Abstract
This paper is concerned with the problem of identifiability of the parameters of a high frequency multivariate autoregressive model from mixed frequency time series data. We demonstrate identifiability for generic parameter values using the population second moments of the observations. In addition we display a constructive algorithm for the parameter values and establish the continuity of the mapping attaching the high frequency parameters to these population second moments. These structural results are obtained using two alternative tools viz. extended Yule Walker equations and blocking of the output process. The cases of stock and flow variables, as well as of general linear transformations of high frequency data, are treated. Finally, we briefly discuss how our constructive identifiability results can be used for parameter estimation based on the sample second moments.
Highlights
In many applications involving multivariate time series data, we encounter mixed frequency (MF) data, i.e., data where the univariate component time series are available at different sampling frequencies
The final aim of the analysis considered here is to directly estimate the parameters of the underlying high frequency model from the available MF data
The central problem considered in this paper is identifiability, i.e., whether, for given, the parameters Ai and ν of the high frequency system are uniquely determined by the population second moments of the observations
Summary
In many applications involving multivariate time series data, we encounter mixed frequency (MF) data, i.e., data where the univariate component time series are available at different sampling frequencies. Harvey and Pierse, 1984; Nijman, 1985; Kohn and Ansley, 1986; Zadrozny, 1990b; Bernanke, Gertler, Watson, Sims, and Friedman, 1997; Chen and Zadrozny, 1998; Marcellino, 1998; Mariano and Murasawa, 2003; Aruoba, Diebold, and Scotti, 2007; Wohlrabe, 2008; Ghysels and Wright, 2009; Marcellino and Schumacher, 2010; Ghysels, 2012) These approaches differ as far as their final aims, the model classes considered and the estimation procedures developed are concerned. This case is simpler than the general case, since here missing observations do not change the autoregressive structure and an explicit description of the (generic) set of all identifiable parameters can be derived. The Appendix consists of the proofs of Theorems 1, 2, 3, 5, 6, 7, and 8
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