Elena Andreou

Rolling-sample volatility estimators: Some new theoretical, simulation, and empirical results

We propose extensions of the continuous record asymptotic analysis for rolling sample variance estimators developed for estimating the quadratic variation of asset returns, referred to as integrated or realized volatility. We treat integrated volatility as a continuous time stochastic process sampled at high frequencies and suggest rolling sample estimators which share many features with spot volatility estimators. We discuss asymptotically efficient window lengths and weighting schemes for estimators of the quadratic variation and establish links between various spot and integrated volatility estimators. Theoretical results are complemented with extensive Monte Carlo simulations and an empirical investigation.

A Comparison of the Statistical Properties of Financial Variables in the USA, UK and Germany Over the Business Cycle

This paper presents business cycle stylized facts for the US, UK and German economies. We examine whether financial variables (interest rates, stock market price indices, dividend yields and monetary aggregates) predict economic activity over the business cycle, and we investigate the nature of any non-linearities in these variables. Leading indicator properties are examined using cross-correlations for both the values of the variables and their volatilities. Our results imply that the most reliable leading indicator across the three countries is the interest rate term structure, although other variables also appear to be useful for specific countries. The volatilities of financial variables may also contain predictive information for production growth as well as production volatility. Non-linearities are uncovered for all financial series, especially in terms of autoregressive conditional heteroscedasticity effects. Strong evidence of mean non-linearity is also found for many financial series and this can be associated with business cycle asymmetries in the mean. This is the case for a number of American and British financial variables, especially interest rates, but the corresponding evidence for Germany is confined largely to the real long-term rate of interest.

Rolling-Sample Volatility Estimators

We propose extensions of the continuous record asymptotic analysis for rolling sample variance estimators developed for estimating the quadratic variation of asset returns, referred to as integrated or realized volatility. We treat integrated volatility as a continuous time stochastic process sampled at high frequencies and suggest rolling sample estimators which share many features with spot volatility estimators. We discuss asymptotically efficient window lengths and weighting schemes for estimators of the quadratic variation and establish links between various spot and integrated volatility estimators. Theoretical results are complemented with extensive Monte Carlo simulations and an empirical investigation.

Statistical Adequacy and the Testing of Trend Versus Difference Stationarity

Abstract The debate on whether macroeconomic series are trend or difference stationary, initiated by Nelson and Plosser [Nelson, C. R.; Plosser, C. I. (1982). Trends and random walks in macroeconomic time series: some evidence and implications. Journal of Monetary Economics10:139–162] remains unresolved. The main objective of the paper is to contribute toward a resolution of this issue by bringing into the discussion the problem of statistical adequacy. The paper revisits the empirical results of Nelson and Plosser [Nelson, C. R.; Plosser, C. I. (1982). Trends and random walks in macroeconomic time series: some evidence and implications. Journal of Monetary Economics10:139–162] and Perron [Perron, P. (1989). The great crash, the oil price shock, and the unit root hypothesis. Econometrica57:1361–1401] and shows that several of their estimated models are misspecified. Respecification with a view to ensuring statistical adequacy gives rise to heteroskedastic AR(k) models for some of the price series. Based on estimated models which are statistically adequate, the main conclusion of the paper is that the majority of the data series are trend stationary.

Structural Breaks in Financial Time Series

This paper reviews the literature on structural breaks in financial time series. The second section discusses the implications of structural breaks in financial time series for statistical inference purposes. In the third section we discuss change-point tests in financial time series, including historical and sequential tests as well as single and multiple break tests. The fourth section focuses on structural break tests of financial asset returns and volatility using the parametric versus nonparametric classification as well as tests in the long memory and the distribution of financial time series. In concluding we provide some areas of future research in the subject.

On Modelling Speculative Prices: The Empirical Literature

Traditionally, financial theory and in particular asset pricing models have assumed (implicitly or explicitly) a certain probabilistic structure for speculative prices. The probabilistic structure is usually defined in terms of specific statistical models and relates to the dependence, heterogeneity and the distribution of such prices. The primary objective of this paper is to trace the development of various statistical models proposed since Bachelier (1900), in an attempt to assess how well these models capture the empirical regularities exhibited by data on speculative prices. Copyright 2001 by Blackwell Publishers Ltd

The behaviour of stock returns and interest rates over the business cycle in the US and UK

The paper studies the dynamic behaviour of the conditional mean and volatility of weekly financial variables in relation to the business cycle for the USA and UK economies. The mean US S&P stock returns steadily increases before a recession, then declines approximately six weeks prior to the trough date. Volatility reaches a local maximum 6 weeks prior to the recession, then peaks with the business cycle peak, but falls prior to the trough where the minimum is reached three weeks before. In the UK the FTSE volatility also falls before a recession but reaches its maximum 10 weeks after the peak date and has its minimum after the trough. Similarly, US interest rates are falling before a recession but there is no clear effect in the UK. The volatility of UK interest rates increases before and after the recession date. Overall more leading indicator information is provided by US stock returns and short interest rates whereas the respective UK variables seem to lag the business cycle phases.

Is Volatility Good for Growth? Evidence from the G7

We provide empirical support for an analytical DSGE model with nominal wage stickiness where growth is driven by learning-by-doing and money shocks and their variance are allowed to impact on long-run output growth. In our theoretical model the variance of monetary shocks has a negative effect on growth, while output volatility is good for growth as a positive relationship exists. Using a bivariate GARCH-M model we test the empirical conditional mean and variance relationships of nominal money and production growth rates in the G7 countries. We corroborate the theoretical model predictions with evidence from Bonferroni multiple tests across the G7.

Residual-Based Rank Specification Tests for AR-GARCH Type Models

This paper derives the asymptotic distribution for a number of rank-based and classical residual specification tests in AR-GARCH type models. We consider tests for the null hypotheses of no linear and quadratic serial residual autocorrelation, residual symmetry, and no structural breaks. For these tests we show that, generally, no size correction is needed in the asymptotic test distribution when applied to AR-GARCH type residuals obtained through QMLE estimation. To be precise, we give exact expressions for the limiting null distribution of the test statistics applied to residuals, and �?nd that standard critical values often lead to conservative tests. For this result, we give simple sufficient conditions. Simulations show that our asymptotic approximations work well for a large number of AR-GARCH models and parameter values. We also show that the rank-based tests often, though not always, have superior power properties over the classical tests, even if they are conservative. We thereby provide a useful extension to the econometrician’s toolkit. An empirical application illustrates the relevance of these tests to the AR-GARCH models for the weekly stock market return indices of some major and emerging countries.

Predicting the VIX and the Volatility Risk Premium: What's Credit and Commodity Volatility Risk Got to Do with It?

This paper presents an innovative approach to extracting factors which are shown to predict the VIX, the S&P 500 Realized Volatility and the Variance Risk Premium. The approach is innovative along two different dimensions, namely: (1) we extract factors from panels of filtered volatilities - in particular large panels of univariate financial asset ARCH-type models and (2) we price equity volatility risk using factors which go beyond the equity class. These are volatility factors extracted from panels of volatilities of short-term funding and long-run corporate spreads as well as volatilities of energy and metals commodities returns and sport/future spreads.