Model Fitting and Forecasting

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

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.

Moving Average Model

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

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.

Linear Dependence and Independence

A short piece on linearly dependent and independent sets of vectors.

Autoregressive Series

We talk about autoregressive models of different orders, and introduce their mean, variance, ACF and PACF values. Its stationarity is also briefly discussed.

Introduction

We introduce some basic ideas of time series analysis and stochastic processes. Of particular importance are the concepts of stationarity and the autocovariance and sample autocovariance functions.

Matrices

Matrix algebra plays an important role in many areas of statistics, such as linear statistical models and multivariate analysis. In this chapter we introduce basic terminology and some basic matrix operations. We also introduce some basic types of matrices.

Linear Models

So far we’ve finished the main materials of this course - estimation and hypothesis testing. The starting point of all the statistical analyses …

Install Dependencies for Puppeteer on Manjaro Linux