Time series data

Summary

• With time series data, our sample is denoted by \(y_1,…,y_T\) . Time naturally orders our sample.
• We denote a specific sample point by \(y_t\) where \(t\) is a value between 1 and \(T\) .
• We model our sample \(y_1,…,y_T\) as a sequence of random variables. A sequence of random variables over time is also called a time series process.
• With time series data, it is no longer reasonable to assume that our sample is a random sample ( a sequence of IID random variables). There will typically be a dependence between two points in time \(y_t\) and \(y_s\) .