Class TransferFunctionOptions<T, TInput, TOutput>

Namespace

AiDotNet.Models.Options

Assembly

AiDotNet.dll

Configuration options for Transfer Function models, which model the dynamic relationship between input (exogenous) and output (endogenous) time series.

public class TransferFunctionOptions<T, TInput, TOutput> : TimeSeriesRegressionOptions<T>

Type Parameters

T

TInput

TOutput

Inheritance

object

ModelOptions

RegressionOptions<T>

TimeSeriesRegressionOptions<T>

TransferFunctionOptions<T, TInput, TOutput>

Inherited Members

TimeSeriesRegressionOptions<T>.LagOrder

TimeSeriesRegressionOptions<T>.IncludeTrend

TimeSeriesRegressionOptions<T>.SeasonalPeriod

TimeSeriesRegressionOptions<T>.AutocorrelationCorrection

TimeSeriesRegressionOptions<T>.ModelType

TimeSeriesRegressionOptions<T>.LossFunction

RegressionOptions<T>.DecompositionMethod

RegressionOptions<T>.UseIntercept

ModelOptions.Seed

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

object.ToString()

Remarks

Transfer Function models extend ARIMA (AutoRegressive Integrated Moving Average) models by incorporating the effects of one or more input (exogenous) time series on an output (endogenous) time series. They are particularly useful for modeling systems where there is a known causal relationship between input and output variables, with possible lagged effects. The transfer function component captures how changes in the input series affect the output series over time, while the ARIMA component models the autocorrelation structure of the output series. These models are widely used in fields such as economics, engineering, and environmental science for applications like dynamic system modeling, intervention analysis, and forecasting with leading indicators. This class provides configuration options for controlling the order of various components in the Transfer Function model.

For Beginners: Transfer Function models help you understand how one time series affects another over time.

When analyzing relationships between time series:

• Simple regression assumes immediate effects (X affects Y at the same time point)
• But in reality, effects often occur with delays (X affects Y after several time periods)
• The effect might also be distributed over multiple time periods

Transfer Function models solve this by:

• Capturing how input variables affect output variables over time
• Modeling both immediate and delayed effects
• Accounting for the autocorrelation in the output series itself
• Combining elements of regression and time series analysis

This approach is useful for:

• Understanding how marketing campaigns affect sales over time
• Modeling how temperature changes affect energy consumption
• Analyzing how policy changes impact economic indicators

This class lets you configure the structure of the Transfer Function model.

Properties

AROrder

Gets or sets the order of the AutoRegressive (AR) component.

public int AROrder { get; set; }

Property Value

int

A non-negative integer, defaulting to 1.

Remarks

This property specifies the order of the AutoRegressive (AR) component in the Transfer Function model. The AR component models the dependency of the current value of the output series on its own past values. An AR order of p means that the current value depends on the p previous values. A higher order allows the model to capture more complex autocorrelation patterns but increases the risk of overfitting and the number of parameters to estimate. The default value of 1 provides a simple AR component suitable for many applications, capturing first-order autocorrelation. The optimal value depends on the autocorrelation structure of the output series after accounting for the effects of the input series.

For Beginners: This setting controls how many past values of the output series influence the current value.

The AutoRegressive (AR) order:

• Determines how many previous values of the output series affect the current value
• Helps the model capture patterns where past values predict future values
• Higher values can model more complex temporal dependencies

The default value of 1 means:

• The model considers the immediate previous value of the output series
• This is sufficient for many time series with simple autocorrelation patterns

Think of it like this:

• Higher values (e.g., 2 or 3): Can capture more complex patterns of autocorrelation
• Lower values (e.g., 0): Ignore autocorrelation in the output series

When to adjust this value:

• Increase it when the output series shows significant autocorrelation at multiple lags
• Decrease it or set to 0 when the output series doesn't show significant autocorrelation
• Consider using autocorrelation and partial autocorrelation functions to guide selection

For example, in quarterly economic data that shows seasonal patterns, you might increase this to 4 to capture year-over-year effects.

InputLagOrder

Gets or sets the order of the input lag in the transfer function.

public int InputLagOrder { get; set; }

Property Value

int

A non-negative integer, defaulting to 1.

Remarks

This property specifies the maximum lag of the input series that affects the output series in the Transfer Function model. An input lag order of r means that the current value of the output series can be affected by the input series values from the current time point up to r time points in the past. A higher order allows the model to capture longer-term effects of the input series but increases the number of parameters to estimate. The default value of 1 allows for immediate and one-period lagged effects, suitable for many applications where the input series has a relatively quick impact on the output series. The optimal value depends on the expected time delay between changes in the input series and their effects on the output series.

For Beginners: This setting controls how many past values of the input series can affect the output series.

The input lag order:

• Determines how many previous values of the input series can affect the current output
• Helps the model capture delayed effects between input and output
• Higher values allow for longer-term effects to be modeled

The default value of 1 means:

• The model considers the current and immediate previous value of the input series
• This is appropriate when input variables have a quick effect on the output

Think of it like this:

• Higher values (e.g., 3 or 4): Can capture effects that take several time periods to manifest
• Lower values (e.g., 0): Only immediate effects are considered

When to adjust this value:

• Increase it when you expect the input series to have delayed effects on the output
• Decrease it when you expect only immediate or short-term effects
• Consider domain knowledge about the expected time delay between cause and effect

For example, in marketing analysis where advertising might affect sales for several months, you might increase this to 3-6 to capture these delayed effects.

MAOrder

Gets or sets the order of the Moving Average (MA) component.

public int MAOrder { get; set; }

Property Value

int

A non-negative integer, defaulting to 1.

Remarks

This property specifies the order of the Moving Average (MA) component in the Transfer Function model. The MA component models the dependency of the current value of the output series on past random shocks or errors. An MA order of q means that the current value depends on the q previous random shocks. A higher order allows the model to capture more complex patterns in the error terms but increases the risk of overfitting and the number of parameters to estimate. The default value of 1 provides a simple MA component suitable for many applications, capturing first-order effects of random shocks. The optimal value depends on the structure of the error terms after accounting for the AR component and the effects of the input series.

For Beginners: This setting controls how many past random shocks influence the current value.

The Moving Average (MA) order:

• Determines how many previous random shocks (errors) affect the current value
• Helps the model capture the lingering effects of unexpected events
• Higher values can model more complex patterns in the error terms

The default value of 1 means:

• The model considers the immediate previous random shock
• This is sufficient for many time series with simple error structures

Think of it like this:

• Higher values (e.g., 2 or 3): Can capture more complex patterns in the error terms
• Lower values (e.g., 0): Ignore the effects of past random shocks

When to adjust this value:

• Increase it when the autocorrelation of residuals shows significant patterns
• Decrease it or set to 0 when the residuals appear to be white noise
• Consider using autocorrelation of residuals to guide selection

For example, in financial time series where shocks often have lingering effects, you might increase this to 2 or 3 to capture these patterns.

Optimizer

Gets or sets the optimizer used for parameter estimation.

public IOptimizer<T, TInput, TOutput>? Optimizer { get; set; }

Property Value

IOptimizer<T, TInput, TOutput>

An instance of a class implementing IOptimizer<T>, or null to use the default optimizer.

Remarks

This property specifies the optimization algorithm used to estimate the parameters of the Transfer Function model. Different optimizers have different strengths and weaknesses in terms of convergence speed, ability to escape local optima, and sensitivity to initial conditions. The default value of null indicates that a default optimizer appropriate for the specific model implementation should be used. Common optimization algorithms for Transfer Function models include maximum likelihood estimation, least squares, and variants of gradient descent. The optimal choice depends on the specific characteristics of the data and the desired trade-off between estimation accuracy and computational efficiency.

For Beginners: This setting determines the algorithm used to find the best model parameters.

The optimizer:

• Controls how the model finds the optimal parameter values
• Different optimizers have different strengths and weaknesses
• Can significantly affect both the quality of results and computation time

The default value of null means:

• The system will choose an appropriate default optimizer
• This is suitable for most applications

Common optimizer types include:

• Gradient-based: Fast but may get stuck in local optima
• Evolutionary: Better at finding global optima but slower
• Bayesian: Efficient for expensive objective functions

When to adjust this value:

• Specify a different optimizer when the default doesn't converge well
• Choose based on whether you prioritize speed or solution quality
• This is an advanced setting that most users can leave as default

For example, if the default optimizer struggles with your complex model, you might specify a more robust optimizer that's less likely to get stuck in local optima.

OutputLagOrder

Gets or sets the order of the output lag in the transfer function.

public int OutputLagOrder { get; set; }

Property Value

int

A non-negative integer, defaulting to 1.

Remarks

This property specifies the order of the denominator polynomial in the transfer function, which determines how the effect of the input series on the output series depends on past values of the output series itself. An output lag order of s means that the effect of the input series on the current output depends on the s previous values of the output. A higher order allows the model to capture more complex dynamic relationships but increases the risk of overfitting and the number of parameters to estimate. The default value of 1 provides a simple dynamic relationship suitable for many applications. The optimal value depends on the complexity of the dynamic relationship between the input and output series.

For Beginners: This setting controls how the effect of inputs depends on past outputs.

The output lag order:

• Determines how the effect of inputs depends on previous output values
• Helps model feedback mechanisms where effects compound or diminish over time
• Higher values allow for more complex dynamic relationships

The default value of 1 means:

• The effect of inputs depends on the immediate previous output value
• This creates a simple dynamic relationship suitable for many systems

Think of it like this:

• Higher values (e.g., 2 or 3): Can model more complex feedback mechanisms
• Lower values (e.g., 0): Effects of inputs don't depend on previous outputs

When to adjust this value:

• Increase it when modeling systems with complex feedback mechanisms
• Decrease it or set to 0 for simpler systems with more direct effects
• Consider domain knowledge about how the system responds to inputs over time

For example, in economic systems where effects often compound over time, you might increase this to 2 to capture how the impact of policy changes depends on the previous state of the economy.