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Ghiglietti, Andrea; Ieva, Francesca; Paganoni, Anna Maria; Aletti, Giacomo
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In functional linear regression, the parameters estimation involves solving a non necessarily wellposed problem, which has points of contact with a range of methodologies, including statistical smoothing, deconvolution and projection on finitedimensional subspaces. We discuss the standard approach based explicitly on functional principal components analysis, nevertheless the choice of the number of basis components remains something subjective and not always properly discussed and justified. In this work we discuss inferential properties of least square estimation in this context, with different choices of projection subspaces, as well as we study asymptotic behaviour increasing the dimension of subspaces.
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By
Bouzebda, S.; Didi, S.; El Hajj, L.
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1 Citations
In the present paper, we are mainly concerned with the nonparametric estimation of the density as well as the regression function, related to stationary and ergodic continuous time processes, by using orthonormal wavelet bases. We provide the strong uniform consistency properties with rates of these estimators, over compact subsets of ℝ^{d}, under a general ergodic condition on the underlying processes. We characterize the asymptotic normality of considered waveletbased estimators under easily verifiable conditions. The asymptotic properties of these estimators are obtained by means of the martingale approach.
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By
Saidane, Mohamed; Lavergne, Christian
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The deficiencies of stationary models applied to financial time series are well documented. A special form of nonstationarity, where the underlying generator switches between (approximately) stationary regimes, seems particularly appropriate for financial markets. We use a dynamic switching (modelled by a hidden Markov model) combined with a linear conditionally heteroskedastic latent factor model in a hybrid mixedstate latent factor model (MSFM) and discuss the practical details of training such models with a new approximated version of the Viterbi algorithm in conjunction with the expectationmaximization (EM) algorithm to iteratively estimate the model parameters in a maximumlikelihood sense. The performance of the MSFM is evaluated on both simulated and financial data sets. On the basis of outofsample forecast encompassing tests as well as other measures for forecasting accuracy, our results indicate that the use of this new method yields overall better forecasts than those generated by competing models.
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By
Wang, Lihong
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2 Citations
This paper studies nonparametric kernel type (smoothed) estimation of quantiles for long memory stationary sequences. The uniform strong consistency and asymptotic normality of the estimates with rates are established. Finite sample behaviors are investigated in a small Monte Carlo simulation study.
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By
Wang, Xinghui; Hu, Shuhe
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In this paper, we consider a stationary autoregressive AR(p) time series
$$y_t=\phi _0+\phi _1y_{t1}+\cdots +\phi _{p}y_{tp}+u_t$$
. A selfweighted Mestimator for the AR(p) model is proposed. The asymptotic normality of this estimator is established, which includes the asymptotic properties under the innovations with finite or infinite variance. The result generalizes and improves the known one in the literature.
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Nkurunziza, Sévérien
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1 Citations
This paper deals with a testing problem for each of the interaction parameters of the Lotka–Volterra ordinary differential equations system~(ODE). In short, when the rates of birth and death are fixed, we would like to test if each interaction parameter is higher or lower than a fixed reference rate. We choose a statistical model where the actual population sizes are modelled as random perturbations of the solutions to this ODE. By assuming that the random perturbations follow correlated Ornstein–Uhlenbeck processes, we propose the uniformly most powerful test concerning each interaction parameter of the ODE and, we establish the asymptotic properties of the test. Further, we illustrate the suggested test on the Canadian mink–muskrat data set.
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By
Battaglia, Francesco; Protopapas, Mattheos K.
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3 Citations
Nonlinear nonstationary models for time series are considered, where the series is generated from an autoregressive equation whose coefficients change both according to time and the delayed values of the series itself, switching between several regimes. The transition from one regime to the next one may be discontinuous (selfexciting threshold model), smooth (smooth transition model) or continuous linear (piecewise linear threshold model). A genetic algorithm for identifying and estimating such models is proposed, and its behavior is evaluated through a simulation study and application to temperature data and a financial index.
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By
Kumar, T. L. Mohan; Prajneshu
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Realworld timeseries are rarely purely linear or nonlinear and often contain both these patterns. Therefore, in this article, we have developed four hybrid models by combining linear seasonal autoregressive integrated moving average (SARIMA) and nonlinear support vector regression (NLSVR) models for timeseries forecasting. Further, particle swarm optimization (PSO), which is a very efficient populationbased global stochastic optimization technique, is employed to estimate the hyperparameters of resultant models. A relevant computer program is written in MATLAB function (m file). The SAS and MATLAB software packages are used for carrying out data analysis. Subsequently, as an illustration, the models are applied to allIndia monthly marine products export timeseries data. Superiority of hybrid models over individual SARIMA and NLSVR models is demonstrated for the data under consideration using root mean square error (RMSE) and mean absolute error (MAE) criteria.
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By
Weba, Michael; Dörmann, Nora
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Let
$$\mu $$
be the expected value of a random variable and
$$\bar{X}_n$$
the corresponding sample mean of n observations. If the transformed expectation
$$f(\mu )$$
is to be estimated by
$$f\left( \bar{X}_n\right) $$
then the delta method is a widely used tool to describe the asymptotic behaviour of
$$f\left( \bar{X}_n\right) $$
. Regarding bias and variance, however, conventional theorems require independent observations as well as boundedness conditions of f being violated even by “simple” functions such as roots or logarithms. It is shown that asymptotic expansions for bias and variance still hold if restrictive boundedness conditions are replaced by considerably weaker requirements upon the global growth of f. Moreover, observations are allowed to be dependent.
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By
Kim, HeeYoung; Weiß, Christian H.; Möller, Tobias A.
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For the modeling of bounded counts, the binomial distribution is a common choice. In applications, however, one often observes an excessive number of zeros and extrabinomial variation, which cannot be explained by a binomial distribution. We propose statistics to evaluate the number of zeros and the dispersion with respect to a binomial model, which is based on the sample binomial index of dispersion and the sample binomial zero index. We apply this index to autocorrelated counts generated by a binomial autoregressive process of order one, which also includes the special case of independent and identically (i. i. d.) bounded counts. The limiting null distributions of the proposed test statistics are derived. A MonteCarlo study evaluates their size and power under various alternatives. Finally, we present two realdata applications as well as the derivation of effective sample sizes to illustrate the proposed methodology.
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