Financial time series including high frequency structures like jumps, spikes and stochastic volatility are usually modeled in an ad-hoc manner by stochastic differential equations together with Levy processes. Estimating the parameters and determining the jump size distributions do not have a precise and universally accepted method. Under these circumstances, complexities and confusions usually arise. This book, approaches to this issue from a very different angle through introducing an autocorrelation one process together with finite number of Fourier series terms. Introduction of Fourier series to estimate the dynamics of the process is not done in an ad-hoc manner or as done before in dealing with seasonality. Here the moving average is transformed to a “moving and fluctuating” average by the help of Fourier series. Instead of adding jump structures to the model which makes the parameter estimation quite cumbersome, our model in discrete time can easily be transformed to a well-known mean reverting continuous time process. Moreover, our alternative model turned out to be a quite powerful and accurate forecasting technique.

Underlying all these questions of right is the question how they are to be secured and maintained. By enforcing the responsibility of the executive and legislature to the community as a whole? Such is the general answer, and it indicates one of the lines of connection between the general theory of liberty and the doctrine of universal suffrage and the sovereignty of the people. The answer, however, does not meet all the possibilities of the case. The people as a whole might be careless of their rights and incapable of managing them. They might be set on the conquest of others, the expropriation of the rich, or on any form of collective tyranny or folly. It is perfectly possible that from the point of view of general liberty and social progress a limited franchise might give better results than one that is more extended. Even in this country it is a tenable view that the extension of the suffrage in 1884 tended for some years to arrest the development of liberty in various directions. On what theory does the principle of popular sovereignty rest, and within what limits does it hold good? Is it a part of the general principles of liberty and equality, or are other ideas involved? These are among the questions which we shall have to examine.

1. T. HOBHOUSE – 1911