Practical Time Series Analysis

Moving average models

The moving average models use dependency between residual errors to forecast values in the next time period. The model helps you adjust for any unpredictable events such as catastrophic events leading to a share market crash leading to share prices falling, which will happen over time and is captured as a moving average process.

The first-order moving average denoted by MA(1) is as follows:

x_t = α - θ₁Є_t-1 + Є_t

The second-order moving average denoted by MA(2) is as follows:

x_t = α - θ₁Є_t-1 - θ₂Є_t-2+ Є_t

The q^th order moving average denoted by MA(q) is as follows:

x_t = α - θ₁Є_t-1 - θ₂Є_t-2 - ... - θ_qЄ_t-q+ Є_t

Here, Є_t is the identically independently-distributed error at time t and follows normal distribution N(0,σ²_Є) with ...