A Test Against Spurious Long Memory, first version: August 2008; this version: April 22, 2009.

This paper proposes a test statistic for the null hypothesis that a given time series is a stationary long memory process against the alternative hypothesis that it is of short memory, affected by regime change or a smoothly varying trend. The proposed test is in the frequency domain and explores the derivatives of the profiled local Whittle likelihood function in a degenerating neighborhood of the origin. The assumptions adopted are the same as in Robinson (1995b), which allow for non-Gaussianity. The resulting null limiting distribution is nuisance parameter free and can be easily simulated. The test is straightforward to implement: no kernel smoothing is required and no estimation of nuisance parameters is necessary. Also, there is no need to specify the number or locations of the different regimes that occur under the alternative hypothesis. Monte Carlo simulation shows that the test has good size, even for relatively small sample sizes, and that it has excellent power against alternatives of interest.

A Stochastic Volatility Model with Random Level Shifts: Theory and Applications to S&P 500 and Nasdaq Indices, (with Pierre Perron), June 2008.

Empirical findings related to the time series properties of stock returns volatility indicate autocorrelations that decay slowly at long lags. In light of this, several long-memory models have been proposed. However, the possibility of level shifts has been advanced as a possible explanation for the appearance of long-memory and there is growing evidence suggesting that it may be an important feature of stock returns volatility. Nevertheless, it remains a conjecture that a model incorporating random level shifts in variance can explain the data well and produce reasonable forecasts. We show that a very simple stochastic volatility model incorporating both a random level shift and a short-memory component indeed provides a better in-sample fit of the data and produces forecasts that are no worse, and sometimes better, than standard stationary short and long-memory models. We use a Bayesian method for inference and develop algorithms to obtain the posterior distributions of the parameters and the smoothed estimates of the two latent components. We apply the model to daily S&P 500 and NASDAQ returns over the period 1980.1-2005.12. Although the occurrence of a level shift is rare, about once every two years, the level shift component clearly contributes most to the total variation in the volatility process. The half-life of a typical shock from the short-memory component is very short, on average between 8 and 14 days. We also show that, unlike common stationary short or long-memory models, our model is able to replicate keys features of the data. For the NASDAQ series, it forecasts better than a standard stochastic volatility model, and for the S&P 500 index, it performs equally well.

An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts, (with Pierre Perron), November 2007. Recently, there has been an upsurge of interest on the possibility of confusing long memory and structural changes in level. Many studies have shown that when a stationary short memory process is contaminated by level shifts the estimate of the fractional differencing parameter is biased away from zero and the autocovariance function exhibits a slow rate of decay, akin to a long memory process. We analyze the properties of the log periodogram estimate of the memory parameter when the jump component is specified by a simple mixture model. Our theoretical results explain many findings reported and uncover new features. Simulations are presented to highlight the properties of the distributions and to assess the adequacy of our approximations. We also show the usefulness of our results to distinguish between long memory and level shifts via an application to the volatility of daily returns for wheat commodity futures. Note: This is a revised version of parts of a working paper entitled "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts and its Implications for Stock Returns Volatility".

Semiparametric Bayesian Inference in Non-Gaussian State Space Models