Spectral properties of temporally aggregated long memory processes

This paper derives the spectral density function of aggregated long memory processes in light of the aliasing effect. The results are different from previous analyses in the literature and a small simulation exercise provides evidence in our favour. The main result point to that flow aggregates from long memory processes shall be less biased than stock ones, although both retain the degree of long memory. This result is illustrated with the daily US Dollar/ French Franc exchange rate series.

A note on Chambers's "long memory and aggregation in macroeconomic time series"

Chambers (1998) explores the interaction between long memory and aggregation. For continuous-time processes, he takes the aliasing effect into account when studying temporal aggregation. For discrete-time processes, however, he seems to fail to do so. This note gives the spectral density function of temporally aggregated long memory discrete-time processes in light of the aliasing effect. The results are different from those in Chambers (1998) and are supported by a small simulation exercise. As a result, the order of aggregation may not be invariant to temporal aggregation, specifically if d is negative and the aggregation is of the stock type.

The aliasing effect, the Fejer Kernel and temporally aggregated long memory processes

This paper derives the spectral density function of aggregated long memory processes in light of the aliasing effect. The results are different from previous analyses in the literature and a small simulation exercise provides evidence in our favour. The main result point to that flow aggregates from long memory processes shall be less biased than stock ones, although both retain the degree of long memory. This result is illustrated with the daily US Dollar/ French Franc exchange rate series.

To cointegrate or not to cointegrate? That's a topological question

We show that for any multivariate I( 1) process which does not cointegrate, it is possible to find another process sufficient1y elose to it where cointegration applies. Closeness is defined in terms of the spectral density matrices of the respective processes in differences, i.e., a metric which takes into account only the information in the (centred) second moments. The result may explain why in practice cointegration is found a bit "too often". Examples developing this point and simulations giving an insight on the metric used are also presented.

Terms of trade, macroeconomic dynamics and default decisions

A evidência empírica aponta que Termos de Troca é uma variável relevante tanto para dinâmica macroeconômica como para o risco de default em países emergentes. No entanto, a literatura de dívida soberana baseada nos trabalhos de Eaton e Gerzovitz (1981) e Arellano (2008) ainda não explorou de forma adequada as conecções entre a dinâmica de termos de troca e incentivos ao default. Nós contribuímos nessa área, introduzindo volatilidade de Termos de Troca no modelo proposto por Mendoza e Yue (2012), no qual as decisões de dívida soberana são vinculadas à um modelo de equilíbrio geral para a economia doméstica. Nós encontramos que uma economia exposta à volatilidade dos termos de troca consegue produzir uma variabilidade do consumo que supera significativamente a variabilidade do produto, característica que constitui um fato estilizado chave de business cycles de países emergentes. Nossos exercícios também mostram que decisões de default são geradas por mudanças bruscas nos termos de troca, mas não necessariamente estão vinculados à estados ruins da economia.