Umberto Triacca

Evidence of recent causal decoupling between solar radiation and global temperature

The Sun has surely been a major external forcing to the climate system throughout the Holocene. Nevertheless, opposite trends in solar radiation and temperatures have been empirically identified in the last few decades. Here, by means of an inferential method—the Granger causality analysis—we analyze this situation and, for the first time, show that an evident causal decoupling between total solar irradiance and global temperature has appeared since the 1960s.

Non-causality: The role of the omitted variables

Abstract In this paper a proof is offered that if a variable Y 3 does not cause a variable Y 1 in the bivariate system ( Y 1 , Y 3 ) and Y 3 causes a variable Y 1 in higher-order system ( Y 1 , Y 2 , Y 3 ), then the omitted variable Y 2 must cause the variable Y 1 in the bivariate system ( Y 1 , Y 2 ) and in the trivariate system ( Y 1 , Y 2 , Y 3 ).

Testing for Equal Predictability of Stationary ARMA Processes

Abstract In this work we use a measure of predictability of a time series following a stationary ARMA process to develop a test of equal predictability of two or more time series. The test is derived by a set of propositions which links the structure of the AR and MA coefficients to the predictability measure. A particular case of this general approach is constituted by time series having a Wold decomposition with weights having the same sign; in this framework the equal predictability is equivalent to parallelism among ARMA models and the null hypothesis of equal predictability is simply a set of linear restrictions. The ARMA representation of the GARCH models presents non-negative weights, so that this test can be extended to verify the equal predictability of squared time series following GARCH structures.

On the variance of the error associated to the squared return as proxy of volatility

In this article we derive, under two different stochastic volatility models, the expression of the variance of the error associate to the use of the squared return as proxy of daily volatility.

Feedback, causality and distance between arma models

The purpose of this paper is to analyze in bivariate vector autoregression the relationship between feedback in stochastic systems, Granger causality and a measure of dissimilarity between ARMA models. In particular, we consider a bivariate vector autoregressive processes of order p (a bivariate VAR(p) process) and we prove if the distance between the univariate ARMA models implied by the VAR representation is greater than a certain number that is a function of p, then Granger causality must exist in at least one direction in the variables.

Measuring persistence in time series of temperature anomalies

Studies on persistence are important for the clarification of statistical properties of the analyzed time series and for understanding the dynamics of the systems which create these series. In climatology, the analysis of the autocorrelation function has been the main tool to investigate the persistence of a time series. In this paper, we propose to use a more sophisticated econometric instrument. Using this tool, we obtain an estimate of the persistence in global land and ocean and hemispheric temperature time series.

On the Hsiao definition of non-causality

Abstract Granger (Granger, C.W.J., 1969. Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37, 424–438.) defined causality between two variables X and Y in terms of predictability. A difficulty with this definition is that it is restricted to one-step ahead prediction. In the presence of a third environment variable Z the non-causality properties depend on the horizon of the involved prediction. Hsiao (Hsaio, C., 1982. Autoregressive modelling and causal ordering of economic variables. Journal of Economic Dynamic and Control 4, 243–259.) proposed a generalization of the Granger notion of causality. The main purpose of this paper is to show that the Hsiao non-causality properties do not depend on the horizon of involved prediction.

COINTEGRATION AND DISTANCE BETWEEN INFORMATION SETS

This paper investigates Granger noncausality and the cointegrating relation between two time series in the Hilbert space framework. This framework allows us to analyze the relationship between cointegration and distance between two information sets. In particular, we prove that if two variables, X and Y , are cointegrated, then the distance between two information sets, concerning the differenced series Δ X and Δ Y , must be less than the standard deviation of Δ X .

Latitudinal variability of the dynamic linkage between temperature and atmospheric carbon dioxide concentrations

In this paper, a novel data-driven approach is used to investigate the presence of spatial differences in the dynamic linkage between temperature and atmospheric carbon dioxide concentrations. This linkage seems to be latitude dependent. The main findings of the study are as follows. In the latitude belts surrounding the equator (0°− 24° N and 0°− 24° S), the link seems very similar. On the opposite, the patterns of the temperature CO2 link in the Arctic is very distant from those concerning the equatorial regions and other latitude bands in the South Hemisphere. This big distance is consistent with the so-called Arctic amplification phenomenon. Further, it is important to underline that this observational data-based analysis provides an independent statistical confirmation of the results from global circulation modelling.

Erratum to ON the variance of the error associated to the squared return as proxy of volatility: [Applied Financial Economics Letters, 2007, 3, 255–7]

This is correct if zt had not been standardized. Given that zt is standardized as we describe at the end of Section II, this expectation should be unity (this mistake has been found by Prof. David Giles). On p. 257 it then follows that the expection of et is zero and we have unbiasedness. This, of course, then affects and simplifies the calculation for the variance that follows. In particular, we have that, if SV-t model (M2) holds, the correct formula for the variance of et, is