Extended Yule-Walker Identification Of Varma Models With Single- Or Mixed Frequency Data

Chen and Zadrozny (1998) developed the linear extended Yule-Walker (XYW) method for determining the parameters of a vector autoregressive (VAR) model with available covariances of mixed-frequency observations on the variables of the model. If the parameters are determined uniquely for available population covariances, then, the VAR model is identified. The present paper extends the original XYW method to an extended XYW method for determining all ARMA parameters of a vector autoregressive moving-average (VARMA) model with available covariances of singleor mixed-frequency observations on the variables of the model. The paper proves that under conditions of stationarity, regularity, miniphaseness, controllability, observability, and diagonalizability on the parameters of the model, the parameters are determined uniquely with available population covariances of singleor mixed-frequency observations on the variables of the model, so that the VARMA model is identified with the singleor mixed-frequency covariances. The paper represents the author's views and does not necessarily represent any official positions of the Bureau of Labor Statistics. The paper was presented at the following conferences and seminars: NBER-NSF Time Series, Washington, 9/13; (EC) on "Mixed-Frequency Econometrics," Nicosia, 12/13; SNDE, New York City, 4/14; CEF, Oslo, 6/14; JSM, Boston, 8/14; KOF, Zurich, 12/14; CFE, Pisa, 12/14; NBP on "Identification in Macroeconomics," Warsaw, 12/14. Affiliated as Research Fellow with the Center for Financial Studies (CFS), Goethe University, Frankfurt, Germany, and with the Center for Economic Studies and Ifo Institute for Economic Research (CESifo), Munich, Germany. The paper has benefitted from comments by Manfred Deistler, Eric Ghysels, Roderick McCrorie, Tucker McElroy, and anonymous referees.