Chapter 2 introduces the baseline version of the VAR model, with its basic statistical assumptions that we examine in the sequel. We first check whether the variables in the VAR can be transformed to meet these assumptions. We analyze the univariate characteristics of the series. Important properties are a bounded spectrum, the order of (seasonal) integration, linearity and normality after the appropriate transformation. Subsequently, these properties are contrasted with the properties of stochastic fractional integration. We suggest data-analytic tools to check the assumption of univariate unit root integration. In an appendix we give a detailed account of unit root tests for stochastic unit root nonstationarity versus deterministic nonstationarity at frequencies of interest. Chapter 3 first discusses local and global influence analysis, which should point out the observations with the most notable impact on the estimates of location and covariance parameters. The results from this analysis can be helpful in spotting the sources of possible problems with the baseline model. After the influence analysis we discuss the merits of various statistical diagnostic tests for the adequacy of the separate regression equations. After one has estimated the unrestricted VAR one should check some overall characteristics of the system. We present several suggestions on how to do this. Chapter 4 deals with common sources of misspecification stemming from problems with seasonality and seasonal adjustment in the multivariate model. We discuss a number of univariate unobserved component models for stochastic seasonality, giving additional insight into the properties of models with unit root nonstationarity. We also suggest a modification of a simple but quite robust seasonal adjustment procedure. Some new data-analytic tools are introduced to examine the seasonal component more closely. Appendix A4.1 discusses the limitations of deterministic modeling of seasonality. Appendix A4.2 treats aspects of backforecasting in models with ...