Time Series data is a series of data points indexed in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time, making it a sequence of discrete-time data. It is widely used in economics, finance, business, science, and engineering, among other fields, for forecasting future trends based on historical data. There are several types of time series data, each with its characteristics and patterns. In this article, I’ll take you through a guide to types of Time Series data and which algorithm you should use for forecasting them.
Types of Time Series Data
There are several types of time series data, each with its characteristics and patterns. Understanding these types is crucial for selecting the appropriate analysis or forecasting algorithm. Below are the types of time series data you should know as a Data Science professional:
- Stationary Time Series
- Non-stationary Time Series
- Cyclical Time Series
Let’s understand all these types and how to select a time series forecasting algorithm for each type.
Stationary Time Series
A stationary time series has properties that do not depend on the time at which the series is observed. Thus, it does not have trend or seasonal effects. Statistical properties such as mean, variance, and autocorrelation are constant over time.
Below is an example of a stationary time series:
The above plot shows a stationary time series where the mean and variance are constant over time, and there’s no discernible trend or seasonality. ARIMA (AutoRegressive Integrated Moving Average) and SES (Simple Exponential Smoothing) are two foundational methods for analyzing stationary time series data.
ARIMA combines three main components: autoregression (AR), differencing (I) to achieve stationarity, and moving average (MA). In the AR part, the model predicts the future value using a linear combination of past values. The I component involves differencing the data one or more times to remove any trends or seasonality and achieve stationarity. The MA part models the error of the prediction as a linear combination of error terms from past predictions. This combination allows ARIMA to capture a wide range of time series patterns in stationary data.
On the other hand, SES focuses on smoothing the data, giving exponentially decreasing weights to past observations as they move further into the past. This method is particularly useful for data without trends or seasonality, as it produces a smoothed version of the time series, emphasizing the most recent trends while naturally dampening older fluctuations, making it ideal for short-term forecasting in stationary series.
Non-Stationary Time Series
A non-stationary time series has properties that change over time. It can include having a trend, seasonality, or both.
- Trend: A trend exists when there is a long-term increase or decrease in the data. It does not have to be linear.
- Seasonality: Seasonality occurs when there are regular patterns of variance at specific regular intervals, such as quarterly, monthly, or daily.
Below are examples of trend and seasonal time series data:
The first plot above demonstrates a time series with a clear trend, showing a long-term increase in the data. The second plot above illustrates seasonality, where patterns repeat at regular intervals. For non-stationary data that exhibits trends, differencing can be used to make the series stationary before applying ARIMA. For data with both trend and seasonality, SARIMA or Holt-Winters can be particularly effective.
ARIMA works on non-stationary data with trends by incorporating an initial differencing step (the “Integrated” part of ARIMA), which transforms the series into a stationary form by removing the trend. This process allows the model to apply the autoregressive (AR) and moving average (MA) components to the differenced data to effectively capture the dependencies and noise patterns in the stationary series.
For non-stationary data with both trends and seasonality, SARIMA (Seasonal ARIMA) extends ARIMA by adding seasonal differencing and additional seasonal AR and MA terms, specifically addressing and modelling the seasonal component of the time series data. It makes SARIMA particularly adept at handling complex patterns that exhibit both trend and seasonality.
On the other hand, the Holt-Winters method, also known as Triple Exponential Smoothing, directly models both trend and seasonality by applying three smoothing equations: one for the level, one for the trend, and one for the seasonal component. This approach allows Holt-Winters to adjust its forecasts based on both the observed trend and seasonality in the data, making it highly effective for time series with clear and consistent seasonal patterns.
Cyclical Time Series
Cyclical patterns occur when there are fluctuations that are not of a fixed frequency. These are often observed in longer datasets and can be thought of as longer-term oscillations, differing from seasonality by not having a fixed period.
Below is an example of a cyclical time series:
The above plot represents a cyclical time series with cycles that are not of a fixed frequency, showing rises and falls that are not of a constant length. It is akin to economic cycles that might last for varying durations beyond a year. Vector Autoregression (VAR) and structural models are sophisticated approaches designed to analyze and forecast cyclical time series, often found in economics and finance, where cycles are not strictly seasonal and may vary in duration.
VAR models the interdependencies and influences between multiple time series simultaneously by using the system’s past values to predict its future values, effectively capturing the cyclical dynamics through the interaction of these series. It makes VAR particularly suited to examining how variables evolve together over time, identifying the lead-lag relationships between them, and understanding the impact of shocks to one variable on the others.
On the other hand, Structural models incorporate theoretical knowledge about the underlying processes generating the data, including potential cyclical behaviours. They break down the time series into components: trend, cycle, seasonality, and irregular components based on economic theory or empirical findings, allowing for the explicit modelling of cyclical patterns and how they are influenced by exogenous variables or structural shifts in the economy.
Summary
So, below are the types of time series data you should know as a Data Science professional:
- Stationary Time Series: A stationary time series has properties that do not depend on the time at which the series is observed. Thus, it does not have trend or seasonal effects. Statistical properties such as mean, variance, and autocorrelation are constant over time.
- Non-Stationary Time Series: A non-stationary time series has properties that change over time. It can include having a trend, seasonality, or both.
- Cyclical Time Series: Cyclical patterns occur when there are fluctuations that are not of a fixed frequency. These are often observed in longer data sets and can be thought of as longer-term oscillations, differing from seasonality by not having a fixed period.
I hope you liked this article on types of time series data and how to choose algorithms for forecasting them. Feel free to ask valuable questions in the comments section below. You can follow me on Instagram for many more resources.
