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CONTRIBUTION À LA PRÉVISION DES PROCESSUS ALÉATOIRES PAR L'ANALYSE HARMONIQUE

机译：调和分析对随机过程预测的贡献

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Historically statisticians had, in the field of the forecast of chronological series, a single series. Few pieces of information provided by the data directed the research for models. The appearance of computers and numerous and powerful means of communication generated a phenomenal number of data. It is not rare any more to have a family of chronological series which we would like to foresee. The forecast of that type(chap) of data,chronological series by chronological series, is unsatisfactory because it does not allow to take into account the information connected with the coherence of the family of trajectories.From 1945 Karhunen and Loeve had suggested a decomposition of a process by means of the base (fi ) of the eigen functions of the operator of covarianceIn1973 Jean Claude Deville uses that decomposition to achieve a study into the constitution of families in France. Our work is in the continuity of those precursors and suggests:1.the implementation of tools of analysis revealing the importance of the temporal components (couple made up of a value and of an eigenvector corresponding of the operator of covariance)2.the global forecast of the data from the continuation of those same components..The decomposition of Karhunem and Loeve makes it possible to write a process whose general term Xi is an elementary process; each elementary process being the product of a random variable and a function. We studied the reaction of the decomposition of Karhunen and Loeve when the time interval T varies and we showed the “proximity”, under certain conditions, of the elementary processes calculated on T and those calculated on T+h. On the other end we defined a strong indicator of loss of information which makes it possible to keep only a finite number of significant elementary processes. It is from those results onwards that we could suggest a method of forecast which observes the following procedure: 1.Décomposition of the process into elementary processes 2.Determination of the number of elementary processes to keep by using the strong index 3.Development of the temporal components kept using the methods of smoothing 4.Reconstitution of the data and forecast of the process To be able to carry out this work we developed a software under Windows which currently proposes a professional version. The two examples we treated (quarterly indexes of the industrial production in France from 1980 to 1988 , the consumption of electricity in France from 1972 to 1980) let us hope, if the data lend themselves to it,in an improvement of the precision.
机译：历史学家在时间序列预测领域中只有一个序列。数据提供的信息很少指导模型研究。计算机的出现和众多强大的通信方式产生了大量的数据。有一个我们希望可以预见的按时间顺序排列的系列不再是罕见的。按时间序列按时间序列对数据类型（章）进行的预测并不令人满意，因为它不允许考虑与轨迹族的连贯性有关的信息。从1945年开始，Karhunen和Loeve提出将1973年，让·克劳德·德维尔（Jean Claude Deville）使用该分解法对法国的家庭构成进行了研究。我们的工作是在这些前兆的连续性上提出，并提出以下建议：1.分析工具的实施揭示了时间成分（由值和与协方差算子相对应的特征向量组成的对偶）的重要性2.全球预测Karhunem和Loeve的分解使得写一个总称Xi为基本过程的过程成为可能。每个基本过程都是随机变量和函数的乘积。我们研究了当时间间隔T变化时Karhunen和Loeve分解的反应，并且在一定条件下，我们显示了在T上计算的基本过程和在T + h上计算的基本过程的“接近度”。另一方面，我们定义了一个强有力的信息丢失指标，该指标使仅保留有限数量的重要基本过程成为可能。从这些结果开始，我们可以提出一种遵循以下过程的预测方法：1.将过程分解为基本过程2.通过使用强指数确定要保留的基本过程的数量3。使用平滑方法保留时间成分。4.重建数据并预测过程为了能够执行此工作，我们在Windows下开发了一个软件，目前正在提供专业版本。我们处理的两个例子（1980年至1988年法国工业生产的季度指数，1972年至1980年法国的电力消耗）使我们希望，如果数据适合，可以提高精度。

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    Cohen Gabriel;

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  • 年度 1999
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