A new bootstrap approach for Gaussian long memory time series.

In this work we introduce a new bootstrap approach based on a result of Ramsey (1974) and on the Durbin-Levinson algorithm to obtain surrogate series from linear Gaussian processes with long range dependence. First we investigate properties of this type of bootstrap, then we apply the method to semi-parametric estimators of the long memory parameter. We find out that the performance of our bootstrap procedure is superior, in terms of MSE, to other established approaches

Bootstrap approaches for estimation and condence intervals of long memory processes.

In this work we investigate an alternative bootstrap approach based on a result of Ramsey (1974) and on the Durbin-Levinson algorithm to obtain surrogate series from linear Gaussian processes with long range dependence. We compare this bootstrap method with other existing procedures in a wide Monte Carlo experiment by estimating, parametrically and semiparametrically, the memory parameter d. We consider Gaussian and non-Gaussian processes to prove the robustness of the method to deviations from Normality. The approach is useful also to estimate condence intervals for the memory parameter d by improving the coverage level of the interval

Frequency Domain Local Bootstrap in long memory time series

Bootstrap techniques in the frequency domain have been proved to be effective instruments to approximate the distribution of many statistics of weakly dependent (short memory) series. However their validity with long memory has not been analysed yet. This paper proposes a Frequency Domain Local Bootstrap (FDLB) based on resampling a locally studentised version of the periodogram in a neighbourhood of the frequency of interest. A bound of the Mallows distance between the distributions of the original and bootstrap periodograms is offered for stationary and non-stationary long memory series. This result is in turn used to justify the use of FDLB for some statistics such as the average periodogram or the Local Whittle (LW) estimator. Finally, the finite sample behaviour of the FDLB in the LW estimator is analysed in a Monte Carlo, comparing its performance with rival alternatives.Research supported by the Spanish Ministry of Science and Innovation and ERDF grants ECO2016-76884-P, ID2019-105183GB-I00 and UPV/EHU Econometrics Research Group (Basque Government grantIT1359-1

Frequency Domain Local Bootstrap in long memory time series

Bootstrap techniques in the frequency domain have been proved to be effective instruments to approximate the distribution of many statistics of weakly dependent (short memory) series. However their validity with long memory has not been analysed yet. This paper proposes a Frequency Domain Local Bootstrap (FDLB) based on resampling a locally studentised version of the periodogram in a neighbourhood of the frequency of interest. A bound of the Mallows distance between the distributions of the original and bootstrap periodograms is offered for stationary and non-stationary long memory series. This result is in turn used to justify the use of FDLB for some statistics such as the average periodogram or the Local Whittle (LW) estimator. Finally, the finite sample behaviour of the FDLB in the LW estimator is analysed in a Monte Carlo, comparing its performance with rival alternatives.Research supported by the Spanish Ministry of Science and Innovation and ERDF grants ECO2016-76884-P, ID2019-105183GB-I00 and UPV/EHU Econometrics Research Group (Basque Government grantIT1359-1

Essays on robust long memory inference

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Long Run And Cyclical Dynamics In The Us Stock Market

This paper examines the long-run dynamics and the cyclical structure of the US stock market using fractional integration techniques. We implement a version of the tests of Robinson (1994a), which enables one to consider unit roots with possibly fractional orders of integration both at the zero (long-run) and the cyclical frequencies. We examine the following series: inflation, real risk-free rate, real stock returns, equity premium and price/dividend ratio, annually from 1871 to 1993. When focusing exclusively on the long-run or zero frequency, the estimated order of integration varies considerably, but nonstationarity is found only for the price/dividend ratio. When the cyclical component is also taken into account, the series appear to be stationary but to exhibit long memory with respect to both components in almost all cases. The exception is the price/dividend ratio, whose order of integration is higher than 0.5 but smaller than 1 for the long-run frequency, and is between 0 and 0.5 for the cyclical component. Also, mean reversion occurs in all cases. Finally, we use six different criteria to compare the forecasting performance of the fractional (at both zero and cyclical frequencies) models with others based on fractional and integer differentiation only at the zero frequency. The results show that the former outperform the others in a number of cases

25 Years of IIF Time Series Forecasting: A Selective Review

We review the past 25 years of time series research that has been published in journals managed by the International Institute of Forecasters (Journal of Forecasting 1982-1985; International Journal of Forecasting 1985-2005). During this period, over one third of all papers published in these journals concerned time series forecasting. We also review highly influential works on time series forecasting that have been published elsewhere during this period. Enormous progress has been made in many areas, but we find that there are a large number of topics in need of further development. We conclude with comments on possible future research directions in this field.Accuracy measures; ARCH model; ARIMA model; Combining; Count data; Densities; Exponential smoothing; Kalman Filter; Long memory; Multivariate; Neural nets; Nonlinearity; Prediction intervals; Regime switching models; Robustness; Seasonality; State space; Structural models; Transfer function; Univariate; VAR.

Long Run and Cyclical Dynamics in the US Stock Market

This paper examines the long-run dynamics and the cyclical structure of various series related to the US stock market using fractional integration. We implement a procedure which enables one to consider unit roots with possibly fractional orders of integration both at the zero (long-run) and the cyclical frequencies. We examine the following series: inflation, real risk-free rate, real stock returns, equity premium and price/dividend ratio, annually from 1871 to 1993. When focusing exclusively on the long-run or zero frequency, the estimated order of integration varies considerably, but nonstationarity is found only for the price/dividend ratio. When the cyclical component is also taken into account, the series appear to be stationary but to exhibit long memory with respect to both components in almost all cases. The exception is the price/dividend ratio, whose order of integration is higher than 0.5 but smaller than 1 for the long-run frequency, and is between 0 and 0.5 for the cyclical component. Also, mean reversion occurs in all cases. Finally, we use six different criteria to compare the forecasting performance of the fractional (at both zero and cyclical frequencies) models with others based on fractional and integer differentiation only at the zero frequency. The results show that the former outperforms the others in a number of cases.stock market, fractional cycles, long memory, Gegenbauer processes