Parameter estimation

In this context, $\nu$ (or, in the time domain, l) are no longer independent variables. They are treated like any of the other parameters: i.e. are assumed to be random variables to be estimated from the observations by fitting a model. Parameter estimation in the frequency domain is best done by fitting models using $\chi^2$statistics (least squares). The MIDAS TSA package contains just one such model, namely Fourier series (SINEFIT/TSA). However, note that with its non-linear least-squares fitting package, MIDAS offers very versatile, dedicated tools for model fitting (see Chapter 8 in Vol. 8 of the MIDAS User Guide).

In the time domain, the most important parameters to be estimated from the data are the correlation length of and time lag between the input signals. This measurement can be done with the command WIDTH/TSA. The correlation length can be obtained as the width of the line centered at zero lag. The time lag can be measured as the center of the corresponding line in the ACF.