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 $y_s$ .