Unit Root Tests in Time Series Volume 2 [electronic resource] : Extensions and Developments /
Patterson, K.author.
Testing for a Unit Root is now an essential part of time series analysis but the literature on the topic is so large that knowing where to start is difficult even for the specialist. This book provides a way into the techniques of unit root testing, explaining the pitfalls and nonstandard cases, using practical examples and simulation analysis.
Description based upon print version of record.
Cover; Half-Title; Title; Copyright; Contents; Detailed Contents; List of Tables; List of Figures; Symbols and Abbreviations; Preface; 1 Some Common Themes; Introduction; 1.1 Stochastic processes; 1.2 Stationarity and some of its implications; 1.2.1 A strictly stationary process; 1.2.2 Stationarity up to order m; 1.3 ARMA(p, q) models; 1.4 The long-run variance; 1.5 The problem of a nuisance parameter only identified under the alternative hypothesis; 1.5.1 Structural stability; 1.5.2 Self-exciting threshold autoregression (SETAR); 1.5.3 Bootstrap the test statistics
1.5.4 Illustration: Hog-corn price1.5.4.i Chow test for temporal structural stability; 1.5.4.ii Threshold autoregression; 1.6 The way ahead; Questions; 2 Functional Form and Nonparametric Tests for a Unit Root; Introduction; 2.1 Functional form: linear versus logs; 2.1.1 A random walk and an exponential random walk; 2.1.2 Simulation results; 2.2 A parametric test to discriminate between levels and logs; 2.2.1 Linear and log-linear integrated processes; 2.2.2 Test statistics; 2.2.2.i The KM test statistics; 2.2.2.ii Critical values; 2.2.2.iii Motivation; 2.2.2.iv Power considerations
2.2.3 Illustrations2.2.3.i Ratio of gold to silver prices; 2.2.3.ii World oil production; 2.3 Monotonic transformations and unit root tests based on ranks; 2.3.1 DF rank-based test; 2.3.2 Rank-score test, Breitung and Gouriéroux (1997); 2.3.2.i Serially correlated errors; 2.3.2.ii Simulation results; 2.4 The range unit root test; 2.4.1 The range and new 'records'; 2.4.1.i The forward range unit root test; 2.4.1.ii Robustness of; 2.4.2 The forward-backward range unit root test; 2.4.3 Robustness of; 2.4.4 The range unit root tests for trending alternatives; 2.5 Variance ratio tests
2.5.1 A basic variance ratio test2.5.2 Breitung variance ratio test; 2.6 Comparison and illustrations of the tests; 2.6.1 Comparison of size and power; 2.6.2 Linear or exponential random walks?; 2.6.3 Empirical illustrations; 2.6.3.i Ratio of gold-silver price (revisited); 2.6.3.ii Air revenue passenger miles (US); 2.7 Concluding remarks; Questions; 3 Fractional Integration; Introduction; 3.1 A fractionally integrated process; 3.1.1 A unit root process with fractionally integrated noise; 3.1.2 Binomial expansion of (1-L)d; 3.1.2.i AR coefficients; 3.1.2.ii MA coefficients
3.1.2.iii The fractionally integrated model in terms of the Gamma function3.1.3 Two definitions of an I(d) process, d fractional; 3.1.3.i Partial summation; 3.1.3.ii Direct definition; 3.1.4 The difference between type I and type II processes; 3.1.5 Type I and type II fBM; 3.1.6 Deterministic components and starting value(s); 3.1.6.i Deterministic components; 3.1.6.ii Starting value(s); 3.2 The ARFIMA(p, d, q) model; 3.2.1 Autocovariances and autocorrelations of the; 3.2.1.i Autocovariances; 3.2.1.ii Autocorrelations; 3.2.1.iii Inverse autocorrelations
3.2.2 Graphical properties of some simple ARFIMA models
Includes bibliographical references and index.
Testing for a Unit Root is now an essential part of time series analysis but the literature on the topic is so large that knowing where to start is difficult even for the specialist. This book provides a way into the techniques of unit root testing, explaining the pitfalls and nonstandard cases, using practical examples and simulation analysis.
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Econometrics.
Probability Theory and Stochastic Processes.
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