Bootstrap Confidence Bands for Forecast Paths

The problem of forecasting from vector autoregressive models has attracted considerable attention in the literature. The most popular non-Bayesian approaches use large sample normal theory or the bootstrap to evaluate the uncertainty associated with the forecast. The literature has concentrated on the problem of assessing the uncertainty of the prediction for a single period. This paper considers the problem of how to assess the uncertainty when the forecasts are done for a succession of periods. It describes and evaluates bootstrap method for constructing confidence bands for forecast paths. The bands are constructed from forecast paths obtained in bootstrap replications with an optimisation procedure used to find the envelope of the most concentrated paths. The method is shown to have good coverage properties in a Monte Carlo study.vector autoregression, forecast path, bootstrapping, simultaneous statistical inference

On the power of direct tests for rational expectations against the alternative of constant gain learning

In this paper we study the power of direct tests for rational expectations against the constant gain learning alternative. The investigation is by means of a Monte Carlo study. The tests considered use quantitative expectations data and qualitative survey data that has been quantified. The main finding is that the power of tests for rational expectations against constant gain learning may be very small, making it impossible to distinguish the hypotheses.adaptive learning, tests for rational expectations, quantification methods, constant gain least squares

Skewness-Adjusted Bootstrap Confidence Intervals and Confidence Bands for Impulse Response Functions

This Article Investigates The Construction Of Skewness-Adjusted Confidence Intervals And Joint Confidence Bands For Impulse Response Functions From Vector Autoregressive Models. Three Different Implementations Of The Skewness Adjustment Are Investigated. The Methods Are Based On A Bootstrap Algorithm That Adjusts Mean And Skewness Of The Bootstrap Distribution Of The Autoregressive Coefficients Before The Impulse Response Functions Are Computed. Using Extensive Monte Carlo Simulations, The Methods Are Shown To Improve The Coverage Accuracy In Small And Medium Sized Samples And For Unit Root Processes For Both Known And Unknown Lag Orders

Choosing the Number of Topics in LDA Models -- A Monte Carlo Comparison of Selection Criteria

Selecting the number of topics in LDA models is considered to be a difficult task, for which alternative approaches have been proposed. The performance of the recently developed singular Bayesian information criterion (sBIC) is evaluated and compared to the performance of alternative model selection criteria. The sBIC is a generalization of the standard BIC that can be implemented to singular statistical models. The comparison is based on Monte Carlo simulations and carried out for several alternative settings, varying with respect to the number of topics, the number of documents and the size of documents in the corpora. Performance is measured using different criteria which take into account the correct number of topics, but also whether the relevant topics from the DGPs are identified. Practical recommendations for LDA model selection in applications are derived

Constructing Joint Confidence Bands for Impulse Response Functions of VAR Models - A Review

Methods for constructing joint confidence bands for impulse response functions which are commonly used in vector autoregressive analysis are reviewed. While considering separate intervals for each horizon individually still seems to be the most common approach, a substantial number of methods have been proposed for making joint inferences about the complete impulse response paths up to a given horizon. A structured presentation of these methods is provided. Furthermore, existing evidence on the small-sample performance of the methods is gathered. The collected information can help practitioners to decide on a suitable confidence band for a structural VAR analysis.Part of the work on this paper was conducted while the first author was a Fernand Braudel Fellow at the European University Institute in Florence. Financial support from the National Science Center (NCN) through MAESTRO 4: DEC-2013/08/A/HS4/00612 is gratefully acknowledged

Badanie dekompozycji wariancji błędów prognozy przy różnych schematach identyfikacji modeli wektorowej autoregresji za pomocą metody Monte Carlo

The goal of the paper is to investigate the estimation precision of forecast error variance decomposition (FEVD) based on stable structural vector autoregressive models identified using short‑run and long‑run restrictions. The analysis is performed by means of Monte Carlo experiments. It is demonstrated that for processes with roots close to one, selected FEVD parameters can be esti­mated more accurately using recursive restrictions on the long‑run multipliers than under recursive restrictions on the impact effects of shocks. This finding contributes to the discussion of pros and cons of using alternative identification schemes by providing counterexamples for the notion that short‑run identifying restrictions lead to smaller estimation errors than long‑run restrictions.Celem artykułu jest zbadanie dokładności estymacji parametrów dekompozycji wariancji błędów prognozy dla strukturalnych modeli wektorowej autoregresji zidentyfikowanych z użyciem restrykcji na parametry krótko‑ i długookresowe. W analizie wykorzystano eksperymenty Monte Carlo. Wykazano, że dla procesów o pierwiastkach, których wartość zbliżona jest do jedności, wybrane parametry dekompozycji wariancji błędów prognozy można oszacować z większą precyzją przy założeniu trójkątnej macierzy mnożników długookresowych niż przy restrykcji trójkątnej macierzy mnożników bezpośrednich. Uzyskane wyniki wnoszą wkład do dyskusji dotyczącej zalet i wad różnych schematów identyfikacji przez wskazanie kontrprzykładów dla hipotezy, że wykorzystanie restrykcji krótkookresowych prowadzi do mniejszych błędów szacunku niż zastosowanie restrykcji na parametry długookresowe.Narodowe Centrum Nauki, MAESTRO 4: DEC-2013/08/A/HS4/0061

Refined Bonferroni prediction bands for autoregressive models

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.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 wielku przypadkach, do uzyskania stosunkowo wąskich pasm predykcyjnych o odpowiednich prawdopodobieństwach zawierania przyszłej trajektorii zmiennej