  Functional data often arise as sequential temporal observations over a
continuous state-space. A set of functional data with a possible change in its
structure may lead to a wrong conclusion if it is not taken in to account. So,
sometimes, it is crucial to know about the existence of change point in a given
sequence of functional data before doing any further statistical inference. We
develop a new methodology to provide a test for detecting a change in the mean
function of the corresponding data. To obtain the test statistic we provide an
alternative estimator of the covariance kernel. The proposed estimator is
asymptotically unbiased under the null hypothesis and, at the same time, has
smaller amount of bias than that of the existing estimator. We show here that
under the null hypothesis the proposed test statistic is pivotal
asymptotically. Moreover, it is shown that under alternative hypothesis the
test is consistent for large enough sample size. It is also found that the
proposed test is more powerful than the available test procedure in the
literature. From the extensive simulation studies we observe that the proposed
test outperforms the existing one with a wide margin in power for moderate
sample size. The developed methodology performs satisfactorily for the average
daily temperature of central England and monthly global average anomaly of
temperatures.
