| A new discrete-time stochastic process model is introduced. The model is suitable for exploring the growth trend of positive time series whose mean and variance are increasing with time. It is shown that the increase in the mean is eventually governed by two numbers, namely the growth order and the growth tendency. A consistent estimator for the growth tendency is derived, assuming that the growth order is known in advance. A particular case of the model utilizes the Pareto distribution and its use is suggested in certain situations where there is a high probability of observing atypically large data. A plot to explore whether the model is suitable for particular data and an application to the S&P 500 stock market index are described. |
