F70TS 2016-17: Assessed Project
1. By simulating white noise data z1, z2, . . . , zn in R for a few values of n, investigate the quality of the Normal approximation
P ≈N2(n−2),16n−29 3 90
used in the turning points test of randomness. [6 Marks]
2. We will construct a test of the hypothesis that our time series data are independent based on the number of runs of increasing values present in the data.
Let k be a fixed integer with k ≥ 1. Suppose we have time series data Y1,Y2,…,Yn. We let Xt be an indicator random variable for the event that a run of k consecutive increasing values begins at time t, so that
Xt =1 ifYt