Statistics

1809 Submissions

[2] viXra:1809.0279 [pdf] replaced on 2018-09-15 17:18:26

Autoregressive and Rolling Moving Average Processes using the K-matrix with Discrete but Unequal Time Steps

Authors: Stephen P. Smith
Comments: 10 Pages.

The autoregressive and rolling moving average time series models are describe with discrete time steps that may be unequal. The standard time series is described, as well as a two-dimensional spatial process that is separable into two one-dimensional processes. The K-matrix representations for each of these are presented, which can then be subjected to standard matrix handling techniques.
Category: Statistics

[1] viXra:1809.0044 [pdf] submitted on 2018-09-02 17:36:12

Stochastic Spline Functions with Unequal Time Steps

Authors: Stephen P. Smith
Comments: 13 Pages.

A piece-wise quadratic spline is introduced as a time series coming with unequal time steps, and where the second derivative of the spline at the junction points is impacted by random Brownian motion. A measurement error is also introduced, and this changes the spline into semi-parametric regression. This makes a total of two dispersion parameters to be estimated by a proposed REML analysis that unitizes the K-matrix. The spline itself only has three location effects that are treated as fixed, and must be estimated. A proposed prediction of a future observation beyond the spline’s end point is presented, coming with a prediction error variance.
Category: Statistics