Class GARCHModelOptions<T>
Configuration options for the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, which is used for analyzing and forecasting volatility in time series data.
public class GARCHModelOptions<T> : TimeSeriesRegressionOptions<T>Type Parameters
TThe numeric type used for calculations (typically double or float).
- Inheritance
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GARCHModelOptions<T>
- Inherited Members
Remarks
GARCH models are specialized time series models designed to capture volatility clustering in financial and economic data. Unlike standard time series models that focus on predicting the mean value, GARCH models specifically model how the variance (volatility) of a time series changes over time, accounting for periods of high and low volatility.
For Beginners: Think of GARCH as a specialized tool for predicting how much something will fluctuate or vary in the future, rather than predicting its exact value. It's particularly useful for financial data like stock prices, where you might want to know not just whether a price will go up or down, but how stable or volatile it will be. For example, GARCH can help predict whether tomorrow's stock price will likely stay close to today's price or might swing dramatically in either direction. This is valuable for risk management and option pricing in finance. The model works by recognizing that periods of high volatility often cluster together (if today is volatile, tomorrow is likely to be volatile too).
Properties
ARCHOrder
Gets or sets the ARCH order (p), which determines how many past squared errors are used to model current volatility.
public int ARCHOrder { get; set; }Property Value
- int
The ARCH order, defaulting to 1.
Remarks
The ARCH component of the model captures how recent shocks (unexpected changes) affect current volatility. The order (p) specifies how many past squared errors are included in the model. Higher values allow the model to capture more complex patterns in how past shocks influence current volatility.
For Beginners: This setting controls how many past surprises or shocks the model considers when predicting today's volatility. With the default value of 1, the model only looks at yesterday's surprise (how far the actual value was from what was expected). Think of it like judging how nervous someone might be based on recent surprises they've experienced. If you set this higher (like 2 or 3), the model will consider surprises from multiple previous days, which might be more accurate but makes the model more complex. For most applications, a value of 1 or 2 works well, capturing the idea that recent surprises affect current volatility.
GARCHOrder
Gets or sets the GARCH order (q), which determines how many past volatility values are used to model current volatility.
public int GARCHOrder { get; set; }Property Value
- int
The GARCH order, defaulting to 1.
Remarks
The GARCH component of the model captures how past volatility levels affect current volatility. The order (q) specifies how many past volatility values are included in the model. Higher values allow the model to capture more persistent patterns in volatility over time.
For Beginners: This setting controls how many past volatility levels the model considers when predicting today's volatility. With the default value of 1, the model only looks at yesterday's volatility. Think of it like judging how rough the sea will be today based on how rough it was yesterday. If you set this higher (like 2 or 3), the model will consider volatility from multiple previous days, which might capture longer-lasting patterns. The combination of ARCH (recent surprises) and GARCH (recent volatility levels) helps the model predict whether things will be stable or unstable in the near future. A GARCH(1,1) model (both orders set to 1) is often sufficient for many applications.
MaxIterations
Gets or sets the maximum number of iterations allowed during parameter estimation.
public int MaxIterations { get; set; }Property Value
- int
The maximum number of iterations, defaulting to 1000.
Remarks
GARCH models are typically estimated using iterative numerical optimization methods. This parameter limits how many iterations the optimization algorithm will perform before stopping, preventing excessively long computation times.
For Beginners: This setting limits how long the model will spend trying to find the best parameters. With the default value of 1000, the model will try up to 1000 rounds of refinement before stopping, even if it hasn't found the perfect solution. Think of it like setting a time limit on a treasure hunt - at some point, you need to stop searching even if you haven't found the absolute best treasure. For simple datasets, the model might find good parameters much sooner than 1000 iterations. You might increase this for complex datasets where the model needs more time to find good parameters, or decrease it if you need faster results and can accept slightly less optimal parameters.
MeanModel
Gets or sets the model used to predict the mean of the time series before modeling volatility.
public ITimeSeriesModel<T>? MeanModel { get; set; }Property Value
- ITimeSeriesModel<T>
The mean model, defaulting to null (which uses a simple mean).
Remarks
GARCH models focus on modeling the variance (volatility) of a time series, but they typically need a separate model to handle the mean prediction. This property allows you to specify a different time series model (like ARIMA) to predict the mean values before the GARCH model analyzes the residuals for volatility patterns.
For Beginners: This setting lets you choose another model to predict the actual values before GARCH predicts the volatility. By default (when null), the model uses a simple average. Think of it like a two-step process: first, predict what value you expect (using this mean model), then predict how far off that prediction might be (using GARCH). For example, you might use an ARIMA model here to predict stock prices, and then GARCH to predict how volatile those prices will be. This combined approach (often called ARIMA-GARCH) is common in financial forecasting because it handles both the direction and the uncertainty of the forecast.
Tolerance
Gets or sets the convergence tolerance for parameter estimation.
public double Tolerance { get; set; }Property Value
- double
The convergence tolerance, defaulting to 0.000001 (1e-6).
Remarks
This parameter determines how small the change in parameter estimates needs to be between iterations for the optimization algorithm to consider that it has converged to a solution. Smaller values require more precise convergence but may increase computation time.
For Beginners: This setting determines how precise the model needs to be before it decides it's found a good solution. With the default value of 0.000001 (one millionth), the model will stop refining its parameters when the improvements between attempts become very tiny. Think of it like deciding when a drawing is "finished" - at some point, additional pencil strokes make such a small difference that it's not worth continuing. A smaller value (like 0.0000001) would make the model more precise but might take longer to finish. A larger value (like 0.0001) would make the model finish faster but with potentially less optimal parameters. The default is a good balance for most applications.