The methods of time series analysis are the main tools used for analysis of price dynamics, as well as for formulating and back-testing trading strategies. Here, we present an overview of the concepts used in this book. For more details, readers can consult Alexander (2001), Hamilton (1994), Taylor (2005), and Tsay (2005).
First, we consider a univariate time series y(t) that is observed at moments t = 0, 1, …, n. The time series in which the observation at moment t takes place depends linearly on several lagged observations at moments t − 1, t − 2, …, t − p
is called the autoregressive process of order p, or AR(p). The white noise ε(t) satisfies the following conditions:
The lag operator Lp = y(t − p) is often used in describing time series. Note that L0 = y(t). Equation (B.1) in terms of the lag operator,
has the form
It is easy to show for AR(1) that
Obviously, contributions of old noise converge with time to zero ...