Statistical tests of stochastic process models used in the financial theory of insurance companies

This paper presents a statistical test allowing the analyst to determine if a given time series is statistically incompatible with being modeled as a linear or log-linear process. Since the commonly used models for financial time series of interest to insurance professionals are linear or log-linear, this paper allows the analyst to verify the linearity of the model under investigation, or else points to the necessity of non-linear modeling. We also show how to test for time series Gaussianity using the same type of statistical test statistic. These results are applied to several financial data sets relevant to the financial operations of insurance companies.