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Introduction to Modern Time Series Analysis

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This book contains the most important approaches to analyze time series which may be stationary or nonstationary. It starts with modeling and forecasting univariate time series and then presents Granger causality tests and vector autoregressive models for multiple stationary time series. It also covers modeling volatilities of financial time series with autoregressive conditional heteroskedastic models.

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Contents
 Preface .................................................................................................. V
1 Introduction and Basics........................................................................ 11.1 The Historical Development of Time Series Analysis ................... 21.2 Graphical Representations of Economic Time Series .................... 51.3 Ergodicity and Stationarity ........................................................... 121.4 The Wold Decomposition............................................................. 21References ............................................................................................ 22
2 Univariate Stationary Processes ........................................................ 272.1 Autoregressive Processes.............................................................. 272.1.1 First Order Autoregressive Processes .................................... 272.1.2 Second Order Autoregressive Processes ............................... 402.1.3 Higher Order Autoregressive Processes ................................ 492.1.4 The Partial Autocorrelation Function .................................... 522.1.5 Estimating Autoregressive Processes .................................... 562.2 Moving Average Processes........................................................... 572.2.1 First Order Moving Average Processes ................................. 582.2.2 Higher Order Moving Average Processes ............................. 642.3 Mixed Processes ........................................................................... 672.3.1 ARMA(1,1) Processes ........................................................... 672.3.2 ARMA(p,q) Processes ........................................................... 732.4 Forecasting.................................................................................... 752.4.1 Forecasts with Minimal Mean Squared Errors ...................... 752.4.2 Forecasts of ARMA(p,q) Processes....................................... 802.4.3 Evaluation of Forecasts ......................................................... 842.5The Relation between Econometric Models and  ARMA Processes.......................................................................... 87References ............................................................................................ 88
3 Granger Causality............................................................................... 933.1 The Definition of Granger Causality ............................................ 953.2 Characterisations of Causal Relations in Bivariate Models.......... 97
VIII Contents
3.2.1 Characterisations of Causal Relations using the Autoregressive and Moving Average Representations ......... 973.2.2 Characterising Causal Relations by Using the Residuals of the Univariate Processes.................................................... 993.3 Causality Tests............................................................................ 1023.3.1 The Direct Granger Procedure............................................. 1023.3.2 The Haugh-Pierce Test ........................................................ 1063.3.3 The Hsiao Procedure ........................................................... 1103.4 Applying Causality Tests in a Multivariate Setting.................... 1143.4.1 The Direct Granger Procedure with More Than Two Variables ............................................................................. 1143.4.2Interpreting the Results of Bivariate Tests in Systems With More Than Two Variables ......................................... 1173.5 Concluding Remarks .................................................................. 118References .......................................................................................... 120
4 Vector Autoregressive Processes ..................................................... 1254.1 Representation of the System ..................................................... 1274.2 Granger Causality ....................................................................... 1364.3 Impulse Response Analysis ........................................................ 1384.4 Variance Decomposition ............................................................ 1444.5 Concluding Remarks .................................................................. 149References .......................................................................................... 150
5 Nonstationary Processes................................................................... 1535.1Forms of Nonstationarity............................................................ 1535.2159Trend Elimination ...................................................................... 5.3 Unit Root Tests ........................................................................... 1635.3.1 Dickey-Fuller Tests ............................................................. 1655.3.2 The Phillips-Perron Test ...................................................... 1715.3.3 Unit Root Tests and Structural Breaks ................................ 1765.3.4 A Test with the Null Hypothesis of Stationarity ................. 1785.4 Decomposition of Time Series ................................................... 1805.5 Further Developments ................................................................ 1875.5.1 Fractional Integration .......................................................... 1875.5.2 Seasonal Integration ............................................................ 1895.6Deterministic versus Stochastic Trends in Economic  Time Series ................................................................................. 191References .......................................................................................... 194
6 Cointegration..................................................................................... 1996.1 Definition and Properties of Cointegrated Processes ................. 203
Contents IX
6.2 Cointegration in Single Equation Models: Representation,  Estimation and Testing ............................................................... 2056.2.1Bivariate Cointegration ....................................................... 2056.2.2 Cointegration with More Than Two Variables.................... 2086.2.3 Testing Cointegration in Static Models ............................... 2096.2.4 Testing Cointegration in Dynamic Models.......................... 2136.3 Cointegration in Vector Autoregressive Models ........................ 2186.3.1 The Vector Error Correction Representation....................... 2196.3.2 The Johansen Approach....................................................... 2226.3.3 Analysis of Vector Error Correction Models....................... 2296.4 Cointegration and Economic Theory.......................................... 234References .......................................................................................... 235
7 Autoregressive Conditional Heteroskedasticity ............................. 2417.1 ARCH Models ............................................................................ 2457.1.1245Definition and Representation............................................. 7.1.2 Unconditional Moments ...................................................... 2487.1.3 Temporal Aggregation......................................................... 2497.2 Generalised ARCH Models ........................................................ 2527.2.1 GARCH Models .................................................................. 2527.2.2 The GARCH(1,1) process ................................................... 2547.2.3 Nonlinear Extensions........................................................... 2577.3 Estimation and Testing ............................................................... 259 7.4 ARCH/GARCH Models as Instruments of Financial  Market Analysis.......................................................................... 261References .......................................................................................... 263
Index of Names and Authors ................................................................ 267
Subject Index.......................................................................................... 271
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