http://homepage.ntu.edu.tw/~ntuperc/docs/publication/2002_25_Lin.pdf

Unit root tests in panel data: asymptotic and finite-sample properties

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root?

Preface1Difference Equations12Lag Operators253Stationary ARMA Processes434Forecasting725Maximum Likelihood Estimation1176Spectral Analysis1527Asymptotic Distribution Theory1808Linear Regression Models2009Linear Systems of Simultaneous Equations23310Covariance-Stationary Vector Processes25711Vector Autoregressions29112Bayesian Analysis35113The Kalman Filter37214Generalized Method of Moments40915Models of Nonstationary Time Series43516Processes with Deterministic Time Trends45417Univariate Processes with Unit Roots47518Unit Roots in Multivariate Time Series54419Cointegration57120Full-Information Maximum Likelihood Analysis of Cointegrated Systems63021Time Series Models of Heteroskedasticity65722Modeling Time Series with Changes in Regime677A Mathematical Review704B Statistical Tables751C Answers to Selected Exercises769D Greek Letters and Mathematical Symbols Used in the Text786Author Index789Subject Index792

https://sisis.rz.htw-berlin.de/inh2007/12357004.pdf

Time series analysis

Any series of observations ordered along a single dimension, such as time, may be thought of as a time series. The emphasis in time series analysis is on studying the dependence among observations at different points in time. What distinguishes time series analysis from general multivariate analysis is precisely the temporal order imposed on the observations. Many economic variables, such as GNP and its components, price indices, sales, and stock returns are observed over time. In addition to being interested in the contemporaneous relationships among such variables, we are often concerned with relationships between their current and past values, that is, relationships over time.

Time Series Analysis

We provide a new and superior measure of U.S. GDP, obtained by applying optimal signal-extraction techniques to the (noisy) expenditure-side and income-side estimates. Its properties - particularly as regards serial correlation - differ markedly from those of the standard expenditure-side measure and lead to substantially-revised views regarding the properties of GDP.

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Improving GDP Measurement: A Measurement-Error Perspective

We estimate a model with latent factors that summarize the yield curve (namely, level, slope, and curvature) as well as observable macroeconomic variables (real activity, inflation, and the stance of monetary policy) Our goal is to provide a characterization of the dynamic interactions between the macroeconomy and the yield curve We find strong evidence of the effects of macro variables on future movements in the yield curve and much weaker evidence for a reverse influence We also relate our results to a traditional macroeconomic approach based on the expectations hypothesis

The macroeconomy and the yield curve: a nonstructural analysis

I. INTRODUCTION There is no one "magic" relevant horizon for risk management. Instead, the relevant horizon will generally vary by asset class (for example, equity versus bonds), industry (banking versus insurance), position in the firm (trading desk versus chief financial officer), and motivation (private versus regulatory), among other things, and thought must be given to the relevant horizon on an application-by-application basis. But one thing is clear: in many risk management situations, the relevant horizons are long--certainly longer than just a few days--an insight incorporated, for example, in Bankers Trust's RAROC system, for which the horizon is one year. Simultaneously, it is well known that short-horizon asset return volatility fluctuates and is highly forecastable, a phenomenon that is very much at the center of modern risk management paradigms. Much less is known, however, about the forecastability of long-horizon volatility, and the speed and pattern with which forecastability decays as the horizon lengthens. A key question arises: Is volatility forecastability important for long-horizon risk management, or is a traditional constant-volatility assumption adequate? In this paper, we address this question, exploring the interface between long-horizon financial risk management and long-horizon volatility forecastability and, in particular, whether long-horizon volatility is forecastable enough such that volatility models are useful for long-horizon risk management. In particular, we report on recent relevant work by Diebold, Hickman, Inoue, and Schuermann (1998); Christoffersen and Diebold (1997); and Diebold, Schuermann, and Stroughair (forthcoming). To assess long-horizon volatility forecastability, it is necessary to have a measure of long-horizon volatility, which can be obtained in a number of ways. We proceed in Section II by considering two ways of converting short-horizon volatility into long-horizon volatility: scaling and formal model-based aggregation. The defects of those procedures lead us to take a different approach in Section III, estimating volatility forecastability directly at the horizons of interest, without making assumptions about the nature of the volatility process, and arriving at a surprising conclusion: Volatility forecastability seems to decline quickly with horizon, and seems to have largely vanished beyond horizons of ten or fifteen trading days. If volatility forecastability is not important for risk management beyond horizons of ten or fifteen trading days, then what is important? The really big movements such as the U.S. crash of 1987 are still poorly understood, and ultimately the really big movements are the most important for risk management. This suggests the desirability of directly modeling the extreme tails of return densities, a task potentially facilitated by recent advances in extreme value theory. We explore that idea in Section IV, and we conclude in Section V. II. OBTAINING LONG-HORIZON VOLATILITIES FROM SHORT-HORIZON VOLATILITIES SCALING AND FORMAL AGGREGATION(1) Operationally, risk is often assessed at a short horizon, such as one day, and then converted to other horizons, such as ten days or thirty days, by scaling by the square root of horizon [for instance, as in Smithson and Minton (1996a, 1996b) or J.P. Morgan (1996)]. For example, to obtain a ten-day volatility, we multiply the one-day volatility by [square root of 10]. Moreover, the horizon conversion is often significantly longer than ten days. Many banks, for example, link trading volatility measurement to internal capital allocation and risk-adjusted performance measurement schemes, which rely on annual volatility estimates. The temptation is to scale one-day volatility by [square root of 252]. It turns out, however, that scaling is both inappropriate and misleading. SCALING WORKS IN lid ENVIRONMENTS Here we describe the restrictive environment in which scaling is appropriate. …

/pdf/horizon-problems-and-extreme-events-in-financial-risk-4oiipz15j0.pdf

Horizon Problems and Extreme Events in Financial Risk Management

It is well known that high-frequency asset returns are fat-tailed relative to the Gaussian distribution tails are typically reduced but not eliminated when returns are standardized by volatilities estimated from popular models such as GARCH. We consider two major dollar exchange rates, and we show that returns standardized instead by the realized volatilities of Andersen, Bollerslev, Diebold and Labys (1999) are very nearly Gaussian. We perform both univariate and multivariate analyses, we trace the different effects of the different standardizations to differences in information sets, and we draw implications for the presence of jumps in exchange rate diffusions.

Francis X. Diebold

Papers

Improving GDP Measurement: A Measurement-Error Perspective

The macroeconomy and the yield curve: a nonstructural analysis

Horizon Problems and Extreme Events in Financial Risk Management

Exchange Rate Returns Standardized by Realized Volatility are (Nearly) Gaussian

On the limitations of comparing mean square forecast errors: Comment