Modelling Trends and Cycles in Economic Time Series

Description

Contents List of Figures 1 Introduction 1.1 Historical Perspective 1.2 Overview of the Book References 2 ‘Classical’ Techniques of Modelling Trends and Cycles 2.1 The Classical Trend-Cycle Decomposition 2.2 Deterministic Trend Models 2.2.1 Linear Trends 2.2.2 Nonlinear Trends 2.2.3 Breaking and Segmented Trends 2.2.4 Smooth Transitions and Fourier Series Approximations 2.3 Estimating Trends Using Moving Averages 2.3.1 Simple Moving Averages 2.3.2 Weighted Moving Averages 2.4 The Cyclical Component 2.4.1 Autoregressive Processes for the Cyclical Component 2.4.2 Estimating the Cyclical Component 2.5 Some Problems Associated with the Classical Approach to Detrending 2.5.1 Further Reading and Background Material References 3 Stochastic Trends and Cycles 3.1 An Introduction to Stochastic Trends 3.2 Determining the Order of Integration of a Time Series 3.3 Some Examples of ARIMA Modelling 3.4 Trend Stationarity Versus Difference Stationarity 3.4.1 Distinguishing Between Trend and Difference Stationarity 3.4.2 Estimating Trends Robustly 3.4.3 Breaking Trends and Unit Root Tests 3.5 Unobserved Component Models and Signal Extraction 3.5.1 Unobserved Component Models 3.5.2 The Beveridge-Nelson Decomposition 3.5.3 Signal Extraction 3.5.4 Basic Structural Models 3.6 Further Reading and Background Material References 4 Filtering Economic Time Series 4.1 Detrending Using Linear Filters 4.1.1 Symmetric Linear Filters 4.1.2 Frequency-Domain Properties of Linear Filters 4.1.3 Designing a Low-Pass Filter 4.1.4 High-Pass and Band-Pass Filters 4.2 The Hodrick-Prescott Filter 4.2.1 The Hodrick-Prescott Filter in Infinite Samples 4.2.2 The Finite Sample H-P Filter 4.2.3 Optimising the Smoothing Parameter and Critiques of H-P Filtering 4.3 Filters and Structural Models 4.3.1 A Structural Model for the H-P Filter 4.3.2 More General Structural Models and Their Filters 4.3.3 Model-Based Filters 4.3.4 Structural Trends and Cycles 4.4 Further Reading and Background Material References 5 Nonlinear and Nonparametric Trend and Cycle Modelling 5.1 Regime Shift Models 5.1.1 Markov Models 5.1.2 STAR Models 5.2 Nonparametric Trends 5.2.1 Smoothing Estimators 5.2.2 Kernel Regression 5.2.3 Local Polynomial Regression 5.3 Nonlinear Stochastic Trends 5.4 Further Reading and Background Material References 6 Multivariate Modelling of Trends and Cycles 6.1 Common Features in Time Series 6.1.1 Specification and Testing of Common Features 6.1.2 Common Cycles and Codependence 6.1.3 Common Deterministic Trends 6.2 Stochastic common trends 6.2.1 Cointegration 6.2.2 Vector Autoregressions with Cointegrated Variables: The VECM 6.2.3 Estimation of VECMs and Tests of Cointegrating Rank 6.2.4 Common Cycles in a VECM 6.3 Multivariate Filtering 6.4 Co-Breaking 6.5 Further Reading and Background Material References 7 Conclusions References Computed Examples Author Index Subject Index