2015/09/04 by Robert Stelzer, Stelzer, Robert, Żywilla fechner +1 · 1 citation
Mathematics · #60G10 #60G51 #62M10 #62M15 #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Probability (math.PR) #Statistics Theory (math.ST) #math.PR #math.ST #msc:60G10 #msc:60G51 #msc:62M10 #msc:62M15 #stat.ME #stat.TH
paper · pdf · doi:10.48550/arxiv.1509.01384
arxiv created 2016/08/15 · arxiv updated 2016/08/16
This paper considers a continuous time analogue of the classical autoregressive moving average processes, Lévy-driven CARMA processes. First we describe limiting properties of the periodogram by means of the so-called truncated Fourier transform if observations are available continuously. The obtained results are in accordance with their counterparts from the discrete-time case. Then we discuss the numerical approximation of the truncated Fourier transform based on non-equidistant high frequency data. In order to ensure convergence of the numerical approximation to the true value of the truncated Fourier transform a certain control on the maximal distance between observations and the number of observations is needed. We obtain both convergence to the continuous time quantity and asymptotic normality under a high-frequency infinite time horizon limit.