[Time series] The difference between multivariate time series and multivariate time series and examples

1. Multivariate time series and multivariate time series

Both multivariate time series and multivariate time series refer to time series data containing multiple variables, but their definitions and characteristics are slightly different.

1.1 Multivariate

Multivariate time series means that a time series data set contains multiple observation variables (such as $y_1$、$y_2$、$y_3$etc.), these variables are correlated in time and are usually generated by the same system. Multivariate time series data can be represented by a matrix, where each column corresponds to a variable and each row corresponds to an observation at a time point. The analysis and modeling of multivariate time series can be done with various time series models, such as ARIMA, VAR and other methods.

1.2 Multivariate

Multivariate time series means that a time series data set contains multiple explanatory variables (such as $x_1$、$x_2$、$x_3$etc.) and a response variable (such as $y$ ), these variables are correlated in time and are usually generated by the same system. Multivariate time series data can also be represented by a matrix, in which except the last column is the observed value of the response variable y, the other columns are explanatory variables$x_1$、$x_2$、$x_3$etc. observed values. The analysis and modeling of multivariate time series can be done with various regression models, such as linear regression, ridge regression, LASSO regression and other methods.

It should be noted that multivariate time series and multivariate time series are somewhat confused and overlapped in some literatures and scenarios, so in practice, it is necessary to select appropriate models and methods for analysis and modeling according to specific data and problems.

2. Examples

2.1 Multivariate

1. 股票价格数据: The stock price data in the stock market usually contains multiple variables, such as the opening price, closing price, highest price, lowest price, etc. of the stock. These variables are correlated in time and can be analyzed and forecasted with multivariate time series models.
2. 气象数据: Meteorological data usually contains multiple variables, such as temperature, humidity, air pressure, wind speed, rainfall, etc. These variables are correlated in time and can be analyzed and forecasted with multivariate time series models.
3. 经济数据: Economic data usually contains multiple variables, such as GDP, unemployment rate, inflation rate, interest rate, etc. These variables are correlated in time and can be analyzed and forecasted with multivariate time series models.
4. 传感器数据: Sensor data usually contains multiple variables, such as temperature, humidity, pressure, light, etc. These variables are correlated in time and can be analyzed and forecasted with multivariate time series models.

It should be noted that there are many examples of multivariate time series, but these examples are only a part of them, and the specific application should be determined according to specific problems and data sets.

2.2 Multivariate

Here are some examples of common multivariate time series:

1. 营销数据: Marketing data usually includes multiple explanatory variables, such as advertising spend, promotional activities, seasonality, etc., and a response variable, such as sales. These variables are correlated in time, and a multivariate time series model can be used to predict changes in sales and analyze which explanatory variables have the greatest impact on sales.
2. 交通数据: Traffic data usually includes multiple explanatory variables, such as road congestion, weather conditions, holidays, etc., and a response variable, such as traffic flow. These variables are correlated in time, and multivariate time series models can be used to predict changes in traffic flow and analyze which explanatory variables have the greatest impact on traffic flow.
3. 医疗数据: Medical data usually includes multiple explanatory variables, such as age, gender, medical history, etc., and a response variable, such as disease prevalence. These variables are correlated in time, and multivariate time series models can be used to predict changes in disease prevalence and analyze which explanatory variables have the greatest impact on prevalence.
4. 环境数据: Environmental data usually includes multiple explanatory variables, such as temperature, humidity, light, etc., and a response variable, such as air quality index. These variables are correlated in time, and a multivariate time series model can be used to predict changes in AQI and analyze which explanatory variables have the greatest impact on AQI.