\documentclass[12pt]{article}
\makeatletter\def\input@path{{../paper/}}\makeatother
\input{../paper/preamble}
\graphicspath{{figures/}{../paper/figures/}}

\title{Online Appendix for\\ ``Faster, Wider, More Fragile? The Evolution of
Intraday Shock Propagation in U.S.\ Equity Markets, 1992--2026''}
\author{}
\date{}

\begin{document}
\maketitle
\tableofcontents
\clearpage

\section{Extended data audit}
\label{app:audit}

\paragraph{Provenance and snapshot.} The data are one-minute OHLCV bars
originally sourced from Finnhub.io and aggregated into 411 monthly files
(January 1992--March 2026). The exact byte-level snapshot is pinned: every
file's SHA-256 checksum was verified at download against the archive's
metadata and re-verified after the full download; the manifest (per-file
checksum, byte size, row count, column schema, timestamp bounds, symbol
count, duplicate count) accompanies the replication package. The archive
carries no explicit licence; the minute data are used for research with
attribution and are not redistributed.

\paragraph{Calendar and timezone.} Observed trading dates match the official
XNYS calendar exactly over the full sample: zero missing sessions, zero dates
outside the calendar, zero weekend observations. Timestamps are UTC at
bar-start; mapping to Eastern Time was verified empirically on both sides of
every daylight-saving transition (the regular session opens at 13:30 UTC in
summer months and 14:30 UTC in winter months throughout). The regular-hours
share of bars by calendar month is flat (96.75\%--97.09\%), ruling out any
DST mishandling: an offset error would displace roughly 15\% of session rows
in March and November. Early-closing sessions are truncated at the true
exchange close; residual post-close prints (7.3\% of morning volume on
2025-12-24 versus 60.4\% on the adjacent full day) are labelled after-hours.

\paragraph{Integrity.} Across \DataRows{} bars: \DataOHLCViol{} OHLC-impossible
bars (1.3 per $10^8$, concentrated 1993--1995), zero non-positive prices, zero
zero-volume or negative-volume bars, \DataDupKeys{} duplicate ticker-minute
keys (1.3 per million; merged as open=first, high=max, low=min, close=last,
volume=sum). Prices are unadjusted for corporate actions; volumes are in
shares (verified against public daily volumes for benchmark securities).

\paragraph{Identity and survivorship.} The panel spans \DataTickers{} tickers
forming \DataSpells{} continuous spells (a gap exceeding 30 calendar days
starts a new spell); \DataMultiSpellTickers{} tickers have multiple spells, so
all long-horizon statements operate within spells. Delisted securities are
present throughout (exits run 800--1,600 per year); the single discrete
coverage expansion (2020, over-the-counter names) is absorbed by fixed-rule
lagged universes.

\paragraph{Corporate actions.} A conservative overnight-ratio screen
(canonical ratios 2 through 8, 10, 20, and 3/2, with their inverses,
$\pm1.5\%$ tolerance, both-day dollar volume $\ge \$50{,}000$, prior close $\ge \$1$)
detects \NSplitEvents{} events (\NSplitFwd{} splits, \NSplitRev{} reverse
splits); event days $\pm1$ trading day are excluded from every return-based
statistic.

\paragraph{Pilot audit.} Before the full download, three pilot months (June
1992, June 2009, December 2025; 58.8~million bars) were audited. Trading-day
counts match the exchange calendar in all three, including the
December~24, 2025 early close; no OHLC-consistency violation, null value,
negative volume, or zero-volume bar occurs; 14 duplicate ticker--minute pairs
(all in inactive over-the-counter names) appear in December 2025. Liquid
securities are densely covered throughout: the four most active tickers in
December 2025 have complete 390-bar regular sessions, and large issuers
already average 277--369 bars per day in June 1992. Volume units were
verified against public daily volumes for benchmark securities.
Figure~\ref{fig:app_pilot_coverage} summarizes raw data volume and per-day
symbol counts, Figure~\ref{fig:app_pilot} the pilot intraday seasonality,
and Table~\ref{tab:pilot_summary} pilot summary statistics for the 500
highest dollar-volume securities in each pilot month.

\begin{figure}[t]
\centering
\includegraphics[width=\textwidth]{figP1_coverage.pdf}
\caption{\textbf{Dataset coverage.} Panel (a): compressed size of each
monthly source file, 1992--2026 (all 411 files of the pinned snapshot). Panel
(b): number of symbols with at least one bar per trading day in the three
pilot months.}
\label{fig:app_pilot_coverage}
\end{figure}

\section{Additional descriptive evidence}
\label{app:descriptive}

Figures~\ref{fig:app_survivorship}--\ref{fig:app_splits} complement the
descriptive results of the main text: universe entry/exit dynamics, dollar
volume concentration, the cross-section of realized volatility, the
stale-price share, and the time series of detected corporate-action events.
Table~\ref{tab:summary_by_decade} reports decade-level summary statistics for
the top-1000 universe.

\begin{figure}[t]
\centering
\includegraphics[width=\textwidth]{figE2_survivorship.pdf}
\caption{\textbf{Universe dynamics.} (a) Active symbols per year; (b) entries
and exits. The shaded band marks the 2020 source-coverage expansion.}
\label{fig:app_survivorship}
\end{figure}

\begin{figure}[t]
\centering
\includegraphics[width=\textwidth]{figE4_concentration.pdf}
\caption{\textbf{Concentration of trading.} (a) Share of aggregate dollar
volume of the top 1\% and 5\% of symbols; (b) Herfindahl index of dollar
volume.}
\label{fig:app_concentration}
\end{figure}

\begin{figure}[t]
\centering
\includegraphics[width=.6\textwidth]{figE6_rv.pdf}
\caption{\textbf{Cross-section of realized volatility.} Median, interquartile
range, and 95th percentile of daily 5-minute realized volatility, lagged
top-1000 universe.}
\label{fig:app_rv}
\end{figure}

\begin{figure}[t]
\centering
\includegraphics[width=.6\textwidth]{figE7_staleness.pdf}
\caption{\textbf{Stale-price share.} Percentage of one-minute returns exactly
zero, lagged top-1000 universe (\ZeroRetNinetySix\% in 1996,
\ZeroRetTwentyFour\% in 2024).}
\label{fig:app_staleness}
\end{figure}

\begin{figure}[t]
\centering
\includegraphics[width=.6\textwidth]{figE9_splits.pdf}
\caption{\textbf{Detected corporate-action events per year.} Forward splits
(up) and reverse splits (down) from the overnight-ratio screen.}
\label{fig:app_splits}
\end{figure}

\input{tables/table2_summary_by_decade}

\clearpage
\section{Additional propagation results}
\label{app:propagation}

Figure~\ref{fig:app_evolution} shows the year-by-year evolution of abnormal
market-wide breadth at $h=5$ and $h=30$ with 95\% day-block bootstrap bands:
the market-wide difference-in-differences is within two standard errors of
zero in essentially every year, not merely on average. The design diagnostics
(pre-event levels, co-arrival classes, pre-level-stratified estimates,
alternative clustering, signed responses) and the decomposition of the
network differential by decade are reported in the main text.

\begin{figure}[t]
\centering
\includegraphics[width=.62\textwidth]{figF2_evolution.pdf}
\caption{\textbf{Evolution of abnormal market-wide propagation.}
$\Delta\Delta$ breadth by year at $h=5$ and $h=30$ minutes, with 95\%
day-block bootstrap intervals.}
\label{fig:app_evolution}
\end{figure}

\begin{figure}[t]
\centering
\includegraphics[width=\textwidth]{figP2_seasonality.pdf}
\caption{\textbf{Pilot-sample intraday seasonality} (June 1992, June 2009,
December 2025; top-500 by within-month dollar volume).}
\label{fig:app_pilot}
\end{figure}

\input{tables/tabP1_pilot_summary}

\clearpage
\section{Computational details and reproducibility}
\label{app:compute}

The pipeline is deterministic end-to-end. All parameters live in versioned
configuration files; the global seed (20260713) governs placebo draws and
bootstrap resampling; every table and figure is generated by a numbered
script from machine-readable intermediate results, and every numerical claim
in the manuscript resolves to a macro generated from those results---no
number is typed by hand. The full run comprises: download and checksum
verification (411 files); per-month integrity audit and daily metadata
construction; clean-panel construction (duplicate resolution, session
labelling with true exchange closes, integrity and corporate-action flags);
universe construction with strictly lagged screens; descriptive aggregation;
shock detection and outcome measurement (\NEventsReal{} events,
\NEventsPlacebo{} placebos); network and co-jump measurement; and estimation.
Every stage operates month-by-month on partitioned columnar files with four
parallel workers on an Apple-silicon workstation; wall-clock times for each
stage are recorded in the run logs of the replication package. The
revision diagnostics (pre-event levels, co-arrival classes, stratified
estimators, alternative clustering) are recomputed from the stored
event-level files in a few minutes without access to the raw minute panel.

\section{Analyses not executed}
\label{app:notdone}

The following checks are referred to in the main text as not executed, so
that no claim rests on them: source thresholds $|z|\ge4$ and $|z|\ge5$;
receiver threshold $|z|>3$; the top-1000 and top-3000 shock universes;
neighbor sets estimated on 5- or 30-minute residual correlations or with a
transaction-time covariance estimator; the pre-event ($t-5$) network
contrast; permuted-network placebos preserving industry and liquidity
composition; propagation measured inside scheduled-announcement windows; a
Hawkes-type model of the co-jump minute series; and a reconciliation of
bar volumes against consolidated-tape volumes to establish the venue scope
of the source. Each requires re-running the detection stage on the raw
minute panel or external data.

\end{document}