Normally when people say “time series” they mean some sort of container where each element has a time stamp associated with it, e.g. the TimeArray in the TimeSeries package. You just have a plain vector and whether there are meaningful differences between using an adjoint or a 1xn matrix likely depends on your application.
Why a row vector as such? A vector is inherently 1D, not either column or row. Even though in the context of linear algebra we tend to use them as though they were columns, it doesn’t have to be that way.