Just follow steps in the instruction using R studio.Both the homework instruction and data required have been attached. I have posted the textbook as well.

hw7.pdf

sdhousepricegr.xlsx

forecasting_for_economics_and_business_1st_by_gloria_gonzale.pdf

Unformatted Attachment Preview

ECON 467

Spring 2019

HW 7

(Due to Shi by 8:30 a.m. on April 1, 2019)

Use the San Diego house price data (data on the growth on the housing prices: G) that I have

posted with this homework. Use the data up to 2008:2 as the estimation sample and the data

in 2008:3 – 2012:2 as the prediction sample.

a. Estimate an AR(4) model of the growth of the housing price in San Diego.

Then using a fixed scheme, make one-period-ahead forecasts based on the model.

Call the forecast FA. The purpose of the exercise is forecast evaluation.

b. Generate a second series of one-period-ahead forecasts that are calculated by

averaging the last two observations. Call it FB.

c. Present a table similar to Table 9.2 in the text book of the two sets of forecasts and

forecast error series along with the actual data.

d. Implement the forecast optimality tests (viz., MPE test, and Information Efficiency

test assuming quadratic loss function) on your two forecasts. Present your results.

(That is, present tables similar to the ones in Table 9.4 in the text book – excluding

the Linex loss function.) Together with regular t-stat include t-stats based on HAC

standard errors too in the table.

e. Implement a descriptive evaluation of the average loss resulting from the two

forecasts. Use RMSE, MAE and MAPE as the measures of the average loss.

Summarize your results in a table like Table 9.6 (excluding Linex loss function) in

the text book.

f. Now statistically test whether the squared error loss from FB is any different from the

loss from FA. Use both regular standard error and HAC standard error. What is your

conclusion?

g. Consider the following two combination forecasts that combine FA and FB forecasts:

i. using equal weights: call this forecast series CF1

ii. using weights equal to the inverse of the MSEs of the forecasts: CF2

In both cases the weights should add up to 1. What are the MSEs of these two

forecasts based on one-period-ahead forecast errors? Compare these MSEs with the

MSEs of FA and FB above. Do you see any improvement in the performance of the

forecasts?

OBS

1975Q2

1975Q3

1975Q4

1976Q1

1976Q2

1976Q3

1976Q4

1977Q1

1977Q2

1977Q3

1977Q4

1978Q1

1978Q2

1978Q3

1978Q4

1979Q1

1979Q2

1979Q3

1979Q4

1980Q1

1980Q2

1980Q3

1980Q4

1981Q1

1981Q2

1981Q3

1981Q4

1982Q1

1982Q2

1982Q3

1982Q4

1983Q1

1983Q2

1983Q3

1983Q4

1984Q1

1984Q2

1984Q3

1984Q4

1985Q1

1985Q2

1985Q3

1985Q4

1986Q1

1986Q2

1986Q3

1986Q4

1987Q1

1987Q2

1987Q3

1987Q4

G

3.875226

2.784185

3.231245

3.026323

0.800703

3.828554

4.758848

8.321665

6.206399

8.27685

5.84781

4.149952

4.963949

4.376981

6.023289

3.121601

6.391586

3.740141

2.591726

1.817442

1.787449

-2.8481

-10.6003

17.50684

4.861545

-1.97747

-7.0395

4.628838

2.53782

-2.60551

-0.36054

1.718688

0.523817

0.430599

1.50887

0.454257

1.057327

1.195765

0.272555

1.564087

1.481622

1.86904

-1.01614

2.910147

2.000959

2.357219

1.48631

2.107113

2.519729

2.445134

2.276081

1988Q1

1988Q2

1988Q3

1988Q4

1989Q1

1989Q2

1989Q3

1989Q4

1990Q1

1990Q2

1990Q3

1990Q4

1991Q1

1991Q2

1991Q3

1991Q4

1992Q1

1992Q2

1992Q3

1992Q4

1993Q1

1993Q2

1993Q3

1993Q4

1994Q1

1994Q2

1994Q3

1994Q4

1995Q1

1995Q2

1995Q3

1995Q4

1996Q1

1996Q2

1996Q3

1996Q4

1997Q1

1997Q2

1997Q3

1997Q4

1998Q1

1998Q2

1998Q3

1998Q4

1999Q1

1999Q2

1999Q3

1999Q4

2000Q1

2000Q2

2000Q3

2000Q4

2.795112

3.945252

4.448373

6.066199

5.131782

5.39785

3.541867

2.642109

0.765248

0.32053

0.622361

-2.15172

-0.90379

-0.53429

-0.34068

0.290253

-0.2094

-1.2832

-0.4109

-2.03926

-2.58309

-0.58374

-1.63463

-1.20494

0.340854

0.331579

-0.57051

-0.92915

-0.86258

-0.30037

-1.54049

-0.46891

0.915116

0.755921

0.198175

-1.41773

1.997965

2.330914

1.592611

1.507377

3.249282

5.516339

1.711208

0.663682

3.711203

3.768753

2.375707

3.234623

3.432154

5.126509

2.849223

2.672024

2001Q1

2001Q2

2001Q3

2001Q4

2002Q1

2002Q2

2002Q3

2002Q4

2003Q1

2003Q2

2003Q3

2003Q4

2004Q1

2004Q2

2004Q3

2004Q4

2005Q1

2005Q2

2005Q3

2005Q4

2006Q1

2006Q2

2006Q3

2006Q4

2007Q1

2007Q2

2007Q3

2007Q4

2008Q1

2008Q2

2008Q3

2008Q4

2009Q1

2009Q2

2009Q3

2009Q4

2010Q1

2010Q2

2010Q3

2010Q4

2011Q1

2011Q2

2011Q3

2011Q4

2012Q1

2012Q2

3.45

3.348252

3.080927

1.422937

5.092976

7.109088

5.802894

3.151133

3.535192

4.303659

5.612785

3.59723

5.843555

9.546292

3.625518

2.159167

0.516565

3.805385

2.019955

-1.03131

-0.34824

-0.34012

-3.49128

-1.84443

0.618136

-1.16976

-4.9801

-7.42473

-6.93466

-3.43053

-5.04084

-6.61976

-3.59545

3.990836

3.516095

1.2723

0.926239

0.261861

-1.79428

-1.91266

-3.08135

0.686884

-2.40045

-0.95467

1.326932

1.328486

FORECASTING FOR ECONOMICS

AND BUSINESS

Gloria González-Rivera

University of California–Riverside

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Library of Congress Cataloging-in-Publication Data

González-Rivera, Gloria.

Forecasting for economics and business / Gloria González-Rivera.

p. cm.

ISBN-13: 978-0-13-147493-2

ISBN-10: 0-13-147493-6

1. Economic forecasting. 2. Economic forecasting—United States. I.

Title.

HB3730.G57 2013

338.5’44—dc23

2011049940

10 9 8 7 6 5 4 3 2 1

ISBN 10: 0-13-147493-6

ISBN 13: 978-0-13-147493-2

To a very special undergraduate,

Vasilios A. Morikis González,

with love

This page intentionally left blank

Brief Contents

1

Introduction and Context

2

Review of the Linear Regression Model

24

3

Statistics and Time Series

52

4

Tools of the Forecaster

79

5

Understanding Linear Dependence: A Link to

Economic Models

103

6

Forecasting with Moving Average (MA) Processes

125

7

Forecasting with Autoregressive (AR) Processes

160

8

Forecasting Practice I

202

9

Forecasting Practice II: Assessment of Forecasts

and Combination of Forecasts

224

Forecasting the Long Term: Deterministic

and Stochastic Trends

255

Forecasting with a System of Equations:

Vector Autoregression

293

12

Forecasting the Long Term and the Short Term Jointly

311

13

Forecasting Volatility I

337

14

Forecasting Volatility II

359

15

Financial Applications of Time-Varying Volatility

395

16

Forecasting with Nonlinear Models: An Introduction

413

10

11

1

vii

This page intentionally left blank

Contents

Preface

MODULE I

xvi

STATISTICS AND TIME SERIES

CHAPTER 1 Introduction and Context

1

1.1

1

1

2

3

4

4

4

5

5

1.2

1.3

1.4

1.5

1.6

What Is Forecasting?

1.1.1 The First Forecaster in History: The Delphi Oracle

1.1.2 Examples of Modern Forecasts

1.1.3 Definition of Forecasting

1.1.4 Two Types of Forecasts

Who Are the Users of Forecasts?

1.2.1 Firms

1.2.2 Consumers and Investors

1.2.3 Government

Becoming Familiar with Economic Time Series:

Features of a Time Series

1.3.1 Trends

1.3.2 Cycles

1.3.3 Seasonality

Basic Notation and the Objective of the Forecaster

1.4.1 Basic Notation

1.4.2 The Forecaster’s Objective

A Road Map for This Forecasting Book

Resources

6

7

8

9

11

11

12

13

14

Key Words

Exercises

16

17

CHAPTER 2 Review of the Linear Regression Model

24

2.1

2.2

24

27

Conditional Density and Conditional Moments

Linear Regression Model

ix

x

Contents

2.3

2.4

Estimation: Ordinary Least Squares

2.3.1 R-squared and Adjusted R-squared

2.3.2 Linearity and OLS

2.3.3 Assumptions of OLS: The Gauss–Markov Theorem

2.3.4 An Example: House Prices and Interest Rates

Hypothesis Testing in a Regression Model

2.4.1 The t-ratio

2.4.2 The F-test

29

32

33

35

38

41

41

44

Key Words

Appendix

Exercises

46

47

49

CHAPTER 3 Statistics and Time Series

52

3.1

Stochastic Process and Time Series

3.1.1 Stochastic Process

3.1.2 Time Series

3.2 The Interpretation of a Time Average

3.2.1 Stationarity

3.2.2 Useful Transformations of Nonstationary Processes

3.3 A New Tool of Analysis: The Autocorrelation Functions

3.3.1 Partial Autocorrelation

3.3.2 Statistical Tests for Autocorrelation Coefficients

3.4 Conditional Moments and Time Series: What Lies Ahead

54

55

56

57

58

62

65

69

71

73

Key Words

Appendix

Exercises

74

74

76

MODULE II MODELING LINEAR DEPENDENCE

FORECASTING WITH TIME SERIES MODELS

CHAPTER 4 Tools of the Forecaster

79

4.1

80

4.2

4.3

The Information Set

4.1.1 Some Information Sets Are More

Valuable Than Others

4.1.2 Some Time Series Are More Forecastable

Than Others

The Forecast Horizon

4.2.1 Forecasting Environments

The Loss Function

4.3.1 Some Examples of Loss Functions

82

84

84

86

89

91

Contents

4.3.2

4.3.3

Examples

Optimal Forecast: An Introduction

Key Words

Appendix

Exercises

xi

91

93

96

97

98

A PAUSE Where Are We and Where Are We Going?

100

Where Are We Going from Here?

How to Organize Your Reading of the Forthcoming Chapters

100

102

CHAPTER 5

A Understanding Linear Dependence:

A Link to Economic Models

5.1

5.2

5.3

5.4

Price Dynamics: The Cob-Web Model (Beginner Level)

5.1.1 The Effect of Only One Supply Shock

5.1.2 The Effect of Many Supply Shocks

5.1.3 A Further Representation of the Dynamics

in the Cob-Web Model

5.1.4 Simulation of the Model, pt = p*(1 – ) + pt-1 + t ,

and Autocorrelation Function

Portfolio Returns and Nonsynchronous

Trading (Intermediate Level)

Asset Prices and the Bid–Ask Bounce

(Advanced Level)

Summary

103

103

105

106

107

109

113

116

121

Key Words

Appendix

Exercises

121

121

123

CHAPTER 6 Forecasting with Moving Average (MA) Processes

125

6.1 A Model with No Dependence: White Noise

6.1.1 What Does This Process Look Like?

6.2 The Wold Decomposition Theorem: The Origin of AR and MA Models

(Advanced Section)

6.2.1 Finite Representation of the Wold Decomposition

6.3 Forecasting with Moving Average Models

6.3.1 MA(1) Process

6.3.2 MA(q) Process

125

126

129

131

133

135

147

Key Words

Appendix

Exercises

157

157

158

xii

Contents

CHAPTER 7 Forecasting with Autoregressive (AR) Processes

160

7.1 Cycles

7.2 Autoregressive Models

7.2.1 The AR(1) Process

7.2.2 AR(2) Process

7.2.3 AR(p) Process

7.2.4 Chain Rule of Forecasting

7.3 Seasonal Cycles

7.3.1 Deterministic and Stochastic Seasonal Cycles

7.3.2 Seasonal ARMA Models

7.3.3 Combining ARMA and Seasonal ARMA Models

162

165

165

173

185

187

188

189

192

197

Key Words

Exercises

200

200

CHAPTER 8 Forecasting Practice I

202

8.1

8.2

202

205

205

8.3

The Data: San Diego House Price Index

Model Selection

8.2.1 Estimation: AR, MA, and ARMA Models

8.2.2 Is the Process Covariance-Stationary,

and Is the Process Invertible?

8.2.3 Are the Residuals White Noise?

8.2.4 Are the Parameters of the Model Statistically Significant?

8.2.5 Is the Model Explaining a Substantial Variation

of the Variable of Interest?

8.2.6 Is It Possible to Select One Model Among Many?

The Forecast

8.3.1 Who Are the Consumers of Forecasts?

8.3.2 Is It Possible To Have Different Forecasts

from the Same Model?

8.3.3 What Is the Most Common Loss Function in Economics

and Business?

8.3.4 Final Comments

206

209

211

211

212

213

213

215

215

221

Key Words

Exercises

221

222

CHAPTER 9 Forecasting Practice II: Assessment of Forecasts

and Combination of Forecasts

224

9.1

Optimal Forecast

9.1.1 Symmetric and Asymmetric Loss Functions

9.1.2 Testing the Optimality of the Forecast

9.2 Assessment of Forecasts

9.2.1 Descriptive Evaluation of the Average Loss

9.2.2 Statistical Evaluation of the Average Loss

225

225

229

238

239

240

Contents

9.3

Combination of Forecasts

9.3.1 Simple Linear Combinations

9.3.2 Optimal Linear Combinations

Key Words

Appendix

Exercises

A PAUSE

xiii

244

244

245

247

248

250

Where Are We and Where Are We Going?

252

Where Are We Going from Here?

253

CHAPTER 10 Forecasting the Long Term: Deterministic

and Stochastic Trends

255

10.1

10.2

Deterministic Trends

10.1.1 Trend Shapes

10.1.2 Trend Stationarity

10.1.3 Optimal Forecast

Stochastic Trends

10.2.1 Trend Shapes

10.2.2 Stationarity Properties

10.2.3 Optimal Forecast

257

258

261

262

270

270

272

279

Key Words

Exercises

291

291

CHAPTER 11 Forecasting with a System of Equations:

Vector Autoregression

293

11.1

11.2

11.3

11.4

11.5

294

294

299

302

305

What Is Vector Autoregression (VAR)?

Estimation of VAR

Granger Causality

Impulse-Response Functions

Forecasting with VAR

Key Words

Exercises

309

309

CHAPTER 12 Forecasting the Long Term and the

Short Term Jointly

311

12.1

12.2

12.3

315

322

327

Finding a Long-Term Equilibrium Relationship

Quantifying Short-Term Dynamics: Vector Error Correction Model

Constructing the Forecast

Key Words

Exercises

332

332

xiv

Contents

A PAUSE

Where Are We and Where Are We Going?

334

Where We Are Going from Here

How to Organize Your Reading of the Forthcoming Chapters

335

336

MODULE III

MODELING MORE COMPLEX DEPENDENCE

CHAPTER 13 Forecasting Volatility I

337

13.1

337

337

13.2

13.3

13.4

13.5

Motivation

13.1.1 The World is Concerned About Uncertainty

13.1.2 Volatility Within the Context of Our

Forecasting Problem

13.1.3 Setting the Objective

Time-Varying Dispersion: Empirical Evidence

Is There Time Dependence in Volatility?

What Have We Learned So Far?

Simple Specifications for the Conditional Variance

13.5.1 Rolling Window Volatility

13.5.2 Exponentially Weighted Moving Average

(EWMA) Volatility

339

340

341

345

353

353

354

355

Key Words

Exercises

357

357

CHAPTER 14 Forecasting Volatility II

359

14.1

360

362

368

370

378

380

14.2

The ARCH Family

14.1.1 ARCH(1)

14.1.2 ARCH(p)

14.1.3 GARCH(1,1)

14.1.4 Estimation Issues for the ARCH Family

Realized Volatility

Key Words

Appendix

Exercises

CHAPTER 15

15.1

390

390

393

Financial Applications of Time-Varying

Volatility

Risk Management

15.1.1 Value-at-Risk (VaR)

15.1.2 Expected Shortfall (ES)

395

395

396

400

Contents

xv

15.2 Portfolio Allocation

15.3 Asset Pricing

15.4 Option Pricing

401

404

406

Key Words

Appendix

Exercises

411

411

412

CHAPTER 16 Forecasting with Nonlinear Models:

An Introduction

413

16.1

16.2

16.3

Nonlinear Dependence

16.1.1 What Is It?

16.1.2 Is There Any Evidence of Nonlinear Dynamics in the Data?

16.1.3 Nonlinearity, Correlation, and Dependence

16.1.4 What Have We Learned So Far?

Nonlinear Models: An Introduction

16.2.1 Threshold Autoregressive Models (TAR)

16.2.2 S …

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