Master time series analysis with this ultimate guide to stationarity and non-stationarity. Explore core concepts like strict vs. weak stationarity, unit root tests (ADF/PP), trend non-stationarity, random walks, and structural breaks. Learn why stationarity is essential for reliable time series forecasting and ARIMA modeling, alongside practical methods to transform non-stationary data using differencing and log transformations. A time series is said to be stationary if its statistical properties (i) mean, (ii) variance, and (iii) autocovariance remain constant over time. Think of it like a river that always flows at the same average depth, with similar fluctuations every season.

Autoregressive (AR) models are fundamental building blocks in time series analysis and forecasting. In an autoregressive model, a variable is predicted using a linear combination of its past (lagged) values. The Autoregressive Model (AR(1) Model) Real-World Example Stationarity Condition: Simulating AR(1) in EViews Statistical Properties of AR(1) Generalization: The AR(p) Model Real-World Example Lag Operator Notation The Autoregressive Model (AR(1) Model) The first-order autoregressive process, AR(1), is defined as: $$Y_t = \phi Y_{t-1} + u_t$$ For simplicity, we assume a zero mean and omit the constant term. $Y_t$ is the value of the series at time $t$.

In this post, I will discuss "Why Does Stationarity Matter"? Whether you are studying econometrics, diving into data science, or building predictive models, time series analysis is a fundamental skill. At the heart of this analysis lies a critical concept: stationarity. Why Does Stationarity Matter? Stationary Time Series Major Analytical Problem When Working with Non-Stationary Time Series How to Detect Stationarity Graphically in EViews Time Series Line Plot Correlogram (ACF and PACF) Non-Stationary Series Issue Identifying Stationarity vs Non-Stationarity Here is a breakdown of why stationarity is the bedrock of reliable predictive modeling, along with a step-by-step guide to visually detecting stationarity in EViews.

A correlogram in Time Series, also known as an Autocorrelation Function (ACF) plot, is a visual tool used in time series analysis to display the correlation of a dataset with itself at different time lags. It is the primary diagnostic tool for determining if a series is stationary or if it contains specific patterns like trends and seasonality. Correlogram in Time Series Short-term Correlogram in Time Series Alternative Time Series Sample Correlogram (Eviews output) Real Life Examples of Correlogram The Weekend Effect in Retail Correlogram of Atmospheric CO2 Levels Correlogram of Heart Rate Variability (HRV)

Explore the differences between Neural ODEs, RNNs, and LSTMs, and learn when each model is best suited for sequential data analysis tasks.

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I am looking forward to giving a keynote talk next Tuesday at the 32nd Irish Conference on Artificial Intelligence and Cognitive Science (AICS 2024), in my old…

Table of Links Background Problem statement Model architecture Training data Results Conclusions Impact statement Future directions Contributions Acknowledgements and References Appendix 6 Conclusions...

Table of Links Abstract and 1. Introduction Related Work Methodology Experimental Setup and Results Conclusion and Future Work \ Acknowledgments Reproducibility statement Impact statement, and References...

In my last post on PHP Zmanim, I said the next thing I’d write about was astronomy calculations. I still plan to do that, but something came up recently that caught my attention, so I’m going to...

Write a function which produces n month moving averages for a year's worth of data.

Department of Mathematical Sciences, Aalborg University