Model-building Strategy

Finding appropriate models for time series is a nontrivial task. We will develop a multistep model-building strategy espoused so well by Box and Jenkins (1976). There are three main steps in the process, each of which may be used several times:
     1. model specification (or identification)
     2. model fitting, and
     3. model diagnostics.

         In model specification (or identification), the classes of time series models are selected that may be appropriate for a given observed series. In this step we look at the time plot of the series, compute many different statistics from the data, and also apply any knowledge of the subject matter in which the data arise, such as biology, business, or ecology. It should be emphasized that the model chosen at this point is tentative and subject to revision later on in the analysis. In choosing a model, we shall attempt to adhere to the principle of parsimony; that is, the model used should require the smallest number of parameters that will adequately represent the time series. Albert Einstein is quoted in Parzen (1982, p. 68) as remarking that “everything should be made as simple as possible but not simpler.”
        The model will inevitably involve one or more parameters whose values must be estimated from the observed series. Model fitting consists of finding the best possible estimates of those unknown parameters within a given model. We shall consider criteria such as least squares and maximum likelihood for estimation.
        Model diagnostics is concerned with assessing the quality of the model that we have specified and estimated. How well does the model fit the data? Are the assumptions of the model reasonably well satisfied? If no inadequacies are found, the modeling may be assumed to be complete, and the model may be used, for example, to forecast future values. Otherwise, we choose another model in the light of the inadequacies found; that is, we return to the model specification step. In this way, we cycle through the three steps until, ideally, an acceptable model is found.
          Because the computations required for each step in model building are intensive, we shall rely on readily available statistical software to carry out the calculations and do the plotting.

Son değiştirme: 12 February 2016, Friday, 20:28