What is a causal process? Can an AR process be called as a causal process since we are inferring a directed graphical model from the time series?
An autoregressive (AR) process is a type of statistical model that describes a time series as a function of its past values. In an AR process, the current value of the time series depends on a linear combination of its past values.
A causal process is a process in which the values of one variable (the cause) determine the values of another variable (the effect). In a causal process, there is a clear direction of causation: the cause occurs before the effect, and changing the cause will affect the effect.
In the context of an AR process, the past values of the time series can be considered the cause, and the current value of the time series can be considered the effect. However, it is important to note that an AR process is not necessarily a causal process. Just because the current value of a time series depends on its past values does not necessarily mean that there is a causal relationship between the two.
To determine whether an AR process is a causal process, it is necessary to consider the underlying data generating process and whether there is a clear direction of causation. For example, if the time series represents the temperature of a room, the past values of the time series (e.g., the temperature at earlier times) could be considered the cause, and the current value of the time series (e.g., the current temperature) could be considered the effect. In this case, the AR process would be a causal process, because the temperature at earlier times determines the current temperature. However, if the time series represents the stock price of a company, it is not clear whether the past values of the time series (e.g., the stock price at earlier times) are the cause or the effect. In this case, the AR process would not be a causal process.
I advise you to start from the in-depth study of a basic text on probability calculation.
The rest will come by itself.
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