hgfalling said:This seems to be kind of a wide-open question. I mean, do you think that the matrices are dependent on time? Are they dependent on only the matrix from the previous time value? On all the previous matrices?
From a modeling standpoint, it seems like all you have is data. There isn't really a reason to assume a priori that any particular model is right, unless you know something extra about the underlying data. So I think you have to use your knowledge about the particular process here in order to formulate a model to predict T(n).
A Transition Matrix of Correlations is a mathematical tool used to analyze the relationship between variables over time. It is a square matrix that shows the correlations between variables at different time points, allowing for the identification of trends and patterns in the data.
To calculate a Transition Matrix of Correlations, the correlation coefficients between all pairs of variables at each time point are calculated. These coefficients are then organized into a square matrix, with each row and column representing a different variable and the values in each cell representing the correlation between those variables at a specific time point.
The purpose of using a Transition Matrix of Correlations is to analyze the relationship between variables over time. It allows for the identification of consistent patterns and trends in the data, as well as changes in the strength and direction of correlations between variables.
One limitation of using a Transition Matrix of Correlations is that it only shows the relationship between two variables at a time, and therefore may not capture the full complexity of a system with multiple variables. Additionally, it assumes that the relationships between variables are linear, which may not always be the case.
A Transition Matrix of Correlations can be interpreted by examining the values in each cell and identifying any consistent patterns or changes over time. A high positive value (close to 1) indicates a strong positive correlation between variables, while a high negative value (close to -1) indicates a strong negative correlation. A value close to 0 indicates little to no correlation between variables. The direction of the correlation can also be determined by the sign of the value (positive = variables move in the same direction, negative = variables move in opposite directions).