trade_classification: Classification and aggregation of high-frequency data

In PINstimation: Estimation of the Probability of Informed Trading

Classification and aggregation of high-frequency data

Description

classify_trades() classifies high-frequency trading data into buyer-initiated and seller-initiated trades using different algorithms, and different time lags (or leads).
aggregate_trades() aggregates high-frequency trading data into aggregated data for provided frequency of aggregation. The aggregation is preceded by a trade classification step which classifies trades using different trade classification algorithms and time lags (or leads).

Usage

classify_trades(data, algorithm = "Tick", timelag = 0, ..., verbose = TRUE)

aggregate_trades(
  data,
  algorithm = "Tick",
  timelag = 0,
  frequency = "day",
  unit = 1,
  ...,
  verbose = TRUE
)

Arguments

data	A dataframe with 4 variables in the following order (timestamp, price, bid, ask).
algorithm	A character string refers to the algorithm used to determine the trade initiator, a buyer or a seller. It takes one of four values ("Tick", "Quote", "LR", "EMO"). The default value is "Tick". For more information about the different algorithms, check the Details section.
timelag	Numeric scalar. Time offset in microseconds used to select the quote matched to each trade for the "Quote", "EMO" and "LR" algorithms. Interpreted in seconds as timelag / 1e6. See Time lags vs. leads in @details for the exact matching rule and edge cases (start/end of sample). Examples: timelag = 5000 is a 5-millisecond lag; timelag = -500000 is a 0.5-second lead.
...	Additional arguments passed to the functions classify_trades() aggregate_trades(). The recognized arguments are fullreport, and is_parallel. Other arguments will be ignored. fullreport is binary variable passed to aggregate_trades() that specifies whether the variable freq is returned. The default value is FALSE. is_parallel is a logical variable passed to classify_trades() that specifies whether the computation is performed using parallel or sequential processing. #' The default value is TRUE. For more details, please refer to the vignette 'Parallel processing' in the package, or online.
verbose	A binary variable that determines whether detailed information about the progress of the trade classification is displayed. No output is produced when verbose is set to FALSE. The default value is TRUE.
frequency	The frequency used to aggregate intraday data. It takes one of the following values: "sec", "min", "hour", "day", "week", "month". The default value is "day".
unit	An integer referring to the size of the aggregation window used to aggregate intraday data. The default value is 1. For example, when the parameter frequency is set to "min", and the parameter unit is set to 15, then the intraday data is aggregated every 15 minutes.

Details

Trade classification algorithms

The argument algorithm takes one of four values:

• "Tick" refers to the tick algorithm: Trade is classified as a buy (sell) if the price of the trade to be classified is above (below) the closest different price of a previous trade.

• "Quote" refers to the quote algorithm: it classifies a trade as a buy (sell) if the trade price of the trade to be classified is above (below) the mid-point of the bid and ask spread. Trades executed at the mid-spread are not classified.

• "LR" refers to LR algorithm as in \insertCiteLeeReady1991;textualPINstimation. It classifies a trade as a buy (sell) if its price is above (below) the mid-spread (quote algorithm), and uses the tick algorithm if the trade price is at the mid-spread.

• "EMO" refers to EMO algorithm as in \insertCiteEllis2000;textualPINstimation. It classifies trades at the bid (ask) as sells (buys) and uses the tick algorithm to classify trades within the then prevailing bid-ask spread.

Time lags vs. leads (timelag)

For the "Quote", "LR" and "EMO" algorithms, classification relies on a quote (bid, ask or midquote) matched to each trade. The argument timelag controls when that quote is taken relative to the trade time:

• Positive lags (timelag > 0): for a trade at time t, the algorithm uses the quote corresponding to the last trade observed at or before ⁠t - |timelag|⁠ seconds. If no such past trade exists, the trade has no matched quote.

• Zero lag (timelag = 0): for a trade at time t, the algorithm uses the quote attached to that trade itself, which in the data setup corresponds to the bid–ask spread just before the trade is executed.

• Negative lags / leads (timelag < 0): for a trade at time t, the algorithm uses the quote corresponding to the last trade observed at or before ⁠t + |timelag|⁠ seconds (a future quote). If no such future trade exists, the trade has no matched quote.

In all cases the time offset is interpreted in seconds as timelag/1e6.

For example, timelag = 500000 corresponds to 0.5 seconds lag, and timelag = -2000000 corresponds to a 2-second lead.

Trades for which no suitable lagged/leading quote exists within the requested window are handled as follows:

• For "Quote", the corresponding trades receive NA classifications.

• For "LR", the quote-based classification is still used where available; trades exactly at the (lagged/leading) midquote fall back to the tick rule. When no midquote exists within the window, the result is NA.

• For "EMO", the bid/ask from the lagged/leading quote is used when available. If no such quote exists, the EMO quote-based step is skipped and the tick rule classification is retained.

LR recommend the use of mid-spread five-seconds earlier ('5-second' rule) mitigating trade misclassifications for many of the 150 NYSE stocks they analyze. On the other hand, in more recent studies such as \insertCitepiwowar2006;textualPINstimation and \insertCiteAktas2014;textualPINstimation, the use of 1-second lagged midquotes are shown to yield lower rates of misclassifications. The default value is set to 0 seconds (no time-lag). Considering the ultra-fast nature of today's financial markets, time-lag is in the unit of milliseconds. Shorter than 1-second lags can also be implemented by entering values such as 100 or 500.

Value

The function classify_trades() returns a dataframe of five variables. The first four variables are obtained from the argument data: timestamp, price, bid, ask. The fifth variable is isbuy, which takes the value TRUE, when the trade is classified as a buyer-initiated trade, and FALSE when the trade is classified as a seller-initiated trade.

The function aggregate_trades() returns a dataframe of two (or three) variables. If fullreport is set to TRUE, then the returned dataframe has three variables ⁠{freq, b, s}⁠. If fullreport is set to FALSE, then the returned dataframe has two variables ⁠{b, s}⁠, and, therefore, can be #'directly used for the estimation of the PIN and MPIN models.

References

\insertAllCited

Examples

# There is a preloaded dataset called 'hfdata' contained in the package.
# It is an artificially created high-frequency trading data. The dataset
# contains  100 000 trades and five variables 'timestamp', 'price',
# 'volume', 'bid', and 'ask'. For more information, type ?hfdata.

xdata <- hfdata
xdata$volume <- NULL

# Use the LR algorithm with a timelag of 0.5 seconds i.e. 500000
# microseconds to classify high-frequency trades in the dataset 'xdata'

lgtrades <- classify_trades(xdata, "LR", timelag = 500000, verbose = FALSE)

# LR algorithm with a 0.5-second lead (-500000 microseconds)

ldtrades <- classify_trades(xdata, "LR", timelag = -500000, verbose = FALSE)

# Compare the number of buyer- and seller-initiated trades between the
# lagged and leading LR classifications.

comparison_tbl <- rbind(
transform(lgtrades, version = "lag of 0.5s"),
transform(ldtrades, version = "lead of 0.5s")
)
comparison_tbl <- with(comparison_tbl,
  aggregate(list(Buys = as.logical(isbuy), Sells = !as.logical(isbuy)),
  by = list(version = version),
  FUN = sum, na.rm = TRUE)
)

show(comparison_tbl)

# Use the EMO algorithm with a timelag of 1 second, i.e. 1000000 microseconds
# to aggregate intraday data in 'xdata' at a frequency of 15 minutes.

emotrades <- aggregate_trades(xdata, algorithm = "EMO", timelag = 1000000,
frequency = "min", unit = 15, verbose = FALSE)

# Use the Quote algorithm with a timelag of 1 second to aggregate intraday
# data in the dataset 'xdata' at a daily frequency.

qtrades <- aggregate_trades(xdata, algorithm = "Quote", timelag = 1000000,
frequency = "day", unit = 1, verbose = FALSE)

# Since the argument 'fullreport' is set to FALSE by default, then the
# output 'qtrades' can be used directly for the estimation of the PIN
# model, namely using pin_ea().

estimate <- pin_ea(qtrades, verbose = FALSE)

# Show the estimate

show(estimate)

PINstimation documentation built on Dec. 18, 2025, 1:07 a.m.