Applied Econometrics: A Simple Introduction

By K.H. Erickson

Applied Econometrics: A Simple Introduction offers a detailed guide to some of the central methods and applications of applied econometrics, with theory, models, calculations, and graphs to support analysis.

S&P 500 equities, GSCI commodities, and US Treasury Bill risk-free rate datasets are assessed for their data distributions, autocorrelation, and stationarity. The Engle-Granger 2 step method, Johansen test and the Vector Error Correction Model test for and correct cointegration.

ARMA models determine the optimal AR and MA processes to model returns data, and GARCH models assess the optimal p and q number of lags to model variance, using the Akaike Information Criterion. Alternative GARCH versions are examined.

Dynamic portfolio strategies are evaluated using Sharpe Ratio portfolio performance evaluation tools, with a focus on the 2007-8 global financial crisis period. Static portfolio strategies are assessed using ARMA return and GARCH variance forecasting. Results are used alongside established financial literature to assess the optimal portfolio strategy.

• Language: English
• Publisher: K.H. Erickson
• Release date: Sep 23, 2015
• ISBN: 9781311537232

Book preview

Applied Econometrics: A Simple Introduction

By K.H. Erickson

Copyright © 2015 K.H. Erickson

All rights reserved.

No part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted in any form or by any means, including electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the author.

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Game Theory

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International Relations

Investment Appraisal

Investment Formulas

Marketing Management Concepts and Tools

Mathematical Formulas for Economics and Business

Methods of Microeconomics

Microeconomics

Table of Contents

1 Introduction

2 Data Selection

3 Price Analysis

3.1 Data Distribution

3.2 Stationarity, and Autocorrelation

3.3 Unit Root Test

3.4 Differenced Data

3.5 Cointegration Tests and Correction

4 Return Analysis

4.1 AR and MA Processes

4.2 Akaike Information Criterion

4.3 ARMA Models, Means and Volatility

5 Volatility Analysis

5.1 GARCH Model

5.2 AIC for GARCH

5.3 GARCH Models, Means and Volatility

6 Portfolio Strategy

6.1 Dynamic Portfolio Strategy

6.2 Static Portfolio Strategy and Forecasting

6.3 Optimum Portfolio Strategy and Conclusions

Bibliography

1 Introduction

This book applies established econometric concepts and methods to a large sample of empirical financial market data, to provide both an insight into the potential real world applications of econometrics, and a detailed examination of the financial investment market over the chosen period. Building on basic econometrics knowledge and theory the book explores the issues which economic and financial data can present in practice. There is extensive use of graphs and model values throughout the book, all calculated with OxMetrics econometric software.

The next section explains the selection of the equities, commodities and risk-free rate of return data which comprise the datasets for this book, and notes how this data will be used to conduct analysis. Three chapters then follow which look at price, return and volatility analysis in turn. Price analysis first examines the distribution of data, then tests for stationarity, using Autocorrelation Functions (ACF) and Partial Autocorrelation Functions (PACF), and a Dickey-Fuller (DF) unit root test. Next data is differenced to ensure stationarity is met, followed by cointegration tests, with the Engle-Granger 2 step method and Error Correction Model (ECM), and the Johansen technique and Vector Error Correction Model (VECM).

Returns are what ultimately motivate financial market investors, and changes in prices are used to give returns for a chapter on return analysis. Return data is examined for Autoregressive (AR) and Moving Average (MA) processes, and the two are combined to form an ARMA model with the Box-Jenkins method. The Akaike Information Criterion (AIC) is then used to calculate the ARMA model which best fits the data, and to find the number of AR and MA lags required to accurately model the equities, commodities, and risk-free rate returns data.

Risk is the other area which concerns investors, and a chapter explores this in depth. With an ARMA model used to model returns a Generalized Autoregressive Conditionally Heteroskedastic (GARCH) model can be used to model the return conditional variance. The Akaike Information Criterion (AIC) is again used to find the optimum number of lags for this GARCH variance model, for each of the equities, commodities, and risk-free rate datasets. After the number of lags is decided GARCH model variations are assessed to improve the accuracy of the conditional variance model further, and the AIC compares EGARCH, GJR-GARCH, and GARCH-M variations. The chosen variation is then used to find the GARCH model variance, and from there the model volatility and risk.

With optimal ARMA and GARCH models selected, and return and volatility mean values calculated for the equities, commodities, and risk-free rate data, the issue of a portfolio management strategy can then be examined. First, a dynamic portfolio management strategy is analysed, using the Sharpe Ratio portfolio performance evaluation tool. The popular strategy to sell off equities and replace them with commodities during market downturns is explored in the midst of the 2007-2008 global financial crisis, as the performance of portfolios which stuck by equities are compared to those which switched to commodities.

A static unchanging portfolio management strategy is examined, using the optimal ARMA and GARCH models calculated earlier, and using the empirical relationship between equities and commodities to determine the portfolio weighting for the different assets. The model’s forecasted returns, volatility and variance are then compared to the actual empirical returns and volatility, to determine the accuracy of forecasts and assess the strategy of holding an unchanging static portfolio.

The final section examines the general issues associated with each of the differing dynamic and static portfolio management strategies. Empirical evidence from this book is combined with theory from literature on the topic, and some conclusions are drawn on the factors driving an effective portfolio management strategy.

2 Data Selection

Three different types of financial data are used as the dataset for this book; equities (stocks and shares); commodities; and risk-free assets. The choice of these three types of data serves several purposes. First, they represent the various main types of investment available to a prospective market investor. Equities represent assets relating to subsections