Chapter 7 Time series

time series is a sequence of data points collected over time, typically at regular intervals, and can be used to study patterns and trends, forecast future values, and model relationships between variables.

There are two main types of time series analysis: univariate and multivariate time series.

Univariate time series analysis involves analyzing a single time series, i.e., a set of observations collected over time for a single variable. The goal of univariate time series analysis is to identify patterns and trends in the data, such as seasonality, cyclical patterns, and long-term trends. It also involves developing statistical models to describe and predict future values of the time series.

Some common techniques used in univariate time series analysis include:

  • Autocorrelation and partial autocorrelation analysis
  • Time series decomposition
  • Stationarity testing
  • Moving averages and exponential smoothing
  • Autoregressive Integrated Moving Average (ARIMA) modeling
  • Seasonal ARIMA modeling (SARIMA)

Multivariate time series analysis involves analyzing multiple time series simultaneously. This type of analysis is used when there are multiple variables that change over time, and the goal is to identify the relationships between these variables and how they change over time. Multivariate time series analysis is commonly used in economics, finance, and engineering, among other fields.

Some common techniques used in multivariate time series analysis include:

  • Vector Autoregression (VAR) modeling
  • Granger causality analysis
  • Multivariate ARIMA modeling

One of the advantages of multivariate time series analysis is that it allows for the modeling of complex relationships between variables, including causal relationships, feedback loops, and nonlinear relationships. However, it can be more complex and computationally demanding than univariate time series analysis.

Overall, time series analysis is a powerful tool for understanding and modeling data that changes over time. Univariate and multivariate time series analysis provide different approaches for analyzing time series data, depending on the research question and the data available.