On the detection of LRD phenomena

A new model-testing paradigm is introduced. The proposed method uses the structure of the autocorrelation function of the model that we would like to fit the data to. We start by estimating the autocorrelation function of the data, and then apply a curve-fitting criterion, which we call the optimization method. If the resultant error is high, then the given process fails the test and may not be considered to follow that particular model. Otherwise, the process is assumed to be long-range dependent following the assumed model with the parameter as estimated. The criteria that we followed to decide whether the error is large or not is the probability of false alarm. For a wide range of the parameter, we develop a relation between the the probability of false alarm and the cutoff to decide how large the error can be. This paradigm is illustrated through the Second-Order Self-Similar (SOSS) model which is an example of a Long-Range Dependent (LRD) model. We perform an empirical study using artificial SOSS data to make a proper decision on the cutoff and to obtain empirical confidence intervals and bias. To better evaluate this proposed method, we tested the method on two sets of real data that are known to be LRD, and on artificial and real data that is known not to be LRD. Although we focus on processes that are LRD, the new method is readily generalizable to other processes. In other words, the new method can be used as a tool to check the validity of a model in characterizing certain process.