Last time we have seen that ARMA models can be integrated (and differentiated) to deal with non-stationarity present in the empirical data. ARIMA model should be sufficient in most cases, but if the empirical data is know to exhibit "true" long-range memory, then ordinary calculus will not work. In those cases one would have to use fractional calculus. Here we will take a brief look at fractional derivatives (and integrals).

Last time we have combined AR(p) and MA(q) models to make ARMA(p, q) model. We are getting quite close to understanding what ARFIMA processes are, but to do that we still have things to look at. This time lets take into account letter I (which stands for "integrated") - lets look at ARIMA models.

In this Numberphile video author and economist Tim Harford talks about where the babies come from and to what conclusions bad statistics can lead us to.

In the last few posts we have talked about how physical models relate to "economical" AR(p) models. Yet our end goal is to about ARFIMA models of which "AR" makes up just about 1/3rd. In this post we introduce you to MA(q) models and show how they combine AR(p) models to make up ARMA(p, q) models.

In the last few posts we have seen that random walk can be written in recursive form, which suggests that random walk is AR(1) process. We have also became familiar with the partial auto-correlation functions. Here in this post we show that PACF can provide an intuition on the order of AR which should be used in modeling the data.