Ignacio N. Lobato

Real and Spurious Long-Memory Properties of Stock-Market Data

We test for the presence of long memory in daily stock returns and their squares using a robust semiparametric procedure of Lobato and Robinson. Spurious results can be produced by nonstationarity and aggregation. We address these problems by analyzing subperiods of returns and using individual stocks. The test results show no evidence of long memory in the returns. By contrast, there is strong evidence in the squared returns.

Long Memory in Stock-Market Trading Volume

This article examines consistent estimation of the long-memory parameters of stock-market trading volume and volatility. The analysis is carried out in the frequency domain by tapering the data instead of detrending them. The main theoretical contribution of the article is to prove a central limit theorem for a multivariate two-step estimator of the memory parameters of a nonstationary vector process. Using robust semiparametric procedures, the long-memory properties of trading volume for the 30 stocks in the Dow Jones Industrial Average index are analyzed. Two empirical results are found. First, there is strong evidence that stock-market trading volume exhibits long memory. Second, although it is found that volatility and volume exhibit the same degree of long memory for most of the stocks, there is no evidence that both processes share the same long-memory component.

A Nonparametric Test for I(0)

There is frequently interest in testing that a scalar or vector time series is I(0), possibly after first-differencing or other detrending, while the I(0) assumption is also taken for granted in autocorrelation-consistent variance estimation. We propose a test for I(0) against fractional alternatives. The test is nonparametric, and indeed makes no assumptions on spectral behaviour away from zero frequency. It seems likely to have good efficiency against fractional alternatives, relative to other nonparametric tests. The test is given large sample justification, subjected to a Monte Carlo analysis of finite sample behaviour, and applied to various empirical data series.

Averaged periodogram estimation of long memory

Abstract This paper discusses estimates of the parameter H ϵ ( 1 2 , 1) which governs the shape of the spectral density near zero frequency of a long memory time series. The estimates are semiparametric in the sense that the spectral density is parameterized only within a neighborhood of zero frequency. The estimates are based on averages of the periodogram over a band consisting of m equally-spaced frequencies which decays slowly to zero as sample size increases. Robinson (1994a) proposed such an estimate of H which is consistent under very mild conditions. We describe the limiting distributional behavior of the estimate and also provide Monte Carlo information on its finite-sample distribution. We also give an expression for the asymptotic mean squared error of the estimate. In addition to depending on the bandwidth number m, the estimate depends on an additional user-chosen number q, but we show that for H ϵ ( 1 2 , 3 4 ) there exists an optimal q for each H, and we tabulate this.

A semiparametric two-step estimator in a multivariate long memory model

This paper analyzes a two-step estimator of the long memory parameters of a vector process. The objective function considered is a semiparametric version of the multivariate Gaussian likelihood function in the frequency domain. In our context, semiparametric refers to the fact that only periodogram ordinates evaluated in a degenerating neighborhood of zero frequency are employed in the estimation procedure. Asymptotic normality is established under mild conditions that do not include Gaussianity. Furthermore, the simplicity of the form of the covariance matrix of the estimates facilitates statistical inference. We include an application of these estimates to exchange rate data.

Testing That a Dependent Process Is Uncorrelated

An analysis is presented of a new testing procedure for the null hypothesis that a stochastic process is uncorrelated when the process is possibly dependent. Unlike with existing procedures, the user does not need to choose any arbitrary number to implement the proposed test. The asymptotic null distribution of the proposed test statistic is not standard, but it is tabulated by means of simulations. The test is compared with two alternative test procedures that require selection of user-chosen numbers on the basis of asymptotic local power and finite sample behavior. Although the asymptotic local power of the proposed test is lower than those corresponding to the alternative tests, in a Monte Carlo study I show that in small samples the test typically better controls the type I error and that the loss of power is not substantial.

TESTING FOR ZERO AUTOCORRELATION IN THE PRESENCE OF STATISTICAL DEPENDENCE

The problem addressed in this paper is to test the null hypothesis that a time series process is uncorrelated up to lag K in the presence of statistical dependence. We propose an extension of the Box–Pierce Q-test that is asymptotically distributed as chi-square when the null is true for a very general class of dependent processes that includes non-martingale difference sequences. The test is based on a consistent estimator of the asymptotic covariance matrix of the sample autocorrelations under the null. The finite sample performance of this extension is investigated in a Monte Carlo study.

Testing for Autocorrelation Using a Modified Box-Pierce Q Test

This article investigates the finite-sample performance of a modified Box-Pierce Q statistic (Q*) for testing that financial time series are uncorrelated without assuming statistical independence. The finite-sample rejection probabilities of the Q* test under the null and its power are examined in experiments using time series generated by an MA (1) process where the errors are generated by a GARCH (1, 1) model and by a long memory stochastic volatility model. The tests are applied to daily currency returns.

Testing the Martingale Difference Hypothesis

Abstract In this paper we consider testing that an economic time series follows a martingale difference process. The martingale difference hypothesis has typically been tested using information contained in the second moments of a process, that is, using test statistics based on the sample autocovariances or periodograms. Tests based on these statistics are inconsistent since they cannot detect nonlinear alternatives. In this paper we consider tests that detect linear and nonlinear alternatives. Given that the asymptotic distributions of the considered tests statistics depend on the data generating process, we propose to implement the tests using a modified wild bootstrap procedure. The paper theoretically justifies the proposed tests and examines their finite sample behavior by means of Monte Carlo experiments.

Debt composition and balance sheet effects of exchange rate volatility in Mexico: a firm level analysis

We use Mexican firm-level data to study the role of currency mismatches in exacerbating the negative effects of a devaluation in the corporate sector and to investigate what drives Mexican firms to borrow in foreign currency. Our results show that large firms and exporters tend to borrow more heavily in foreign currency. The presence of foreign currency denominated debt poses a significant risk to balance sheets at the time of devaluation. Our findings suggest that in Mexico, the balance sheet effects of a devaluation far outweigh the competitiveness effects.