Enum DecompositionComponentType

Namespace

AiDotNet.Enums

Assembly

AiDotNet.dll

Represents the different components that can be extracted when decomposing a time series.

public enum DecompositionComponentType

Fields

Cycle = 3

Repeating patterns with a variable or changing period, unlike the fixed periods of seasonal components.

For Beginners: The Cycle component represents repeating patterns that don't have a fixed time period.

Unlike seasonality (which occurs at fixed intervals like every December), cycles have varying lengths:

• Business cycles (boom and bust) might last 2-10 years
• Housing market cycles might expand and contract over varying timeframes
• Sunspot activity follows cycles of approximately 11 years, but the exact length varies

Think of cycles as repeating patterns where you can't precisely predict when the next one will occur.

Identifying cycles helps you understand medium to long-term patterns that aren't tied to the calendar.

IMF = 6

Intrinsic Mode Functions - components extracted using Empirical Mode Decomposition (EMD) methods.

For Beginners: IMF stands for Intrinsic Mode Function, which is a special type of component extracted using a technique called Empirical Mode Decomposition (EMD).

Unlike traditional decomposition that separates data into trend, seasonality, and residuals, EMD breaks down the data into a collection of IMFs, each representing oscillations at different time scales.

Think of IMFs as layers of waves with different frequencies:

• Lower-order IMFs (IMF1, IMF2) capture fast oscillations (high-frequency components)
• Higher-order IMFs capture slower oscillations (low-frequency components)
• The final residual typically represents the overall trend

EMD and IMFs are particularly useful for:

• Analyzing non-linear and non-stationary time series
• Data where patterns change over time
• Complex signals with multiple overlapping cycles

This approach is more advanced but can reveal patterns that traditional decomposition methods might miss.

Irregular = 5

Random, unpredictable fluctuations in the data (similar to Residual but used in specific decomposition methods).

The Irregular component represents random variations that can't be attributed to trend, seasonality, or cycles.

This term is often used in specific decomposition methods (especially X-12-ARIMA and SEATS) and is functionally similar to the Residual component.

Think of it as the unpredictable "noise" in your data after accounting for all identifiable patterns.

Analyzing the irregular component helps you:

• Identify outliers or unusual events
• Assess the volatility or unpredictability in your data
• Evaluate how well your decomposition has captured the systematic patterns

Residual = 2

The irregular variation or "noise" remaining after other components have been extracted.

The Residual component (sometimes called "noise" or "error") represents the random, unpredictable fluctuations in your data that can't be explained by trend, seasonality, or cycles.

Think of it as the "unexplained" part of your data - the random ups and downs that don't follow any pattern.

Examples of what might cause residuals:

• Unexpected events (like a surprise promotion causing a sales spike)
• Measurement errors
• Random consumer behavior
• Small factors that individually aren't significant enough to model

Analyzing residuals helps you:

• Check if your decomposition captured all important patterns
• Identify unusual events or outliers
• Assess the randomness and unpredictability in your data

Seasonal = 1

Repeating patterns or cycles with a fixed, known period (e.g., daily, weekly, monthly, yearly).

The Seasonal component captures regular, predictable patterns that repeat at fixed intervals.

Think of it as patterns that occur at specific times, like:

• Higher retail sales during December holidays
• Higher ice cream sales in summer months
• Higher website traffic during business hours
• Lower energy usage on weekends

The key characteristic of seasonality is that it happens at known, fixed intervals (daily, weekly, monthly, quarterly, yearly).

Identifying seasonality helps you plan for predictable fluctuations and adjust your forecasts accordingly.

Trend = 0

The long-term progression or general direction of the time series.

The Trend component represents the long-term movement in the data, showing whether values are generally increasing, decreasing, or staying stable over time.

Think of it as the "big picture" direction of your data when you ignore short-term fluctuations.

Examples:

• Population growth showing a steady increase over decades
• A company's revenue gradually increasing year over year
• Global temperature rising slowly over many years

Identifying the trend helps you understand the fundamental direction of your data and make long-term forecasts.

TrendCycle = 4

A combined component that includes both the long-term trend and cyclical patterns.

For Beginners: The TrendCycle component combines the long-term trend and cyclical patterns into a single component.

This is often used when:

• It's difficult to separate the trend from cycles
• You're more interested in the overall direction including medium-term fluctuations
• The decomposition method doesn't distinguish between trends and cycles

Think of it as the "smoothed" version of your data with short-term seasonality and noise removed, but keeping both the long-term direction and medium-term fluctuations.

For example, in economic data, the TrendCycle might show both the general economic growth (trend) and the business cycles of expansion and recession together.

Remarks

For Beginners: Time series decomposition is like breaking down a complex song into its individual instruments.

When analyzing data that changes over time (like stock prices, temperature readings, or website traffic), it's often helpful to separate the data into simpler components to better understand what's happening.

For example, retail sales data might contain:

• A general upward trend due to business growth
• Seasonal patterns (higher sales during holidays)
• Random fluctuations due to unpredictable factors

Decomposing the data helps you see each of these patterns separately, making it easier to:

• Understand what's driving changes in your data
• Make better forecasts
• Identify unusual events or anomalies