Leveraging time series analysis for trend recognition

Time Series Analysis

The Time Series Analysis capability within the Signal analytics module empowers security professionals to gain deeper insights into the selected signals by examining their behavior and patterns over time. This analysis technique focuses on understanding the temporal dynamics and trends within the signals, like seasonality, periodic events, or long-term trends that may not be readily apparent through visual inspection.

For time-series analysis, we do the following analysis -

1. Trend analysis – Seasonality detection

2. Outlier detection

3. Change point detection

4. Motif detection

5. Forecasting

Trend analysis – Seasonality detection

Seasonality in a time series is a regular pattern that repeats over a fixed period. For example, imagine you have a dataset that records the daily temperature in a city over a year. If you plot this data on a graph with time on the x-axis and temperature on the y-axis, you'll see a pattern repeating itself. For example, you might notice that the temperature tends to be high during the summer months and low during the winter months. This repeating pattern is what we call seasonality.

Seasonality refers to regular and predictable patterns that occur at fixed intervals within a time series. These patterns can repeat on a daily, weekly, monthly, quarterly, or yearly basis, depending on the nature of the data. In the example of the temperature data, the repeating pattern occurs every year since it follows the four seasons.

Outlier detection

Outlier detection in a time series refers to the process of identifying observations that significantly deviate from the expected or normal behavior of the data. Outliers are data points that are unusually different from the majority of the other data points in the series.

Change point detection

Imagine you have a dataset that records the daily temperature in a city over several years. You might want to know if there were any significant changes or shifts in the temperature patterns during this time. Change point detection in time series analysis is the process of identifying points or moments in the data where there is a noticeable change or shift in the underlying behavior.

Motif detection

Imagine you have a sequence of numbers representing the daily temperature in a city recorded over a long period. You might notice that certain patterns in the temperature readings repeat themselves at different points in the sequence. For example, you might observe that the temperature rises sharply for a few days, then stays high for a while before dropping suddenly. This repeating pattern is what we call a motif.

In time series analysis, motif detection refers to the process of finding these recurring patterns within a time series dataset. These patterns can be of different lengths and shapes, but they have the property of repeating or appearing multiple times in the data.

Motif detection is important because it helps us identify significant subsequences within a time series that exhibit interesting behavior or hold important information. By detecting motifs, we can gain insights into recurring events or patterns that occur in the data and use that knowledge for various purposes.

For example, in weather forecasting, motif detection can help identify recurring weather patterns, such as heatwaves or cold spells, which can be useful for predicting future weather conditions. In financial analysis, motif detection can help identify repeated patterns in stock prices, which can aid in making investment decisions.

To summarize, motif detection in time series analysis involves finding recurring patterns or motifs within a time series dataset. These motifs can provide valuable insights into repeated events or patterns, and their detection can be helpful in various applications such as weather forecasting, finance, and many others.

How is motif detection different from seasonality detection, since both seem to identify repeating patterns?

Motif detection and seasonality detection are indeed related in that they both involve identifying repeating patterns in time series data. However, they differ in several key aspects:

1. Scope of Patterns: Seasonality detection focuses specifically on identifying patterns that repeat at fixed intervals, such as daily, weekly, monthly, or yearly cycles. It is concerned with capturing regular, predictable variations in the data. On the other hand, motif detection aims to find repeating patterns more generally, without constraints on the length or periodicity of the patterns. Motifs can be of any length and can repeat at irregular intervals within the time series.

2. Purpose and Interpretation: Seasonality detection primarily seeks to understand and model the cyclic behavior inherent in the data. It helps us uncover periodic effects that can be utilized for forecasting, anomaly detection, or understanding the underlying factors influencing the time series. Motif detection, on the other hand, focuses on the discovery of interesting or meaningful subsequences within the time series. The motifs may represent specific events, behaviors, or unique occurrences that are worth further investigation or analysis.

3. Analysis Techniques: Seasonality detection often relies on spectral analysis techniques like the Fourier Transform or its fast variant, FFT, to decompose the time series into its frequency components. It looks for significant peaks in the frequency spectrum to identify dominant seasonal patterns. In contrast, motif detection employs various algorithms and approaches such as pattern matching, subsequence clustering, or data mining techniques to identify repeated patterns within the time series. It typically involves comparing subsequences and measuring their similarity or distance.

4. Application Focus: Seasonality detection is particularly useful for understanding cyclic phenomena and making predictions based on historical patterns. It finds application in fields like climate science, finance, and retail, where the cyclic nature of the data is essential for decision-making. Motif detection, on the other hand, is more general and can be applied in various domains, such as biological sequences, signal processing, anomaly detection, or event recognition, where finding repeated patterns is of interest.

In summary, while both motif detection and seasonality detection involve identifying repeating patterns, they differ in terms of the nature of the patterns, the analysis techniques employed, their intended purposes, and the specific applications they serve.

Forecasting 

Forecasting uses the information from past observations in the time series to make educated guesses about what will happen in the future. It helps us understand and predict how the data might change or behave over time.

In Resolution Intelligence Cloud, forecasting helps you predict the number of incoming signals in the coming days (let's say tomorrow).