First-order moving average processes associated by interval exchange maps
Keywords:
moving average process, interval exchange map, strictly stationary process, covariance function.Abstract
Abstract—In present work we investigate the nonlinear first-order
moving average processes associated by interval exchange maps h.
Let random process X := {Xn, n ≥ 1} defined by
Xn+1(h) := h(ξn) +ξn+1 , n ∈ Z,
where bξ := {ξn, n ≥ 1} is independent, identically uniformly distributed on interval [0,1] random sequence. We investigate the random process X for stationarity and find their distribution function
and autocovariance function.
References
Coelho Z., Lopes A., da Rocha L.F.Absolutely continuous invariant measures for a class of affine interval exchange maps // American Mathematical Society. 1995. Vol. 123, No 11. P. 3533.
P.J.Brockwell, R.A.Davis.: Introduction to Time Series and Forecasting. 3rd edition. Springer Texts in Statistics, Springer International Publishing Switzerland, 2016.
A.Klenke.: Probability Theory: A Comprehensive Course. Springer , 2007.
D.C.Montgomery, C.L.Jennings, M.Kulahci.: Introduction to Time Series Analysis and Forecasting (Wiley Series in Probability and Statistics). 2nd edition. Wiley Interscience, 2015.
S.Zhang, Z.Lin, X.Zhang. A Least Squares Estimator for Levy-Driven Moving Averages Based Discrete Time
Observations // Communications in Statistics-Theory and Methods. 2013. Vol. 44, No 6.
P.J.Brockwell. Recent results in the theory and aplications of CARMA processes // Ann.Inst. Stat.Math. 2014. Vol. 66, P. 637-685.
R.G.Laha, V.K.Rohatgi.: Probability Theory. Dover Publications, 2020.
H.Pishro-Nik.: Introduction to Probability, Statistics and Random Processes. Kappa Research, LLC, 2014
