Testing for long memory in the presence of non-linear deterministic trends with Chebyshev polynomials

AbstractThis paper examines the interaction between non-linear deterministic trends and long run dependence by means of employing Chebyshev time polynomials and assuming that the detrended series displays long memory with the pole or singularity in the spectrum occurring at one or more possibly non-zero frequencies. The combination of the non-linear structure with the long memory framework produces a model which is linear in parameters and therefore it permits the estimation of the deterministic terms by standard OLS-GLS methods. Moreover, the orthogonality property of Chebyshev’s polynomials makes them especially attractive to approximate non-linear structures of data. We present a procedure which allows us to test (possibly fractional) orders of integration at various frequencies in the presence of the Chebyshev trends with no effect on the standard limit distribution of the method. Several Monte Carlo experiments are conducted and the results indicate that the method performs well. An empirical application, using data of real exchange rates is also carried out at the end of the article.

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Long Memory and Parity Reversion in Real Exchange Rate

Malaysian Management Journal ◽

10.32890/mmj.7.2.2003.8613 ◽

2020 ◽

Author(s):

Abd. Ghafar Ismail ◽

Wahi Ismail

Keyword(s):

Exchange Rate ◽

Exchange Rates ◽

Purchasing Power Parity ◽

Long Memory ◽

Real Exchange Rates ◽

Power Parity ◽

Equilibrium Relation ◽

Long Memory Process ◽

Long Run ◽

Floating Exchange Rate

This paper examines the post Bretton Woods experience of the Malaysian Ringgit. In this period, Malaysia moved from a managed to a floating exchange rate environment.We examine persistence in real exchange rates by estimating fractionally integrated ARIMA models and find evidence of long memory, which induces persistence though this long memory need not be associated with a unit root. The results show that three out of four exchange rates being examined display mean reversion. The long memory process re-establishes the Purchasing Power Parity as a meaningful concept of long-run equilibrium relation between the exchange rate and relative prices.

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What Goes Up Might Not Come Down: Modeling Directional Asymmetry with Large-N, Large-T Data

Sociological Methodology ◽

10.1177/00811750211046307 ◽

2021 ◽

pp. 008117502110463

Author(s):

Ryan P. Thombs ◽

Xiaorui Huang ◽

Jared Berry Fitzgerald

Keyword(s):

Fixed Effects ◽

Directional Asymmetry ◽

Cross Sectional ◽

Monte Carlo Experiments ◽

Long Run ◽

Large N ◽

Fixed Effects Estimator ◽

Cross Sectional Dependence ◽

Using Data ◽

Heterogeneous Panel

Modeling asymmetric relationships is an emerging subject of interest among sociologists. York and Light advanced a method to estimate asymmetric models with panel data, which was further developed by Allison. However, little attention has been given to the large- N, large- T case, wherein autoregression, slope heterogeneity, and cross-sectional dependence are important issues to consider. The authors fill this gap by conducting Monte Carlo experiments comparing the bias and power of the fixed-effects estimator to a set of heterogeneous panel estimators. The authors find that dynamic misspecification can produce substantial biases in the coefficients. Furthermore, even when the dynamics are correctly specified, the fixed-effects estimator will produce inconsistent and unstable estimates of the long-run effects in the presence of slope heterogeneity. The authors demonstrate these findings by testing for directional asymmetry in the economic development–CO2 emissions relationship, a key question in macro sociology, using data for 66 countries from 1971 to 2015. The authors conclude with a set of methodological recommendations on modeling directional asymmetry.

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Investigating in the J-curve phenomenon in Tunisia- ARDL bound test approach

Journal of Economics and Behavioral Studies ◽

10.22610/jebs.v12i5(j).3077 ◽

2020 ◽

Vol 12 (5(J)) ◽

pp. 23-32

Author(s):

Elham Shubaita ◽

Muhammad Mar’i ◽

Mehdi Seraj

Keyword(s):

Trade Balance ◽

Real Exchange Rates ◽

Distributed Model ◽

Long Run ◽

J Curve ◽

Short Run ◽

Using Data ◽

Bound Test ◽

The Relationship ◽

Ardl Bound Test

This paper investigates the relationship between trade balance, real exchange rates, and incomes in Tunisia by adopting the autoregressive distributed model (ARDL) by using data over the period of 1980 to 2018. We also used the bound test cointegration between variables at a 10% significant level. Our findings show that the Tunisia economy does not match the Marshall-Lerner condition in the long run, that provides an accurate description of the particular situation for which a country currency devaluation or depreciation its currency under both fixed or floating regime is predicted to enhance the trade balance of a country, which means there is no j-curve phenomenon in the long run, which tries to differentiate between the change of short-run and long-run effects in the change of exchange rate on the trade balance. Our findings match the Marshall-Lerner condition in the short run and can confirm the existing j-curve in the case of Tunisia.

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