In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

A voluminous literature has emerged for modeling the temporal dependencies in financial market volatility using ARCH and stochastic volatility models. While most of these studies have documented highly significant in-sample parameter estimates and pronounced intertemporal volatility persistence, traditional ex-post forecast evaluation criteria suggest that the models provide seemingly poor volatility forecasts. Contrary to this contention, we show that volatility models produce strikingly accurate interdaily forecasts for the latent volatility factor that would be of interest in most financial applications. New methods for improved ex-post interdaily volatility measurements based on high-frequency intradaily data are also discussed.

https://faculty.washington.edu/ezivot/econ589//////AndersenBollerslevIER1998.pdf

Answering the skeptics: yes, standard volatility models do provide accurate forecasts*

This bestselling and thoroughly classroom-tested textbook is a complete resource for finance students. A comprehensive and illustrated discussion of the most common empirical approaches in finance prepares students for using econometrics in practice, while detailed case studies help them understand how the techniques are used in relevant financial contexts. Worked examples from the latest version of the popular statistical software EViews guide students to implement their own models and interpret results. Learning outcomes, key concepts and end-of-chapter review questions (with full solutions online) highlight the main chapter takeaways and allow students to self-assess their understanding. Building on the successful data- and problem-driven approach of previous editions, this third edition has been updated with new data, extensive examples and additional introductory material on mathematics, making the book more accessible to students encountering econometrics for the first time. A companion website, with numerous student and instructor resources, completes the learning package.

Introductory Econometrics for Finance

A complete theory for evaluating interval forecasts has not been worked out to date. Most of the literature implicitly assumes homoskedastic errors even when this is clearly violated, and proceed by merely testing for correct unconditional coverage. Consequently, I set out to build a consistent framework for conditional interval forecast evaluation, which is crucial when higher-order moment dynamics are present. The new methodology is demonstrated in an application to the exchange rate forecasting procedures advocated in risk management.

Evaluating Interval Forecasts.

Non-Gaussian processes of Ornstein–Uhlenbeck (OU) type offer the possibility of capturing important distributional deviations from Gaussianity and for flexible modelling of dependence structures. This paper develops this potential, drawing on and extending powerful results from probability theory for applications in statistical analysis. Their power is illustrated by a sustained application of OU processes within the context of finance and econometrics. We construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive OU processes, and we study these models in relation to financial data and theory.

Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics

A common assumption in the academic literature and in the actual supervision of banking systems worldwide is that franchise value plays a key role in limiting bank risk-taking. As the underlying source of franchise value is assumed to be market power, reduced competition has been considered to promote banking stability. Boyd and De Nicolo (2005) propose an alternative view where concentration in the loan market could lead to increased borrower debt loads and a corresponding increase in loan defaults that undermine bank stability. Martinez-Miera and Repullo (2007) encompass both approaches by proposing a nonlinear relationship between competition and bank risk-taking. Using unique datasets for the Spanish banking system, we examine the empirical nature of that relationship. After controlling for macroeconomic conditions and bank characteristics, we find that standard measures of market concentration do not affect the ratio of non-performing commercial loans (NPL), our measure of bank risk. However, using Lerner indexes based on bank-specific interest rates, we find a negative relationship between loan market power and bank risk. This result provides evidence in favor of the franchise value paradigm.

/pdf/how-does-competition-impact-bank-risk-taking-41ddkrzgvl.pdf

How Does Competition Impact Bank Risk-Taking?

https://www.frbsf.org/economic-research/files/wp07-23bk.pdf

How does competition affect bank risk-taking?

It is obvious that forecasts are of great importance and widely used in economics and finance. Quite simply, good forecasts lead to good decisions. The importance of forecast evaluation and combination techniques follows immediately -- forecast users naturally have a keen interest in monitoring and improving forecast performance. More generally, forecast evaluation figures prominently in many questions in empirical economics and finance. We provide selective account of forecast evaluation and combination methods. First we discuss evaluation of a single forecast, and in particular, evaluation of whether and how it may be improved. Second, we discuss the evaluation and comparison of the accuracy of competing forecasts. Third, we discuss whether and how a set of forecasts may be combined to produce a superior composite forecast. Fourth, we describe a number of forecast evaluation topics of particular relevance in economics and finance, including methods for evaluating direction-of-change forecasts, probability forecasts and volatility forecasts.

Forecast Evaluation and Combination

I. CURRENT REGULATORY FRAMEWORK In August 1996, the U.S. bank regulatory agencies adopted the market risk amendment (MRA) to the 1988 Basle Capital Accord. The MRA, which became effective in January 1998, requires that commercial banks with significant trading activities set aside capital to cover the market risk exposure in their trading accounts. (For further details on the market risk amendment, see Federal Register [1996].) The market risk capital requirements are to be based on the value-at-risk (VaR) estimates generated by the banks' own risk management models. In general, such risk management, or VaR, models forecast the distributions of future portfolio returns. To fix notation, let Yt denote the log of portfolio value at time t. The k-period-ahead portfolio return is Et+ k = Yt \-Yt Conditional on the information available at time t, Et+ k is a random variable with distribution fi + k. Thus, VaR model m is characterized by fmt+k, its forecast of the distribution of the k-period-ahead portfolio return. VaR estimates are the most common type of forecast generated by VaR models. A VaR estimate is simply a specified quantile (or critical value) of the forecasted fmt + k The VaR estimate at time t derived from model m for a k-period-ahead return, denoted VaRm,(k,a), is the critical value that corresponds to the lower a percent tail of fmt + k In other words, VaR estimates are forecasts of the maximum portfolio loss that could occur over a given holding period with a specified confidence level. Under the "internal models" approach embodied in the MRA, regulatory capital against market risk exposure is based on VaR estimates generated by banks' own VaR models using the standardizing parameters of a ten-day holding period (k = 10) and 99 percent coverage (ox = 1 ). A bank's market risk capital charge is thus based on its own estimate of the potential loss that would not be exceeded with 1 percent certainty over the subsequent twoweek period. The market risk capital that bank m must hold for time t + 1, denoted MCRmt+ t, is set as the larger of VaRat( 10,1 ) or a multiple of the average of the previous sixty VaRmt( 10,1) estimates, that is, estimates for a one-day holding period (k = 1) and 99 percent coverage, denoted VaR mt( 1,1 ) or simply VaRmt. Smt is a step function that depends on the number of exceptions (that is, occasions when the portfolio return Et + I is less than VaRmt ) observed over the last 250 trading days. The possible number of exceptions is divided into three zones. Within the green zone of four or fewer exceptions, a VaR model is deemed "acceptably accurate," and Smt remains at its minimum value of three. Within the yellow zone of five to nine exceptions, Smt increases incrementally with the number of exceptions. Within the red zone of ten or more exceptions, the VaR model is deemed to be "inaccurate," and Smt increases to its maximum value of four. II. ALTERNATIVE EVALUATION METHODS Given the obvious importance of VaR estimates to banks and now their regulators, evaluating the accuracy of the models underlying them is a necessary exercise. To date, two hypothesis-testing methods for evaluating VaR estimates have been proposed: the binomial method, currently the quantitative standard embodied in the MRA, and the interval forecast method proposed by Christoffersen (forthcoming). For these tests, the null hypothesis is that the VaR estimates in question exhibit a specified property characteristic of accurate VaR estimates. If the null hypothesis is rejected, the VaR estimates do not exhibit the specified property, and the underlying VaR model can be said to be "inaccurate." If the null hypothesis is not rejected, then the model can be said to be "acceptably accurate." However, for these evaluation methods, as with any hypothesis test, a key issue is their statistical power, that is, their ability to reject the null hypothesis when it is incorrect. If the hypothesis tests exhibit low power, then the probability of misclassifying an inaccurate VaR model as "acceptably accurate" will be high. …

/pdf/methods-for-evaluating-value-at-risk-estimates-23c4xge8vx.pdf

Methods for Evaluating Value-at-Risk Estimates

Differences between yields on comparable-maturity U.S. Treasury nominal and real debt, the so-called breakeven inflation (BEI) rates, are widely used indicators of inflation expectations. However, better measures of inflation expectations could be obtained by subtracting inflation risk premiums from the BEI rates. We provide such decompositions using an estimated affine arbitrage-free model of the term structure that captures the pricing of both nominal and real Treasury securities. Our empirical results suggest that long-term inflation expectations have been well anchored over the past few years, and inflation risk premiums, although volatile, have been close to zero on average.

/pdf/inflation-expectations-and-risk-premiums-in-an-arbitrage-g79w1y4urt.pdf

Jose A. Lopez

Papers

How Does Competition Impact Bank Risk-Taking?

How does competition affect bank risk-taking?

Forecast Evaluation and Combination

Methods for Evaluating Value-at-Risk Estimates

Inflation Expectations and Risk Premiums in an Arbitrage-Free Model of Nominal and Real Bond Yields †