x̄ - > Idea that the time between trades was correlated with the existence of new information, providing our basis for looking at trade time instead of clock time

"The idea that the time between trades was correlated with the existence of new information, providing our basis for looking at trade time instead of clock time. It seems reasonable that the more relevant a piece of news is, the more volume it attracts. By drawing a sample every occasion the market exchanges a constant amount of volume, we attempt to mimic the arrival to the market of news of comparable relevance. If a particular piece of news generates twice as much volume as another piece of news, we will draw twice as many observations, thus doubling its weight in the sample.” (Easley, Lopéz de Prado & O’Hara, 2012a)

The quoted statement refers to a methodology for analyzing trade data to identify the arrival of new information in financial markets. The authors propose using trade time instead of clock time to measure the interval between trades. They argue that this time interval is correlated with the existence of new information.

To implement this methodology in R, you would typically have access to a dataset containing trade data, including the time of each trade and the corresponding volume. Here's an outline of how you can approach this analysis using R:

1. Load the necessary libraries:

```R

library(dplyr)   # for data manipulation

library(ggplot2) # for visualizations

```

2. Read the trade data into a data frame:

```R

trade_data <- read.csv("trade_data.csv")  # Replace "trade_data.csv" with the actual file name and path

```

3. Calculate the time between consecutive trades:

```R

trade_data <- trade_data %>%

  mutate(trade_time = as.POSIXct(trade_time)) %>%   # Convert trade_time to POSIXct format

  arrange(trade_time) %>%                           # Sort the data by trade_time

  mutate(time_diff = difftime(trade_time, lag(trade_time), units = "secs"))

```

4. Calculate the cumulative volume up to each trade:

```R

trade_data <- trade_data %>%

  mutate(cumulative_volume = cumsum(volume))

```

5. Determine the constant amount of volume for each sample:

```R

total_volume <- max(trade_data$cumulative_volume)

num_samples <- 100  # Specify the desired number of samples

sample_volume <- total_volume / num_samples

```

6. Sample the data based on the specified volume:

```R

sampled_data <- trade_data %>%

  mutate(sample = floor(cumulative_volume / sample_volume)) %>%

  group_by(sample) %>%

  sample_n(size = n() / num_samples)

```

7. Perform further analysis on the sampled data to study the impact of news:

```R

# Example analysis: Plot the relationship between time difference and volume

ggplot(sampled_data, aes(x = time_diff, y = volume)) +

  geom_point() +

  labs(x = "Time Difference", y = "Volume")

```

The code outlined above provides a general framework to implement the methodology described in the quote. You may need to adapt and customize it according to the specific structure and requirements of your trade data.