Modelling Trends and Cycles in Economic Time Series

by Mills, Terence C.

• ISBN13: 9781403902092
• ISBN10: 1403902097
• Format: Paperback
• Copyright: 2003-09-17
• Publisher: Palgrave Macmillan

Summary

Modelling trends and cycles in economic time series has a long history, with the use of linear trends and moving averages forming the basic tool kit of economists until the 1970s. Several developments in econometrics then led to an overhaul of the techniques used to extract trends and cycles from time series. Terence Mills introduces these various approaches to allow students and researchers to appreciate the variety of techniques and the considerations that underpin their choice for modelling trends and cycles.

Author Biography

Terence C. Mills is Professor of Applied Statistics and Econometrics, Department of Economics, Loughborough University, UK.

Table of Contents

List of Tables and Figures	ix
Series Editor's Foreword	xi
1 Introduction	1	(12)
1.1 Historical perspective	1	(9)
1.2 Overview of the book	10	(3)
2 'Classical' Techniques of Modelling Trends and Cycles	13	(26)
2.1 The classical trend-cycle decomposition	13	(1)
2.2 Deterministic trend models	14	(4)
2.2.1 Linear trends	14	(1)
2.2.2 Nonlinear trends	15	(1)
2.2.3 Segmented trends and smooth transitions	16	(2)
Example 2.1 A linear trend for US output per capita	18	(1)
Example 2.2 Fitting deterministic trends to UK output	19	(3)
Example 2.3 Fitting a smooth transition to US stock prices	22	(1)
2.3 Estimating trends using moving averages	23	(2)
2.3.1 Simple moving averages	23	(1)
2.3.2 Weighted moving averages	24	(1)
Example 2.4 Weighted moving average trends for US stock prices	25	(1)
2.4 The cyclical component	26	(4)
2.4.1 Autoregressive processes for the cyclical component	26	(4)
2.4.2 Estimating the cyclical component	30	(1)
Example 2.5 The cyclical component of US output per capita	30	(1)
Example 2.6 The cyclical component of UK output	31	(1)
Example 2.7 The cyclical component of US stock prices	32	(1)
2.5 Some problems associated with the 'classical' approach	33	(1)
Example 2.8 Simulating the Slutsky-Yule effect	34	(2)
Further reading and background material	36	(3)
3 Stochastic Trends and Cycles	39	(36)
3.1 An introduction to stochastic trends	39	(9)
3.2 Determining the order of integration of a time series	48	(2)
3.3 Some examples of ARIMA modelling	50	(1)
Example 3.1 Modelling the dollar/sterling exchange rate	50	(1)
Example 3.2 Modelling the FTA All Share index	50	(2)
Example 3.3 Modelling US output	52	(2)
3.4 Trend stationarity versus difference stationarity	54	(4)
Example 3.4 Testing TS versus DS processes for UK equities and US output	58	(1)
3.5 Unobserved component models and signal extraction	59	(5)
3.5.1 Unobserved component models	59	(2)
3.5.2 The Beveridge-Nelson decomposition	61	(3)
Example 3.5 Decomposing UK equities and US output	64	(6)
3.5.3 Signal extraction	66	(1)
3.5.4 Basic structural models	67	(3)
Example 3.6 Basic structural models for UK equities and US output	70	(2)
Further reading and background material	72	(3)
4 Filtering Economic Time Series	75	(28)
4.1 Detrending using linear filters	75	(1)
4.1.1 Symmetric linear filters	75	(1)
Example 4.1 The simple MA filter	76	(5)
4.1.2 Frequency-domain properties of linear filters	77	(4)
Example 4.2 The gain and phase of the simple MA and first differencing filters	81	(1)
Example 4.3 Spurious cyclical behaviour	82	(9)
4.1.3 Designing a low-pass filter	84	(3)
4.1.4 High-pass and band-pass filters	87	(4)
Example 4.4 Band-pass business cycle filters	91	(1)
4.2 The Hodrick-Prescott filter	92	(5)
4.2.1 The Hodrick-Prescott filter in infinite samples	92	(2)
4.2.2 The finite sample H-P filter	94	(1)
4.2.3 Optimising the smoothing parameter	95	(2)
Example 4.5 Band-pass and Hodrick-Prescott cycles for US output	97	(1)
Example 4.6 H-P filtering of UK output	97	(1)
4.3 Filters and structural models	97	(4)
4.3.1 A structural model for the H-P filter	97	(2)
4.3.2 The Butterworth filter	99	(2)
Further reading and background material	101	(2)
5 Nonlinear and Nonparametric Trend Modelling	103	(20)
5.1 Regime shift models	103	(4)
5.1.1 Markov models	103	(4)
Example 5.1 A Markov switching model for US output	107	(5)
5.1.2 STAR models	107	(5)
Example 5.2 A STAR model for UK output	112	(2)
5.2 Nonparametric trends	114	(3)
5.2.1 Smoothing estimators	114	(3)
5.2.2 Kernel regression	117	(1)
5.2.3 Local polynomial regression
Example 5.3 nonparametric trends in US stock prices	117	(2)
5.3 Nonlinear stochastic trends	119	(1)
Further reading and background material	120	(3)
6 Multivariate Modelling of Trends and Cycles	123	(26)
6.1 Common features in time series	123	(4)
6.1.1 Specification and testing for common features	123	(2)
6.1.2 Common cycles and codependence	125	(2)
Example 6.1 Is there a common cycle in US and Canadian output?	127	(1)
6.1.3 Common deterministic trends	127	(1)
Example 6.2 Common trends in the Victorian economy	128	(1)
6.2 Common trends and cycles in a VAR framework	128	(6)
Example 6.3 Common trends and cycles in the UK macroeconomy	134	(3)
6.3 Multivariate basic structural models	137	(2)
6.3.1 Common trends	137	(2)
6.3.2 Common cycles	139	(1)
Example 6.4 A multivariate BSM of the UK macroeconomy	139	(3)
6.4 Multivariate filtering	142	(2)
Example 6.5 Multivariate detrending of UK consumption and output using a common trend restriction	144	(1)
Further reading and background material	145	(4)
7 Conclusions	149	(2)
Computed Examples	151	(10)
References	161	(10)
Author Index	171	(2)
Subject Index	173