Towards a raw-data dynamic structural model with its descriptive applications

Regarding the current development in multivariate time series analysis, this article contributes to the theory of dynamic structural equation model (DSEM) with an estimation procedure performed on raw data and macroeconomic uses. The analytical formulas for the score vector as well as blocks of the Hessian matrix are solved employing the differential, a viable alternative to matrix derivatives. Optimal terms have been used in the maximum likelihood (ML) technique based on a modified Newton iteration algorithm, undergoing selections from different calculus applications. Despite the relatively high dimension of the induced covariance matrix, singularity issues, or an initial evaluation in observed form, these issues are executed in subsequent numerical experiments directed at the tourism industry. The processing of the full latent system in European countries is supported by several procedures utilized as special cases. The general usefulness of methods, contributed by the fluctuating action of both the consumer price index and trade openness, is particularly interesting.