Refined Bonferroni Prediction Bands for Autoregressive Models

• Autorzy: Anna Staszewska-Bystrova

Warianty tytułu

Zmodyfikowane pasma predyjkcyjne Bonferroniego dla modeli autoregresyjnych

• Języki publikacji: EN

Abstrakty

EN

Joint prediction bands are often constructed using Bonferroni's inequality. The drawback of such bands may be their large width and excessive coverage probability. The paper proposes two refinements to the basic Bonferroni method of constructing bootstrap prediction bands. These are based on higher order inequalities and optimization of the width of the band. The procedures are applied to the problem of predicting univariate autoregressive processes. Their properties are studied by means of Monte Carlo experiments. It is shown that the proposed methods lead, in many scenarios, to obtaining relatively narrow prediction bands with desired coverage probabilities. (original abstract)

Pasma predykcyjne konstruuje się często z użyciem nierówności Bonferroniego. Wadą takich pasm może być ich duża rozpiętość i zawyżone prawdopodobieństwo zawierania przyszłej trajektorii prognozowanej zmiennej. W artykule zaproponowano dwie poprawki dla metody konstrukcji bootstrapowych pasm predykcyjnych Bonferroniego wykorzystujące nierówności wyższego rzędu i procedurę minimalizacji szerokości pasma. Metody zastosowano do prognozowania jednowymiarowych procesów autoregresyjnych. Ich właściwości zbadano za pomocą eksperymentów Monte Carlo. Wykazano, że zaproponowane procedury prowadzą, w wielu przypadkach, do uzyskania stosunkowo wąskich pasm predykcyjnych o odpowiednich prawdopodobieństwach zawierania przyszłej trajektorii zmiennej. (abstrakt oryginalny)

Słowa kluczowe

EN

Autoregression models; Forecasting methodology; Nonparametric estimation; Bootstrap

PL

Modele autoregresji; Metodologia prognozowania; Estymacja nieparametryczna; Metody samowsporne

• Czasopismo: Przegląd Statystyczny
• Rocznik: 2018
• Tom: 65
• Numer: z. 2
• Strony: 155--172

Twórcy

autor

Anna Staszewska-Bystrova

• University of Lodz, Poland

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