Related papers: Forecasting under Long Memory and Nonstationarity

Time series data is prevalent across numerous fields, necessitating the development of robust and accurate forecasting models. Capturing patterns both within and between temporal and multivariate components is crucial for reliable…

Time series modeling techniques based on deep learning have seen many advancements in recent years, especially in data-abundant settings and with the central aim of learning global models that can extract patterns across multiple time…

We consider the residual empirical process in random design regression with long memory errors. We establish its limiting behaviour, showing that its rates of convergence are different from the rates of convergence for to the empirical…

This paper tackles one of the most fundamental goals in functional time series analysis which is to provide reliable predictions for future functions. Existing methods for predicting a complete future functional observation use only…

We present the results of a simulation study into the properties of 12 different estimators of the Hurst parameter, $H$, or the fractional integration parameter, $d$, in long memory time series. We compare and contrast their performance on…

Memory-augmented neural networks consisting of a neural controller and an external memory have shown potentials in long-term sequential learning. Current RAM-like memory models maintain memory accessing every timesteps, thus they do not…

We present a perfect simulation algorithm for stationary processes indexed by Z, with summable memory decay. Depending on the decay, we construct the process on finite or semi-infinite intervals, explicitly from an i.i.d. uniform sequence.…

Mid-term electricity load forecasting (LF) plays a critical role in power system planning and operation. To address the issue of error accumulation and transfer during the operation of existing LF models, a novel model called error…

Fueled by their remarkable ability to tackle diverse tasks across multiple domains, large language models (LLMs) have grown at an unprecedented rate, with some recent models containing trillions of parameters. This growth is accompanied by…

Many existing mortality models follow the framework of classical factor models, such as the Lee-Carter model and its variants. Latent common factors in factor models are defined as time-related mortality indices (such as $\kappa_t$ in the…

Forecasting is an indispensable element of operational research (OR) and an important aid to planning. The accurate estimation of the forecast uncertainty facilitates several operations management activities, predominantly in supporting…

An efficient estimator is constructed for the quadratic covariation or integrated co-volatility matrix of a multivariate continuous martingale based on noisy and nonsynchronous observations under high-frequency asymptotics. Our approach…

Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high…

We propose a nonstationary functional time series forecasting method with an application to age-specific mortality rates observed over the years. The method begins by taking the first-order differencing and estimates its long-run covariance…

Foundation Models (FMs) have become the hallmark of modern AI, however, these models are trained on massive data, leading to financially expensive training. Updating FMs as new data becomes available is important, however, can lead to…

We study the generalized dynamic factor model in a long-memory setting. Unlike most recent work, which assumes a finite-dimensional factor space and short memory, our framework allows the factor space to be infinite-dimensional and the…

Introduction: Long-term time series forecasting (LTSF) has gained significant attention in recent years. While various specialized designs exist for capturing temporal dependency, recent studies have shown that even a single linear layer…

For long memory time series models with uncorrelated but dependent errors, we establish the asymptotic normality of the Whittle estimator under mild conditions. Our framework includes the widely used FARIMA models with GARCH-type…

In lifelong learning, data are used to improve performance not only on the present task, but also on past and future (unencountered) tasks. While typical transfer learning algorithms can improve performance on future tasks, their…

We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly-decaying…