What is cross correlation time series?

Cross correlation is a statistical method used to measure the similarity between two time series. It involves comparing the values of two time series at different points in time and calculating their correlation coefficient. Cross correlation can be used to identify the time lag between two time series, which can be useful in predicting future values and patterns.

The cross correlation between two time series is calculated as follows:

rxy(k) = (1/n) * Σ(xi - x_avg) * (yi+k - y_avg)

where rxy(k) is the correlation coefficient between the two time series, xi and yi are the values of the two time series at time i, k is the time lag between the two time series, x_avg and y_avg are the mean values of the two time series, and n is the number of data points.

The cross correlation function can be visualized using a scatter plot or a correlation matrix. A positive correlation coefficient indicates a positive correlation between the two time series (i.e., they tend to move in the same direction), while a negative correlation coefficient indicates a negative correlation (i.e., they tend to move in opposite directions).

Cross correlation is widely used in various fields, including economics, finance, engineering, and meteorology. It is used to analyze the relationship between different economic variables, to predict stock prices, to detect patterns in signal processing, and to forecast weather patterns, among other applications.