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


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


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.

Tarot cards.
Time series
Sep 14, 2020 | 15 min read

Model Fitting and Forecasting

This model-building strategy consists of three steps: model specification (identification), model fitting, and model diagnostics.

Model toy cars.
Time series
Sep 13, 2020 | 8 min read

ARMA Model

The mean, variance, ACF and PACF of ARMA models. The backshift operator is introduced, and the stationarity and invertibility of the general ARMA(p, q) model is discussed.

Crowd in London underground.
Time series
Sep 5, 2020 | 6 min read

Moving Average Model

The mean, variance, ACF and PACF of moving average models. Instead of stationarity, a new property called invertibility is introduced.

Ocean clouds seen from space.
Linear algebra
Aug 31, 2020 | 8 min read

Vector Space

We introduce some basic terminology - vector space, subspace, span, basis, and dimension. These concepts lay the foundation for future discussions on matrices and matrix properties.