Description: A bivariate time series is a dataset consisting of two variables that are observed and recorded over time. This type of series allows for the analysis of the relationship and interaction between the two variables, providing a more comprehensive view of the phenomena being studied. Bivariate time series are fundamental in statistical analysis, as they help identify patterns, trends, and correlations that may not be evident when observing each variable in isolation. For example, studying the relationship between temperature and electricity consumption can reveal how both factors vary over time and influence each other. The main characteristics of bivariate time series include seasonality, trend, and autocorrelation, which are essential for making forecasts and informed decisions across various disciplines such as economics, meteorology, and engineering. The ability to model and analyze these interactions is crucial for better understanding complex systems and for data-driven decision-making.