Modelling Trends and Cycles in Economic Time Series

Cover......Page 1
Contents......Page 6
List of Tables and Figures......Page 10
Series Editor's Foreword......Page 12
1.1 Historical perspective......Page 14
1.2 Overview of the book......Page 23
2.1 The classical trend-cycle decomposition......Page 26
2.2.1 Linear trends......Page 27
2.2.2 Nonlinear trends......Page 28
2.2.3 Segmented trends and smooth transitions......Page 29
Example 2.1 A linear trend for US output per capita......Page 31
Example 2.2 Fitting deterministic trends to UK output......Page 32
Example 2.3 Fitting a smooth transition to US stock prices......Page 35
2.3.1 Simple moving averages......Page 36
2.3.2 Weighted moving averages......Page 37
Example 2.4 Weighted moving average trends for US stock prices......Page 38
2.4.1 Autoregressive processes for the cyclical component......Page 39
Example 2.5 The cyclical component of US output per capita......Page 43
Example 2.6 The cyclical component of UK output......Page 44
Example 2.7 The cyclical component of US stock prices......Page 45
2.5 Some problems associated with the 'classical' approach......Page 46
Example 2.8 Simulating the Slutsky–Yule effect......Page 47
Further reading and background material......Page 49
3.1 An introduction to stochastic trends......Page 52
3.2 Determining the order of integration of a time series......Page 61
Example 3.2 Modelling the FTA All Share index......Page 63
Example 3.3 Modelling US output......Page 65
3.4 Trend stationarity versus difference stationarity......Page 67
Example 3.4 Testing TS versus DS processes for UK equities and US output......Page 71
3.5.1 Unobserved component models......Page 72
3.5.2 The Beveridge–Nelson decomposition......Page 74
Example 3.5 Decomposing UK equities and US output......Page 77
3.5.3 Signal extraction......Page 79
3.5.4 Basic structural models......Page 80
Example 3.6 Basic structural models for UK equities and US output......Page 83
Further reading and background material......Page 85
4.1.1 Symmetric linear filters......Page 88
Example 4.1 The simple MA filter......Page 89
4.1.2 Frequency-domain properties of linear filters......Page 90
Example 4.2 The gain and phase of the simple MA and first differencing filters......Page 94
Example 4.3 Spurious cyclical behaviour......Page 95
4.1.3 Designing a low-pass filter......Page 97
4.1.4 High-pass and band-pass filters......Page 100
Example 4.4 Band-pass business cycle filters......Page 104
4.2.1 The Hodrick–Prescott filter in infinite samples......Page 105
4.2.2 The finite sample H–P filter......Page 107
Example 4.5 Band- pass and Hodrick–Prescott cycles for US output......Page 108
4.3.1 A structural model for the H–P filter......Page 110
4.3.2 The Butterworth filter......Page 112
Further reading and background material......Page 114
5.1.1 Markov models......Page 116
5.1.2 STAR models......Page 120
Example 5.2 A STAR model for UK output......Page 125
5.2.1 Smoothing estimators......Page 127
5.2.2 Kernel regression......Page 128
Example 5.3 nonparametric trends in US stock prices......Page 130
5.3 Nonlinear stochastic trends......Page 132
Further reading and background material......Page 133
6.1.1 Specification and testing for common features......Page 136
6.1.2 Common cycles and codependence......Page 138
6.1.3 Common deterministic trends......Page 140
6.2 Common trends and cycles in a VAR framework......Page 141
Example 6.3 Common trends and cycles in the UK macroeconomy......Page 147
6.3.1 Common trends......Page 150
Example 6.4 A multivariate BSM of the UK macroeconomy......Page 152
6.4 Multivariate filtering......Page 155
Example 6.5 Multivariate detrending of UK consumption and output using a common trend restriction......Page 157
Further reading and background material......Page 158
7 Conclusions......Page 162
Computed Examples......Page 164
References......Page 174
Author Index......Page 184
Subject Index......Page 186