About
Method of Moments is the simplest parameter estimation approach for ARMA models, though not necessarily the most efficient.
The core idea is to equate sample moments with theoretical moments and solve the resulting equations for unknown parameters.
Simplest Example
Estimating the mean of a stationary process by using the sample mean .
Advantages
- Computationally simple
- Provides closed-form solutions for AR models
- Serves as good initial estimates for more sophisticated methods
Limitations
- For MA models, produces less accurate estimates
- May fail to find real solutions (e.g., MA(1) when )
- Results in nonlinear equations for higher-order MA models
- Does not use all information in the data (only first and second moments)