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 zero mean and σ²_Є variance. The Є_t component represents error in time t and the α  and Є notations represent mean intercept and error coefficients, respectively. The moving average time series model with q^th order is represented as MA(q). The preceding relations...