Introduction

Traditional event studies measure abnormal returns at a daily frequency, but many corporate events — earnings announcements, regulatory decisions, central-bank communications — have effects that materialize within minutes or hours. Intraday event studies capture these short-lived dynamics by operating on high-frequency (tick or bar) data.

The EventStudy package supports two intraday workflows:

1. Task-based preparation via IntradayEventStudyTask and prepare_intraday_event_study(), which compute intraday returns and assign estimation/event windows.
2. Non-parametric significance testing via nonparametric_intraday_test(), which implements the methodology of Rinaudo & Saha (2014) in pure R.

This vignette walks through both.

Data Structure

The non-parametric test requires three inputs:

The time column should be a character representation of the intraday time (e.g., "10:15", "14:30"), consistent across all days. The abnormalReturn column contains the pre-computed abnormal return for each bar.

library(tibble)

# Estimation window: 20 days x 50 bars per day
estimation_window <- tibble(
  day  = rep(1:20, each = 50),
  time = rep(sprintf("%02d:%02d", 10L + 1:50 %/% 60L, 1:50 %% 60L), 20),
  abnormalReturn = rnorm(1000, 0, 0.001)
)

# Event window: single day, same 50 bars
event_window <- tibble(
  time = sprintf("%02d:%02d", 10L + 1:50 %/% 60L, 1:50 %% 60L),
  abnormalReturn = rnorm(50, 0, 0.001)
)

# Event times to test
event_times <- c("10:10", "10:30")

The IntradayEventStudyTask

For studies where you want to use the full pipeline (return computation, window assignment), start with IntradayEventStudyTask:

library(EventStudy)

# Firm intraday data
firm_data <- tibble(
  symbol    = "FIRM_A",
  timestamp = seq(as.POSIXct("2020-06-15 09:30:00", tz = "UTC"),
                  by = "1 min", length.out = 500),
  price     = 100 * cumprod(1 + rnorm(500, 0, 0.001))
)

# Index intraday data
index_data <- tibble(
  symbol    = "INDEX_1",
  timestamp = seq(as.POSIXct("2020-06-15 09:30:00", tz = "UTC"),
                  by = "1 min", length.out = 500),
  price     = 1000 * cumprod(1 + rnorm(500, 0, 0.0008))
)

# Request table
request <- tibble(
  event_id                 = 1L,
  firm_symbol              = "FIRM_A",
  index_symbol             = "INDEX_1",
  event_timestamp          = as.POSIXct("2020-06-15 14:30:00", tz = "UTC"),
  group                    = "Earnings",
  event_window_start       = -30L,
  event_window_end         = 30L,
  shift_estimation_window  = -31L,
  estimation_window_length = 120L
)

# Create task and prepare
task <- IntradayEventStudyTask$new(firm_data, index_data, request)
ps   <- ParameterSet$new()
task <- prepare_intraday_event_study(task, ps)

The prepared task contains returns (firm_returns, index_returns) and window flags (event_window, estimation_window) in the nested data column.

Non-Parametric Test

The nonparametric_intraday_test() function implements the algorithm of Rinaudo & Saha (2014). The key idea:

1. For each event time, accumulate cumulative abnormal returns (CARs) observation-by-observation on the event day.
2. In parallel, accumulate CARs for the same time range on each estimation day.
3. After an initial window (default 5 bars), compare the event-day CAR to the empirical percentile of the estimation-day CARs.
4. If the event-day CAR falls outside the confidence band, the event is significant at that point. The algorithm continues extending the window as long as significance holds.
5. When significance is lost, the window stops growing.

This approach is non-parametric: no distributional assumptions are needed. The confidence band comes directly from the empirical distribution of estimation-day CARs.

results <- nonparametric_intraday_test(
  estimation_window = estimation_window,
  event_window      = event_window,
  event_times       = event_times,
  p                 = 0.05,
  init_window       = 5L,
  upper             = FALSE
)

Parameters:

• p: Significance level (default 0.05). Smaller values require more extreme event-day CARs.
• init_window: Number of bars to accumulate before the first significance check (default 5).
• upper: If TRUE, test the upper tail (positive abnormal returns); if FALSE (default), test the lower tail (negative abnormal returns).

Interpreting Results

The function returns a named list of tibbles, one per event time:

results[["10:10"]]
#> # A tibble: 12 x 4
#>       id      CAR       CI    fitCI
#>    <int>    <dbl>    <dbl>    <dbl>
#>  1     1 -0.00823 -0.00654 -0.00671
#>  2     2 -0.00912 -0.00701 -0.00698
#>  ...

When an event time is not significant, the result is a single-row tibble with all values equal to zero:

results[["10:30"]]
#> # A tibble: 1 x 4
#>      id   CAR    CI fitCI
#>   <int> <dbl> <dbl> <dbl>
#> 1     1     0     0     0

The fitCI column applies a degree-4 polynomial smoothing to the raw CI values. This removes noise from the empirical percentile boundary and produces cleaner confidence bands for visualization.

Plotting Results

The CAR path with confidence bands can be visualized with ggplot2:

library(ggplot2)

plot_np_result <- function(result_tbl, event_time) {
  if (nrow(result_tbl) <= 1 && result_tbl$CAR[1] == 0) {
    message("Event at ", event_time, " is not significant.")
    return(invisible(NULL))
  }

  ggplot(result_tbl, aes(x = id)) +
    geom_line(aes(y = CAR), colour = "steelblue", linewidth = 1) +
    geom_line(aes(y = fitCI), colour = "firebrick", linetype = "dashed",
              linewidth = 0.8) +
    geom_ribbon(aes(ymin = fitCI, ymax = 0), alpha = 0.1, fill = "firebrick") +
    labs(
      title = paste("Non-Parametric Intraday CAR — Event at", event_time),
      x     = "Bars after event",
      y     = "Cumulative Abnormal Return"
    ) +
    theme_minimal()
}

# Plot the first significant event
plot_np_result(results[["10:10"]], "10:10")

References

• Rinaudo, J.B. & Saha, A. (2014). Non-parametric intraday event studies.
• MacKinlay, A.C. (1997). Event Studies in Economics and Finance. Journal of Economic Literature, 35(1), 13–39.