection, and validation through
# placebo tests - the complete event study workflow.
#
# ## Learning Objectives
# After completing this notebook, you will be able to:
# - LO1: Construct data-driven counterfactuals using BSTS models
# - LO2: Select appropriate control series that avoid spillover contamination
# - LO3: Measure cumulative effects and interpret posterior credible intervals
# - LO4: Validate event study results using placebo tests
#
# ## Cross-References
# - **Upstream**: ETF Universe data (Chapter 3), macro data (Chapter 5)
# - **Downstream**: Strategy evaluation (Chapter 16), risk events (Chapter 19)
# - **Related**: [`01_library_overview`](01_library_overview.ipynb) (library selection), [`07_tigramite_time_series`](07_tigramite_time_series.ipynb) (time series)
#
# ## Key Concepts
# 1. **Counterfactual construction**: Build "synthetic twin" of what would have happened
# 2. **Control series selection**: Choose correlated but unaffected time series
# 3. **Causal impact measurement**: Difference between actual and counterfactual
# 4. **Placebo validation**: Verify model doesn't find false positives
#
# **Prerequisites**: [`01_library_overview`](01_library_overview.ipynb) for library context;
# ETF OHLCV data from Ch2 data pipeline

# %% [markdown]
# ## Setup

# %%
"""Measure the causal impact of FOMC announcements on bond ETFs with BSTS."""

import importlib
import os

os.environ.setdefault("CUDA_VISIBLE_DEVICES", "-1")
os.environ.setdefault("ABSL_MIN_LOG_LEVEL", "3")
os.environ.setdefault("GLOG_minloglevel", "3")
os.environ.setdefault("TF_CPP_MIN_LOG_LEVEL", "3")
os.environ.setdefault("TF_ENABLE_ONEDNN_OPTS", "0")

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from IPython.display import display
from matplotlib.patches import Patch

from data.etfs.loader import load_etfs
from utils.reproducibility import set_global_seeds
from utils.style import COLORS, FIGSIZE, show_with_alt

_saved_stderr_fd = os.dup(2)
_null_fd = os.open(os.devnull, os.O_WRONLY)
os.dup2(_null_fd, 2)
try:
    tf = importlib.import_module("tensorflow")
    CausalImpact = importlib.import_module("causalimpact").CausalImpact
finally:
    os.dup2(_saved_stderr_fd, 2)
    os.close(_null_fd)
    os.close(_saved_stderr_fd)

tf.config.set_visible_devices([], "GPU")
tf.get_logger().setLevel("ERROR")


# %%
# Production defaults - Papermill injects overrides for CI

# %% [markdown]
# ## Configuration
#
# ### Window Length Justification (Brodersen et al., 2015)
#
# **Pre-period (60 trading days, ~3 months)**:
# - Sufficient to learn stable control relationships
# - Short enough to avoid regime changes (Fed policy cycles ~6 months)
# - This notebook reports the 60-day baseline only; a sensitivity sweep
#   over pre_days ∈ {45, 60, 90} and post_days ∈ {10, 20, 30} is left
#   to the reader as the BSTS MCMC fit is the bottleneck.
#
# **Post-period (20 trading days, ~1 month)**:
# - Allows 2-3 weeks for bond-market repricing
# - Captures full policy transmission to yields
# - Balances impact capture vs contamination from subsequent events
#
# ## Causal Design Contract
#
# | Element                   | This notebook                                                                                       |
# |---------------------------|-----------------------------------------------------------------------------------------------------|
# | Unit                      | Trading day in the IEF + control-ETF panel                                                          |
# | Treatment                 | FOMC announcement on the event date (discrete event)                                                |
# | Outcome                   | Cumulative abnormal log return on IEF over the 20-trading-day post-window                           |
# | Controls                  | Daily log returns of VEA, EFA, DBC entered into the BSTS counterfactual model                        |
# | Effect modifiers          | None - separate event studies per FOMC date                                                          |
# | Identification assumption | Controls move with IEF in the pre-period and are *not affected by the FOMC event* in the post-window |
# | Main failure modes        | Control spillover (Fed shocks the dollar and global risk; international ETFs are not unaffected); placebo-date contamination by other macro releases; daily bars mix pre- and post-announcement trading |
# | Estimand                  | Cumulative abnormal log return attributable to the FOMC event; reported with the BSTS posterior credible interval |
#
# The panel is whatever `TARGET_ETF` and `CONTROL_ETFS` name in the parameters
# cell. This table describes the production defaults - IEF against VEA, EFA and
# DBC - which is what the committed run studies; change those parameters and the
# unit, outcome and controls change with them.
#
# FOMC decisions are announced before the market close. The event-day close-to-close
# return therefore contains both the pre-announcement portion of that trading day and
# the post-announcement response. This timing is part of the estimand, not a claim that
# the full event-day return was known when the announcement occurred.
#
# ### Control Selection Rationale
#
# Fed decisions can affect broad US financial markets. Using SPY or VNQ as
# controls is problematic because they may react to the same announcement.
# The argument rests on two categories, international and commodity, rather than
# on the particular tickers, so `CONTROL_ETFS` should cover both. The default set
# and the panel the CI run substitutes are both two international controls and one
# commodity control. The defaults are:
# - **International ETFs** (VEA, EFA): Correlated through global risk factors
#   but less directly affected by FOMC (which targets US policy rates)
# - **Commodities** (DBC): Affected by USD but different transmission mechanism
#
# **Caveat - control affectedness is real**: This is the *plausible* control
# set, not an unaffected one. FOMC announcements move the dollar, global
# risk appetite, global yields, and commodities through cross-border
# capital flows and the dollar funding channel. The placebo test and the
# per-event spillover test below bound the residual contamination; a
# more conservative design would use non-US sovereign-bond ETFs or a
# local-level model with no ETF controls and a longer pre-window.

# %% tags=["parameters"]
# Production defaults - Papermill injects overrides for CI
SEED = 42
PRE_PERIOD_DAYS = 60
POST_PERIOD_DAYS = 20
START_DATE = "2020-01-01"
END_DATE = "2024-06-01"
TARGET_ETF = "IEF"
# Control ETFs: international + commodity (see rationale in markdown above)
CONTROL_ETFS = ["VEA", "EFA", "DBC"]
# Zero means all configured dates; CI injects smaller positive limits.
MAX_FOMC_EVENTS = 0
MAX_PLACEBO_DATES = 0

# %%
set_global_seeds(SEED)
tf.random.set_seed(SEED)

# Selected FOMC announcement dates
FOMC_EVENTS = [
    ("2023-03-22", "25bp hike amid banking stress"),
    ("2023-07-26", "25bp hike"),
    ("2023-11-01", "Hold decision"),
    ("2024-03-20", "Hold, revised projections"),
]

# Selected trading days with no FOMC announcement
PLACEBO_DATES = [
    "2023-02-15",
    "2023-04-12",
    "2023-05-10",
    "2023-06-07",
    "2023-08-16",
    "2023-09-13",
    "2023-10-11",
    "2023-12-06",
    "2024-01-17",
    "2024-02-14",
    "2024-04-10",
    "2024-05-08",
]

if MAX_FOMC_EVENTS > 0:
    FOMC_EVENTS = FOMC_EVENTS[:MAX_FOMC_EVENTS]
if MAX_PLACEBO_DATES > 0:
    PLACEBO_DATES = PLACEBO_DATES[:MAX_PLACEBO_DATES]

# %% [markdown]
# ## 1. Load ETF Price Data
#
# We need daily prices for the target ETF and its controls - IEF against VEA,
# EFA and DBC by default. Data loaded from curated ETF universe (book data
# pipeline).

# %%

tickers = [TARGET_ETF] + CONTROL_ETFS

print(f"Loading {tickers} from curated ETF universe...")
print(f"Date range: {START_DATE} to {END_DATE}")

# Load and filter data
df = load_etfs(symbols=tickers, start_date=START_DATE, end_date=END_DATE).select(
    ["symbol", "timestamp", "close"]
)

# Pivot to wide format at the pandas boundary required by CausalImpact.
raw_prices = (
    df.pivot(on="symbol", index="timestamp", values="close")
    .sort("timestamp")
    .to_pandas()
    .set_index("timestamp")
)

# %% [markdown]
# The target and controls are daily log returns, so summing the post-period point effects
# estimates a cumulative abnormal log return. A specification on log price *levels* would
# sum level gaps in log-point-days instead, which is not the estimand declared above.

# %%
data = np.log(raw_prices).diff().dropna()

# %%
# Ensure all required columns exist
missing = [t for t in tickers if t not in data.columns]
if missing:
    raise ValueError(f"Curated ETF data is missing required symbols: {missing}")
DATA_AVAILABLE = True
print(f"Loaded data shape: {data.shape}")
print(f"Date range: {data.index.min()} to {data.index.max()}")
print(data.tail())

# %% [markdown]
# ## 2. BSTS Event Study Functions
#
# The event study workflow has three stages:
# 1. **Window computation**: Define pre/post periods from event date
# 2. **BSTS estimation**: Run the `tfcausalimpact` Bayesian structural time series
# 3. **Dispatcher**: Assemble per-event results into a comparable summary
#
# `tfcausalimpact` (Willian Fuks, 2025) is the actively maintained TFP port of the
# original Google R package. It implements BSTS and exposes the posterior columns
# used below.

# %% [markdown]
# ### The Analysis Window
#
# Compute pre/post periods and filter data for the analysis window.


# %%
def _compute_analysis_window(data, target, controls, event_date, pre_days, post_days):
    """Compute exact pre/post windows by trading-day index position."""
    event_dt = pd.to_datetime(event_date).normalize()
    cols = [target] + controls
    available = data[cols].dropna()
    # Normalize the index to tz-naive calendar dates so a tz-aware or
    # non-midnight bar still matches a naive calendar event date. All
    # downstream slicing and comparisons then share one calendar-date scale.
    cal_index = available.index
    if cal_index.tz is not None:
        cal_index = cal_index.tz_localize(None)
    available = available.set_axis(cal_index.normalize(), axis=0)
    idx = available.index

    event_pos = idx.searchsorted(event_dt)
    if event_pos >= len(idx):
        return None, None, None, f"Event date {event_date} is after the data range"
    if idx[event_pos] != event_dt:
        return None, None, None, f"Event date {event_date} is not a trading day in the data"

    pre_start_pos = max(0, event_pos - pre_days)
    post_end_pos = min(len(idx), event_pos + post_days)

    analysis_data = available.iloc[pre_start_pos:post_end_pos]
    pre_period_data = analysis_data[analysis_data.index < event_dt]
    post_period_data = analysis_data[analysis_data.index >= event_dt]

    if len(pre_period_data) < 20 or len(post_period_data) < 3:
        return None, None, None, f"Insufficient pre/post data for {event_date}"

    pre_period = [str(pre_period_data.index.min().date()), str(pre_period_data.index.max().date())]
    post_period = [
        str(post_period_data.index.min().date()),
        str(post_period_data.index.max().date()),
    ]

    return analysis_data, pre_period, post_period, None


# %% [markdown]
# ### Running BSTS with `tfcausalimpact`
#
# Bayesian BSTS engine faithful to the original Google R package. Provides
# posterior credible intervals - a probability statement about the parameter -
# rather than frequentist confidence intervals.


# %% [markdown]
# #### Extracting the Posterior Effect
#
# Normalize column naming differences across `tfcausalimpact` versions.

# %%
TFP_EFFECT_COLUMNS = {
    "point": ["point_effects_means", "point_effects", "point_effect"],
    "cum_mean": [
        "post_cum_effects_means",
        "post_cum_effects",
        "point_effect_cumulative",
    ],
    "cum_lower": ["post_cum_effects_lower", "point_effect_cumulative_lower"],
    "cum_upper": ["post_cum_effects_upper", "point_effect_cumulative_upper"],
}


# %%
def _extract_tfp_effect_stats(impact_data, post_start):
    """Extract effect estimates and credible-interval-based significance.

    Significance is determined by whether the 95% credible interval on the
    cumulative post-period effect excludes zero. The sample fraction of
    positive point-estimate rows is not a Bayesian posterior and cannot drive
    a valid significance test.
    """
    post_impact = impact_data.loc[pd.to_datetime(post_start) :]

    def _resolve(key, reducer):
        for name in TFP_EFFECT_COLUMNS[key]:
            if name in post_impact.columns:
                series = post_impact[name].dropna()
                if not series.empty:
                    return reducer(series)
        return None

    impact_mean = _resolve("point", lambda s: float(s.mean()))
    cumulative = _resolve("cum_mean", lambda s: float(s.iloc[-1]))
    cum_lower = _resolve("cum_lower", lambda s: float(s.iloc[-1]))
    cum_upper = _resolve("cum_upper", lambda s: float(s.iloc[-1]))

    required = [impact_mean, cumulative, cum_lower, cum_upper]
    if any(value is None for value in required):
        raise KeyError(f"Unsupported tfcausalimpact inference columns: {list(impact_data.columns)}")

    significant = (
        cum_lower is not None and cum_upper is not None and (cum_lower > 0 or cum_upper < 0)
    )

    return {
        "impact_mean": impact_mean,
        "cumulative_impact": cumulative,
        "cumulative_lower": cum_lower,
        "cumulative_upper": cum_upper,
        "significant": significant,
    }


# %% [markdown]
# #### The BSTS Runner
#
# Execute BSTS inference and normalize outputs for downstream validation.


# %%
def _run_bsts(
    analysis_data,
    pre_period,
    post_period,
    event_date,
    pre_period_data,
    post_period_data,
):
    """Run a single BSTS event study via tfcausalimpact."""
    ci_data = analysis_data.copy()
    ci_data.index = pd.to_datetime(ci_data.index)
    ci = CausalImpact(ci_data, pre_period, post_period)

    summary = ci.summary()
    report = ci.summary(output="report")

    impact_data = ci.inferences
    if impact_data is None:
        raise RuntimeError("tfcausalimpact returned no inference data")

    effect_stats = _extract_tfp_effect_stats(impact_data, post_period[0])

    return {
        "library": "tfcausalimpact",
        "event_date": event_date,
        "pre_period": pre_period,
        "post_period": post_period,
        "pre_days": len(pre_period_data),
        "post_days": len(post_period_data),
        "impact_mean": effect_stats["impact_mean"],
        "cumulative_impact": effect_stats["cumulative_impact"],
        "cumulative_lower": effect_stats["cumulative_lower"],
        "cumulative_upper": effect_stats["cumulative_upper"],
        "significant": effect_stats["significant"],
        "summary": summary,
        "report": report,
        "ci_object": ci,
    }


# %% [markdown]
# ### The Event Study Dispatcher


# %%
def run_event_study(data, target, controls, event_date, pre_days=60, post_days=20):
    """Run a BSTS event study on `target` with `controls`."""
    analysis_data, pre_period, post_period, error = _compute_analysis_window(
        data,
        target,
        controls,
        event_date,
        pre_days,
        post_days,
    )
    if error:
        raise ValueError(error)

    event_dt = pd.to_datetime(event_date)
    pre_data = analysis_data[analysis_data.index < event_dt]
    post_data = analysis_data[analysis_data.index >= event_dt]

    return _run_bsts(
        analysis_data,
        pre_period,
        post_period,
        event_date,
        pre_data,
        post_data,
    )


# %% [markdown]
# ## 3. Spillover Validation
#
# The counterfactual is built from the controls, so a control that responds to the
# announcement carries part of the effect into the thing the effect is measured against.
# This section runs the same BSTS specification with each control as the target and the
# remaining controls as its predictors, and flags a control whose own post-period interval
# excludes zero.
#
# **What the test can and cannot see.** A control is judged against the other controls, so
# the flag fires on a control that moves *differently* from them. A Fed announcement that
# moves all three through the same dollar and global-risk channel moves each one's
# predictors with it, and none of the three is flagged - which is the contamination that
# matters most for the target's counterfactual. Read a clean result as "no differential
# response among the controls", not as "the controls were unaffected". The design that
# would answer the stronger question needs a control set with no plausible exposure to US
# policy rates at all, and the caveat under Control Selection Rationale says what that
# would cost.


# %%
def validate_control_spillover(data, controls, event_date, pre_days=60, post_days=20):
    """
    Check whether control series respond to the intervention (spillover).

    A control is flagged as contaminated when its own BSTS post-period
    cumulative effect has a 95% credible interval that excludes zero.
    """
    spillover_results = {}

    for control in controls:
        other_controls = [c for c in controls if c != control]

        if len(other_controls) < 1:
            raise ValueError("Spillover validation requires at least two controls")

        result = run_event_study(data, control, other_controls, event_date, pre_days, post_days)
        impact = result["impact_mean"]
        significant = result["significant"]
        spillover_results[control] = {
            "impact": impact,
            "significant": significant,
            "has_spillover": significant,
        }

    return spillover_results


# %%
if DATA_AVAILABLE:
    print("\n" + "=" * 60)
    print("SPILLOVER VALIDATION (PER EVENT)")
    print("=" * 60)
    print("Checking whether control series respond to each FOMC event.")
    print(
        "Rule: a control is flagged when its post-period cumulative-effect "
        "95% credible interval excludes zero."
    )
    print(
        "We report control validity per event because a spillover verdict does "
        "not transfer across announcement dates."
    )

    spillover_per_event = {}
    event_control_status = []

# %%
if DATA_AVAILABLE:
    for event_date, description in FOMC_EVENTS:
        spillover = validate_control_spillover(
            data, CONTROL_ETFS, event_date, PRE_PERIOD_DAYS, POST_PERIOD_DAYS
        )
        spillover_per_event[event_date] = spillover

        contaminated_for_event = []
        for control, result in spillover.items():
            has_spillover = result["has_spillover"]
            if has_spillover:
                contaminated_for_event.append(control)
            event_control_status.append(
                {
                    "event_date": event_date,
                    "control": control,
                    "mean_daily_effect": result["impact"],
                    "significant_ci": result["significant"],
                    "status": "SPILLOVER" if has_spillover else "OK",
                }
            )
        if contaminated_for_event:
            print(f"  {event_date}: spillover on {contaminated_for_event} ({description})")
        else:
            print(f"  {event_date}: no spillover ({description})")

# %%
if DATA_AVAILABLE:
    spillover_df = pd.DataFrame(event_control_status)
    display(spillover_df)

    # Aggregate: a control is treated as "warned" if it shows spillover on
    # any FOMC event. Downstream code references `spillover_warnings`.
    spillover_warnings = sorted(
        {row["control"] for row in event_control_status if row["status"] == "SPILLOVER"}
    )

    if spillover_warnings:
        print(f"\nControls flagged on at least one event: {spillover_warnings}")
        print(
            "Event estimates can be re-estimated without the affected controls "
            "for those events, or the events marked as not credible."
        )
    else:
        print("\nNo interval-based spillover flag on any event.")
else:
    spillover_warnings = []
    spillover_df = pd.DataFrame()
    spillover_per_event = {}
    event_control_status = []

# %% [markdown]
# ## 4. Analyze Key FOMC Events
#
# We analyze the response to selected Fed announcements in bond ETFs.

# %%
if DATA_AVAILABLE:
    event_results = []

    print("\n" + "=" * 60)
    print("FOMC EVENT ANALYSIS")
    print("=" * 60)

    for event_date, description in FOMC_EVENTS:
        result = run_event_study(
            data,
            TARGET_ETF,
            CONTROL_ETFS,
            event_date,
            pre_days=PRE_PERIOD_DAYS,
            post_days=POST_PERIOD_DAYS,
        )

        result["description"] = description
        event_results.append(result)

# %%
if DATA_AVAILABLE:
    event_rows = [
        {
            "event_date": r["event_date"],
            "description": r["description"],
            "mean_daily_effect": r["impact_mean"],
            "cum_impact": r["cumulative_impact"],
            "cum_lower": r["cumulative_lower"],
            "cum_upper": r["cumulative_upper"],
            "significant": r["significant"],
        }
        for r in event_results
    ]
    event_df = pd.DataFrame(event_rows)
    display(event_df)
else:
    print("Skipping event analysis - required ETF data not available")
    event_results = []
    event_df = pd.DataFrame()

# %% [markdown]
# The chart reports the estimand in log-return units. Intervals that cross zero
# do not distinguish the event response from posterior uncertainty; intervals
# that exclude zero remain conditional on the no-spillover assumption.

# %%
if not event_df.empty:
    _event_values = event_df["cum_impact"].to_numpy()
    _event_errors = np.vstack(
        [
            _event_values - event_df["cum_lower"].to_numpy(),
            event_df["cum_upper"].to_numpy() - _event_values,
        ]
    )
    _event_colors = [
        COLORS["amber"] if flag else COLORS["blue"] for flag in event_df["significant"]
    ]
    fig, ax = plt.subplots(figsize=FIGSIZE["single_tall"], constrained_layout=True)
    _event_bars = ax.bar(event_df["event_date"], _event_values, color=_event_colors, width=0.65)
    for bar, flag in zip(_event_bars, event_df["significant"], strict=True):
        bar.set_hatch("//" if flag else "")
    ax.errorbar(
        event_df["event_date"],
        _event_values,
        yerr=_event_errors,
        fmt="none",
        color=COLORS["neutral"],
        capsize=4,
    )
    ax.axhline(0, color=COLORS["neutral"], linewidth=0.8)
    ax.set_ylabel("Cumulative abnormal log return")
    ax.set_xlabel("FOMC announcement date")
    ax.set_title(
        "Cumulative abnormal log return around each FOMC announcement",
        loc="left",
        color=COLORS["blue"],
        fontweight="bold",
    )
    ax.legend(
        handles=[
            Patch(facecolor=COLORS["amber"], hatch="//", label="Interval excludes zero"),
            Patch(facecolor=COLORS["blue"], label="Interval includes zero"),
        ],
        frameon=False,
    )
    show_with_alt(
        fig,
        "Bar chart with one bar per FOMC announcement date, showing the cumulative abnormal "
        "log return the BSTS counterfactual assigns to that event, each with a vertical "
        "credible-interval bar. Bars whose interval excludes zero are drawn in amber with "
        "diagonal hatching, the rest in blue, and a legend states which is which.",
    )

# %% [markdown]
# **Interpretation**: The FOMC event results above show whether the target ETF
# (IEF by default) moved significantly after rate decisions, after constructing a
# counterfactual from its controls. The causal impact estimates capture the *additional*
# movement attributable to the announcement beyond what correlated assets predicted.
# The uncertainty intervals, rather than a macro narrative about each date, determine
# whether the model distinguishes an event response from market-wide risk.
# Credible intervals that include zero indicate the model cannot distinguish the
# event effect from noise.

# %% [markdown]
# ## 5. Placebo Test Validation
#
# Run the same analysis on 12 dates with no Fed announcement. A
# "significant" cumulative impact on any of these dates means the model
# is misspecified. With so few placebo dates the empirical rate is a
# coarse diagnostic rather than a precise Type I estimate: a single
# flagged window moves it by a large step, and its denominator is not the
# twelve dates listed but however many of them survive the FOMC screen
# applied below, which is the count printed beside the rate. We therefore
# report it as a *placebo false-positive rate*, not a multiple-testing FDR.
#
# **Caveat - macro contamination of placebo dates**: "No FOMC announcement"
# is necessary but not sufficient. A clean placebo date for a Fed/bond
# event study should also avoid CPI prints, payrolls, Treasury refunding
# announcements, FOMC minutes, banking stress headlines, and other
# macro releases that move the rates curve. The 12 dates below are not
# screened for these - they are illustrative, and a publication-grade
# placebo test would filter against a macro-calendar exclusion list
# before computing the rate.

# %%
if DATA_AVAILABLE:
    placebo_results = []

    print("\n" + "=" * 60)
    print("PLACEBO TESTS")
    print("=" * 60)
    print(f"Testing {len(PLACEBO_DATES)} placebo dates with no Fed announcement.")

    for placebo_date in PLACEBO_DATES:
        result = run_event_study(
            data,
            TARGET_ETF,
            CONTROL_ETFS,
            placebo_date,
            pre_days=PRE_PERIOD_DAYS,
            post_days=POST_PERIOD_DAYS,
        )

        placebo_results.append(result)

# %% [markdown]
# A placebo date is only a placebo if its post-window is clear of the announcements this
# notebook is studying. The windows are twenty trading days long and the FOMC meets every
# six to eight weeks, so a date chosen for being on no announcement can still sit a fortnight
# ahead of one, and its "false positive" would then be a true effect measured from the wrong
# origin. The screen below is against `FOMC_EVENTS`, the four dates this notebook treats as
# events; the wider macro calendar in the caveat above is not screened, so a window this
# check calls clear is clear of those four dates and nothing more.


# %%
def post_window_events(date, index, post_days, event_dates):
    """FOMC dates falling inside the post-window a study of `date` would use."""
    idx = pd.DatetimeIndex(index)
    if idx.tz is not None:
        idx = idx.tz_localize(None)
    idx = idx.normalize()
    pos = idx.searchsorted(pd.to_datetime(date))
    window = idx[pos : pos + post_days]
    return [d for d in event_dates if pd.to_datetime(d) in window]


# %%
if DATA_AVAILABLE and placebo_results:
    _fomc_dates = [d for d, _ in FOMC_EVENTS]
    placebo_df = pd.DataFrame(
        [
            {
                "placebo_date": r["event_date"],
                "mean_daily_effect": r["impact_mean"],
                "cum_impact": r["cumulative_impact"],
                "cum_lower": r["cumulative_lower"],
                "cum_upper": r["cumulative_upper"],
                "significant": r["significant"],
                "window_events": ", ".join(
                    post_window_events(r["event_date"], data.index, POST_PERIOD_DAYS, _fomc_dates)
                ),
            }
            for r in placebo_results
        ]
    )
    placebo_df["clean_window"] = placebo_df["window_events"] == ""

    clean = placebo_df[placebo_df["clean_window"]]
    n_false_positives = int(clean["significant"].sum())
    n_total = len(clean)
    placebo_false_positive_rate = n_false_positives / n_total if n_total else None
    n_contaminated = len(placebo_df) - n_total

    if n_contaminated:
        print(
            f"{n_contaminated} of {len(placebo_df)} placebo windows contain an FOMC date "
            f"from this notebook's own event list; the rate below excludes them."
        )
    if n_total:
        print(
            f"Placebo false-positive rate: "
            f"{n_false_positives}/{n_total} = {placebo_false_positive_rate:.1%}"
        )
    else:
        print("No placebo window is clear of this notebook's FOMC dates; no rate to report.")
elif DATA_AVAILABLE:
    placebo_false_positive_rate = None
    placebo_df = pd.DataFrame()
else:
    placebo_results = []
    placebo_false_positive_rate = None
    placebo_df = pd.DataFrame()

# %% [markdown]
# A valid design should rarely produce credible intervals excluding zero on
# dates without an FOMC announcement. This chart makes both the false-positive
# count and the uncertainty behind each placebo estimate visible.

# %%
if not placebo_df.empty:
    _placebo_values = placebo_df["cum_impact"].to_numpy()
    _placebo_errors = np.vstack(
        [
            _placebo_values - placebo_df["cum_lower"].to_numpy(),
            placebo_df["cum_upper"].to_numpy() - _placebo_values,
        ]
    )
    _placebo_colors = [
        COLORS["negative"] if flag else COLORS["blue"] for flag in placebo_df["significant"]
    ]
    fig, ax = plt.subplots(figsize=FIGSIZE["single_tall"], constrained_layout=True)
    _placebo_bars = ax.bar(
        placebo_df["placebo_date"], _placebo_values, color=_placebo_colors, width=0.7
    )
    for bar, flag, clean in zip(
        _placebo_bars, placebo_df["significant"], placebo_df["clean_window"], strict=True
    ):
        bar.set_hatch("//" if flag else "")
        if not clean:
            # A window holding an FOMC date is not a placebo; it stays on the chart so the
            # screen is visible, outlined rather than filled like the dates that count.
            bar.set_alpha(0.35)
            bar.set_edgecolor(COLORS["neutral"])
            bar.set_linewidth(1.5)
    ax.errorbar(
        placebo_df["placebo_date"],
        _placebo_values,
        yerr=_placebo_errors,
        fmt="none",
        color=COLORS["neutral"],
        capsize=3,
    )
    ax.axhline(0, color=COLORS["neutral"], linewidth=0.8)
    ax.tick_params(axis="x", rotation=45)
    ax.set_ylabel("Cumulative abnormal log return")
    ax.set_xlabel("Placebo date")
    ax.set_title(
        "Cumulative abnormal log return around each placebo date",
        loc="left",
        color=COLORS["blue"],
        fontweight="bold",
    )
    show_with_alt(
        fig,
        "Bar chart with one bar per placebo date, showing the cumulative abnormal log return "
        "the same BSTS specification assigns to a date with no FOMC announcement, each with a "
        "vertical credible-interval bar. Bars whose interval excludes zero are drawn in red "
        "with diagonal hatching, the rest in blue, and bars for windows that contain one of "
        "the notebook's FOMC dates are faded and outlined because they are excluded from the "
        "false-positive rate.",
    )

# %% [markdown]
# ## 6. Results Summary

# %%
n_events_significant = sum(1 for r in event_results if r.get("significant", False))
# The rate is over the screened windows, so the count reported beside it has to be too.
n_placebo_screened = int(placebo_df["clean_window"].sum()) if not placebo_df.empty else 0
n_placebo_significant = (
    int(placebo_df.loc[placebo_df["clean_window"], "significant"].sum())
    if not placebo_df.empty
    else 0
)

results_summary = {
    "library_used": "tfcausalimpact",
    "target_etf": TARGET_ETF,
    "control_etfs": CONTROL_ETFS,
    "pre_period_days": PRE_PERIOD_DAYS,
    "post_period_days": POST_PERIOD_DAYS,
    "events_analyzed": len(event_results),
    "events_significant": n_events_significant,
    "placebo_tests_run": len(placebo_results),
    "placebo_windows_clear_of_fomc": n_placebo_screened,
    "placebo_false_positives": n_placebo_significant,
    "placebo_false_positive_rate": placebo_false_positive_rate,
    "spillover_warnings": spillover_warnings if "spillover_warnings" in dir() else [],
}

pfpr_str = (
    f"{placebo_false_positive_rate:.1%}" if placebo_false_positive_rate is not None else "N/A"
)

# %%
print("\n" + "=" * 60)
print("SUMMARY: FED ANNOUNCEMENT BSTS EVENT STUDY")
print("=" * 60)

print(f"""
CONFIGURATION:
  Pre-period: {PRE_PERIOD_DAYS} trading days (~3 months)
  Post-period: {POST_PERIOD_DAYS} trading days (~1 month)
  Target: {TARGET_ETF}
  Controls: {", ".join(CONTROL_ETFS)}

VALIDATION:
  Spillover check: {"FLAG: " + str(spillover_warnings) if spillover_warnings else "No interval-based flag"}
  Placebo tests: {len(placebo_results)} run, {n_placebo_screened} clear of the FOMC dates
  Placebo false-positive rate: {pfpr_str}

EVENT RESULTS:
  Events analyzed: {len(event_results)}
  Significant impacts: {n_events_significant}

INTERPRETATION GUIDANCE:
  - Interpret event results only when placebo false positives are rare
    and no interval-based control spillover is detected
  - Passing these diagnostics does not prove that controls are unaffected
  - Credible intervals capture posterior uncertainty
  - Consider sensitivity to window length choices
""")

# %% [markdown]
# ## Key Takeaways
#
# 1. **BSTS constructs a counterfactual** from pre-event target-control
#    relationships and reports the post-event gap with posterior uncertainty.
# 2. **The cumulative estimand has return units** because the model uses daily log
#    returns; summing post-period point effects yields cumulative abnormal log return.
# 3. **Placebo and control-as-target tests are diagnostics, not proofs**. Passing
#    their interval rules does not establish that global controls are unaffected.
# 4. **Daily timing remains a limitation**. A close-to-close event-day return mixes
#    trading before and after the afternoon announcement.
# 5. **A placebo date is only a placebo if its window is one.** The dates here are screened
#    against the four announcements this notebook studies, and against nothing else; CPI
#    prints, payrolls and refunding announcements still sit inside some of these windows,
#    and window length remains untested at a single pre and post setting.
#
# Continue with `07_tigramite_time_series` for time-series causal discovery. See
# Section 15.5 for BSTS identification assumptions and event-study interpretation.

```