Related papers: Guessing the output of a stationary binary time se…
Predictive process monitoring is concerned with the analysis of events produced during the execution of a business process in order to predict as early as possible the final outcome of an ongoing case. Traditionally, predictive process…
Let $X_1,X_2,\ldots $ be independent random variables observed sequentially and such that $X_1,\ldots,X_{\theta-1}$ have a common probability density $p_0$, while $X_\theta,X_{\theta+1},\ldots $ are all distributed according to $p_1\neq…
Statistical inference for time series such as curve estimation for time-varying models or testing for existence of change-point have garnered significant attention. However, these works are generally restricted to the assumption of…
A long noted difficulty when assessing the reliability (or calibration) of forecasting systems is that reliability, in general, is a hypothesis not about a finite dimensional parameter but about an entire functional relationship. A…
Given a Wiener process with unknown and unobservable drift, we try to estimate this drift as effectively but also as quickly as possible, in the presence of a quadratic penalty for the estimation error and of a fixed, positive cost per unit…
Many applications require the ability to judge uncertainty of time-series forecasts. Uncertainty is often specified as point-wise error bars around a mean or median forecast. Due to temporal dependencies, such a method obscures some…
We develop an estimator for the high-dimensional covariance matrix of a locally stationary process with a smoothly varying trend and use this statistic to derive consistent predictors in non-stationary time series. In contrast to the…
The problem of filtering of finite-alphabet stationary ergodic time series is considered. A method for constructing a confidence set for the (unknown) signal is proposed, such that the resulting set has the following properties: First, it…
Methods of estimation and forecasting for stationary models are well known in classical time series analysis. However, stationarity is an idealization which, in practice, can at best hold as an approximation, but for many time series may be…
In this paper an approach to modelling nonstationary binary sequences, i.e., predicting the probability of upcoming symbols, is presented. After studying the prediction model we evaluate its performance in two non-artificial test cases.…
Non-stationary time series with non-linear trends are frequently encountered in applications. We consider here the feasibility of accurately forecasting the signals of multiple such time series considering jointly when the number of…
The prediction of a binary sequence is a classic example of online machine learning. We like to call it the 'stock prediction problem,' viewing the sequence as the price history of a stock that goes up or down one unit at each time step. In…
Bayesian sequence prediction is a simple technique for predicting future symbols sampled from an unknown measure on infinite sequences over a countable alphabet. While strong bounds on the expected cumulative error are known, there are only…
For a zero-mean, unit-variance second-order stationary univariate Gaussian process we derive the probability that a record at the time $n$, say $X_n$, takes place and derive its distribution function. We study the joint distribution of the…
Performance estimation aims at estimating the loss that a predictive model will incur on unseen data. These procedures are part of the pipeline in every machine learning project and are used for assessing the overall generalisation ability…
A new general procedure for a priori selection of more predictable events from a time series of observed variable is proposed. The procedure is applicable to time series which contains different types of events that feature significantly…
In a sequential regression setting, a decision-maker may be primarily concerned with whether the future observation will increase or decrease compared to the current one, rather than the actual value of the future observation. In this…
Two series of binary observations $x_1,x_1,...$ and $y_1,y_2,...$ are presented: at each time $n\in\N$ we are given $x_n$ and $y_n$. It is assumed that the sequences are generated independently of each other by two B-processes. We are…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
Let $X=(X_t)_{t\geq 0}$ be a known process and $T$ an unknown random time independent of $X$. Our goal is to derive the distribution of $T$ based on an iid sample of $X_T$. Belomestny and Schoenmakers (2015) propose a solution based the…