Time Series Analysis And Forecasting
The concept of time series is used in many industries and areas of research. There are thousands of them in industries like commerce, technology, healthcare, energy, and finance.
Considering the inherent time element in trading and the financial/economic indicators, this section focuses on the finance industry. A business’s profits over time or other measured key performance indicators are a great example of time series data. Consequently, the time series analysis techniques described in the following article can be utilized in almost any profession where time series analysis is required.
To model or forecast time series, there are different approaches. Methods based on statistical analysis and machine learning are the most commonly used.
Prior to the advent of computing power and more granular data, statistical approaches dominated the field of time series modeling. In production, time series models are now being run with ML-based approaches, due to recent advancements in computing power and more comprehensive data collection. The classical statistical approaches still have relevance, especially when ML models struggle to learn patterns from limited training data (e.g., monthly data from only three years ago). Furthermore, statistical approaches have been successful in winning several recent M-Competitions, which is the largest time series forecasting competition initiated by Spyros Makridakis.
The purpose of this article is to introduce you to the fundamentals of time series modelling. Decomposition methods are used to deconstruct time series and explore the constituent elements within it. A discussion of stationarity, testing methods, and methods to attain stationarity in non-stationary series follows.
Using time series decomposition, data is broken down into its constituent components, such as trend, seasonality, and residual variation. As a result of this technique, underlying patterns and variations in the data are understood, providing useful information for forecasting.
A time series decomposition helps us understand the data by breaking it into different components. In this process, insights are gained into the complexity of the model and methods required to capture or model each component effectively.
An example can provide a better understanding of the possibilities. Think of a time series that shows an increasing or decreasing trend. Separating trend components from other series can be accomplished using decomposition. By removing the trend from the time series, the time series can become stationary. When the other components have been modeled, the trend can be added back to the model if desired. If we have sufficient data or suitable features, our algorithm can model the trend independently. In a time series, there are systematic and non-systematic components. In addition to exhibiting consistency, the systematic components can be described and modeled. On the other hand, it is not possible to directly model the non-systematic components.
A time series has the following components: The level refers to the series’ average value. Secondly, The trend represents the overall direction of the series over a long period, such as whether it is increasing or decreasing. In other words, seasonality is a variation in the series resulting from predictable and repeating short-term cycles. There is a fixed period and a known duration for these cycles.
Non-systematic components of a series can be described as noise, which refers to random variations. Among other things, it includes all the fluctuations that remain after removing other components. Traditional approaches typically employ additive or multiplicative models for decomposing time series.
It is the structure of the model y(t) that determines whether the model is additive or subtractive. This means the value at time ‘t’ is the sum of baseline level, trend, seasonal variation, and noise. A linear model exhibits consistency in magnitude as changes occur over time. In addition, a linear trend can be seen as a straight line. The cycle width (frequency) and height (amplitude) remain constant over time.
A multiplicative model has the following defining attributes: The model’s equation, represented as y(t) = level * trend * seasonality * noise, states that the value at a given time ‘t’ is the result of multiplying the base level, the prevailing trend, the cyclical variation (seasonality), and random disturbances (noise). Multiplicative models differ from linear models in that their values change over time in an unpredictable manner. It is possible, for instance, to see exponential changes. Observed trends in this model are curvilinear and nonlinear. A non-linear seasonality is also present in this model, where frequency and amplitude of cycles increase or decrease over time.