Special Functions and Their Applications. By N. N. Lebedev, translated by R. A. Silverman. Pp. xii, 308. 96s. 1965. (Prentice-Hall)

This textbook provides an introduction to econometrics through a grounding in probability theory and statistical inference. The emphasis is on the concepts and ideas underlying probability theory and statistical inference, and on motivating the learning of them both at a formal and an intuitive level. It encourages the mastering of fundamental concepts and theoretical perspectives which guide the formulation and solution of problems in econometric modelling. This makes it an ideal introduction to empirical econometric modelling and the more advanced econometric literature. It is recommended for use on courses giving students a thorough grounding in econometrics at undergraduate or graduate level.

Statistical Foundations of Econometric Modelling

We study how the structure of housing finance affects the transmission of monetary policy shocks. We document three main facts: first, the features of residential mortgage markets differ markedly across industrialized countries; second, and according to a wide range of indicators, the transmission of monetary policy shocks to residential investment and house prices is significantly stronger in those countries with larger flexibility/development of mortgage markets; third, the transmission to consumption is stronger only in those countries where mortgage equity release is common and mortgage contracts are predominantly of the variable-rate type. We build a two-sector DSGE model with price stickiness and collateral constraints and analyze how the response of consumption and residential investment to monetary policy shocks is affected by alternative values of two institutional features: (i) down-payment rate; (ii) interest rate mortgage structure (variable vs. fixed rate). In line with our empirical evidence, the sensitivity of both variables to monetary policy shocks increases with lower values of the down-payment rate and is larger under a variable- rate mortgage structure.

Housing Finance and Monetary Policy

We document three facts concerning how the structure of housing finance affects the monetary transmission mechanism: first, the characteristics of residential mortgage markets differ markedly across industrialized countries; second, the impact of monetary policy shocks to residential investment and house prices is significantly stronger in those countries with larger flexibility/development of mortgage markets; third, the transmission to consumption is stronger only in those countries where mortgage equity release is common and mortgage contracts are predominantly of the variable-rate type. We then build a two-sector DSGE model with financial constraints to rationalize those facts.

/pdf/housing-finance-and-monetary-policy-4rvlxjxbb3.pdf

Housing finance and monetary policy

1 Elements of Stochastic Processes.- 1.1 Introduction.- 1.2 Stochastic Processes.- 1.3 Limit Theorems.- Problems.- 2 Local Asymptotic Normality for Stochastic Processes.- 2.1 General Results for Local Asymptotic Normality.- 2.2 Local Asymptotic Normality for Linear Processes.- Problems.- 3 Asymptotic Theory of Estimation and Testing for Stochastic Processes.- 3.1 Asymptotic Theory of Estimation and Testing for Linear Processes.- 3.1.1 Asymptotic Theory Based on a Gaussian Likelihood.- 3.1.2 Asymptotic Theory of Estimation and Testing Based on LAN Results.- 3.2 Asymptotic Theory for Nonlinear Stochastic Models.- 3.2.1 Nonlinear Models.- 3.2.2 Probability Structure of Nonlinear Models.- 3.2.3 Statistical Testing and Estimation Theory for Nonlinear Models.- 3.2.4 Asymptotic Theory Based on the LAN Property.- 3.2.5 Model Selection Problems.- 3.2.6 Nonergodic Models.- 3.3 Asymptotic Theory for Continuous Time Processes.- 3.3.1 Stochastic Integrals and Diffusion Processes.- 3.3.2 Asymptotic Theory for Diffusion Processes.- 3.3.3 Diffusion Processes and Autoregressions with Roots.- Near Unity.- 3.3.4 Continuous Time ARMA Processes.- 3.3.5 Asymptotic Theory for Point Processes.- Problems.- 4 Higher Order Asymptotic Theory for Stochastic Processes.- 4.1 Introduction to Higher Order Asymptotic Theory.- 4.2 Valid Asymptotic Expansions.- 4.3 Higher Order Asymptotic Estimation Theory for Discrete Time Processes in View of Statistical Differential Geometry.- 4.4 Higher Order Asymptotic Theory for Continuous Time Processes.- 4.5 Higher Order Asymptotic Theory for Testing Problems.- 4.6 Higher Order Asymptotic Theory for Normalizing Transformations.- 4.7 Generalization of LeCam's Third Lemma and Higher Order Asymptotics of Iterative Methods.- Problems.- 5 Asymptotic Theory for Long-Memory Processes.- 5.1 Some Elements of Long-Memory Processes.- 5.2 Limit Theorems for Fundamental Statistics.- 5.3 Estimation and Testing Theory for Long-Memory Processes.- 5.4 Regression Models with Long-Memory Disturbances.- 5.5 Semiparametric Analysis and the LAN Approach.- Problems.- 6 Statistical Analysis Based on Functionals of Spectra.- 6.1 Estimation of Nonlinear Functionals of Spectra.- 6.2 Application to Parameter Estimation for Stationary Processes.- 6.3 Asymptotically Efficient Nonparametric Estimation of Functionals of Spectra in Gaussian Stationary Processes.- 6.4 Robustness in the Frequency Domain Approach.- 6.4.1 Robustness to Small Trends of Linear Functionals of a Periodogram.- 6.4.2 Peak-Insensitive Spectrum Estimation.- 6.5 Numerical Examples.- Problems.- 7 Discriminant Analysis for Stationary Time Series.- 7.1 Basic Formulation.- 7.2 Standard Methods for Gaussian Stationary Processes.- 7.2.1 Time Domain Methods.- 7.2.2 Frequency Domain Methods.- 7.2.3 Admissible Linear Procedure: Case of Unequal Mean Vectors and Covariance Matrices.- 7.3 Discriminant Analysis for Non-Gaussian Linear Processes.- 7.4 Nonparametric Approach for Discriminant Analysis.- 7.5 Parametric Approach for Discriminant Analysis.- 7.6 Derivation of Spectral Expressions to Divergence Measures Between Gaussian Stationary Processes.- 7.7 Miscellany.- Problems.- 8 Large Deviation Theory and Saddlepoint Approximation for Stochastic Processes.- 8.1 Large Deviation Theorem 538 8.2 Asymptotic Efficiency for Gaussian Stationary Processes:Large Deviation Approach.- 8.2.1 Asymptotic Theory of Neyman-Pearson Tests.- 8.2.2 Bahadur Efficiency of Estimator.- 8.2.3 Stochastic Comparison of Tests.- 8.3 Large Deviation Results for an Ornstein-Uhlenbeck Process.- 8.4 Saddlepoint Approximations for Stochastic Processes.- Problems.- A.1 Mathematics.- A.2 Probability.- A.3 Statistics.

Asymptotic theory of statistical inference for time series

We investigate the presence of significant electricity forward risk premia, using data from three major continental European energy markets - German, Dutch and French. We introduce the risk premium in the framework of a standard electricity spot/forward unobserved factor model, and derive the implied forward price behaviour. We then assess the term-structure and time-evolution of the risk premia for each of the markets.

Risk Premia in Electricity Forward Prices

Optimal asymmetric kernels

Kernels are typically justified as a smoothing device in nonparametric analysis. We provide alternative interpretations which could lead to the use of asymmetric kernels. We thus derive the class of optimal asymmetric kernels, and analyse its main properties. We illustrate numerically its optimality by showing how well it fares in locating the mode and tail quantiles of some common asymmetric densities.

Optimal Asymmetric Kernels

The finite-sample null distribution of the Jarque–Bera Lagrange multiplier test for normality differs considerably from the asymptotic χ2(2). However, asymptotic critical values are commonly used in applied work, even for relatively small sample sizes. Here, very accurate response surface approximations are developed for the 10% and 5% critical values of the test, which enable correct practical implementation.

/pdf/finite-sample-quantiles-of-the-jarque-bera-test-zkye7c6968.pdf

Finite-sample quantiles of the Jarque–Bera test

We develop a flexible multifactor stochastic model with Markov regime-switching spikes, for daily spot and forward electricity. The model captures various stylized features of power prices, including mean reversion and seasonal patterns, and short- lived spikes. Parameters are estimated through a practical two-step procedure, that combines pre-calibration of deterministic elements and spikes, and state-space estimation of diffusive factors. We use several results on affine jump diffusions to combine the spike and diffusive components, and to provide convenient closed-form solutions for important power derivatives. We also propose a simple nonparametric model for hourly spot prices, based on hourly profile sampling from historical data. This model can reproduce complicated intraday patterns, and enables fast numerical pricing of hourly options. We illustrate the performance of the daily and hourly models using data from the Amsterdam Power Exchange.

Steve Lawford

Papers

Risk Premia in Electricity Forward Prices

Optimal asymmetric kernels

Optimal Asymmetric Kernels

Finite-sample quantiles of the Jarque–Bera test

Practical stochastic modelling of electricity prices