Mirrored alleyway in Switzerland.
Linear algebra
Oct 12, 2020 | 6 min read

Matrix Inverse

...for a nonsingular matrix. We talk about left and right inverses, *the* matrix inverse and orthogonal matrices.

Beer collection.
Time series
Oct 9, 2020 | 13 min read

Variability of Nonstationary Time Series

Using the Box-Cox power transformation to stabilize the variance. At the end of this section, the standard procedure for fitting an ARIMA model is discussed.

Petri dish with bacteria samples.
Time series
Oct 7, 2020 | 9 min read

Unit Root Test

A test that helps us determine whether differencing is needed or not. We also talk about over-differencing (don't do it!) and model selection (AIC/BIC and MAPE).

Night sky with stars.
Linear algebra
Oct 7, 2020 | 4 min read

Matrix Trace

Such a simple concept with so many properties and applications!

Lego!
Time series
Oct 5, 2020 | 9 min read

ARIMA Models

Combining differencing and ARMA models and we get ARIMA. The procedures of estimation, diagnosis and forecasting are very similar as that of ARMA models.

74 Bowne St, Brooklyn, NY
Linear algebra
Sep 30, 2020 | 7 min read

Linear Space of Matrices

The column space, row space and rank of a matrix and their properties.

Stock charts.
Time series
Sep 30, 2020 | 13 min read

Mean Trend

We introduce detrending and differencing, two methods that aim to remove the mean trends in time series.

Corner of a building.
Linear algebra
Sep 29, 2020 | 5 min read

Orthogonalization

Introducing the Gram-Schmidt process, a method for constructing an orthogonal basis given a non-orthogonal basis.

Projection on the Sydney Opera House.
Linear algebra
Sep 22, 2020 | 7 min read

Projection

Geometrically speaking, what is the projection of a vector onto another vector, and the projection of a vector onto a subspace?

Lots of arrows.
Linear algebra
Sep 15, 2020 | 6 min read

Definitions in Arbitrary Linear Space

This chapter provides an introduction to some fundamental geometrical ideas and results. We start by giving definitions for norm, distance, angle, inner product and orthogonality. The Cauchy-Schwarz inequality comes useful in many settings.