Dimensions.
Linear algebra
Nov 18, 2020
10 min read

Eigenvalues and Eigenvectors

If you’re a statistics major (or any science major really), you must have heard of these two words before. In this chapter, we’re going to …

Music mixing dials.
Time series
Nov 17, 2020
9 min read

Spectral Analysis

We talk about a method that helps us find the periodicity of a time series -- the spectral density.

Ship breaking down icebergs.
Linear algebra
Nov 4, 2020
15 min read

Quadratic Form

This long post covers the quadratic form and the positive definiteness of matrices. The decomposition of symmetric matrices is slightly touched on, and the entire post is mainly to prepare for the next chapter -- eigenvalues and eigenvectors.

Smooth waves.
Time series
Nov 2, 2020
14 min read

Decomposition and Smoothing Methods

Decomposition procedures to extract trend, seasonal and other components from a time series. Smoothing techniques like moving average and Lowess are often used, and exponential smoothing (Holt-Winters) is another powerful tool.

A box of keys.
Linear algebra
Oct 26, 2020
6 min read

Determinant

The determinant is a very important concept for square matrices, and its properties are key to various other notions such as block matrices and matrix inverses.

Shadows of a green plant.
Linear algebra
Oct 23, 2020
4 min read

Projection Matrix

We introduce idempotent matrices and the projection matrix. Both are very important concepts in statistical analyses such as linear regression.

Pragser Wildsee, Italy
Linear algebra
Oct 21, 2020
4 min read

Generalized Inverse

The generalized matrix inverse that applies to any $m \times n$ matrix.

Aerial view of a forest road in autumn.
Time series
Oct 13, 2020
17 min read

Seasonal Time Series

We introduce seasonal differencing, seasonal ARMA models, and combine them to get SARIMA models.

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.