Modelling Financial Time Series by Stephen J. Taylor
Pub. Date: April 2008 268pp





SynopsisThis book contains several innovative models for the prices of financial assets. First published in 1986, it is a classic text in the area of financial econometrics. It presents ARCH and stochastic volatility models that are often used and cited in academic research and are applied by quantitative analysts in many banks. Another often-cited contribution of the first edition is the documentation of statistical characteristics of financial returns, which are referred to as stylized facts.  This second edition takes into account the remarkable progress made by empirical researchers during the past two decades from 1986 to 2006. In the new Preface, the author summarizes this progress in two key areas: firstly, measuring, modelling and forecasting volatility; and secondly, detecting and exploiting price trends.

Product Details

Pub. Date: April 2008 Publisher: World Scientific Publishing Company, Incorporated
• Format: Hardcover, 268pp
• Sales Rank: 280,933

ISBN-13: [url=]9789812770844[/url]
• ISBN: [url=]9812770844[/url]
• Edition Number: 2

Table of Contents

Preface to the 2nd edition     xv
Preface to the 1st edition     xxv
Introduction     1
Financial time series     1
About this study     2
The world's major financial markets     3
Examples of daily price series     4
A selective review of previous research     8
Important questions     8
The random walk hypothesis     8
The efficient market hypothesis     10
Daily returns     12
Models     13
Models in this book     15
Stochastic processes     16
General remarks     16
Stationary processes     16
Autocorrelation     17
Spectral density     18
White noise     19
ARMA processes     20
Gaussian processes     23
Linear stochastic processes     23
Their definition     23
Autocorrelation tests     24
Features of Financial Returns     26
Constructing financial time series     26
Sources     26
Time scales     27
Additional information     27
Using futures contracts     28
Prices studied     28
Spot prices     28
Futures prices     30
Commodity futures     30
Financial futures     31
Extended series     32
Average returns and risk premia     32
Annual expected returns     33
Common stocks and ordinary shares     35
Spot commodities     36
Spot currencies     36
Commodity futures     36
Standard deviations     38
Risks compared     39
Futures and contract age     40
Calendar effects     41
Day-of-the-week     41
Stocks     41
Currencies     41
Agricultural futures     42
Standard deviations     42
Month-of-the-year effects for stocks     43
Skewness     44
Kurtosis     44
Plausible distributions     45
Autocorrelation     48
First-lag     49
Lags 1 to 30     50
Tests     50
Non-linear structure     52
Not strict white noise     52
A characteristic of returns      52
Not linear     56
Consequences of non-linear structure     57
Summary     58
Autocorrelation caused by day-of-the-week effects     58
Autocorrelations of a squared linear process     60
Modelling Price Volatility     62
Introduction     62
Elementary variance models     63
Step change, discrete distributions     63
Markov variances, discrete distributions     64
Step variances, continuous distributions     65
Markov variances, continuous distributions     66
A general variance model     67
Notation     69
Modelling variance jumps     69
Modelling frequent variance changes not caused by prices     70
General models     70
Stationary models     72
The lognormal, autoregressive model     73
Modelling frequent variance changes caused by past prices     75
General concepts     75
Caused by past squared returns     76
Caused by past absolute returns     78
ARMACH models     78
Modelling autocorrelation and variance changes     79
Variances not caused by returns     81
Variances caused by returns     82
Parameter estimation for variance models     83
Parameter estimates for product processes     84
Lognormal AR(1)     86
Results     88
Parameter estimates for ARMACH processes     90
Results     92
Summary     93
Results for ARCH processes     95
Forecasting Standard Deviations     97
Introduction     97
Key theoretical results     98
Uncorrelated returns     98
Correlated returns     100
Relative mean square errors     100
Stationary processes     100
Forecasts: methodology and methods     101
Benchmark forecast     101
Parametric forecasts     101
Product process forecasts     102
ARMACH forecasts     103
EWMA forecasts     103
Futures forecasts     104
Empirical RMSE     105
Forecasting results     106
Absolute returns     106
Conditional standard deviations     107
Two leading forecasts     108
More distant forecasts     108
Conclusions about stationarity      110
Another approach     110
Recommended forecasts for the next day     110
Examples     113
Summary     114
The Accuracy of Autocorrelation Estimates     116
Introduction     116
Extreme examples     117
A special null hypothesis     118
Estimates of the variances of sample autocorrelations     119
Some asymptotic results     120
Linear processes     121
Non-linear processes     122
Interpreting the estimates     123
The estimates for returns     124
Accurate autocorrelation estimates     126
Rescaled returns     127
Variance estimates for recommended coefficients     128
Exceptional series     130
Simulation results     130
Autocorrelations of rescaled processes     131
Summary     132
Testing the Random Walk Hypothesis     133
Introduction     133
Test methodology     134
Distributions of sample autocorrelations     135
Asymptotic limits     136
Finite samples     136
A selection of test statistics      137
Autocorrelation tests     137
Spectral tests     138
The runs test     140
The price-trend hypothesis     141
Price-trend autocorrelations     141
An example     142
Price-trend spectral density     143
Tests for random walks versus price-trends     143
Consequences of data errors     145
Results of random walk tests     146
Stocks     150
Commodities and currencies     152
About the rest of this chapter     156
Some test results for returns     157
Power comparisons     159
Testing equilibrium models     161
Stocks     161
Simulation results     163
Tests     165
Other equilibrium models     166
Conclusion     166
Institutional effects     167
Limit rules     167
Bid-ask spreads     169
Results for subdivided series     169
Conclusions     170
Summary     172
Correlation between test values for two related series     172
Forecasting Trends in Prices     174
Introduction      174
Price-trend models     174
A non-linear trend model     176
A linear trend model     176
Estimating the trend parameters     178
Methods     178
Futures     179
Spots     181
Accuracy     183
Some results from simulations     183
Estimates     183
A puzzle solved     185
Forecasting returns: theoretical results     185
The next return     186
More distant returns     187
Sums of future returns     187
Empirical forecasting results     188
Benchmark forecasts     188
Price-trend forecasts     189
Summary statistics     189
Futures     190
Spots     192
Further forecasting theory     193
Expected changes in prices     193
Forecasting the direction of the trend     194
Forecasting prices     194
Summary     194
Evidence Against the Efficiency of Futures Markets     196
Introduction     196
The efficient market hypothesis     197
Problems raised by previous studies      199
Filter rules     199
Benchmarks     200
Significance     201
Optimization     201
Problems measuring risk and return     201
Returns     201
Risk     202
Necessary assumptions     203
Trading conditions     203