Modeling and large sample estimation for multi-casting autoregression

Multi-casting autoregression (MCAR, for short) is suggested as a natural extension of the bifurcating autoregressive (BAR) model (cf. [Cowan, R., Staudte, R.G., 1986. The bifurcating autoregression model in cell lineage studies. Biometrics 42, 769-783]) in order to analyze multi-splitting tree-structured data. Pathwise stationarity of the MCAR model is discussed. Least squares estimation for the autoregressive parameter is considered and relevant limiting distribution is derived, in particular, for the pathwise explosive case. These results can be regarded as generalizations of those for standard stationary and explosive AR(1) time series. A simulation study is conducted to illustrate our results.