ARTIFICIAL INTELLIGENCE + MODERN ROBOTICS

Introduction to data science Part 19: Time series and LLMs

The Age of AI has brought us Time-series Reasoning

Part A: Definitions

A time series is a series of data points indexed in time order. It is ubiquitous in our everyday understanding of the modern world. We take a look at its presence in Finance/Econometrics and Robotics.

(a) In Finance and Econometrics, time-series data as those by yahoofinance are simply known as historical data.

(b) In Robotics, time-series data means any stream of measurements recorded over time; from, say, t = 1 to t = T.

Part B: Partitions of a time series

A given time series is thought to consist of 3 systematic components (level, trend, seasonality) and 1 non-systematic component called noise.

Level is the baseline value around which the series fluctuates; trend is a long-term increase or decrease; and seasonality consists of regular, repeating patterns (e.g. the change caused by seasonal factors such as fluctuations in use and demand of an item). Then, we have stationarity, which is a property of a time series without a changing trend or seasonality.

• Trends and seasonality affect forecasts negatively. Error metrics of models when trends are present will usually be higher than when there are no trends; the same is the case when there is seasonality vs when there is no seasonality. As such, it is easier to forecast a stationary time series. Stationarity, in basic English, refers to how stable the values of a time series are. Stationary data means that the statistical structure of the data series is independent of time. As such, a stationary variable’s structure doesn’t evolve with time. A stationary time-series will not have any kind of increasing or decreasing pattern, and its points will generally hover around the same value, its unconditional mean i.e. a stationary time-series is mean-reverting. It’s because of this characteristic that a simple mechanism like the EWMA, which estimates the mean, is helpful for forecasts. Stationarity is important in time-series modelling because it allows preserving model stability i.e. a model whose parameters and structure are stable over time. Consider the crazy situation: If you want to build a model in which averaging is used, what mean will you pick to use if your data is non-stationary? Now, stationarity matters because it provides a framework in which averaging (used in AutoRegressive and Moving Average processes) can be properly used to describe a time-series behaviour.

Part C: AI arena

AI conferences: Can we put AI in any stuff?

Time-series analysis is the broad study of time-dependent data to understand its underlying patterns. On the other hand, time-series forecasting is a specific application of time-series analysis focused on predicting future values of a time series.

Now, as a matter of fact, time-series forecasting has the traditional goal of separating the pattern of a series from the noise by understanding the pattern’s trend and its seasonality. But, relying only on extrapolating past numerical trends can fail when underlying dynamics change — this is in the traditional time-series analysis! Now, according to the paper Toward Reasoning-Centric Time-Series Analysis, Large Language Models (LLMs) present the opportunity to include semantic/contextual inputs beyond numeric fitting. Without caring for computational costs, the authors of the paper say that “Reasoning over time series involves analysing observed data in context, leveraging prior domain knowledge to uncover underlying dynamics, explain the emergence of temporal patterns, and ultimately support practical decision-making.”

Different kinds of time-series reasoning essential for segmenting a time series:

(i) Drift is a slow, gradual, and persistent change in the underlying properties of a time series. Along with understanding regime shifts, drift can be understood also by Adaptation Reasoning.

(ii) Level can be understood by Quantitative Reasoning (e.g. When is the peak? We need to support precise predictions here!!)

(iii) Trend refers to a long-term movement of a time series in a particular direction. It can be made interpretable by Semantic Reasoning (How do we describe what’s happening?). The trend can also be understood by Counterfactual Reasoning (What if X hadn’t happened?), and Relational Reasoning (What causes what?)

• A time-series with trend is non-stationary because its mean changes in time. With linear trend, time-series points will approximately follow a line. It’s also possible to have higher order trends, such as quadratic trend where points follow a parabola.

(iv) Seasonality (aka periodicity) can be understood by Commonsense Reasoning (What typically happens in similar cases?)

(v) Noise can be understood by Abductive Reasoning (What unseen cause best explains this effect?)

Sources:

Apart from the paper, internet articles.

Google Images.