Time series foundation models (TSFMs) are widely used as generic feature extractors, yet the notion of non-stationarity in their embedding spaces remains poorly understood. Recent work often conflates non-stationarity with distribution shift, blurring distinctions fundamental to classical time-series analysis and long-standing methodologies such as statistical process control (SPC). In SPC, non-stationarity signals a process leaving a stable regime - via shifts in mean, variance, or emerging trends - and detecting such departures is central to quality monitoring and change-point analysis. Motivated by this diagnostic tradition, we study how different forms of distributional non-stationarity - mean shifts, variance changes, and linear trends - become linearly accessible in TSFM embedding spaces under controlled conditions. We further examine temporal non-stationarity arising from persistence, which reflects violations of weak stationarity due to long-memory or near-unit-root behavior rather than explicit distributional shifts. By sweeping shift strength and probing multiple TSFMs, we find that embedding-space detectability of non-stationarity degrades smoothly and that different models exhibit distinct, model-specific failure modes.

Inflation remains a persistent challenge for many African countries. This research investigates the critical role of machine learning (ML) in understanding and managing inflation in Ghana, emphasizing its significance for the country's economic stability and growth. Utilizing a comprehensive dataset spanning from 2010 to 2022, the study aims to employ advanced ML models, particularly those adept in time series forecasting, to predict future inflation trends. The methodology is designed to provide accurate and reliable inflation forecasts, offering valuable insights for policymakers and advocating for a shift towards data-driven approaches in economic decision-making. This study aims to significantly advance the academic field of economic analysis by applying machine learning (ML) and offering practical guidance for integrating advanced technological tools into economic governance, ultimately demonstrating ML's potential to enhance Ghana's economic resilience and support sustainable development through effective inflation management.

About one century ago, quantitative analysis and forecasting services were made available to businesses and the general public (Dominguez et al., 1988). Irving Fisher (1867-1947) spearheaded this initiative, pioneering data-driven forecasting practices grounded in theoretical foundations. His renowned theories, namely the monetary quantity theory, inflation-deflation theory, and index theory, were supported by statistical evidence. For example, Fisher (1925) was one of the earliest attempts to understand the source of business cycles in association with the price level (inflation), and Fisher (1926) was the first to report "a statistical relation between unemployment and price changes", today better known as the Phillips curve. Statistical inference is crucial for integrating economic theory and empirical data, which has become a tradition upheld by successive generations of researchers. In today's era of big data, we have unprecedented access to a vast amount of digital information about the economy. Recent advancements in statistical inference have uncovered new empirical patterns in prediction practices using datasets with temporal features. This paper aims at a plain quest: in a high dimensional linear predictive regression model when the number of potential regressors is larger than the sample size, how to conduct asymptotically valid statistical inference for a regressor of particular interest. To the best of our knowledge, no paper has solved this question before.

Sales Forecasting determines how the company invests and grows to create a massive impact on company valuation. This is part 2, and you will learn how to do sales prediction using Time Series. I'm working on Part 3 where I will be implementing Deep Learning and Part 4 where I will be implementing a supervised ML model. Now let's look at the moving average, as it gives you an overall idea of the trends in the dataset, it's useful in long-term forecasting. Rolling mean/ Standard Deviation-- helps in understanding short-term trends in data and outliers.

The global financial crisis and Covid recession have renewed discussion concerning trend-cycle discovery in macroeconomic data, and boosting has recently upgraded the popular HP filter to a modern machine learning device suited to data-rich and rapid computational environments. This paper sheds light on its versatility in trend-cycle determination, explaining in a simple manner both HP filter smoothing and the consistency delivered by boosting for general trend detection. Applied to a universe of time series in FRED databases, boosting outperforms other methods in timely capturing downturns at crises and recoveries that follow. With its wide applicability the boosted HP filter is a useful automated machine learning addition to the macroeconometric toolkit.

Finance is a lucrative industry and in recent years it has heavily used data science, machine learning, deep learning, and several other computational techniques to maximize results. An important category of work within finance is stocks that resemble the equity market. In this story, I will attempt to use R for analyzing stocks through visualizations, creating predictions for future stock prices based on historical data, and then use the concept of Sharpe Ratio to create an optimal return-giving portfolio of stocks. I will walk through the complete process of using Data Visualization concepts in R to build a trading strategy. Along the way I will also introduce concepts about time series analysis, data stationarity and perform predictions.

In the previous blog, we discussed a predictive model for house prices using Machine Learning algorithms. In this blog, we are going to discuss the time series forecasting on Zillow economics data using a statistical modeling approach. The project was implemented in September 2019 and forecasting of house prices was done for the next year that is 2020. The code could be reused by changing the span of forecasting that is year for forecasting or duration of forecasting. The results discussed in this blog are for the year 2020.

Established recurrent neural networks are well-suited to solve a wide variety of prediction tasks involving discrete sequences. However, they do not perform as well in the task of dynamical system identification, when dealing with observations from continuous variables that are unevenly sampled in time, for example due to missing observations. We show how such neural sequence models can be adapted to deal with variable step sizes in a natural way. In particular, we introduce a time-aware and stationary extension of existing models (including the Gated Recurrent Unit) that allows them to deal with unevenly sampled system observations by adapting to the observation times, while facilitating higher-order temporal behavior. We discuss the properties and demonstrate the validity of the proposed approach, based on samples from two industrial input/output processes.

Stationarity is an important concept in time series analysis. For a concise (but thorough) introduction to the topic, and the reasons that make it important, take a look at my previous blog post on the topic. As such, the ability to determine if a time series is stationary is important. Rather than deciding between two strict options, this usually means being able to ascertain, with high probability, that a series is generated by a stationary process. In this brief post, I will cover several ways to do just that.

This article develops a statistical test for the null hypothesis of strict stationarity of a discrete time stochastic process. When the null hypothesis is true, the second order cumulant spectrum is zero at all the discrete Fourier frequency pairs present in the principal domain of the cumulant spectrum. The test uses a frame (window) averaged sample estimate of the second order cumulant spectrum to build a test statistic that has an asymptotic complex standard normal distribution. We derive the test statistic, study the size and power properties of the test, and demonstrate its implementation with intraday stock market return data. The test has conservative size properties and good power to detect varying variance and unit root in the presence of varying variance.