The Likelihood of a Continuous-time Vector Autoregressive Model

This paper provides a method that weakens conditions under which the exact likelihood of a continuous-time vector autoregressive model can be derived. In particular, the method does not require the restrictions extant methods impose on discrete data that limit the applicability of continuous-time methods to real economic time series. The method applies generally to higher-order continuous-time systems involving mixed stock and flow data.Continuous-time, Vector autoregression, Exact likelihood, Time series

The shine of precious metals around the global financial crisis

Figuerola-Ferretti thanks the Spanish Ministry of Education and Science for support under grants MICINN ECO2010-19357, ECO2012-36559 and ECO2013-46395, and McCrorie, The Carnegie Trust for the Universities of Scotland under grant no. 31935.We analyze the price behavior of the main precious metals – gold, silver, platinum and palladium – before, during and in the aftermath of the 2007–08 financial crisis. Using the mildly explosive/multiple bubble technology developed by Phillips, Shi and Yu (2015, International Economic Review 56(4), 1043–1133), we find significant, short periods of mildly explosive behavior in the spot and futures prices of all four metals. Fewer periods are detected using exchange-rate adjusted prices, and almost none when deflated prices are used. We assess whether these findings are indicative of bubble behavior. Convenience yield is shown to have little efficacy in this regard, while other fundamental proxy variables and position data offer only very limited evidence against prices having been anything other than fundamentals-driven. Possible exceptions are in gold in the run-up to the highpoint of the financial crisis, and in silver and palladium around the launch of specific financial products. Some froth, however, is reported and discussed for each metal.PostprintPeer reviewe

Robert Neumann’s Hochstaplernovelle: the imaginary Balkans, Mediterranean and Central Europe

Hochstaplernovelle, Robert Neumann’s novella published in 1930, can be read as a distinct genre variety of the trickster theme (a topic popular in German literature), but is also analytically interesting due to its troubled representation of the Balkan complex. Consequently, this article focuses on the function of the Balkan discourse in Neumann’s fictional prose as well as its localization at the Mediterranean (nowadays Croatian) coastline of the former Dual Monarchy. Strategies of fictionalization employed in the novella point to a polyvalent potential of the Balkan discourse. The notion of Balkanism is understood and analysed as a discursive formation: references to older Balkan discourses from the cultural and historic space of the former monarchy quoted in the novella can therefore be described in terms of “nesting Orientalism” (Bakic-Hayden), a phenomenon in symbolic geography

Moments in Pearson’s four-step uniform random walk problem and other applications of very well-poised generalized hypergeometric series

This paper considers the representation of odd moments of the distribution of a four-step uniform random walk in even dimensions, which are based on both linear combinations of two constants representable as contiguous very well-poised generalized hypergeometric series and as even moments of the square of the complete elliptic integral of the first kind. Neither constants are currently available in closed form. New symmetries are found in the critical values of the L-series of two underlying cusp forms, providing a sense in which one of the constants has a formal counterpart. The significant roles this constant and its counterpart play in multidisciplinary contexts is described. The results unblock the problem of representing them in terms of lower-order generalized hypergeometric series, offering progress towards identifying their closed forms. The same approach facilitates a canonical characterization of the hypergeometry of the parbelos, adding to the characterizations outlined by Campbell, D'Aurozio and Sondow (2020, The American Mathematical Monthly 127(1) , 23-32). The paper also connects the econometric problem of characterizing the bias in the canonical autoregressive model under the unit root hypothesis to very well-poised generalized hypergeometric series. The confluence of ideas presented reflects a multidisciplinarity that accords with the approach and philosophy of Prasanta Chandra Mahalanobis.Peer reviewe

Moments in Pearson’s four-step uniform random walk problem and other applications of very well-poised generalized hypergeometric series

This paper considers the representation of odd moments of the distribution of a four-step uniform random walk in even dimensions, which are based on both linear combinations of two constants representable as contiguous very well-poised generalized hypergeometric series and as even moments of the square of the complete elliptic integral of the first kind. Neither constants are currently available in closed form. New symmetries are found in the critical values of the L-series of two underlying cusp forms, providing a sense in which one of the constants has a formal counterpart. The significant roles this constant and its counterpart play in multidisciplinary contexts is described. The results unblock the problem of representing them in terms of lower-order generalized hypergeometric series, offering progress towards identifying their closed forms. The same approach facilitates a canonical characterization of the hypergeometry of the parbelos, adding to the characterizations outlined by Campbell, D'Aurozio and Sondow (2020, The American Mathematical Monthly 127(1), 23-32). The paper also connects the econometric problem of characterizing the bias in the canonical autoregressive model under the unit root hypothesis to very well-poised generalized hypergeometric series. The confluence of ideas presented reflects a multidisciplinarity that accords with the approach and philosophy of Prasanta Chandra Mahalanobis

The role of Skorokhod space in the development of the econometric analysis of time series

This paper discusses the fundamental role played by Skorokhod space, through its underpinning of functional central limit theory, in the development of the paradigm of unit roots and co-integration. This paradigm has fundamentally affected the way economists approach economic time series as was recognized by the award of the Nobel Memorial Prize in Economic Sciences to Robert F. Engle and Clive W.J. Granger in 2003. Here, we focus on how P.C.B. Phillips and others used the Skorokhod topology to establish a limiting distribution theory that underpinned and facilitated the development of methods of estimation and testing of single equations and systems of equations with possibly integrated regressors. This approach has spawned a large body of work that can be traced back to Skorokhod's conception of fifty years ago. Much of this work is surprisingly confined to the econometrics literature

Estimating continuous-time models on the basis of discrete data via an exact discrete analog

This paper offers a perspective on A.R. Bergstrom's contribution to continuous-time modeling, focusing on his preferred method of estimating the parameters of a structural continuous-time model using an exact discrete-time analog. Some inherent difficulties in this approach are discussed, which help to explain why, in spite of his prescience, the methods around his time were not universally adopted as he had hoped. Even so, it is argued that Bergstrom's contribution and legacy is secure and retains some relevance today for the analysis of macroeconomic and financial time series.</p