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 and Projects
- Logic. Mathematics. Code. Automatic Verification such as Lean Proven or Frama-C.
- Languages in Anki.
Summary
FAQ
Worked examples
Reference Notes
Analysis
White noise
Autocorrelation
Dynamic Time Warping
DTW Windows
Transformations
Calendar adjustments
Population adjustments
Inflation adjustments
Mathematical transformations
log
Box-Cox transformations Box & Cox, 1964
Bias adjustments
back-transformed
Data windowing
Windowing operations
https://pandas.pydata.org/docs/user_guide/window.html#window-exponentially-weighted
https://www.oreilly.com/radar/the-world-beyond-batch-streaming-101/
https://www.oreilly.com/radar/the-world-beyond-batch-streaming-102/
https://softwaremill.com/windowing-in-big-data-streams-spark-flink-kafka-akka/
Exercises and Projects
Summary
FAQ
Reference Notes
Exploratory analysis
Time series graphics
Frequency
Annual, Quartely, Monthly, Weekly, Bussiness days
No time based
Time series patterns
Trend
Seasonal
Cyclic
Seasonal plots
Seasonal subseries plots
Scatterplots
Lag plots
Exercises and Projects
Summary
Design decisions
FAQ
Reference Notes
Curve fitting and signal estimation
Function approximation
Time series forecasting and prediction
The forecaster’s toolbox
Residual diagnostics
Evaluating models
Backtesting
Prediction intervals
Some simple forecasting methods
Judgmental forecasts
Time series regression models
TIme series decomposition
Exponential smoothing
ARIMA models
Forecasting hierarchical or grouped time series
Advanced forecasting methods?
Complex seasonality
Vector autoregressions
Bootstrapping and bagging
Deep learning models
Exercises and Projects
Summary
Design decisions
FAQ
Reference Notes
Time series classification
https://www.timeseriesclassification.com/
The classifier’s toolbox
Evaluating models
Anomaly detection
Time series segmentation
Practical issues dealing with stocastic processes
Weekly, daily and sub-daily data
Time series of counts
Ensuring forecasts stay within limits
Forecast combinations
Prediction combinations
Prediction intervals for aggregates
Backcasting
Very long and very short time series
Forecasting on training and test sets
Visualization in real-time
Grafana
Metabase
Storage
Postgres and TimeseriesDB
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].
- Nielsen, A. (2020). Practical time series analysis: Prediction with statistics and machine learning. O’Reilly.
- Atwan, T. A. (2022). Time Series Analysis with Python Cookbook: Practical Recipes for Exploratory Data Analysis, Data Preparation, Forecasting, and Model Evaluation. Packt Publishing.
- Hyndman, R.J., & Athanasopoulos, G. (2018) Forecasting: principles and practice, 2nd edition, OTexts: Melbourne, Australia. https://otexts.com/fpp2/. Accessed on 12 January, 2023
- Bickel, P. J., & Doksum, K. A. (1981). An analysis of transformations revisited. Journal of the American Statistical Association, 76(374), 296–311.
- Box, G. E. P., & Cox, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Society. Series B, Statistical Methodology, 26(2), 211–252. [DOI]