A comparison between parallel algorithms for system parameter estimation in dynamic linear models (Q2711705)

A recursive estimation algorithm for the system parameters of dynamic linear models is proposed. Usually, a dynamic linear model describes a relationship between a sequence of \(c\)-variate (\(c\geq 1\)) observable random vectors \(y_{t}\) and a sequence of \(k\)-variate (\(k\geq 1 \)) unobservable random vectors \(x_{t}\) (usually referred to as the state vector), \(t=1,2,\dots,\) given by the following stochastic system: NEWLINE\[NEWLINEx_{t} =M_{t}x_{t-1}+u_{t},\quad y_{t}=H_{t}x_{t}+v_{t},NEWLINE\]NEWLINE where \(H_{t}\) is a known matrix, \(v_{t}\equiv WN(0,R_{t})\) is the vector of measurement errors, and \(u_{t}\equiv WN(0,Q_{t})\) is the system error vector. In many applications, the system parameter \(\theta _{t}:=vec(M_{t}^{'})\) is not known. When dealing with high-frequency time series, statistical procedures giving reliable estimates of unknown parameters \(\theta_{t}\) and forecasts in real time are required. For its estimation, many methods have been proposed, but only two methods, based on the extended Kalman filter and on parallel processing, are recursive. The recursive estimation methods are usually preferred to maximum likelihood estimators. The recursive estimation method proposed in this paper is compared with some other algorithms via Monte Carlo simulations. Consistency properties of the algorithms are also verified empirically.