What are we learning about the long-run?

An attempt is made to link together earlier definitions of the long-run found in micro and macro economics with recent developments in econometrics; specifically cointegration. It is suggested that the links are not strong and that most of the previous work in econometric theory has been unnecessarily over-precise. Unit root processes can be replaced by processes that approximate them without loss of interpretation. The possibility of embedding cointegration theory into a very general non linear theory is suggested. An example uses a nonIinear relationship between UK short and long run interest rate proposed by Frank Paish

Time Series Analysis, Cointegration, and Applications

The two prize winners in Economics this year would describe themselves as "Econometricians," so I thought that I should start by explaining that term. One can begin with the ancient subject of Mathematics which is largely concerned with the discovery of relationships between deterministic variables using a rigorous argument. (A deterministic variable is one whose value is known with certainty.) However, by the middle of the last millennium it became clear that some objects were not deterministic, they had to be described with the use of probabilities, so that Mathematics grew a substantial sub-field known as "Statistics." This later became involved with the analysis of data and a number of methods have been developed for data having what may be called "standard properties."time series; cointegration

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.

What are we learning about the long-run?.

An attempt is made to link together earlier definitions of the long-run found in micro and macro economics with recent developments in econometrics; specifically cointegration. It is suggested that the links are not strong and that most of the previous work in econometric theory has been unnecessarily over-precise. Unit root processes can be replaced by processes that approximate them without loss of interpretation. The possibility of embedding cointegration theory into a very general non linear theory is suggested. An example uses a nonIinear relationship between UK short and long run interest rate proposed by Frank Paish.The long-run in microeconomics; The long-run in macroeconomics; Cointegration; Approximating unit roots; Cointegration in nonlinear models;

Investigating the relationship between gold and silver prices

This paper analyze the long-run relationship between gold and silver prices. The three main questions addressed are: the influence of a large bubble from 1979:9 to 1980:3 on the cointegration relationship, the extent to which by including error correction terms in a nonlinear way we can beat the random walk model out-of sample and, the existence of a strong simultaneous relationship between the rates of return of gold and silver. Different efficient single equation estimation techniques are required for each of the three questions and this is explained within a simple bivariante cointegration system. With monthly data from 1971 to 1990, it is found that cointegration could have occurred during some periods and specially during the bubble and post-bubble periodo However, dummy variables for the intercept of the long-ron relationships are needed during the full sample. For the price of gold the nonlinear models perform better than the random walk in-sample and out-of-sample. In-sample nonlinear models for the price of silver perform better than the random walk but this predictive capacity is lost out-of sample, mainly due to the structural change that occurs (reduction) in the variance of the out-of sample models. The in-sample and out-of sample predictive capacity of the nonlinear models is reduced when the variables are in logs. Clear and strong evidence is found for a simultaneous relationship between the rates of return of gold and silver. In the three type of relationships that we have analyzed between the prices of gold and silver, the dependence is less out-of sample, possibly meaning that the two markets are becoming separated

Modeling Amazon Deforestation for Policy Purposes

Brazil has long ago removed most of the perverse government incentives that stimulated massive deforestation in the Amazon in the 70s and 80s, but one highly controversial policy remains: Road building. While data is now abundantly available due to the constant satellite surveillance of the Amazon, the analytical methods typically used to analyze the impact of roads on natural vegetation cover are methodologically weak and not very helpful to guide public policy. This paper discusses the respective weaknesses of typical GIS analysis and typical municipality level regression analysis, and shows what would be needed to construct an ideal model of deforestation processes. It also presents an alternative approach that is much less demanding in terms of modeling and estimation and more useful for policy makers as well.Deforestation, Amazon, Brazil, econometric modeling

Is Seasonal Adjustment a Linear or Nonlinear Data Filtering Process?

In this paper, we investigate whether seasonal adjustment procedures are, at least approximately, linear data transformations. This question is important with respect to many issues including estimation of regression models with seasonally adjusted data. We focus on the X-11 program and first review the features of the program that might be potential sources of nonlinearity. We rely on simulation evidence, involving linear unobserved component ARIMA models, to assess the adequacy of the linear approximation. We define a set of properties for the adequacy of a linear approximation to a seasonal adjustment filter. These properties are examined through statistical tests. Next, we study the effect of X-11 seasonal adjustment on regression statistics assessing the statistical significance of the relationship between economic variables in the same spirit as Sims (1974) and Wallis (1974). These findings are complemented with several empirical examples involving economic data. Nous examinons si la procédure d'ajustement X-11 est approximativement linéaire. Il y a potentiellement plusieurs sources de non-linéarité dans cette procédure. Le but de l'étude est de savoir si ces sources sont effectivement assez importantes pour affecter, par exemple, des résultats d'estimation dans des modèles de régression linéaire. La seule façon de répondre à cette question est par estimation. Nous proposons plusieurs critères qu'on peut utiliser pour juger si une procédure d'ajustement est approximativement linéaire. Nous examinons également par simulation des propriétés de tests dans le modèle de régression dans le même esprit que Sims (1974) et Wallis (1974).X-11 program; Nonlinearity, X-11 program ; Nonlinearity