Estimation of parameters in exponential autoregressive models.
This paper discusses the estimation of parameters in second order exponential autoregressive models.
Estimation of parameters of RCA with exponential marginals.
Estimation of the Distribution Function of Noise in Stationary Processes.
Estimation of variances in a heteroscedastic RCA(1) model
The paper concerns with a heteroscedastic random coefficient autoregressive model (RCA) of the form . Two different procedures for estimating or , respectively, are described under the special seasonal behaviour of . For both types of estimators strong consistency and asymptotic normality are proved.
Estimation paramétrique d'un processus de diffusion avec retards
Estimation récursive des paramètres d'un modèle de régression, variant au cours du temps
Estimation semi-paramétrique d'un modèle autorégressif stationnaire multiindice non nécessairement causal
Every continuous first order autoregressive stochastic process is a Gaussian process
EWMA historical volatility estimators
Expolynomial Smoothing of Autocorrelated Time Series.
Exponential smoothing and resampling techniques in time series prediction
Time series analysis deals with records that are collected over time. The objectives of time series analysis depend on the applications, but one of the main goals is to predict future values of the series. These values depend, usually in a stochastic manner, on the observations available at present. Such dependence has to be considered when predicting the future from its past, taking into account trend, seasonality and other features of the data. Some of the most successful forecasting methods are...
Exponential smoothing based on L-estimation
Robust methods similar to exponential smoothing are suggested in this paper. First previous results for exponential smoothing in 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...
Exponential smoothing for irregular data
Various types of exponential smoothing for data observed at irregular time intervals are surveyed. Double exponential smoothing and some modifications of Holt’s method for this type of data are suggested. A real data example compares double exponential smoothing and Wright’s modification of Holt’s method for data observed at irregular time intervals.
Exponential smoothing for irregular time series
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 m for irregular data is derived. A similar method using a DLS **discounted least squares** estimation of polynomial trend of order m is derived as well. Maximum likelihood parameters estimation for forecasting...
Exponential smoothing for time series with outliers
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...
Extrapolation in fractional autoregressive models
The naïve and the least-squares extrapolation are investigated in the fractional autoregressive models of the first order. Some explicit formulas are derived for the one and two steps ahead extrapolation.
Extrapolations in non-linear autoregressive processes
We derive a formula for -step least-squares extrapolation in non-linear AR processes and compare it with the naïve extrapolation. The least- squares extrapolation depends on the distribution of white noise. Some bounds for it are derived that depend only on the expectation of white noise. An example shows that in general case the difference between both types of extrapolation can be very large. Further, a formula for least-squares extrapolation in multidimensional non-linear AR() process is derived....