<p><br/></p><p>1 Introduction and Basics........................................................................1<br/>1.1 The Historical Development of Time Series Analysis ...................2<br/>1.2 Graphical Representations of Economic Time Series ....................5<br/>1.3 Ergodicity and Stationarity ...........................................................12<br/>1.4 The Wold Decomposition.............................................................21<br/>References ............................................................................................22<br/>2 Univariate Stationary Processes ........................................................27<br/>2.1 Autoregressive Processes..............................................................27<br/>2.1.1 First Order Autoregressive Processes....................................27<br/>2.1.2 Second Order Autoregressive Processes ...............................40<br/>2.1.3 Higher Order Autoregressive Processes ................................49<br/>2.1.4 The Partial Autocorrelation Function ....................................52<br/>2.1.5 Estimating Autoregressive Processes ....................................56<br/>2.2 Moving Average Processes...........................................................57<br/>2.2.1 First Order Moving Average Processes.................................58<br/>2.2.2 Higher Order Moving Average Processes .............................64<br/>2.3 Mixed Processes ...........................................................................67<br/>2.3.1 ARMA(1,1) Processes ...........................................................67<br/>2.3.2 ARMA(p,q) Processes ...........................................................73<br/>2.4 Forecasting....................................................................................75<br/>2.4.1 Forecasts with Minimal Mean Squared Errors ......................75<br/>2.4.2 Forecasts of ARMA(p,q) Processes.......................................80<br/>2.4.3 Evaluation of Forecasts .........................................................84<br/>2.5 The Relation between Econometric Models and<br/>ARMA Processes..........................................................................87<br/>References ............................................................................................ 88<br/>3 Granger Causality...............................................................................93<br/>3.1 The Definition of Granger Causality ............................................95<br/>3.2 Characterisations of Causal Relations in Bivariate Models..........97<br/>VIII Contents<br/>3.2.1 Characterisations of Causal Relations using the<br/>Autoregressive and Moving Average Representations .........97<br/>3.2.2 Characterising Causal Relations by Using the Residuals<br/>of the Univariate Processes....................................................99<br/>3.3 Causality Tests............................................................................102<br/>3.3.1 The Direct Granger Procedure.............................................102<br/>3.3.2 The Haugh-Pierce Test ........................................................106<br/>3.3.3 The Hsiao Procedure ...........................................................110<br/>3.4 Applying Causality Tests in a Multivariate Setting....................114<br/>3.4.1 The Direct Granger Procedure with More Than Two<br/>Variables .............................................................................114<br/>3.4.2 Interpreting the Results of Bivariate Tests in Systems<br/>With More Than Two Variables .........................................117<br/>3.5 Concluding Remarks ..................................................................118<br/>References ..........................................................................................120<br/>4 Vector Autoregressive Processes .....................................................125<br/>4.1 Representation of the System .....................................................127<br/>4.2 Granger Causality .......................................................................136<br/>4.3 Impulse Response Analysis ........................................................138<br/>4.4 Variance Decomposition ............................................................144<br/>4.5 Concluding Remarks ..................................................................149<br/>References ..........................................................................................150<br/>5 Nonstationary Processes...................................................................153<br/>5.1 Forms of Nonstationarity............................................................153<br/>5.2 Trend Elimination ......................................................................159<br/>5.3 Unit Root Tests...........................................................................163<br/>5.3.1 Dickey-Fuller Tests .............................................................165<br/>5.3.2 The Phillips-Perron Test......................................................171<br/>5.3.3 Unit Root Tests and Structural Breaks ................................176<br/>5.3.4 A Test with the Null Hypothesis of Stationarity .................178<br/>5.4 Decomposition of Time Series ...................................................180<br/>5.5 Further Developments ................................................................187<br/>5.5.1 Fractional Integration ..........................................................187<br/>5.5.2 Seasonal Integration ............................................................189<br/>5.6 Deterministic versus Stochastic Trends in Economic<br/>Time Series .................................................................................191<br/>References ..........................................................................................194<br/>6 Cointegration.....................................................................................199<br/>6.1 Definition and Properties of Cointegrated Processes .................203<br/>Contents IX<br/>6.2 Cointegration in Single Equation Models: Representation,<br/>Estimation and Testing ...............................................................205<br/>6.2.1 Bivariate Cointegration .......................................................205<br/>6.2.2 Cointegration with More Than Two Variables....................208<br/>6.2.3 Testing Cointegration in Static Models ...............................209<br/>6.2.4 Testing Cointegration in Dynamic Models..........................213<br/>6.3 Cointegration in Vector Autoregressive Models ........................218<br/>6.3.1 The Vector Error Correction Representation.......................219<br/>6.3.2 The Johansen Approach.......................................................222<br/>6.3.3 Analysis of Vector Error Correction Models.......................229<br/>6.4 Cointegration and Economic Theory..........................................234<br/>References ..........................................................................................235<br/>7 Autoregressive Conditional Heteroskedasticity .............................241<br/>7.1 ARCH Models ............................................................................245<br/>7.1.1 Definition and Representation.............................................245<br/>7.1.2 Unconditional Moments ......................................................248<br/>7.1.3 Temporal Aggregation.........................................................249<br/>7.2 Generalised ARCH Models ........................................................252<br/>7.2.1 GARCH Models ..................................................................252<br/>7.2.2 The GARCH(1,1) process ...................................................254<br/>7.2.3 Nonlinear Extensions...........................................................257<br/>7.3 Estimation and Testing ...............................................................259<br/>7.4 ARCH/GARCH Models as Instruments of Financial<br/>Market Analysis..........................................................................261<br/>References ..........................................................................................263<br/>Index of Names and Authors ................................................................267<br/>Subject Index..........................................................................................27</p>