Long-memory process and aggregation of AR(1) stochastic processes: A new characterization

Contemporaneous aggregation of individual AR(1) random processes might lead to different properties of the limit aggregated time series, in particular, long memory (Granger, 1980). We provide a new characterization of the series of autoregressive coefficients, which is defined from the Wold representation of the limit of the aggregate stochastic process, in the presence of long-memory features. Especially the infinite autoregressive stochastic process defined by the almost sure representation of the aggregate process has a unit root in the presence of the long-memory property. Finally we discuss some examples using some well-known probability density functions of the autoregressive random parameter in the aggregation literature. JEL Classification Code: C2, C13

Support and distribution inference from noisy data

We consider noisy observations of a distribution with unknown support. In the deconvolution model, it has been proved recently [19] that, under very mild assumptions, it is possible to solve the deconvolution problem without knowing the noise distribution and with no sample of the noise. We first give general settings where the theory applies and provide classes of supports that can be recovered in this context. We then exhibit classes of distributions over which we prove adaptive minimax rates (up to a log log factor) for the estimation of the support in Hausdorff distance. Moreover, for the class of distributions with compact support, we provide estimators of the unknown (in general singular) distribution and prove maximum rates in Wasserstein distance. We also prove an almost matching lower bound on the associated minimax risk

A theoretical framework for trading experiments

A general framework is suggested to describe human decision making in a certain class of experiments performed in a trading laboratory. We are in particular interested in discerning between two different moods, or states of the investors, corresponding to investors using fundamental investment strategies, technical analysis investment strategies respectively. Our framework accounts for two opposite situations already encountered in experimental setups: i) the rational expectations case, and ii) the case of pure speculation. We consider new experimental conditions which allow both elements to be present in the decision making process of the traders, thereby creating a dilemma in terms of investment strategy. Our theoretical framework allows us to predict the outcome of this type of trading experiments, depending on such variables as the number of people trading, the liquidity of the market, the amount of information used in technical analysis strategies, as well as the dividends attributed to an asset. We find that it is possible to give a qualitative prediction of trading behavior depending on a ratio that quantifies the fluctuations in the model

Une étude asymptotique probabiliste des coefficients d’une série entière

19 pages, texte en françaisInternational audienceFollowing the ideas of Rosenbloom [7] and Hayman [5], Luis B ́aez-Duarte gives in [1] a probabi- listic proof of Hardy-Ramanujan's asymptotic formula for the partitions of an integer. The main principle of the method relies on the convergence in law of a family of random variables to a gaussian variable. In our work we prove a theorem of the Liapounov type (Chung [2]) that justifies this convergence. To obtain simple asymptotic formulæ a condition of the so-called strong Gaussian type defined by Luis B ́aez-Duarte is required; we demonstrate this in a situation that make it possible to obtain a classical asymptotic formula for the partitions of an integer with distinct parts (Erd ̈os-Lehner [4], Ingham [6])

P. Terencio Afro, Comedias, El Heautontimorumenos, Formión, texto revisado y traducido por Lisardo Rubio, Cathedratico de la Universitad de Barcelona, vol. II., 1961

Miniconi Pierre. P. Terencio Afro, Comedias, El Heautontimorumenos, Formión, texto revisado y traducido por Lisardo Rubio, Cathedratico de la Universitad de Barcelona, vol. II., 1961. In: Revue des Études Anciennes. Tome 65, 1963, n°1-2. pp. 201-204

Trümpy (Hans). Kriegerische Fachausdrücke im griechischen Epos ( Untersuchungen zum Wortschatze Homers)

Miniconi Pierre. Trümpy (Hans). Kriegerische Fachausdrücke im griechischen Epos ( Untersuchungen zum Wortschatze Homers). In: Revue belge de philologie et d'histoire, tome 31, fasc. 2-3, 1953. pp. 545-550