Stochastic processes

Preface

Prerequisites

Learning ethics

Introduction

What is a stochastic process?

Space of states

A time series is a stochastic process indexed by a discrete monotonic increasing set.

Type of stochastic dependence between random variables

https://stats.stackexchange.com/questions/126791/is-a-time-series-the-same-as-a-stochastic-process

1.1 La ecuación de regresión lineal simple poblacional
1.2 Diagrama de dispersión
1.3 Estimación de la ecuación de regresión lineal simple
1.4 Confiabilidad de las predicciones
1.5 Prueba de hipótesis acerca del coeficiente de regresión

2.1 Modelo de regresión múltiple
2.2 Notación matricial
2.3 Prueba de hipótesis para los parámetros del modelo

3.1 Supuestos de la correlación simple
3.2 Coeficiente de correlación lineal poblacional
3.3 Coeficiente de correlación lineal muestral
3.4 Prueba de hipótesis acerca del coeficiente de correlación lineal

4.1 Elementos de una serie de tiempo
4.2 Tipos de series de tiempo
4.3 Estructura de una serie de tiempo
4.3.1 Tendencia
4.3.2 Estacionalidad
4.3.3 Movimientos cíclicos
4.3.4 Variaciones inesperadas
4.4 Modelos para el análisis de series de tiempo
4.4.1 Modelos de media cero
4.4.2 Caminata aleatoria
4.4.3 Modelos de tendencia
4.4.4 Modelos de estacionalidad

Why does time serie analysis matter to you?

Research

Ecosystem

Standards, jobs, industry, roles, …

Python libraries

https://github.com/lmmentel/awesome-time-series

https://github.com/rjt1990/pyflux

https://github.com/facebook/prophet

https://github.com/blue-yonder/tsfresh

https://www.aeon-toolkit.org/en/latest/

https://github.com/ethanrosenthal/skits

https://github.com/dmbee/seglearn

Story

FAQ

Worked examples

Characteristics of time series

The nature of time series data

Classic

Static covariates

Time series can contain static data.

Hierarchical time series

Exercises

  1. Logic. Mathematics. Code. Automatic Verification such as Lean Proven or Frama-C.
  1. Languages in Anki.

Projects

Summary

FAQ

Reference Notes

Analysis

Exploratory analysis

Curve fitting and signal estimation

Function approximation

Time series forecasting and prediction

Time series classification

https://www.timeseriesclassification.com/

Time series segmentation

Next steps

Explainable time series models

https://www.youtube.com/watch?v=e5qs9PG0HFM&list=PLH3Ao8RnwtkTtqDeRum-t-GD1OP0pm_kv

References

1. Shumway, Robert H., and Stoffer, David S. Time Series Analysis and Its Applications: With R Examples, Third Edition. Springer Verlag. Available here.
2.
Bisgaard, Søren, and Kulahci, Murat. Time Series Analysis and Forecasting by Example, 1st Edition. John Wiley & Sons. Available here.
3.
Beck, V.L. (2017). Linear Regression: Models, Analysis, and Applications. Nova Science Publishers. Available at: EBSCOhost.
4.
Bingham, N. H., & Fry, J. M. (2010). Regression: Linear Models in Statistics. Springer. Available at: Springer Link [Clásica].
5.
Bowerman, B.L., O'Connell, R.T., Koehler, A.B. (2007). Pronósticos, series de tiempo y regresión: un enfoque aplicado. Ed. Cengage Learning. [Clásico].
6.
Ciaburro, G. (2018). Regression Analysis with R: Design and Develop Statistical Nodes to Identify Unique Relationships Within Data at Scale. Packt Publishing. Available at: EBSCOhost.
7.
Giuseppe, C. (2018). Regression Analysis with R: Design and Develop Statistical Nodes to Identify Unique Relationships Within Data at Scale. Packt Publishing. Available at: EBSCOhost.
8.
Tattar, P.N. (2017). Statistical Application Development with R and Python - Second Edition. Vol 2nd ed. Packt Publishing.
9.
Stanimirović, I. (2020). Correlation and Regression Analysis: Applications for Industrial Organizations. Arcler Press. Available at: EBSCOhost.
10.
Pal, D.A. (2017). Practical Time Series Analysis. Packt Publishing. Available at: EBSCOhost.
11.
Montgomery, D.C., Peck, E.A., Vining, G. (2002). Introducción al análisis de regresión lineal. Ed. Grupo Patria Cultural. [Clásico].

  1. Nielsen, A. (2020). Practical time series analysis: Prediction with statistics and machine learning. O’Reilly.
  1. Atwan, T. A. (2022). Time Series Analysis with Python Cookbook: Practical Recipes for Exploratory Data Analysis, Data Preparation, Forecasting, and Model Evaluation. Packt Publishing.