Complete Solutions Manual – Time Series Analysis With Applications in R (2nd Ed) by Cryer & Chan, NEWEST VERSION

Solutions Manual –

Time Series Analysis With Applications In R
By Cryer & Chan


2nd Edition

,x Contents


CHAPTER 1 INTRODUCTION ...................................... 1
1.1 Examples Of Time Series ........................................... 1
1.2 A Model-Building Strategy .......................................... 8
1.3 Time Series Plots In History ........................................ 8
1.4 An Overview Of The Book ........................................... 9
Exercises ................................................................... 10

CHAPTER 2 FUNDAMENTAL CONCEPTS ...................... 11
2.1 Time Series And Stochastic Processes .......................... 11
2.2 Means, Variances, And Covariances ............................ 11
2.3 Stationarity ......................................................... 16
2.4 Summary ............................................................ 19
Exercises ................................................................... 19
Appendix A: Expectation, Variance, Covariance, And Correlation . 24

CHAPTER 3 TRENDS .......................................... 27
3.1 Deterministic Versus Stochastic Trends ........................ 27
3.2 Estimation Of A Constant Mean .................................. 28
3.3 Regression Methods............................................... 30
3.4 Reliability And Efficiency Of Regression Estimates ............ 36
3.5 Interpreting Regression Output .................................. 40
3.6 Residual Analysis .................................................. 42
3.7 Summary ............................................................ 50
Exercises ................................................................... 50

CHAPTER 4 MODELS FOR STATIONARY TIME SERIES ...... 55
4.1 General Linear Processes ......................................... 55
4.2 Moving Average Processes ....................................... 57
4.3 Autoregressive Processes ......................................... 66
4.4 The Mixed Autoregressive Moving Average Model ............ 77
4.5 Invertibility ......................................................... 79
4.6 Summary ............................................................ 80
Exercises ................................................................... 81
Appendix B: The Stationarity Region For An Ar(2) Process.......... 84
Appendix C: The Autocorrelation Function For Arma(P,Q). ......... 85

Ix


CHAPTER 5 MODELS FOR NONSTATIONARY TIME SERIES . 87
5.1 Stationarity Through Differencing................................ 88

, 5.2 Arima Models ..................................................... 92
5.3 Constant Terms In Arima Models ............................... 97
5.4 Other Transformations ............................................ 98
5.5 Summary ..........................................................102
Exercises .................................................................103
Appendix D: The Backshift Operator ..................................106

CHAPTER 6 MODEL SPECIFICATION .......................... 109
6.1 Properties Of The Sample Autocorrelation Function ......... 109
6.2 The Partial And Extended Autocorrelation Functions.........112
6.3 Specification Of Some Simulated Time Series ................117
6.4 Nonstationarity ...................................................125
6.5 Other Specification Methods ....................................130
6.6 Specification Of Some Actual Time Series .....................133
6.7 Summary ..........................................................141
Exercises ................................................................. 141

CHAPTER 7 PARAMETER ESTIMATION ....................... 149
7.1 The Method Of Moments.........................................149
7.2 Least Squares Estimation ....................................... 154
7.3 Maximum Likelihood And Unconditional Least Squares ......158
7.4 Properties Of The Estimates ..................................... 160
7.5 Illustrations Of Parameter Estimation........................... 163
7.6 Bootstrapping Arima Models ...................................167
7.7 Summary ..........................................................170
Exercises .................................................................170

CHAPTER 8 MODEL DIAGNOSTICS............................ 175
8.1 Residual Analysis ................................................. 175
8.2 Overfitting And Parameter Redundancy ........................185
8.3 Summary ..........................................................188
Exercises ................................................................. 188

9.1 Minimum Mean Square Error Forecasting ..................... 191
9.2 Deterministic Trends ............................................. 191
9.3 Arima Forecasting ............................................... 193
9.4 Prediction Limits .................................................. 203
9.5 Forecasting Illustrations ......................................... 204
9.6 Updating Arima Forecasts ...................................... 207
9.7 Forecast Weights And Exponentially Weighted
Moving Averages .................................................. 207
9.8 Forecasting Transformed Series ................................ 209

, xii Contents

9.9 Summary Of Forecasting With Certain Arima Models ....... 211
9.10 Summary ........................................................... 213
Exercises .................................................................. 213
Appendix E: Conditional Expectation ................................. 218
Appendix F: Minimum Mean Square Error Prediction .............. 218
Appendix G: The Truncated Linear Process .......................... 221
Appendix H: State Space Models ...................................... 222

CHAPTER 10 SEASONAL MODELS........................... 227
10.1 Seasonal Arima Models ......................................... 228
10.2 Multiplicative Seasonal Arma Models.......................... 230
10.3 Nonstationary Seasonal Arima Models ....................... 233
10.4 Model Specification, Fitting, And Checking .................... 234
10.5 Forecasting Seasonal Models ................................... 241
10.6 Summary ........................................................... 246
Exercises .................................................................. 246

CHAPTER 11 TIME SERIES REGRESSION MODELS......... 249
11.1 Intervention Analysis ............................................. 249
11.2 Outliers ............................................................ 257
11.3 Spurious Correlation ............................................. 260
11.4 Prewhitening And Stochastic Regression ...................... 265
11.5 Summary ........................................................... 273
Exercises .................................................................. 274


CHAPTER 12 TIME SERIES MODELS OF
HETEROSCEDASTICITY ........................... 277
12.1 Some Common Features Of Financial Time Series ..........278
12.2 The Arch(1) Model...............................................285
12.3 Garch Models .................................................... 289
12.4 Maximum Likelihood Estimation ................................298
12.5 Model Diagnostics ................................................301
12.6 Conditions For The Nonnegativity Of The
Conditional Variances ............................................307
12.7 Some Extensions Of The Garch Model .......................310
12.8 Another Example: The Daily Usd/Hkd Exchange Rates ....311
12.9 Summary ..........................................................315
Exercises ................................................................. 316
Appendix I: Formulas For The Generalized Portmanteau Tests ....318

CHAPTER 13 INTRODUCTION TO SPECTRAL ANALYSIS ..... 319