Table of Contents

Class NeuralNetworkARIMAOptions<T>

Namespace
AiDotNet.Models.Options
Assembly
AiDotNet.dll

Configuration options for Neural Network ARIMA (AutoRegressive Integrated Moving Average) models, which combine traditional statistical time series methods with neural networks for improved forecasting.

public class NeuralNetworkARIMAOptions<T> : TimeSeriesRegressionOptions<T>

Type Parameters

T
Inheritance
NeuralNetworkARIMAOptions<T>
Inherited Members

Remarks

Neural Network ARIMA is a hybrid approach that extends traditional ARIMA models by incorporating neural networks to capture complex nonlinear patterns in time series data. This approach leverages both the statistical foundation of ARIMA for handling linear dependencies, seasonality, and trends, while using neural networks to model nonlinear relationships that traditional ARIMA cannot capture. The resulting model can provide more accurate forecasts for time series with complex patterns, regime shifts, or other nonlinear dynamics that are common in real-world data.

For Beginners: Neural Network ARIMA combines two powerful approaches for predicting future values in a time series:

Imagine you're trying to predict tomorrow's temperature:

  • ARIMA is like using mathematical formulas that look at recent temperatures and patterns
  • Neural Networks are like having a smart system that can learn complex relationships from data
  • Neural Network ARIMA combines both approaches to get better predictions

Traditional ARIMA is good at capturing:

  • How today's temperature relates to yesterday's (AR - AutoRegressive)
  • How random fluctuations from previous days affect today (MA - Moving Average)

But it struggles with complex patterns like:

  • When a cold front arrives, temperatures might drop suddenly but then recover differently than normal
  • How humidity and cloud cover might interact in non-obvious ways to affect temperature

The neural network part helps capture these complex relationships, while the ARIMA part ensures the basic time patterns are properly handled. This combination often produces better forecasts than either approach alone.

This class lets you configure both the ARIMA components and the neural network that will work together to make predictions.

Properties

AROrder

Gets or sets the AutoRegressive (AR) order, which determines how many previous time steps are used as inputs to predict the current value.

public int AROrder { get; set; }

Property Value

int

The AR order, defaulting to 1.

Remarks

The AR order specifies the number of lagged observations of the time series itself that are included in the model as predictors. This parameter is crucial for capturing direct dependencies between current values and past values. Higher AR orders allow the model to capture longer-term dependencies but increase model complexity and computational requirements. The optimal AR order often depends on the inherent memory of the process generating the time series.

For Beginners: This setting determines how many previous time points the model looks at to make predictions.

Imagine predicting today's temperature:

  • AR order = 1: Only yesterday's temperature is considered
  • AR order = 7: An entire week of previous temperatures is considered

The default value of 1 means:

  • The model only looks at the most recent value to predict the next one
  • This is often a good starting point for many time series

You might want a higher value if:

  • Your data shows patterns that depend on values from multiple time periods ago
  • The series has weekly, monthly, or other cyclic patterns
  • You have enough data to support learning these longer-term relationships

You might want to keep it at 1 if:

  • You have limited data
  • The most recent value is the strongest predictor
  • You're dealing with a fast-changing time series where older values become irrelevant quickly

AR stands for "AutoRegressive" - using the series' own past values to predict its future.

DifferencingOrder

The order of differencing applied to the time series data.

public int DifferencingOrder { get; set; }

Property Value

int

Remarks

Specifies how many times the differencing operation is applied to the time series to achieve stationarity. Differencing helps remove trends and seasonality by computing differences between consecutive observations.

For Beginners: This determines how the model handles trends in your data.

Imagine you're tracking daily temperatures:

  • If temperatures are steadily rising over time (a trend), it's harder to predict exact values
  • Differencing transforms the data to focus on changes rather than absolute values
  • For example, instead of predicting "it will be 75°F tomorrow," the model might work with "it will be 2°F warmer than today"

The differencing order tells the model how many times to apply this transformation:

  • Order 0: Use the original values (no differencing)
  • Order 1: Use the differences between consecutive values
  • Order 2: Use the differences of the differences

Higher orders help handle more complex trends, but too high may introduce unnecessary complexity.

ExogenousVariables

Gets or sets the number of exogenous (external) variables to include in the model.

public int ExogenousVariables { get; set; }

Property Value

int

The number of exogenous variables, defaulting to 0.

Remarks

Exogenous variables are external factors not part of the time series itself but that may influence its behavior. This parameter specifies how many such variables are incorporated into the model. Including relevant exogenous variables can significantly improve forecast accuracy by accounting for external drivers of the time series. When this value is set to a positive number, the model expects these additional variables to be provided during training and forecasting.

For Beginners: This setting determines how many external factors (beyond the time series itself) the model will consider.

Going back to our temperature example:

  • Time series data: Historical daily temperatures
  • Exogenous variables might include: humidity, cloud cover, wind speed

The default value of 0 means:

  • The model only looks at the time series itself
  • No external factors are considered

You might want to increase this value if:

  • You know there are specific external factors that influence your data
  • You have reliable data for these external factors
  • These external factors help explain sudden changes or patterns in your data

For example, if you're forecasting:

  • Retail sales, exogenous variables might include: holidays, promotions, weather
  • Energy demand, exogenous variables might include: temperature, day of week, special events
  • Stock prices, exogenous variables might include: interest rates, sector indices, news sentiment

Adding exogenous variables can make your model much more accurate, but requires having this additional data available both for training and when making future predictions.

LaggedPredictions

Gets or sets the number of lagged predictions to use as inputs to the neural network.

public int LaggedPredictions { get; set; }

Property Value

int

The number of lagged predictions, defaulting to 1.

Remarks

This parameter determines how many of the model's own previous predictions are fed back into the neural network as inputs for making the next prediction. This creates a recurrent structure even in feedforward networks, allowing the model to capture temporal dependencies that span multiple time steps. Using lagged predictions can improve performance in cases where future values depend not just on past observations but on how those observations were predicted.

For Beginners: This setting controls how many of the model's own previous predictions it uses to make new predictions.

This is different from AR order:

  • AR order uses actual historical values from your data
  • LaggedPredictions uses the model's own previous predictions

The default value of 1 means:

  • The model considers its most recent prediction when making a new one
  • This helps create continuity in forecasts

You might want a higher value if:

  • You're making longer-term forecasts
  • The way values change over time is as important as the values themselves
  • Your time series has momentum that should persist in forecasts

You might want to keep it at 1 if:

  • You're primarily interested in short-term forecasts
  • You want to minimize error accumulation
  • You prefer simpler model behavior

This feature helps the neural network portion develop a "memory" of its own predictions, which can lead to more coherent forecasting sequences.

MAOrder

Gets or sets the Moving Average (MA) order, which determines how many previous error terms are used in the prediction model.

public int MAOrder { get; set; }

Property Value

int

The MA order, defaulting to 1.

Remarks

The MA order specifies the number of lagged forecast errors that are included in the model. This component captures the relationship between the current value and previous random shocks to the system. MA terms help model the short-term effects of unexpected events or noise in the time series. Higher MA orders allow the model to account for longer-lasting effects of past disturbances but can make the model more difficult to estimate reliably.

For Beginners: This setting determines how many previous prediction errors the model considers.

Continuing with our temperature example:

  • Suppose yesterday the model predicted 75°F but it was actually 78°F (an error of +3°F)
  • The MA part lets the model learn from this error

The default value of 1 means:

  • The model only considers the most recent prediction error
  • This helps adjust for recent unexpected changes

You might want a higher value if:

  • Your data shows that effects from unexpected events tend to linger
  • The time series has persistent errors in one direction
  • You notice that after a big miss, the model continues to miss in following periods

You might want to keep it at 1 if:

  • Errors tend to be random and don't show patterns
  • You want to keep the model simpler
  • You have limited data

MA stands for "Moving Average" - though it's not actually taking averages of the data, but rather modeling how unexpected shocks continue to affect future values.

NeuralNetwork

Gets or sets the neural network to use in the hybrid model.

public INeuralNetwork<T>? NeuralNetwork { get; set; }

Property Value

INeuralNetwork<T>

The neural network instance, defaulting to null (in which case a default network will be created).

Remarks

This property allows specification of a custom neural network architecture to be used within the hybrid ARIMA model. When provided, this neural network will be used to model the nonlinear components of the time series after the linear ARIMA components have been applied. The network should accept inputs that conform to the AR order, MA order, and exogenous variables specified, and produce outputs suitable for the forecasting task. If left null, a default architecture appropriate for the specified parameters will be created automatically.

For Beginners: This setting lets you provide your own custom neural network instead of using the default one.

The neural network is the "smart" part of the model that learns complex patterns:

  • It takes inputs (past values, errors, external factors)
  • It processes them through layers of interconnected nodes
  • It produces predictions based on patterns it learned during training

The default value of null means:

  • The system will automatically create a suitable neural network for you
  • This is convenient and works well in many cases

You might want to provide your own network if:

  • You have expertise in neural network design
  • Your time series has very specific characteristics that need a specialized architecture
  • You want to experiment with different network structures

For example, you might create:

  • A deeper network with more layers for very complex data
  • A network with specific activation functions suited to your data characteristics
  • A network with dropout or regularization to prevent overfitting

If you're new to neural networks, it's recommended to start with the default (null) and let the system create an appropriate network automatically.

OptimizeParameters

Gets or sets a value indicating whether the model should attempt to optimize its parameters during training.

public bool OptimizeParameters { get; set; }

Property Value

bool

Remarks

When enabled, the model may use the configured Optimizer (or a default optimizer) to refine AR/MA coefficients and neural network parameters beyond their initial estimates.

For Beginners: Turning this on tells the model to spend extra time trying to find better parameter values. This can improve accuracy, but it can also make training take longer.

Optimizer

Gets or sets the optimizer to use for training the neural network component.

public IOptimizer<T, Matrix<T>, Vector<T>>? Optimizer { get; set; }

Property Value

IOptimizer<T, Matrix<T>, Vector<T>>

The optimizer instance, defaulting to null (in which case a default optimizer will be used).

Remarks

This property allows specification of the optimization algorithm to be used when training the neural network portion of the model. The optimizer controls how the network's weights are updated based on the calculated gradients during backpropagation. Different optimizers have various properties regarding convergence speed, likelihood of finding global optima, and behavior in the presence of noisy gradients. If left null, a default optimizer (typically a variant of stochastic gradient descent with momentum) will be used.

For Beginners: This setting determines the method used to train the neural network part of your model.

Think of training a neural network like descending a mountain to find the lowest point:

  • The optimizer is the strategy you use to navigate downhill
  • Different strategies have different tradeoffs in speed, accuracy, and reliability

The default value of null means:

  • The system will choose a standard optimizer for you
  • This is usually Adam or SGD with momentum, which work well for many problems

You might want to provide your own optimizer if:

  • Your model is getting stuck in training
  • You need faster convergence
  • You're dealing with a particularly challenging dataset

Common optimizer options include:

  • Adam: Good all-around performer that adapts learning rates
  • SGD with momentum: Simple but effective, especially with proper tuning
  • RMSProp: Good for non-stationary objectives
  • Nesterov Accelerated Gradient: Helps avoid overshooting minima

If you're new to time series forecasting, start with the default (null) optimizer and only change it if you encounter specific training issues.

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