Nonstationary Mean Research Articles

Core Inflation Rate for China and the ASEAN-10 Countries: Smoothed Signal for Score-Driven Local Level Plus Scale Models

Abstract We use a score-driven minimum mean-squared error (MSE) signal extraction method and perform inflation smoothing for China and the ASEAN-10 countries. Our focus on China and ASEAN-10 countries is motivated by the significant historical variation in inflation rates, e.g. during the 1997 Asian Financial Crisis, the 2007–2008 Financial Crisis, the COVID-19 Pandemic, and the Russian Invasion of Ukraine. Some advantages of the score-driven signal extraction method are that it uses dynamic mean and volatility filters, it considers stationary or non-stationary mean dynamics, it is computationally fast, it is robust to extreme observations, it uses information-theoretically optimal updating mechanisms for both mean and volatility, it uses closed-form formulas for smoothed signals, and parameters are estimated by using the maximum likelihood (ML) method for which the asymptotic properties of estimates are known. In the empirical application, we present the political and economic conditions for each country and analyze the evolution and determinants of the core inflation rate.

СОВРЕМЕННЫЕ И БУДУЩИЕ ИЗМЕНЕНИЯ КЛИМАТА ЛЕНИНГРАДСКОЙ ОБЛАСТИ И ИХ ВЛИЯНИЕ НА АГРОКЛИМАТИЧЕСКИЕ ХАРАКТЕРИСТИКИ

Based on the long-term time series of observations at the weather stations in the Leningrad oblast, current changes in monthly mean air temperatures and precipitation, as well as in the agroclimatic characteristics of the growing season are assessed using statistical models of nonstationary means. The spatial distribution of these changes is determined. The most suitable physical and mathematical climate model is selected based on the comparison of observational data with the results of the CMIP historical experiment. Based on the identified systematic model errors, the scenario values of air temperature and precipitation are corrected, and the agroclimatic characteristics until the end of the 21st century for different parts of the region are obtained on their basis. An estimated future yield and recommendations for the output of the most promising agricultural products are given.

A federated learning-based approach to recognize subjects at a high risk of hypertension in a non-stationary scenario

BackgroundTransferring data across nodes could raise concerns about data security and privacy. Federated learning is a tech- nological remedy for these problems. However, in a real federated scenario, there are two main issues: 1) it is difficult to collect locally a large and representative dataset, and 2) the data are non-stationary, where non-stationary means that the data increase in size over time, which may generate catastrophic forgetting events affecting the learning process. ObjectiveThe aim of this paper is to investigate and assess the performance and behavior of a federated model during the occurrence of catastrophic forgetting events within the context of a non-stationary data scenario. MethodsTo achieve this objective, the performance of a proposed federated learning approach has been evaluated in terms of the continuous flow of data in order to train a time series-based model. Results and ConclusionThe results demonstrate the goodness of the solution in terms of performance, with improvements ranging from 2% to 28%. This indicates the benefits that the proposed approach brings to a node in terms of recovering from a catastrophic forgetting event, also taking into account the fact that the probability of catastrophic forgetting is higher at the beginning of the learning process.

Estimating high-resolution Red Sea surface temperature hotspots, using a low-rank semiparametric spatial model

In this work, we estimate extreme sea surface temperature (SST) hotspots, that is, high threshold exceedance regions, for the Red Sea, a vital region of high biodiversity. We analyze high-resolution satellite-derived SST data comprising daily measurements at 16,703 grid cells across the Red Sea over the period 1985–2015. We propose a semiparametric Bayesian spatial mixed-effects linear model with a flexible mean structure to capture spatially-varying trend and seasonality, while the residual spatial variability is modeled through a Dirichlet process mixture (DPM) of low-rank spatial Student’s t processes (LTPs). By specifying cluster-specific parameters for each LTP mixture component, the bulk of the SST residuals influence tail inference and hotspot estimation only moderately. Our proposed model has a nonstationary mean, covariance, and tail dependence, and posterior inference can be drawn efficiently through Gibbs sampling. In our application, we show that the proposed method outperforms some natural parametric and semiparametric alternatives. Moreover, we show how hotspots can be identified, and we estimate extreme SST hotspots for the whole Red Sea, projected until the year 2100, based on the Representative Concentration Pathways 4.5 and 8.5. The estimated 95% credible region, for joint high threshold exceedances include large areas covering major endangered coral reefs in the southern Red Sea.

Non-stationary Stochastic Multi-armed Bandit Problems with External Information on Stationarity

Multi-armed bandit problem is a fundamental mathematical problem in sequential optimization and reinforcementlearning that has a variety of application such as online recommendation system and clinical trial design. Multiarmedbandit problem can describe a situation in which a player tries to select a good choice sequentially from givencandidate choices to maximize the cumulative reward. In this paper, we consider the non-stationary multi-armed banditproblems. Non-stationary means the reward distribution of each arm varies with time. We point out that in somereal application, we can utilize information on the change of reward distribution. Especially we consider the type ofinformation that may restrict the rounds at which the reward distribution changes. Against such scenario, we proposea novel strategy called PM policy. The proposed policy is based on existing CUSUM-UCB policy and M-UCB policythat do not consider external information. Though such existing policies monitor all arms to detect the change ofreward distribution, our policy monitors only important arms and rounds. As a result, the ratio of unnecessary monitoringis reduced, and an efficient search can be performed. The regret bound of the proposed policy is described. Wealso show the effectiveness of the proposed method by numerical experiments.

Stationarity in the variability of arid precipitation: A case study of arid Central Asia

Precipitation is particularly scarce in arid Central Asia (CA), and is expected to be severely impacted by future warming, and the assessment of the stationarity of precipitation variability is important for managing surface water resources in this region. In this study, we investigated the statistics of stationarity in the totals and extremes of precipitation in CA based on the longest observational records (1881–2006), tree-ring reconstructed records (1756–2012 and 1760–2015), and the Coupled Model Intercomparison Project 5 (CMIP5) simulations, applying the autocorrelation function and testing criteria established based on the statistical definitions of stationarity. We analyzed the longest daily precipitation record (Tashkent station, 1881–2006) and found that the autocorrelation coefficient of the precipitation totals (PRCPTOT) and annual maximum 1-day precipitation amount (Rx1day) were statistically insignificant for all lags, implying stationary behavior. Regionally, nearly all the Global Historical Climatology Network-Daily Database (GHCN-D) observatory sites (1925–2005) indicated likely stationary behavior. The reconstructed records were also indistinguishable from a random process. For the CMIP5 models, the simulated and projected PRCPTOT closely approximated a purely random process; however, the projected Rx1day maintained non-stationary means in most of the models under the representative concentration pathway (RCPs), implying that extreme events would increase in the future. The mean precipitation changes (ΔP) can be expressed as an exponential function depending on the length of the successive mean periods (μ) and variance (σ2). The ΔP of the next decade is projected to be within ±14.8% of the previous decades mean annual PRCPTOT over CA. The higher the RCPs, the higher the ΔP over CA. The results show that the detection and prediction of precipitation change will be challenging in arid CA.

Changing Expected Returns Can Induce Spurious Serial Correlation

Changing expected returns can induce spurious autocorrelation in returns and possible bias in other financial models. We show why this happens with some simple examples and then investigate its prevalence in actual equity data. Assets may undergo changes in expected returns for a variety of reasons. Hence, autocorrelations computed from extended records can be subject to spurious bias. The bias might be difficult to measure because of noise but a re-sampling method (the bootstrap) discloses its rather ubiquitous presence in US equity data. Turning the phenomenon on its head, return serial correlation in an efficient market is evidence of changing expected returns. Estimated risk measures such as “beta” might also be subject to bias induced by non-stationary mean returns, but the direction of the bias is more ambiguous.

Short-Range Forecasting of Coronavirus Disease 2019 (COVID-19) During Early Onset at Various Levels of Geographic Granularity Using Seven Different Methods

Background: The coronavirus disease 2019 (COVID-19) spread rapidly across the world since its appearance in Wuhan city, Hubei province, China in December 2019. We explore the effectiveness of forecasting methods during early onset for COVID-19 case counts over the upcoming seven-days at the county, health district, and state levels. Our goal is to assess which forecasting methods can aid decision makers about anticipated one-, three-, and seven-day case growth.Methods: We apply forecasting methods across VA’s counties and independent cities, its health districts, and the state using data reported by the The New York Times. We forecast one-, three-, and seven-days forward using: (1) a naïve approach; (2) Holt-Winters exponential smoothing (HW); (3) growth rate (Growth); (4) moving average (MA); (5) autoregressive (AR); (6) autoregressive moving average (ARMA); and (7) autoregressive integrated moving average (ARIMA). Using Median Absolute Error (MdAE) and Median Absolute Percentage Error (MdAPE), we compare the resulting 216698 forecasts to VA’s historical data through April 22, 2020.Findings: Single-day MA forecast with three-day lookback obtains the lowest MdAE and is statistically significantly different than 66 percent of evaluated alternatives at each geographic level. Furthermore, methods assuming stationary means of prior days’ case counts outperform methods with assumptions of weak- or non-stationarity. Finally, for an individual forecasting method, MdAPE evaluation reveals in most cases statistically significant differences across geographic levels demonstrating that there is not a one-size-fits-all solution to short-term COVID-19 forecasting.Interpretation: For decision makers applying short-term forecasts of COVID-19: (1) MA is an effective option for forecasting cumulative case counts one-, three-, and seven-days forward; (2) methods assuming stationarity of means in prior-observations are more effective than methods assuming weak- or non-stationary means; and (3) the intended level of geographic resolution should be a factor in selecting the appropriate forecasting method.Funding Statement: This work received no external funding.Declaration of Interests: All authors declare no competing interests.

Multipoint reconstruction of wind speeds

Abstract. The most intermittent behaviour of atmospheric turbulence is found for very short timescales. Based on a concatenation of conditional probability density functions (cpdf's) of nested wind speed increments, inspired by a Markov process in scale, we derive a short-time predictor for wind speed fluctuations around a non-stationary mean value and with a corresponding non-stationary variance. As a new quality this short-time predictor enables a multipoint reconstruction of wind data. The used cpdf's are (1) directly estimated from historical data from the offshore research platform FINO1 and (2) obtained from numerical solutions of a family of Fokker–Planck equations in the scale domain. The explicit forms of the Fokker–Planck equations are estimated from the given wind data. A good agreement between the statistics of the generated and measured synthetic wind speed fluctuations is found even on timescales below 1 s. This shows that our approach captures the short-time dynamics of real wind speed fluctuations very well. Our method is extended by taking the non-stationarity of the mean wind speed and its non-stationary variance into account.

Universal behavior in non-stationary Mean Field Games

Mean Field Games provide a powerful framework to analyze the dynamics of a large number of controlled objects in interaction. Though these models are much simpler than the underlying differential games they describe in some limit, their behavior is still far from being fully understood. When the system is confined, a notion of “ergodic state” has been introduced that characterizes most of the dynamics for long optimization times. Here we consider a class of models without such an ergodic state, and show the existence of a scaling solution that plays a similar role. Its universality and scaling behavior can be inferred from a mapping to an electrostatic problem.

Does Hollywood Make Too Many R-Rated Movies?: Risk, Stochastic Dominance, and the Illusion of Expectation

This paper estimates the probability distributions of budgets, revenues, returns and profits to G-, PG-, PG13-, and R-rated movies. The distributions are non-Gaussian and show a self-similar stable Paretian form with non-finite variance and non-stationary mean. We stochastically rank these distributions to investigate film critic Michael Medved's argument that Hollywood overproduces R-rated movies. The evidence shows that the industry's critics and its shareholders can agree that Hollywood does make too many trashy movies. The profit distributions have aysmmetric tails which means that Hollywood could trim its downside risk while increasing its upside possibilities by shifting production dollars out of R-rated movies into G, PG, and even PG13 movies. Stars who are willing to appear in edgy, counterculture R-rated movies for their prestige value may induce an illusion of expectation leading a studio to greenlight movies that have biased expectations.

Laplace domain method for evaluating mean-square response of simple oscillators to nonstationary excitation

Evaluating mean-square response of linear systems to nonstationary excitation has been extensively studied, but exact closed-form solutions under various assumptions have been rarely available. This paper derives exact closed-form solutions for the mean-square response of simple oscillators subjected to nonstationary excitation which is formulated as the multiplication of a stationary excitation characterized by an arbitrary spectral density function (PSD) and an envelope function being the sum of several exponential functions. Special attention is given to the envelope function as the sum of two exponential functions because of its practical importance. While analytically evaluating the nonstationary mean square response of a SDOF (single-degree-of-freedom) system subjected to a nonstationary stochastic excitation requires carrying out a triple integral, traditional methods would conduct tedious calculus in the time, frequency or time–frequency domain. In contrast, the proposed method – much more efficient than traditional methods – primarily operates in the Laplace domain (complex plane) based on pole–residue formulations. Another advantage of the proposed pole–residue method is that meaningful physical and mathematical insights could be gained in the solution procedure. For demonstrating the effectiveness and versatility of the proposed method, two cases of the input PSD function are studied: (1) a modulated white noise process, and (2) a modulated correlated process. The correctness of the exact closed-form solutions is verified numerically by Monte Carlo simulations.

Long-range dependence, nonlinear trend, and breaks in historical sea surface and land air surface global and regional temperature anomalies

The global temperature series is a major indicator of climate change, whereas this indicator has undergone shift in trend over the twentieth century, changing from linear trend to nonlinear trend as a result of structural breaks. This paper investigates global and regional sea surface (SS) and land air surface (LS) temperature series from 1880 to 2016 by means of fractional integration technique. The results show that temperature series are described by trend stationary process, mostly in long memory range in the case of LS temperature while in the case of SS temperature, temperature series are in nonstationary mean reverting range for global and hemispheric temperature as well as for three other regional locations. By applying the multiple structural break test, the trend line is found breaking in many dates, locking up into many regimes which can be described using nonlinear trend structure. Nonlinear trend, based on Chebyshev inequality in the fractional integration framework, shows that global and regional temperature series can be represented using nonlinear trend up to the third order since this further lowers the integration order to long memory range in both SS and LS temperature series.

A Stochastic source model for the 2015 Mw 7.9 Gorkha, Nepal, Earthquake using Multi-Dimensional Ensemble Empirical Mode Decomposition technique

The present study aims at developing a new strategy to model the spatial variability of slip on the rupture plane using multi-dimensional ensemble empirical mode decomposition (MEEMD) technique. Here, the earthquake slip distribution is split into finite number of empirical modes of oscillation called the intrinsic mode functions (IMFs). This help in identifying the fluctuation component and trend in the slip data. The trend is positive and characterizes the nonstationary mean of the slip distribution. The fluctuation component can be modelled as a stationary random field using an exponential power spectral density function. The trend can be modeled as an elliptic patch. This new technique is demonstrated for the slip distribution of the recent Nepal Earthquake, 2015. It is observed that the new model can be used to simulate the spatial complexity of slip distribution of any earthquake.

Analytical Reduced Models for the Non-stationary Diabatic Atmospheric Boundary Layer

Geophysical boundary-layer flows feature complex dynamics that often evolve with time; however, most current knowledge centres on the steady-state problem. In these atmospheric and oceanic boundary layers, the pressure gradient, buoyancy, Coriolis, and frictional forces interact to determine the statistical moments of the flow. The resulting equations for the non-stationary mean variables, even when succinctly closed, remain challenging to handle mathematically. Here, we derive a simpler physical model that reduces these governing unsteady Reynolds-averaged Navier–Stokes partial differential equations into a single first-order ordinary differential equation with non-constant coefficients. The reduced model is straightforward to solve under arbitrary forcing, even when the statistical moments are non-stationary and the viscosity varies in time and space. The model is successfully validated against large-eddy simulation for, (1) time-variable pressure gradients, and (2) linearly time-variable buoyancy. The new model is shown to have a superior performance compared to the classic Blackadar solutions (and later improvements on these solutions), and it covers a much wider range of conditions.

Continuous Time Spot Rate Models with a Nonstationary Mean

We present a model in which the interest rate reverts to a nonstationary stochastic mean. In our model, the stochastic mean is subject to a sequence of permanent shocks that can better capture the source of nonlinearity in the drift than extant models. We find that our model provides a better fit to observed interest rates relative to a large number of alternative models. In particular, the Vasicek model with a nonstationary mean outperforms constant elasticity of volatility models. The implied bond option price from our model accounts for the downward bias in existing bond option valuation models.

Surface Stress with Non-stationary Weak Winds and Stable Stratification

The behaviour of turbulent transport in the weak-wind, stably-stratified, boundary layer over land is examined in terms of the non-stationarity of the wind field using measurements from three field programs. These field programs include towers ranging from 12 to 20 m in height and an extensive horizontal network of sonic anemometers. The relationship of the friction velocity to the stratification and non-stationary submeso motions is investigated from several points of view and nominally quantified. The relationship of the turbulence to the stratification is less systematic than expected partly due to enhancement of the turbulence by submeso motions. Cause and effect relationships are difficult to isolate because the non-stationary momentum flux significantly modifies the profile of the non-stationary mean flow. The link between the turbulence and accelerations at the surface is examined in terms of the changing vertical structure of the wind profile and sudden increases in the downward transport of momentum.

Linear and segmented trends in sea surface temperature data

This paper deals with the analysis of the MET Office Hadley Centre's sea surface temperature data set (HadSST3) by using long-range dependence techniques. We incorporate linear and segmented trends using fractional integration, and thus permitting long memory behavior in the detrended series. The results indicate the existence of warming trends in the three series examined (Northern and Southern Hemispheres along with global temperatures), with orders of integration which are in the range (0.5, 1) and thus implying nonstationary long memory and mean reverting behavior. This is innovative compared with other works that assume short memory behavior in the detrended series. Allowing for segmented trends two features are observed: increasing values in the degree of dependence of the series across time and significant warming trends from 1940 onwards.

On the Estimation of Lagrangian Diffusivity: Influence of Nonstationary Mean Flow

Abstract Eddy–mean flow decomposition is crucial to the estimation of Lagrangian diffusivity based on drifter data. Previous studies have shown that inhomogeneous mean flow induces shear dispersion that increases the estimated diffusivity with time. In the present study, the influences of nonstationary mean flows on the estimation of Lagrangian diffusivity, especially the asymptotic behavior, are investigated using a first-order stochastic model, with both idealized and satellite-based oceanic mean flows. Results from both experiments show that, in addition to inhomogeneity, nonstationarity of mean flows that contain slowly varying signals, such as a seasonal cycle, also cause large biases in the estimates of diffusivity within a time lag of 2 months if a traditional binning method is used. Therefore, when assessing Lagrangian diffusivity over regions where a seasonal cycle is significant [e.g., the Indian Ocean (IO) dominated by monsoon winds], inhomogeneity and nonstationarity of the mean flow should be simultaneously taken into account in eddy–mean flow decomposition. A temporally and spatially continuous fit through the Gauss–Markov (GM) estimator turns out to be very efficient in isolating the effects of inhomogeneity and nonstationarity of the mean flow, resulting in estimates that are closest to the true diffusivity, especially in regions where strong seasonal cycles exist such as the eastern coast of Somalia and the equatorial IO.

On the colour and spin of epistemic error (and what we might do about it)

Abstract. Disinformation as a result of epistemic error is an issue in hydrological modelling. In particular the way in which the colour in model residuals resulting from epistemic errors should be expected to be non-stationary means that it is difficult to justify the spin that the structure of residuals can be properly represented by statistical likelihood functions. To do so would be to greatly overestimate the information content in a set of calibration data and increase the possibility of both Type I and Type II errors. Some principles of trying to identify periods of disinformative data prior to evaluation of a model structure of interest, are discussed. An example demonstrates the effect on the estimated parameter values of a hydrological model.