Modelling trends and cycles in economic time series
In: Palgrave texts in econometrics
Intro -- 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.