Article 3: Complete Guide to Time Series Models
Published: 2023-10-28 08:45:13

## **COMPLETE GUIDE TO TIME SERIES MODELS**


**PRELIMINARIES**

Time series analysis is a detailed way of analysing a sequence of data points collected over a period of time. To carry this analysis, analysts record data points at consistent intervals over a given period of time rather than just recording the data points at random or sporadically.
Time series data is pervasive in various fields like financial markets, economics, energy, healthcare, environmental sciences and many more. 
To measure time series, it requires one to build a time series model that helps analyse and forecast the future. In this models, time is often the independent variable, and the goal is usually to make a prediction for the future. Understanding and effectively modeling time-dependent data is crucial for making informed decisions and predictions. 
In this comprehensive guide, we will explore different characteristics and types of time series models in data science. 

**CHARACTERISTICS OF TIME SERIES MODELS**
In order to have an understanding of how time series models work, it is paramount to explore their main characteristics as detailed below; 

**1.	Stationarity**
It refers to the statistical properties of a time series remaining constant over time. It has three main statistical characteristics, i.e. mean, variance, and autocorrelation, which do not exhibit significant changes with respect to time. Stationarity is crucial because many time series models and statistical techniques assume or work better with stationary data. 
If a time series is found to be non-stationary, appropriate transformations like differencing or using models designed for non-stationary data (e.g., vector autoregression for integrated time series) may be applied to address the non-stationarity and make the data amenable to analysis and forecasting.

**2.	Seasonality**
It refers to recurring, predictable patterns or fluctuations that occur at regular intervals within a given time frame (i.e daily, weekly, monthly, or yearly patterns). These patterns are often associated with seasonal, environmental, or calendar-related factors and can have a significant impact on the behaviour of the data.
By accounting for seasonality, analysts can better capture the true underlying dynamics of the data and make more informed decisions in various applications, including business forecasting, economic analysis, and environmental monitoring.

**3.	Autocorrelation**
Also known as serial correlation, is a statistical concept in time series that quantitifies the degree of similarity between a time series and a lagged version of itself. In short, it assesses the correlation between a data point and previous data points in the same time series.
It is used to identify patterns and relationships within a time series. It is an essential concept in time series analysis because it helps to detect and understand underlying structures, trends, and seasonality in the data.

**TYPES OF TIME SERIES MODELS**

**1.	Autoregressive Integrated Moving Average (ARIMA) Models:** 

ARIMA models usually combine autoregressive, differencing, and moving average components to model a wide range of time series data. ARIMA (p, d, q) models are useful for handling non-stationary data and capturing both short-term and long-term dependencies.

**Note:** 
_**p (Autoregressive Order):**_ The autoregressive order, denoted as 'p,' refers to the number of lagged observations included in the model to predict the current value.

_**d (Integrated Order):**_ The differencing order, denoted as 'd,' represents the number of differences required to make the time series data stationary.

_**q (Moving Average Order):**_ The moving average order, denoted as 'q,' indicates the number of lagged forecast errors included in the model to predict the current value.

**2.	Autoregressive (AR) Models:**
AR are a class of time series models that rely on the linear relationship between a data point and its past values. In AR(p) models, the current value is a linear combination of the previous p values. AR models are used when the time series exhibits autocorrelation and may have a stationary behavior.

**3.	Moving Average (MA) Models:**
MA are other classes of linear time series models that focus on the relationship between a data point and past forecast errors. In MA(q) models, the current value depends on the previous q forecast errors. They are used to capture short-term variations in a time series.

**4.	Vector Autoregression (VAR) Models:**
VAR models are used for multivariate time series data, where multiple variables are interrelated. They use the past values of all variables in the system to make predictions.

**5.	Seasonal Autoregressive Integrated Moving Average (SARIMA) Models:**
SARIMA models extend ARIMA models that incorporate seasonal components. They are designed to handle time series data with seasonal patterns or periodic, like weekly, monthly, or annual cycles.

**6.	Exponential Smoothing Models:**
These methods include the simple exponential smoothing, Holt-Winters exponential smoothing and Holt's linear exponential smoothing. They are used to record different levels of trend and seasonality in time series data.

**7.	Long Short-Term Memory (LSTM) and Recurrent Neural Networks (RNNs):** 
Deep learning models like LSTMs and RNNs are used capture complex temporal dependencies in time series data. They are effective when dealing with non-linear and high-dimensional time series.

**8.	Bayesian Structural Time Series (BSTS) Models:** 
BSTS are Bayesian state space models that provide a powerful framework for time series decomposition, forecasting, and uncertainty estimation. They offer a flexible and powerful framework for decomposing time series data into its constituent components, modeling complex dependencies, and generating forecasts while accounting for uncertainty.

**9.	State Space Time Series Models (SSTSM):** 
They are a class of statistical models that combine elements of both state space models and time series models. These models are designed to handle complex time-dependent data with the added capability of capturing the underlying dynamics of the system generating the data.

**10.	Prophet Time Series Model:** 
It is an open-source forecasting tool developed by Facebook. It is designed for time series data with strong seasonal and holiday patterns. It is designed to make forecasting easy and approachable, especially for users without advanced expertise in time series analysis. It can handle missing data and outliers and is easy to use for quick forecasting tasks.

**11.	Generalized Autoregressive Conditional Heteroskedasticity (GARCH) Models:** 
They are a class of time series models used to analyze and forecast volatility in financial time series data. These models are especially important in the field of finance, where understanding and forecasting volatility is crucial for risk management, option pricing, portfolio optimization, and other financial applications.

**APPLICATIONS OF TIME SERIES MODELS**

Time series models are suitably used in a wide range of fields;

**1.	Finance**
Financial analysts can leverage time series models to record sales, Stock Price Forecasting, risk management, Interest Rate Forecasting, Credit Scoring, asset allocation and many.

**2.	Healthcare**
They can help analyze historical data, detect patterns, forecast future trends, and support decision-making in various aspects of the healthcare industry. They contribute to more efficient resource allocation, improved patient care, better financial planning, and enhanced public health responses.

**3.	Energy**
They are used to analyze, forecast, and optimize various aspects of energy production, consumption, and distribution. They are a vital tool for the energy sector, contributing to more efficient energy production, distribution, and consumption.

**4.	Agriculture**
They to analyse historical data, make predictions, and support decision-making for crop management, resource allocation, and sustainable farming practices. E.g they can take into account seasonal temperatures, the number of rainy days each month and other variables over the course of years, allowing agricultural workers to assess environmental conditions and ensure a successful harvest.

**5.	Cybersecurity**
They are essential for identifying, mitigating, and responding to cyber threats. IT and cybersecurity teams can develop patterns in user behavior with time series models, allowing them to be aware of when behavior doesn’t align with normal trends.

**CONCLUSION**
Time series modeling is an indispensable skill in the data scientist's toolkit. This guide has provided a comprehensive overview of time series models in data science, covering data characteristis, types and real world applications.  With use of this knowledge, data scientists can take advantage of the power of time series data to make informed decisions, identify trends, and make accurate predictions in a wide range of applications. Whether you are working in finance, energy, healthcare, or any other industry, mastering time series analysis is a valuable asset in your data science journey.