Robust methods similar to exponential smoothing are suggested in this paper. First previous results for exponential smoothing in L1
are generalized using the regression quantiles, including a generalization to more parameters. Then a method based on the classical sign test is introduced that should deal not only with outliers but also with level shifts, including a detection of change points. Properties of various approaches are investigated by means of a simulation study. A real data example is used as an illustration.
The paper deals with extensions of exponential smoothing type methods for univariate time series with irregular observations. An alternative method to Wright's modification of simple exponential smoothing based on the corresponding ARIMA process is suggested. Exponential smoothing of order for irregular data is derived. A similar method using a DLS () estimation of polynomial trend of order is derived as well. Maximum likelihood parameters estimation for forecasting methods in irregular time series is suggested. The suggested methods are compared with the existing ones in a simulation numerical study.
Recursive time series methods are very popular due to their numerical simplicity. Their theoretical background is usually based on Kalman filtering in state space models (mostly in dynamic linear systems). However, in time series practice one must face frequently to outlying values (outliers), which require applying special methods of robust statistics. In the paper a simple robustification of Kalman filter is suggested using a simple truncation of the recursive residuals. Then this concept is applied mainly to various types of exponential smoothing (recursive estimation in Box-Jenkins models with outliers is also mentioned). The methods are demonstrated using simulated data.
The robust recursive algorithm for the parameter estimation and the volatility prediction in GARCH models is suggested. It seems to be useful for various financial time series, in particular for (high-frequency) log returns contaminated by additive outliers. The proposed procedure can be effective in the risk control and regulation when the prediction of volatility is the main concern since it is capable to distinguish and correct outlaid bursts of volatility. This conclusion is demonstrated by simulations and real data examples presented in the paper.