Non-stationarities in stock returns

The paper outlines a methodology for analyzing daily stock returns that relinquishes the assumption of global stationarity. Giving up this common working hypothesis reflects our belief that fundamental features of the financial markets are continuously and significantly changing. Our approach approximates locally the non-stationary data by stationary models. The methodology is applied to the S&P 500 series of returns covering a period of over seventy years of market activity. We find most of the dynamics of this time series to be concentrated in shifts of the unconditional variance. The forecasts based on our non-stationary unconditional modeling were found to be superior to those obtained in a stationary long memory framework or to those based on a stationary Garch(1,1) data generating process.stock returns, non-stationarities, locally stationary processes, volatility, sample autocorrelation, long range dependence, Garch(1,1) data generating process.

The cost of sustainability on optimal portfolio choices

We examine the impact of including sustainability related constraints on optimal portfolio selection. Our analysis covers an investment set containing the components of the S&P500 index from 1993 to 2008. The optimizations are performed according to the classical mean-variance approach while sustainability constraints are introduced by eliminating from the investment pool those assets that do not comply to given social responsibility criteria (screening). We compare the efficient frontiers with and without screening. The analysis is performed on the three main dimensions of sustainability, namely Environmental, Social and Governance. We find that socially responsible screening implies a small loss in terms of Sharpe Ratio even though it has a strong impact on the market capitalization of the optimal port-folio. The spanning test shows that the ex-post differences between the two frontiers, when short selling is not allowed, are significant only in the case of Environmental screeningSocially responsible investments, optimal portfolios, screening.

Is GARCH(1,1) as good a model as the Nobel prize accolades would imply?

This paper investigates the relevance of the stationary, conditional, parametric ARCH modeling paradigm as embodied by the GARCH(1,1) process to describing and forecasting the dynamics of returns of the Standard & Poors 500 (S&P 500) stock market index. A detailed analysis of the series of S&P 500 returns featured in Section 3.2 of the Advanced Information note on the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel reveals that during the period under discussion, there were no (statistically significant) differences between GARCH(1,1) modeling and a simple non-stationary, non-parametric regression approach to next-day volatility forecasting. A second finding is that the GARCH(1,1) model severely over-estimated the unconditional variance of returns during the period under study. For example, the annualized implied GARCH(1,1) unconditional standard deviation of the sample is 35% while the sample standard deviation estimate is a mere 19%. Over-estimation of the unconditional variance leads to poor volatility forecasts during the period under discussion with the MSE of GARCH(1,1) 1-year ahead volatility more than 4 times bigger than the MSE of a forecast based on historical volatility. We test and reject the hypothesis that a GARCH(1,1) process is the true data generating process of the longer sample of returns of the S&P 500 stock market index between March 4, 1957 and October 9, 2003. We investigate then the alternative use of the GARCH(1,1) process as a local, stationary approximation of the data and find that the GARCH(1,1) model fails during significantly long periods to provide a good local description to the time series of returns on the S&P 500 and Dow Jones Industrial Average indexes. Since the estimated coefficients of the GARCH model change significantly through time, it is not clear how the GARCH(1,1) model can be used for volatility forecasting over longer horizons. A comparison between the GARCH(1,1) volatility forecasts and a simple approach based on historical volatility questions the relevance of the GARCH(1,1) dynamics for longer horizon volatility forecasting for both the S&P 500 and Dow Jones Industrial Average indexes.stock returns, volatility, Garch(1,1), non-stationarities, unconditional time-varying volatility, IGARCH effect, longer-horizon forecasts

When did the 2001 recession really start?

The paper develops a non-parametric, non-stationary framework for business-cycle dating based on an innovative statistical methodology known as Adaptive Weights Smoothing (AWS). The methodology is used both for the study of the individual macroeconomic time series relevant to the dating of the business cycle as well as for the estimation of their joint dynamic. Since the business cycle is defined as the common dynamic of some set of macroeconomic indicators, its estimation depends fundamentally on the group of series monitored. We apply our dating approach to two sets of US economic indicators including the monthly series of industrial production, nonfarm payroll employment, real income, wholesale-retail trade and gross domestic product (GDP). We find evidence of a change in the methodology of the NBER’s Business-Cycle Dating Committee an extended set of five monthly macroeconomic indicators replaced in the dating of the last recession the set of indicators emphasized by the NBER’s Business- Cycle Dating Committee in recent decades. This change seems to seriously affect the continuity in the outcome of the dating of business cycle. Had the dating been done on the traditional set of indicators, the last recession would have lasted one year and a half longer. We find that, independent of the set of coincident indicators monitored, the last economic contraction began in November 2000, four months before the date of the NBER’s Business-Cycle Dating Committee.business cycle, non-parametric smoothing, non-stationarity

The IGARCH e®ect: Consequences on volatility forecasting and option trading

This paper studies the integrated Garch (IGARCH) e®ect, a phenomenon often encountered when estimating conditional auto-regressive models on ¯nancial time series. The analysis of twelve indexes of major ¯nancial markets provides empirical evidence of its well-spread presence especially in periods of market turbulence. We examine its impact on volatility forecasting and on trading and hedging options. We show that a strong IGARCH e®ect may have relevant consequences on trading and on risk management.stock returns, volatility forecasting, GARCH(1,1), IGARCH effect, option hedging

Why does the GARCH(1,1) model fail to provide sensible longer- horizon volatility forecasts?

The paper investigates from an empirical perspective aspects related to the occurrence of the IGARCH effect and to its impact on volatility forecasting. It reports the results of a detailed analysis of twelve samples of returns on financial indexes from major economies (Australia, Austria, Belgium, France, Germany, Japan, Sweden, UK, and US). The study is conducted in a novel, non-stationary modeling framework proposed in Starica and Granger (2005). The analysis shows that samples characterized by more pronounced changes in the unconditional variance display stronger IGARCH effect and pronounced differences between estimated GARCH(1,1) unconditional variance and the sample variance. Moreover, we document particularly poor longer-horizon forecasting performance of the GARCH(1,1) model for samples characterized by strong discrepancy between the two measures of unconditional variance. The periods of poor forecasting behavior can be as long as four years. The forecasting behavior is evaluated through a direct comparison with a naive non-stationary approach and is based on mean square errors (MSE) as well as on an option replicating exercise.stock returns, volatility forecasting, GARCH(1,1), IGARCH effect, hedging, non-stationary, longer horizon forecasting

Changes of structure in financial time series and the GARCH model

In this paper we propose a goodness of fit test that checks the resemblance of the spectral density of a GARCH process to that of the log-returns. The asymptotic behavior of the test statistics are given by a functional central limit theorem for the integrated periodogram of the data. A simulation study investigates the small sample behavior, the size and the power of our test. We apply our results to the S&P500 returns and detect changes in the structure of the data related to shifts of the unconditional variance. We show how a long range dependence type behavior in the sample ACF of absolute returns might be induced by these shifts.integrated periodogram, spectral distribution, functional central limit theorem, Kiefer--Muller process, Brownian bridge, sample autocorrelation, change point, GARCH process, long range dependence, IGARCH, non-stationarity

A simple non-stationary model for stock returns

The aim of the present peper is to show the example of the S&P 500 return series that a simple non-stationary model seem to fit the data significantly better than conventional GARCH-type models outperforming them also in forecasting the distribution of tomorrow\u27s return. Instead of a complex endogenous specification of the conditional variance, we assume that the volatility dynamics is exogenous. Since no obvious canadidates explanatory exogenous variables are at hand, we model the volatility as deterministic. This approach leads to a structurally simple regression-type model. Special attention is paid to the accurate descripion of the tails of the innovations

Long range dependence effects and ARCH modelling

Our study supports the hypothesis of global non-stationarity of the return time series. We bring forth both theoretical and empirical evidence that the long range dependence (LRD) type behavior of the sample ACF and the periodogram of absolute return series and the IGARCH effect documented in the econometrics literature could be due to the impact of non-stationarity on statistical instruments and estimation procedures. In particular, contrary to the common-hold belief that the LRD characteristic and the IGARCH phenomena carry meaningful information about the price generating process, these so-called stylized facts could be just artifacts due to structural changes in the data. The effect that the switch to a different regime has on the sample ACF and the periodogram is theoretically explained and empirically documented using time series that were the object of LRD modeling efforts (S&P500, DEM/USD FX) in various publications.sample autocorrelation, change point, GARCH process, long range dependence.