An exclusive study of a general class of multichannel stacking filters is made. They are designed in the time domain as optimum multichannel Wiener filters for various models of random stationary processes and include some known stacking filters as special cases. It is shown that filters of this class may be specified as two- and three-dimensional velocity filters, polarisation filters and stacking filters for the rejection or enhancement of signals with differential normal moveout. The two- and three-dimensional Fourier transforms are used as valuable tools for the characterisation of velocity filters. Transforms for special differential moveout filters are also given. The concept of a stacking filter transfer function is defined and it is shown under which conditions it can be obtained from the two- or three-dimensional Fourier transform of a filter. It gives a deep insight into the filter characteristics. A discussion of the given multichannel normal equations shows how to select special time windows to obtain zero phase transfer functions. Zero phase stacking filter components do not necessarily guarantee zero phase transfer functions, while non-zero phase components may give phasefree transfer functions. Some rules for the characteristics of the class of filters are presented. They are used in the design of special velocity filters, which have superior properties over known velocity filters. A study of the presented multichannel normal equations leads as well to the discovery of the 'scaling effect'. This effect helps to reduce computer calculations of filters. It also explains observations connected with their characterisation and application. Because the filter design depends on a host of design parameters, computational experiments were done to show in which way important parameters influence filter characteristics. A short re-appraisal of the basic theory of time series analysis is given. The theory of continuous and discrete stacking filters is also reviewed.