Uniform Moment Bounds of Fisher’s Information with Applications to Time Series by Ngai
نویسنده
چکیده
In this paper, a uniform (over some parameter space) moment bound for the inverse of Fisher’s information matrix is established. This result is then applied to develop moment bounds for the normalized least squares estimate in (nonlinear) stochastic regression models. The usefulness of these results is illustrated using time series models. In particular, an asymptotic expression for the mean squared prediction error of the least squares predictor in autoregressive moving average models is obtained. This asymptotic expression provides a solid theoretical foundation for some model selection criteria.
منابع مشابه
A Hybrid Time Series Clustering Method Based on Fuzzy C-Means Algorithm: An Agreement Based Clustering Approach
In recent years, the advancement of information gathering technologies such as GPS and GSM networks have led to huge complex datasets such as time series and trajectories. As a result it is essential to use appropriate methods to analyze the produced large raw datasets. Extracting useful information from large data sets has always been one of the most important challenges in different sciences,...
متن کاملTREND-CYCLE ESTIMATION USING FUZZY TRANSFORM OF HIGHER DEGREE
In this paper, we provide theoretical justification for the application of higher degree fuzzy transform in time series analysis. Under the assumption that a time series can be additively decomposed into a trend-cycle, a seasonal component and a random noise, we demonstrate that the higher degree fuzzy transform technique can be used for the estimation of the trend-cycle, which is one of the ba...
متن کاملMoment Bounds and Mean Squared Prediction Errors of Long-memory Time Series1 by Ngai
A moment bound for the normalized conditional-sum-of-squares (CSS) estimate of a general autoregressive fractionally integrated moving average (ARFIMA) model with an arbitrary unknown memory parameter is derived in this paper. To achieve this goal, a uniform moment bound for the inverse of the normalized objective function is established. An important application of these results is to establis...
متن کاملNew analytical bounds on the average undershoot in an infinite horizon (s, S) inventory system
We provide new bounds on the average undershoot in an infinite horizon (s, S) inventory system with i.i.d demands with known moments up to order three. The two moment bound improves on Lorden’s bound (Ann. Math. Stat. 1970) for small values of S – s and low values of the coefficient of variation. The three moment bound provides further improvement for negatively skewed demands. The bounds are s...
متن کاملMachine learning algorithms for time series in financial markets
This research is related to the usefulness of different machine learning methods in forecasting time series on financial markets. The main issue in this field is that economic managers and scientific society are still longing for more accurate forecasting algorithms. Fulfilling this request leads to an increase in forecasting quality and, therefore, more profitability and efficiency. In this pa...
متن کامل