Estimation in the Time Domain

This chapter talks about the unknown parameters (μ, Φ1,…, Φp, θ1,…, θq, σ2)' and the unknown orders (p,d,q) in the autoregressive integrated moving average (ARIMA) model. It discusses the estimation of these parameters from a time-domain perspective. The chapter describes several statistical procedures used to estimate these parameters which include classical method of moments, autoregressive models (AR), moving average models (MA), autoregressive moving average model (ARMA) and the method of maximum likelihood estimates (MLE). It also discusses two commonly used methods of order selection criterion, the final prediction error (FPE) and the Akaike's information criterion (AIC). Another commonly used order selection criterion is the Bayesian information criterion (BIC), which attempts to correct the overfitting nature of the AIC. Finally, the chapter highlights three stages of model building: model specification (choosing ARIMA), model identification (estimation) and model checking (diagnostic). Controlled Vocabulary Terms autoregressive integrated moving average process; autoregressive model; autoregressive moving average process; maximum likelihood estimator; moving average model; time domain