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

Seasonal Time Series

In the last chapter, we learned about how to deal with mean and variance changes in time series data. Periodic patterns are also frequently observed, …

Linear algebra
Oct 12, 2020
3 min read

Matrix Inverse

... for a nonsingular matrix.

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).

Linear algebra
Oct 7, 2020
4 min read

Matrix Trace

The trace of a square matrix $\boldsymbol{A}: n \times n$ is the sum of the diagonals: $$ tr(\boldsymbol{A}) = \sum_{i=1}^n a_{ii} $$ The trace is …

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.

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 28, 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 21, 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?