Data Generation

All data generation methods use the makedata function with different structs containing input parameters.

Parametric Data Generation

Log Diffusion

Creating a time series with the log diffusion model for asset prices (also known as Geometric Brownian Motion) uses the LogDiffInput struct.

Note: drift (expected value of returns) and volatility are in terms of the implicit time period for the whole simulated data set. For example, when simulating a year of prices, drift represents the yearly expected return.

For simulating a year of daily and hourly prices, assuming there are 252 trading days in a year and 6 hours in a trading day.

# creating a LogDiffInput struct with input parameters
daily_input = LogDiffInput(; 
    nTimeStep=252, 
    initial=50, 
    volatility=.3,
    drift=.08
);

hourly_input = LogDiffInput(; 
    nTimeStep=252*6, 
    initial=50, 
    volatility=.3,
    drift=.08
);

# creating 2 new datasets with 2 timeseries each
daily_timeseries = makedata(daily_input, 2) 
hourly_timeseries = makedata(hourly_input, 2)

Non-Parametric Data Generation

Time-Series Bootstrapping

Time-series bootstrapping samples with replacement from blocks of the original time-series dataset. The three bootstraps included in Bruno are Stationary, MovingBlock, and CircularBlock.

All time series bootstraps use the BootstrapInput struct with parameters.

• Stationary bootstrap (Politis and Romano, 1994) uses expnentially distributed blocksizes.
• MovingBlock uses constant sized blocks that do not wrap around the time-series.
• CircularBlock uses constant sized blocks that wrap around the time-series.