What is this about?

What is an AR Model? An Auto Regressive Model, or simply an AR-Model, is a statistical model for time series. The main assumption is that the value in time $t+1$ is a linear combination of the $p$ previous values. The $p$ parameter is called the order of the model. Hence an auto regressive model of order $p$ can be concisily referred to as an $AR(p)$ model. Given $\{x_t\}_{t=0}^{n}$ data points the main assumption of an AR($p$) model is expresed through the following equation: ...

What is a Fractional Integral? It was shown a previous post how to define and calculate a function’s $\alpha$-th fractional integral, where $\alpha$ is a non-negative real number. Using this technique one can also define a function’s $\alpha$-th primitive. Now one will be able to see what such a primitive actually looks like through three examples. Recall that the $\alpha$-th primitive of $f_0$ is defined as $$ f_{\alpha}(x) := \frac{1}{\Gamma(\alpha)} \int_0^{x} (x - s)^{\alpha-1} f_0(s) ds. $$ ...

Hermann Weyl Hermann Klaus Hugo Weyl was a german mathematician born in 1885. His doctorate was awarded at the University of Göttingen under the supervision of David Hilbert. Moreover, Weyl was an important member of the Institute for Advanced Study, in Princeton. In the paper Bemerkungen zum Begriff des Differentialquotienten gebrochener Ordnung Weyl introduced the concept of fractional integral. The paper’s title can be unofficially and amateurly translated as Notes on the Concept of Fractional Derivative. ...