Table of Contents

Class SARIMAOptions<T>

Namespace
AiDotNet.Models.Options
Assembly
AiDotNet.dll

Configuration options for Seasonal Autoregressive Integrated Moving Average (SARIMA) models, which extend ARIMA models to incorporate seasonal components in time series data.

public class SARIMAOptions<T> : TimeSeriesRegressionOptions<T>

Type Parameters

T

The data type used in matrix operations for the time series model.

Inheritance
SARIMAOptions<T>
Inherited Members

Remarks

SARIMA (Seasonal Autoregressive Integrated Moving Average) is a sophisticated time series forecasting model that extends the ARIMA (Autoregressive Integrated Moving Average) framework to handle seasonal patterns in data. It is particularly useful for time series that exhibit both trend and seasonality, such as monthly sales data, quarterly economic indicators, or daily web traffic with weekly patterns. The model is denoted as SARIMA(p,d,q)(P,D,Q)m, where p, d, q are the non-seasonal parameters (autoregressive order, differencing order, and moving average order), P, D, Q are the corresponding seasonal parameters, and m is the seasonal period. This class provides configuration options for all these parameters, allowing fine-tuning of the SARIMA model to best capture the specific characteristics of the time series being analyzed.

For Beginners: SARIMA helps predict future values in time series data that has seasonal patterns.

Time series data shows how values change over time, like:

  • Monthly sales figures
  • Daily temperature readings
  • Quarterly company earnings

Many time series have seasonal patterns:

  • Retail sales spike during holidays
  • Ice cream consumption increases in summer
  • Energy usage follows daily and yearly cycles

SARIMA is designed to capture both:

  • The overall trend in your data
  • The repeating seasonal patterns

It does this by combining:

  • Regular ARIMA components that handle short-term patterns and trends
  • Seasonal components that handle repeating patterns at fixed intervals

This class lets you configure exactly how the SARIMA model analyzes your time series data, including how many past values to consider and how to handle seasonality.

Properties

D

Gets or sets the differencing order (d) of the non-seasonal component.

public int D { get; set; }

Property Value

int

A non-negative integer, defaulting to 0.

Remarks

The differencing order (d) specifies how many times the time series is differenced to achieve stationarity. Differencing involves computing the differences between consecutive observations and is used to remove trends from the data. A value of 0 means no differencing is applied, which is appropriate for already stationary series. A value of 1 applies first-order differencing, which can remove linear trends. A value of 2 applies second-order differencing, which can remove quadratic trends. Higher values are rarely needed in practice. The default value of 0 assumes that the time series is already stationary or that any non-stationarity will be addressed by other components of the model. Statistical tests like the Augmented Dickey-Fuller test can help determine the appropriate differencing order.

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

Differencing means taking the difference between consecutive values:

  • It helps remove trends and make the data more stable (stationary)
  • Each level of differencing removes a more complex trend

The default value of 0 means:

  • No differencing is applied
  • The model assumes your data doesn't have strong trends or that other components will handle them

Different values mean:

  • D=0: No trend removal (use when data has no trend or when you want to preserve the trend)
  • D=1: Removes linear trends (like steady growth or decline)
  • D=2: Removes quadratic trends (like accelerating growth or decline)

When to adjust this value:

  • Increase to 1 when your data shows clear upward or downward trends
  • Increase to 2 when trends are changing (accelerating or decelerating)
  • Keep at 0 when data fluctuates around a constant level

For example, with steadily increasing monthly sales data, setting D=1 would help the model focus on the patterns in the growth rather than the absolute values.

MaxIterations

Gets or sets the maximum number of iterations for the parameter estimation algorithm.

public int MaxIterations { get; set; }

Property Value

int

A positive integer, defaulting to 1000.

Remarks

This property specifies the maximum number of iterations allowed for the numerical optimization algorithm used to estimate the SARIMA model parameters. SARIMA models are typically fitted using maximum likelihood estimation, which requires an iterative optimization procedure. This parameter prevents the algorithm from running indefinitely in cases where convergence is difficult to achieve. The default value of 1000 is sufficient for most applications to achieve convergence. However, for particularly complex models or difficult datasets, more iterations may be required. Conversely, for simpler models or when approximate solutions are acceptable, fewer iterations may be sufficient. If the algorithm reaches this maximum without converging according to the Tolerance criterion, it will return the best solution found so far, possibly with a warning.

For Beginners: This setting limits how long the algorithm will try to find the best model parameters.

SARIMA uses an iterative process to find the optimal parameters:

  • It starts with initial estimates and gradually improves them
  • Each iteration refines the parameters to better fit your data
  • The process continues until the improvements become very small or the maximum iterations is reached

The default value of 1000 means:

  • The algorithm will try up to 1000 rounds of refinement
  • This is usually more than enough for most time series
  • If it reaches this limit without converging, it returns the best solution found so far

When to adjust this value:

  • Increase it (e.g., to 2000 or 5000) for complex seasonal patterns or if you get convergence warnings
  • Decrease it (e.g., to 500) when you need faster results and approximate solutions are acceptable

For example, when fitting a SARIMA model to complex economic data with multiple seasonal patterns, you might need to increase this value to ensure the algorithm finds the optimal solution.

P

Gets or sets the autoregressive order (p) of the non-seasonal component.

public int P { get; set; }

Property Value

int

A non-negative integer, defaulting to 1.

Remarks

The autoregressive order (p) determines how many lagged observations are included in the model. It represents the number of past time points that directly influence the current value. A higher p value allows the model to capture more complex autocorrelation patterns but increases the risk of overfitting and computational complexity. The default value of 1 means that the model includes the influence of the immediately preceding observation, which is sufficient for many time series with simple autocorrelation structures. For time series with more complex dependencies on past values, a higher p value might be appropriate. Model selection techniques like AIC (Akaike Information Criterion) or BIC (Bayesian Information Criterion) are often used to determine the optimal p value.

For Beginners: This setting controls how many previous time points directly influence the current prediction.

The P value determines:

  • How many past observations the model uses to predict the current value
  • How directly the model captures the relationship between current and past values

The default value of 1 means:

  • The model considers the immediate previous value (t-1) when predicting the current value (t)
  • This works well for many simple time series

Think of it like this:

  • P=1: Today's temperature depends on yesterday's temperature
  • P=2: Today's temperature depends on both yesterday's and the day before's temperatures
  • P=3: Extends this pattern to three previous days

When to adjust this value:

  • Increase it (to 2, 3, etc.) when you believe values depend on multiple previous time points
  • Keep it low (0 or 1) for simpler patterns or to avoid overfitting with limited data

For example, in stock price prediction, a P value of 2 or 3 might capture short-term momentum effects where recent price movements influence current price changes.

Q

Gets or sets the moving average order (q) of the non-seasonal component.

public int Q { get; set; }

Property Value

int

A non-negative integer, defaulting to 1.

Remarks

The moving average order (q) determines how many lagged forecast errors are included in the model. It represents the number of past random shocks (unexpected events or innovations) that influence the current value. A higher q value allows the model to capture more complex patterns in the residuals but increases the risk of overfitting and computational complexity. The default value of 1 means that the model includes the influence of the immediately preceding forecast error, which is sufficient for many time series with simple error structures. For time series with more complex error patterns, a higher q value might be appropriate. As with the autoregressive order, model selection techniques like AIC or BIC are often used to determine the optimal q value.

For Beginners: This setting controls how the model handles unexpected events or shocks in your data.

The Q value determines:

  • How many past "surprises" or errors influence the current prediction
  • How the model accounts for unexpected events that caused previous predictions to be off

The default value of 1 means:

  • The model considers the most recent prediction error when making new predictions
  • This helps adjust for recent unexpected events

Think of it like this:

  • Q=1: If yesterday's weather was unexpectedly rainy, today's forecast adjusts for that surprise
  • Q=2: Adjusts for surprises from both yesterday and the day before
  • Q=3: Extends this pattern to three previous days

When to adjust this value:

  • Increase it when unexpected events have lingering effects over multiple time periods
  • Keep it low when shocks to the system are quickly absorbed

For example, in retail sales, a Q value of 2 might help account for how unexpected events (like a promotion or supply shortage) affect sales for a couple of periods afterward.

SeasonalD

Gets or sets the seasonal differencing order (D) of the model.

public int SeasonalD { get; set; }

Property Value

int

A non-negative integer, defaulting to 0.

Remarks

The seasonal differencing order (D) specifies how many times the time series is seasonally differenced to achieve seasonal stationarity. Seasonal differencing involves computing the differences between observations separated by the seasonal period and is used to remove seasonal trends from the data. A value of 0 means no seasonal differencing is applied, which is appropriate for series without seasonal trends. A value of 1 applies first-order seasonal differencing, which can remove seasonal patterns that change linearly over time. Higher values are rarely needed in practice. The default value of 0 assumes that any seasonal patterns in the time series are stable over time or will be addressed by other components of the model. Statistical tests and visual inspection of seasonal plots can help determine the appropriate seasonal differencing order.

For Beginners: This setting controls how the model handles changing seasonal patterns.

Seasonal differencing compares values across seasons:

  • It helps remove changing seasonal patterns
  • It's like comparing "this January vs. last January" instead of "January vs. December"

The default value of 0 means:

  • No seasonal differencing is applied
  • The model assumes seasonal patterns are stable over time

Different values mean:

  • SeasonalD=0: No seasonal trend removal (seasons have consistent patterns)
  • SeasonalD=1: Removes changing seasonal patterns (when seasonal effects grow or shrink over time)

When to adjust this value:

  • Increase to 1 when seasonal patterns are getting stronger or weaker over time
  • Keep at 0 when seasonal patterns are consistent year after year

For example, if holiday sales spikes are getting larger each year, setting SeasonalD=1 would help the model account for this growing seasonal effect.

SeasonalP

Gets or sets the seasonal autoregressive order (P) of the model.

public int SeasonalP { get; set; }

Property Value

int

A non-negative integer, defaulting to 1.

Remarks

The seasonal autoregressive order (P) determines how many seasonally lagged observations are included in the model. It represents the number of past seasonal time points that directly influence the current value. For example, with monthly data and a seasonal period of 12, a P value of 1 means that the value from the same month in the previous year influences the current value. A higher P value allows the model to capture more complex seasonal autocorrelation patterns but increases the risk of overfitting and computational complexity. The default value of 1 is sufficient for many seasonal time series with simple seasonal autocorrelation structures. For time series with more complex seasonal dependencies, a higher P value might be appropriate.

For Beginners: This setting controls how previous seasons influence the current prediction.

The SeasonalP value determines:

  • How many previous seasonal periods directly influence the current value
  • How the model captures year-over-year (or season-over-season) patterns

The default value of 1 means:

  • The model considers the same time point from the previous season
  • For monthly data with 12-month seasonality, January 2023 is influenced by January 2022

Think of it like this:

  • SeasonalP=1: This month's sales depend on the same month last year
  • SeasonalP=2: This month's sales depend on the same month from both last year and two years ago

When to adjust this value:

  • Increase it when you believe multiple previous seasons influence the current season
  • Keep it at 1 for most seasonal patterns, as one previous season is often sufficient

For example, in tourism data, a SeasonalP of 1 would capture how summer tourism this year is related to summer tourism last year.

SeasonalPeriod

Gets or sets the number of time points in one seasonal cycle.

public int SeasonalPeriod { get; set; }

Property Value

int

A positive integer, defaulting to 12 (monthly seasonality).

Remarks

The seasonal period defines the number of time points that make up one complete seasonal cycle in the data. It represents the periodicity of the seasonal pattern. Common values include 12 for monthly data with yearly seasonality, 4 for quarterly data with yearly seasonality, 7 for daily data with weekly seasonality, or 24 for hourly data with daily seasonality. The default value of 12 is appropriate for monthly data with yearly seasonality, which is common in many business and economic applications. This property overrides the SeasonalPeriod property inherited from the base class to provide a more appropriate default value for SARIMA models. The correct specification of the seasonal period is crucial for the model to properly capture the seasonal patterns in the data.

For Beginners: This setting defines how long one complete seasonal cycle is in your data.

The SeasonalPeriod tells the model how many time points make up a complete cycle:

  • For monthly data: 12 (default) means a yearly seasonal pattern
  • For quarterly data: 4 would mean a yearly seasonal pattern
  • For daily data: 7 would mean a weekly seasonal pattern
  • For hourly data: 24 would mean a daily seasonal pattern

This value is critical because it tells the model exactly how far back to look for seasonal patterns:

  • With monthly data and SeasonalPeriod=12, January is compared with previous Januaries
  • With daily data and SeasonalPeriod=7, Mondays are compared with previous Mondays

When to adjust this value:

  • Change it to match the natural cycle in your data
  • Common values: 12 (monthly), 4 (quarterly), 7 (daily with weekly pattern), 24 (hourly)

For example, if analyzing weekly sales data over multiple years, you might set this to 52 to capture yearly seasonality (52 weeks in a year).

SeasonalQ

Gets or sets the seasonal moving average order (Q) of the model.

public int SeasonalQ { get; set; }

Property Value

int

A non-negative integer, defaulting to 1.

Remarks

The seasonal moving average order (Q) determines how many seasonally lagged forecast errors are included in the model. It represents the number of past seasonal random shocks that influence the current value. For example, with monthly data and a seasonal period of 12, a Q value of 1 means that the forecast error from the same month in the previous year influences the current value. A higher Q value allows the model to capture more complex seasonal error patterns but increases the risk of overfitting and computational complexity. The default value of 1 is sufficient for many seasonal time series with simple seasonal error structures. For time series with more complex seasonal error patterns, a higher Q value might be appropriate.

For Beginners: This setting controls how unexpected seasonal events influence the current prediction.

The SeasonalQ value determines:

  • How many past seasonal "surprises" or errors influence the current prediction
  • How the model accounts for unexpected events that happened in previous seasons

The default value of 1 means:

  • The model considers the prediction error from the same time in the previous season
  • For monthly data, an unexpected spike last December affects this December's prediction

Think of it like this:

  • SeasonalQ=1: If last Christmas had unexpectedly high sales, this Christmas's forecast adjusts for that
  • SeasonalQ=2: Adjusts for surprises from both last Christmas and the Christmas before that

When to adjust this value:

  • Increase it when seasonal shocks have effects that persist across multiple years
  • Keep it at 1 for most cases, as one seasonal period is often sufficient

For example, in energy consumption data, a SeasonalQ of 1 would help account for how an unusually cold winter last year might inform predictions for this winter.

Tolerance

Gets or sets the convergence tolerance for the parameter estimation algorithm.

public double Tolerance { get; set; }

Property Value

double

A positive double value, defaulting to 1e-5 (0.00001).

Remarks

This property specifies the convergence criterion for the numerical optimization algorithm used to estimate the SARIMA model parameters. The algorithm terminates when the relative change in the log-likelihood function or parameter estimates between consecutive iterations is less than this tolerance value. A smaller tolerance requires more precise convergence, potentially leading to more accurate parameter estimates but requiring more iterations. A larger tolerance allows for earlier termination, potentially saving computational resources at the cost of less precise parameter estimates. The default value of 1e-5 (0.00001) provides a good balance between precision and computational efficiency for most applications. For high-precision requirements, a smaller value might be appropriate, while for exploratory analysis or when computational resources are limited, a larger value might be used.

For Beginners: This setting determines how precise the final solution needs to be.

During the iterative process, the algorithm keeps refining its solution:

  • It compares each new solution to the previous one
  • When the improvement becomes smaller than the tolerance value, it stops
  • This indicates the solution has stabilized and further iterations won't improve much

The Tolerance value (default 0.00001 or 1e-5) means:

  • The algorithm will stop when improvements between iterations are very small
  • A smaller value requires more precision (and usually more iterations)
  • A larger value allows the algorithm to stop earlier with an approximate solution

When to adjust this value:

  • Decrease it (e.g., to 1e-6 or 1e-7) when you need extremely precise parameter estimates
  • Increase it (e.g., to 1e-4 or 1e-3) when you need faster results and can accept slight imprecision

For example, in a production forecasting system where small prediction improvements have significant financial impact, you might use a smaller tolerance to ensure maximum precision.

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