In this paper, a synthesis of the recently advanced Lagrange multiplier (LM)-based tests for the null of no cointegration which account for different patterns of breaks in the cointegrating relationship is provided. The limiting distributions of the test statistics are not only invariant to an intercept break and a break in the cointegrating vector, but are also invariant to a trend break in a ...

For independent random variables, the order of growth of the convergent series Sn is studied in this paper. More specifically, if the series Sn converges almost surely to a random variable, the tail series is a well-defined sequence of random variables and converges to 0 almost surely. For the almost surely convergent series Sn, a tail series strong law of large numbers (SLLN) is constructed by...

In this paper the solution of the Volterra integro-differential equations of fractional order is presented. The proposed method consists in constructing the functional series, sum of which determines the function giving the solution of considered problem. We derive conditions under which the solution series, constructed by the method is convergent. Some examples are presented to verify convergen...