On parameter estimation for locally stationary long-memory processes

We consider parameter estimation for time-dependent locally stationary long-memory processes. The asymptotic distribution of an estimator based on the local infinite autoregressive representation is derived, and asymptotic formulas for the mean squared error of the estimator, and the asymptotically optimal bandwidth are obtained. In spite of long memory, the optimal bandwidth turns out to be of the order n^(-1/5) and inversely proportional to the square of the second derivative of d. In this sense, local estimation of d is comparable to regression smoothing with iid residuals.long memory, fractional ARIMA process, local stationarity, bandwidth selection

Optimal Convergence Rates in Nonparametric Regression with Fractional Time Series Errors

Optimal rate of convergence, nonparametric regression, long memory, antipersistence.

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.

Efficient wald tests for fractional unit roots

In this article we introduce efficient Wald tests for testing the null hypothesis of the unit root against the alternative of the fractional unit root. In a local alternative framework, the proposed tests are locally asymptotically equivalent to the optimal Robinson Lagrange multiplier tests. Our results contrast with the tests for fractional unit roots, introduced by Dolado, Gonzalo, and Mayoral, which are inefficient. In the presence of short range serial correlation, we propose a simple and efficient two-step test that avoids the estimation of a nonlinear regression model. In addition, the first-order asymptotic properties of the proposed tests are not affected by the preestimation of short or long memory parameters.Publicad

Efficient wald tests for fractional unit roots

In this article we introduce efficient Wald tests for testing the null hypothesis of unit root against the alternative of fractional unit root. In a local alternative framework, the proposed tests are locally asymptotically equivalent to the optimal Robinson (1991, 1994a) Lagrange Multiplier tests. Our results contrast with the tests for fractional unit roots introduced by Dolado, Gonzalo and Mayoral (2002) which are inefficient. In the presence of short range serial correlation, we propose a simple and efficient two-step test that avoids the estimation of a nonlinear regression model. In addition, the first order asymptotic properties of the proposed tests are not affected by the pre-estimation of short or long memory parameter

Detecting long-range dependence in non-stationary time series

An important problem in time series analysis is the discrimination between non-stationarity and longrange dependence. Most of the literature considers the problem of testing specific parametric hypotheses of non-stationarity (such as a change in the mean) against long-range dependent stationary alternatives. In this paper we suggest a simple approach, which can be used to test the null-hypothesis of a general non-stationary short-memory against the alternative of a non-stationary long-memory process. The test procedure works in the spectral domain and uses a sequence of approximating tvFARIMA models to estimate the time varying long-range dependence parameter. We prove uniform consistency of this estimate and asymptotic normality of an averaged version. These results yield a simple test (based on the quantiles of the standard normal distribution), and it is demonstrated in a simulation study that - despite of its semi-parametric nature - the new test outperforms the currently available methods, which are constructed to discriminate between specific parametric hypotheses of non-stationarity short- and stationarity long-range dependence.Comment: Keywords and phrases: spectral density, long-memory, non-stationary processes, goodness-of-fit tests, empirical spectral measure, integrated periodogram, locally stationary process, approximating model

A SIMPLE FRACTIONALLY INTEGRATED MODEL WITH A TIME-VARYING LONG MEMORY PARAMETER Dt

This paper generalizes the standard long memory modeling by assuming that the long memory parameter d is stochastic and time varying: we introduce a STAR process on this parameter characterized by a logistic function. We propose an estimation method of this model. Some simulation experiments are conducted. The empirical results suggest that this new model offers an interesting alternative competing framework to describe the persistent dynamics in modelling some financial series.Long-memory, Logistic function, STAR