Adrian Pagan

A Simple Test for Heteroscedasticity and Random Coefficient Variation

A simple test for heteroscedastic disturbances in a linear regression model is developed using the framework of the Lagrangian multiplier test. For a wide range of heteroscedastic and random coefficient specifications, the criterion is given as a readily computed function of the OLS residuals. Some finite sample evidence is presented to supplement the general asymptotic properties of Lagrangian multiplier tests.

Alternative Models for Conditional Stock Volatility

This paper compares several statistical models for monthly stock return volatility. The focus is on U.S. data from 1834-19:5 because the post-1926 data have been analyzed in more detail by others. Also, the Great Depression had levels of stock volatility that are inconsistent with stationary models for conditional heteroskedasticity, We show the importance of nonlinearities in stock return behavior that are not captured by conventional ARCH or GARCH models. We also show the nonstationariry of stock volatility, even over the 1834-1925 period.

Dissecting the cycle: a methodological investigation ☆

Following Burns and Mitchell we define the cycle as a pattern in the level of aggregate economic activity. An algorithm to locate turning points is developed, as is a new measure of pro-cyclicality. A link between turning points and the moments of the series is established thereby providing the statistical foundation that Burns and Mitchells work lacked. Using these tools we are able to dissect cycles in terms of the contributions made by trend growth, volatility, serial correlation and non-linear effects. We dissect several models and find little evidence that certain non-linear effects are important to the nature of business cycles.

The econometrics of financial markets

Abstract The paper provides a survey of the work that has been done in financial econometrics in the past decade. It proceeds by first establishing a set of stylized facts that are characteristics of financial series and then by detailing the range of techniques that have been developed to model series which possess these characteristics. Both univariate and multivariate models are considered.

Two Stage and Related Estimators and Their Applications

This paper aims to provide a unified treatment of the properties of two stage estimators. General conditions are set forth for consistency, efficiency and correct inferences. Applications of the general theorems are made to models with expectations and diagnostic tests. The general approach frequently enables much simpler derivation of existing results, and provides a number of new ones.

Diagnostic tests as residual analysis

Many applied workers are strongly oriented to residual analysis for assessing model adequacy. Formal test statistics of adequacy however are frequently derived from likelihood theory, particularly through Lagrange Multipliers. In contraGt, the present paper derives the formal statistics by concentrating Upon the distribution of residuals. It is shown that most existing tests can be derived in this way from a few elementary principles of specification analysis. One advantage of this alternative methodology is that it highlights some difficulties in existing approaches and simultaneously indicates a resolution of them; a good example being testing for heteroscedasticity in simultaneous equations. Other issues such as independence and robustness of diagnostic tests are also easily explored within the proposed framework.

The Phillips Curve in Australia

In this paper we discuss the development of Phillips curves in Australia over the forty years since Phillips first estimated one using Australian data. We examine the central issues faced by researchers estimating Australian Phillips curves. These include the distinction between the short and long-run trade-offs between inflation and unemployment, and the changing level of the non-accelerating inflation rate of unemployment (NAIRU), particularly in the 1970s. We estimate Phillips curves for prices and unit labour costs in Australia over the past three decades. These Phillips curves allow the NAIRU to change through time, and include a role for import prices and ‘speed-limit’ effects. The paper concludes by presenting an extended discussion of the changing role of the Phillips curve in the intellectual framework used to analyse inflation within the Reserve Bank of Australia over the past three decades.

Estimating the Density Tail Index for Financial Time Series

The tail index of a density has been widely used as an indicator of the probability of getting a large deviation in a random variable. Most of the theory underlying popular estimators of it assume that the data are independently and identically distributed (i.i.d.). However, many recent applications of the estimator have been to financial data, and such data tend to exhibit long-range dependence. We show, via Monte Carlo simulations, that conventional measures of the precision of the estimator, which are based on the i.i.d. assumption, are greatly exaggerated when such dependent data are used. This conclusion also has implications for estimates of the likelihood of getting some extreme values, and we illustrate the changed conclusions one would get using equity return data.

A Survey of Some Recent Econometric Methods

This survey is written mainly for the applied economist though we hope that the specialist econometrician will find something of interest too. Our aim has been to try to bring the applied worker as up to date as possible, and in the process to improve the quality of applied work, by providing access to the latest ideas in econometrics. We have tried to describe and explain in a relatively non-technical way the main developments that have taken place in the last ten years. Partly for reasons of space the survey is by no means exhaustive but it does cover a wide range of topics in both time-series and cross-section analysis. Among the subjects covered are the followoing: the nature of data (including integrated and fractionally integrated data), four estimation methods (maximum likelihood, method of moments, M-estimators and non-parametric estimation), inference (with stationary and integrated regressors), a comparison of various model evaluation principles, the formulation of models (including dynamic specification, cointegration and conditional expectations in mean and variance). Copyright 1989 by Royal Economic Society.

Testing for covariance stationarity in stock market data

Abstract This paper proposes several non-parametric tests for covariance stationarity and applies them to common stock return data from 1834–1987. Recursive variance plots, post-sample prediction tests, Cumulative Sum (henceforth, CUSUM) tests and modified scaled range tests all show strong non-stationarity in stock returns, primarily due to the large increase in volatility during the Great Depression. These tests should be useful as diagnostics for data where the assumptions underlying the desired statistical procedure require stationarity.