Data Generators

Abstract supertype for all data generation inputs to use with makedata() function. Use subtypes(DataGenInput) for a list of all possible data generation inputs.

LogDiffInput(nTimeStep, initial, volatility, drift)
LogDiffInput(;kwargs...)

Contains parameters that are used by makedata() to synthesize data from a log-normal diffusion process of the form.

\[P_{t+1} = P_t \cdot e^{drift + volatility \cdot v}\]

Where P_t is the value of the data at timestep t. The drift and volatility represent the mean and standard deviation of a normal distribution. The equation given above expresses them as such by letting v be a draw from a standard normal distribution which is then shifted and scaled by the drift and volatility terms.

Arguments

• nTimeStep: The number of time steps to synthesize.
• initial: The assumed value at the 0th time step. Default: 100.
• volatility: The price volatility as a standard deviation in terms of implied time period. Defaults to 0.3.
• drift: The drift parameter describes the mean of the log-normal diffusion process

given in terms of the entire implied time period (if simulating a year, drift would be annual expected return). Defaults to 0.02.

Example

input1 = LogDiffInput(250, 100, .05, .1)

# initialize first input with default values
input2 = LogDiffInput(250)

# initialize a second input with zero volatility
kwargs = Dict(:nTimeStep=>250, :initial=>100, :volatility=>.05, :drift=>.1)
input3 = LogDiffInput(;kwargs...)

BootstrapInput(input_data, bootstrap_method::<:TSBootMethod; kwargs...)
BootstrapInput{T <: TSBootMethod}(; kwargs...)

Contains the parameters needed to perform block bootstrap of type T to be used by makedata() function. T can be any subtype of TSBootMethod: Stationary, MovingBlock, or CircularBlock.

Keyword Arguments

• input_data: data to be resampled. Must be a 1-D array
• bootstrap_method: Type of time series bootstrap to use. Must be subtype of TSBootMethod.
• n: size of resampled output data. Default: 100
• block_size: block size to use. Defaults to the optimal block length using opt_block_length()

Examples

input_data = [1,2,4,3,5,7,6,3];
kwargs = Dict(:n=>20);
input1 = BootstrapInput(input_data, Stationary; kwargs...)

kwargs = Dict(:input_data=>input_data, :n=>20, :block_size=>4);
input2 = BootstrapInput{MovingBlock}(;kwargs...)

makedata(Input::LogDiffInput, nSimulation::Integer)

generates data according to the DataGenInput struct provided

Possible DataGenInput types are

• ::LogDiffInput
• ::BootstrapInput{MovingBlock}
• ::BootstrapInput{CircularBlock}
• ::BootstrapInput{Stationary}

Arguments

• Input<:DataGenInput: struct with parameters to generate data
• nSimulation: the number of simulations to run.

Outputs

• data: nTimeStep x nSimulation array, where each column contains the data for one simulation, and each row contains data for each timestep

Example

nTimeStep = 100;
input1 = LogDiffInput(nTimeStep);

# create a dataset using the log diffusion model
data1 = makedata(input1, 1)

# create another dataset with 2 simulation runs using a startionary bootstrap 
input2 = BootstrapInput(data1, Stationary; n=100);
data2 = makedata(input2, 2)

factory(widget::Widget, bootstrap_method::TSBootMethod, nWidgets::Signed)

Creates nWidgets using a given bootstrap_method. If a widget of type "Stock" is passed in then the widget factory will use a given bootstrap method to produce n "Stock" widgets. All widgets use first difference.

Positional Inputs

• widget::Widget: A concrete widget struct. See the Widget documentation for more.
• bootstrap_method: A subtype of TSBootMethod: Stationary, MovingBlock, or CircularBlock.
• nWidgets: The amount of widgets you want widget factory to return.

Example

prices = [1,2,5,9,8,10,5,3];
widget = Stock(prices)

list_of_widgets = factory(widget, Stationary, 2)

opt_block_length(array, bootstrap_method::TSBootMethod)

Computes the optimal block length for a time series block bootstrap using the methods defined by Politis and White (2004).

If bootstrap method other than Stationary or CircularBlock is used, the function defaults to CircularBlock

Examples

using Distributions: Normal

# create ar(1) data set
ar1 = [1.0];
for _ in 1:799
    push!(ar1, ar1[end] * 0.7 + rand(Normal()))
    end

# find optimal block lengths
st_bl = opt_block_length(ar1, Stationary)
cb_bl = opt_block_length(ar1, CircularBlock)