Joint Tests for Long Memory and Non-linearity: The Case of Purchasing Power Parity

A pervasive finding of unit roots in macroeconomic data often runs counter to intuition regarding the stochastic nature of the process under consideration. Two econometric techniques have been utilized in an attempt to resolve the finding of unit roots, namely long memory and models that depart from linearity. While the use of long memory and stochastic regime switching models have developed almost independently of each other, it is now clear that the two modeling techniques can be intimately linked. In particular, both modeling techniques have been used in isolation to study the dynamics of the real exchange rate. To determine the importance of each technique in this context, I employ a testing and estimation procedure that allows one to jointly test for long memory and non-linearity (regime switching behavior) of the STAR variety. I find that there is substantial evidence of non-linear behavior for the real exchange rate for many developing and European countries, with little evidence for ESTAR non-linearity for countries outside the European continent including Japan and Canada. In cases where non-linearity is found, I also find significant evidence of long memory for the majority of the countries in my sample. Thus, long memory and non-linearity can also be viewed as compliments rather than substitutes. On the other hand, a combination of long memory and non-linearity may be a promising research avenue for pursuing an answer to the paradoxreal exchange rates, long memory, ESTAR non-linearity

Long Memory Regressors and Predictive Regressions: A two-stage rebalancing approach

Predictability tests with long memory regressors may entail both size distortion and incompatibility between the orders of integration of the dependent and independent variables. Addressing both problems simultaneously, this paper proposes a two-step procedure that rebalances the predictive regression by fractionally differencing the predictor based on a first-stage estimation of the memory parameter. Extensive simulations indicate that our procedure has good size, is robust to estimation error in the first stage, and can yield improved power over cases in which an integer order is assumed for the regressor. We also extend our approach beyond the standard predictive regression context to cases in which the dependent variable is also fractionally integrated, but not cointegrated with the regressor. We use our procedure to provide a valid test of forward rate unbiasedness that allows for a long memory forward premium

Inference for likelihood-based estimators of generalized long-memory processes

Despite a recent proliferation of research using cyclical long memory, surprisingly little is known regarding the asymptotic properties of likelihood-based methods. Estimators have been studied in both the time and frequency domains for the Gegenbauer autoregressive moving average process (GARMA). However, a full set of asymptotic results for all parameters has only been proposed by Chung (1996a,b), who present somewhat tenuous results without an initial consistency proof. In this paper, we review the GARMA process and the properties of frequency and time domain likelihood-based estimators using Monte Carlo analysis. The results demonstrate the strong efficacy of both estimators and generally sup- port the proposed theory of Chung for the parameter governing the cycle length. Important caveats await. The results show that asymptotic confidence bands can be unreliable in very small samples under weak long memory, and the distribution theory under the null of an infinitely long cycle appears to be unusable. Possible solutions are proposed, including the use of narrower confidence bands and the application of theory under the alternative of finite cycles

Conditional Sum of Squares Estimation of Multiple Frequency Long Memory Models

We review the multiple frequency Gegenbauer autoregressive moving average model, which is able to reproduce a wide range of autocorrelation functions. Extending the result of Chung (1996a), we propose the asymptotic distributions for a conditional sum of squares estimator of the model parameters. The parameters that determine the cycle lengths are asymptotically independent, converging at rate T for finite cycles. This result does not hold generally, most notably for the differencing parameters associated with the cycle lengths. Remaining parameters are typically not independent and converge at the standard rate of T1/2. We present simulation results to explore small sample properties of the estimator, which strongly support most distributional results while also highlighting areas that merit additional exploration. We demonstrate the applicability of the theory and estimator with an application to IBM trading volume

Inference for likelihood-based estimators of generalized long-memory processes

Despite a recent proliferation of research using cyclical long memory, surprisingly little is known regarding the asymptotic properties of likelihood-based methods. Estimators have been studied in both the time and frequency domains for the Gegenbauer autoregressive moving average process (GARMA). However, a full set of asymptotic results for all parameters has only been proposed by Chung (1996a,b), who present somewhat tenuous results without an initial consistency proof. In this paper, we review the GARMA process and the properties of frequency and time domain likelihood-based estimators using Monte Carlo analysis. The results demonstrate the strong efficacy of both estimators and generally sup- port the proposed theory of Chung for the parameter governing the cycle length. Important caveats await. The results show that asymptotic confidence bands can be unreliable in very small samples under weak long memory, and the distribution theory under the null of an infinitely long cycle appears to be unusable. Possible solutions are proposed, including the use of narrower confidence bands and the application of theory under the alternative of finite cycles

Inference for likelihood-based estimators of generalized long-memory processes

Despite a recent proliferation of research using cyclical long memory, surprisingly little is known regarding the asymptotic properties of likelihood-based methods. Estimators have been studied in both the time and frequency domains for the Gegenbauer autoregressive moving average process (GARMA). However, a full set of asymptotic results for all parameters has only been proposed by Chung (1996a,b), who present somewhat tenuous results without an initial consistency proof. In this paper, we review the GARMA process and the properties of frequency and time domain likelihood-based estimators using Monte Carlo analysis. The results demonstrate the strong efficacy of both estimators and generally sup- port the proposed theory of Chung for the parameter governing the cycle length. Important caveats await. The results show that asymptotic confidence bands can be unreliable in very small samples under weak long memory, and the distribution theory under the null of an infinitely long cycle appears to be unusable. Possible solutions are proposed, including the use of narrower confidence bands and the application of theory under the alternative of finite cycles

Conditional Sum of Squares Estimation of Multiple Frequency Long Memory Models

We review the multiple frequency Gegenbauer autoregressive moving average model, which is able to reproduce a wide range of autocorrelation functions. Extending the result of Chung (1996a), we propose the asymptotic distributions for a conditional sum of squares estimator of the model parameters. The parameters that determine the cycle lengths are asymptotically independent, converging at rate T for finite cycles. This result does not hold generally, most notably for the differencing parameters associated with the cycle lengths. Remaining parameters are typically not independent and converge at the standard rate of T1/2. We present simulation results to explore small sample properties of the estimator, which strongly support most distributional results while also highlighting areas that merit additional exploration. We demonstrate the applicability of the theory and estimator with an application to IBM trading volume

Down but not out in posterior cingulate cortex : Deactivation yet functional coupling with prefrontal cortex during demanding semantic cognition

The posterior cingulate cortex (pCC) often deactivates during complex tasks, and at rest is often only weakly correlated with regions that play a general role in the control of cognition. These observations led to the hypothesis that pCC contributes to automatic aspects of memory retrieval and cognition. Recent work, however, has suggested that the pCC may support both automatic and controlled forms of memory processing and may do so by changing its communication with regions that are important in the control of cognition across multiple domains. The current study examined these alternative views by characterising the functional coupling of the pCC in easy semantic decisions (based on strong global associations) and in harder semantic tasks (matching words on the basis of specific non-dominant features). Increasingly difficult semantic decisions led to the expected pattern of deactivation in the pCC; however, psychophysiological interaction analysis revealed that, under these conditions, the pCC exhibited greater connectivity with dorsolateral prefrontal cortex (PFC), relative to both easier semantic decisions and to a period of rest. In a second experiment using different participants, we found that functional coupling at rest between the pCC and the same region of dorsolateral PFC was stronger for participants who were more efficient at semantic tasks when assessed in a subsequent laboratory session. Thus, although overall levels of activity in the pCC are reduced during external tasks, this region may show greater coupling with executive control regions when information is retrieved from memory in a goal-directed manner

Maternal DNA Methylation Regulates Early Trophoblast Development

This work was funded by the BBSRC, Wellcome Trust, MRC, the EC Network of Excellence EpiGeneSys, the EC BLUEPRINT project, the Centre for Trophoblast Research, and CIHR (grant MOP-119357 to L.L.). M.R.B. is a Sir Henry Dale Fellow (101225/Z/13/Z), jointly funded by the Wellcome Trust and the Royal Society