Simple Autoregressive Process Research Articles

Deep Learning Based Predictive Beamforming Design

This paper investigates deep learning techniques to predict transmit beamforming based on only historical channel data without current channel information in the multiuser multiple-input-single-output downlink. This will significantly reduce the channel estimation overhead and improve the spectrum efficiency especially in high-mobility vehicular communications. Specifically, we propose a joint learning framework that incorporates channel prediction and power optimization, and produces prediction for transmit beamforming directly. In addition, we propose to use the attention mechanism in the Long Short-Term Memory Recurrent Neural Networks to improve the accuracy of channel prediction. Simulation results using both a simple autoregressive process model and the more realistic 3GPP spatial channel model verify that our proposed predictive beamforming scheme can significantly improve the effective spectrum efficiency compared to traditional channel estimation and the method that separately predicts channel and then optimizes beamforming.

An enhanced stochastic operating cycle description including weather and traffic models

• The new stochastic operating cycle includes models for the weather and traffic. • A primary model for the weather category is introduced to account for seasonality. • A regression analysis is made to investigate spread in CO 2 emissions. • It is found that both seasonal and traffic settings influence CO 2 emissions. The present paper extends the concept of a stochastic operating cycle (sOC) by introducing additional models for weather and traffic. In regard to the weather parameters, dynamic models for air temperature, atmospheric pressure, relative humidity, precipitation, wind speed and direction are included. The traffic models is instead based on a macroscopic approach which describes the density dynamically by means of a simple autoregressive process. The enhanced format is structured in a hierarchical fashion, allowing for ease of implementation and modularity. The novel models are parametrised starting from data available from external databases. The possibility of generating synthetic data using the statistical descriptors introduced in the paper is also discussed. To investigate the impact of the novel parameters over energy efficiency, a sensitivity analysis is conducted with a combinatorial test design. Simulation results show that both seasonality and traffic conditions are responsible for introducing major variations in the CO 2 emissions.

Temperature and Precipitation Variance in CMIP5 Simulations and Paleoclimate Records of the Last Millennium

Abstract Accurate assessments of future climate impacts require realistic simulation of interannual–century-scale temperature and precipitation variability. Here, well-constrained paleoclimate data and the latest generation of Earth system model data are used to evaluate the magnitude and spatial consistency of climate variance distributions across interannual to centennial frequencies. It is found that temperature variance generally increases with time scale in patterns that are spatially consistent among models, especially over the mid- and high-latitude oceans. However, precipitation is similar to white noise across much of the globe. When Earth system model variance is compared to variance generated by simple autocorrelation, it is found that tropical temperature variability in Earth system models is difficult to distinguish from variability generated by simple autocorrelation. By contrast, both forced and unforced Earth system models produce variability distinct from a simple autoregressive process over most high-latitude oceans. This new analysis of tropical paleoclimate records suggests that low-frequency variance dominates the temperature spectrum across the tropical Pacific and Indian Oceans, but in many Earth system models, interannual variance dominates the simulated central and eastern tropical Pacific temperature spectrum, regardless of forcing. Tropical Pacific model spectra are compared to spectra from the instrumental record, but the short instrumental record likely cannot provide accurate multidecadal–centennial-scale variance estimates. In the coming decades, both forced and natural patterns of decade–century-scale variability will determine climate-related risks. Underestimating low-frequency temperature and precipitation variability may significantly alter our understanding of the projections of these climate impacts.

Analysis of the simulated global temperature using a simple energy balance stochastic model

This work presents a study of the response of the simulated global temperature variability to additive and multiplicative stochastic parameterizations of heat fluxes, along with a description of the long-term variability in terms of simple autoregressive processes. The Earth's global temperature was simulated using a globally averaged energy balance climate model coupled to a thermodynamic ocean model. It was found that simple autoregressive processes explain the temperature variability in the case of additive parameterizations; whereas in the case of multiplicative parameterizations, the description of the temperature variability would involve higher order autoregressive processes, suggesting the presence of complex feedback mechanisms originated by the multiplicative forcing. Also, it was found that multiplicative parameterizations produced a rich structure that emulates closely observed climate processes. Finally, a new approach to describe the stability in the steady state of a general one-dimensional stochastic system, through its potential function, was proposed. From an analytical expression of the potential function, further insight into the description of a stochastic system was provided.

On the Predictive Content of Nonlinear Transformations of Lagged Autoregression Residuals and Time Series Observations

Abstract Although many macroeconomic time series are assumed to follow nonlinear processes, nonlinear models often do not provide better predictions than their linear counterparts. Furthermore, nonlinear models easily become very complex and difficult to estimate. The aim of this study is to investigate whether simple nonlinear extensions of autoregressive processes are able to provide more accurate forecasting results than linear models. Therefore, simple autoregressive processes are extended by means of nonlinear transformations (quadratic, cubic, sine, exponential functions) of lagged time series observations and autoregression residuals. The proposed forecasting models are applied to a large set of macroeconomic and financial time series for 10 European countries. Findings suggest that these models, including nonlinear transformation of lagged autoregression residuals, are able to provide better forecasting results than simple linear models. Thus, it may be possible to improve the forecasting accuracy of linear models by including nonlinear components. This is especially true for time series that are positively tested for nonlinear characteristics and longer forecast horizons.

Time-Varying NAIRU and Some of Its Determinants—A Semi-Structural Approach: Evidence from Eastern European Economies

The results of structural estimates of the hybrid New Keynesian Phillips curve are used to calibrate a semistructural state-space model that is then used to estimate a time-varying NAIRU. In the first version, the NAIRU is estimated as a simple autoregressive process. In the second, the state equation is enriched by two exogenous variables: long-term unemployment rate and labor costs. The results show that very long-term unemployment plays a statistically significant role in the explanation of the NAIRU, but even so, the majority of the fluctuations of the estimated NAIRU are explained by the autoregressive process itself.

STOCHASTIC DESCRIPTION OF THE HIGH-FREQUENCY CONTENT OF DAILY SUNSPOTS AND EVIDENCE FOR REGIME CHANGES

The irregularity index λ is applied to the high-frequency content of daily sunspot numbers ISSN. This λ is a modification of the standard maximal Lyapunov exponent. It is computed here as a function of embedding dimension m, within four-year time windows centered at the maxima of Schwabe cycles. The λ(m) curves form separate clusters (pre-1923 and post-1933). This supports a regime transition and narrows its occurrence to cycle 16, preceding the growth of activity leading to the Modern Maximum. The two regimes are reproduced by a simple autoregressive process AR(1), with the mean of Poisson noise undergoing 11 yr modulation. The autocorrelation a of the process (linked to sunspot lifetime) is a ≈ 0.8 for 1850-1923 and ≈0.95 for 1933-2013. The AR(1) model suggests that groups of spots appear with a Poisson rate and disappear at a constant rate. We further applied the irregularity index to the daily sunspot group number series for the northern and southern hemispheres, provided by the Greenwich Royal Observatory (RGO), in order to study a possible desynchronization. Correlations between the north and south λ(m) curves vary quite strongly with time and indeed show desynchronization. This may reflect a slow change in the dimension of an underlying dynamical system. The ISSN and RGO series of group numbers do not imply an identical mechanism, but both uncover a regime change at a similar time. Computation of the irregularity index near the maximum of cycle 24 will help in checking whether yet another regime change is under way.

TRACING THE DYNAMICS OF COMPETITION: EVIDENCE FROM COMPANY PROFITS

This article proposes a simple approach to analyzing profit dynamics, which allows for time‐varying persistence of profits. The time series model is a simple autoregressive process where the dynamics of the persistence parameter follow an autoregressive process. Using the longest time series available on profits for more than a hundred U.S. firms, we find that there is ample evidence of time variation in the persistence parameter. (JEL L00, C22)

Real-time flow forecasting in the absence of quantitative precipitation forecasts: A multi-model approach

Summary In situations where Quantitative Precipitation Forecasts (QPF) over lead-times are not readily available, but lead-time flow forecasts are required, models based either solely on the recorded flow data series, or on the recorded series of flow and past rainfall are needed. For the first input scenario considered, involving the flow series only, five lumped models which are based on the simple autoregressive process and artificial neural networks are used. For the second input scenario, involving two recorded series, i.e. rainfall and runoff, two linear transfer function type models and two models based on artificial neural networks are employed. Using a multi-model approach, the outputs of the models in each scenario are combined using three techniques of combination, namely, the simple and the weighted average methods and the neural network method. The Nash–Sutcliffe model efficiency index, the Root Mean Square Error and the Mean Relative Error are used to assess the relative performance of the models and combinations. Daily recorded flow and rainfall data of two rivers, one in France and the other in Ireland, are used to generate flow forecasts up to six day lead-times. For the French catchment, it is observed that, among the individual forecasting models utilising only the observed flows, the best forecast efficiency in verification for lead-times of one and two days is achieved by the simple autoregressive model whereas for the higher lead-times, the neural network model performs best. In contrast, among the models employing both observed flow and rainfall, the linear transfer function model utilising departures from the seasonal means produces the highest efficiency. For the Irish catchment, the neural network models employing the departures from the seasonal means are consistently best in verification for both scenarios, namely, using observed flow only and using both the observed flow and rainfall series. For both scenarios, the performance is better when both rainfall and flow data are used rather than the flow data only. In both scenarios of application, all three methods of model output combination produce very similar efficiency values which are generally better than the efficiencies of the individual models used in the combinations.

The real exchange rate in Brazil Mean reversion or random walk in the long run?

This paper studies the behavior of the real exchange rate in Brazil over the longest possible period for which data are available: 1855–1990. Does the real exchange rate follow a random walk or does it revert to its mean, possibly nonstationary, level? The evidence is mixed. Formal tests can not reject the hypothesis of nonstationary behavior, although the judgement is borderline. However, time-series identification favors a stationary interpretation, and simple autoregressive processes for the real exchange rate yield extremely robust and satisfactory estimates.

Seasonal Integration and the Evolving Seasonals Model

In this paper it is argued that describing seasonal patterns as an evolving seasonals model in which the coefficients attached to seasonal trigonometric terms follow simple autoregressive processes can be very useful when one is faced with the task of extending well known results obtained for non-seasonal time series to the seasonal case. Such a perspective gains its utility from the fact that this evolving seasonal Model (ESM) can be decomposed into quantities that are non-seasonal and the behaviour of these variables can be examined with standard techniques. It emerges that this strategy will deliver methods currently in use for the analysis of seasonal series, and is also flexible enough to suggest some new alternatives.

Quasi-Stationary and Transient Periods in the Northern Hemisphere Circulation Series

In this paper, persistence characteristics of the Northern Hemisphere (NH) extratropical circulation have been studied. A simple method, based on the speed with which the atmosphere moves in the phase space (PSS, measured by 2-day lag distances), was adopted to partition the circulation data series into 5-day or longer quasi-stationary periods (QSP) and alternating transition periods (TP). The method is based on the assumptions that large-scale circulation regimes often develop abruptly and that during their development transient activity is either unchanged or enhanced. The partitioning results reveal that a whole cycle of QSP and TP on the hemisphere has an average duration of 20 days with considerable amount of variability. The average length of a QSP-TP cycle is not sensitive to changes of a relatively wide range in the PSS limit value employed in the method. In this range of limit values, the average length of the cycle changes less than 17%, while the ratio between the length of QSP and TP increases dramatically from 0.73 to 4.42. The partitioning results are statistically very similar for three complementary sectors of the hemisphere. However, we found very little synchronicity in the changes in the three sectors. The correlation between changes in any of the three sectors and on the whole hemisphere is at a much higher level, around 0.75. Although the length of the cycle on height values at individual grid points is in the range we can expect from a red-noise process, this cycle length is considerably (20%) shorter than that in a larger region or on the whole hemisphere. This is an indication that the persistence characteristics of larger-scale circulation, due to spatial interactions, show more persistence than, and cannot be well modeled by, a simple autoregressive process. Statistical tests indicate that the hemispheric QSPs are largely temporally uncorrelated and cannot be results of a random partitioning method. All these results suggest that the basic assumption about the regime-like behavior of the atmosphere is at least partially true: large-scale regime changes are indeed accompanied with higher speed of changes in the circulation phase space. Further evidence is presented that the circulation patterns in the phase space are distributed as a multivariate normal distribution in a phase-average sense (i.e., as a function of distance from the mean). Hence, the characteristic distance between neighboring circulation patterns is smaller close to the climate mean than farther away from it. As a consequence that had to be considered in this study, the day-to-day changes in the circulation (an inverse measure of persistence) are also smaller close to the climate mean. It is also argued that phase-average multinormality is the primary characteristic of the distribution of circulation patterns in the phase space and any secondary characteristic (local density maximum) should be searched for and interpreted in this context.

Strong representations for LAD estimators in linear models

Consider the standard linear modely i =z i β+e i ,i=1, 2,...,n, where zi denotes theith row of ann x p design matrix,β∈ℝ p is an unknown parameter to be estimated ande i are independent random variables with a common distribution functionF. The least absolute deviation (LAD) estimate $$\tilde \beta $$ of β is defined as any solution of the minimization problem $$\sum\limits_{i = 1}^n { \left| {y_i - z_i \tilde \beta } \right| = \inf \left\{ {\sum\limits_{i = 1}^n { \left| {y_i - z_i \beta } \right|:\beta \in \mathbb{R}^p } } \right\}} .$$ In this paper Bahadur type representations are obtained for $$\tilde \beta $$ under very mild conditions onF near zero and onz i,i=1,...,n. These results are extended to the case, when {e i} is a mixing sequence. In particular the results are applicable when the residualse i form a simple autoregressive process.

An Empirical Investigation of the Adaptive-Filtering Learning Factor

Acceptance of the adaptive-filtering parameter-estimation process has been mixed. Much of the variability between studies may result from the particular learning factor selected and may be further affected by the type of standardization used. The author presents a modification of the Makridakis and Wheelwright adaptive-filtering algorithm. This modified algorithm provides superior performance and simplifies the selection of the learning factor when used with simple autoregressive processes.

Estimation of seemingly unrelated regression with lagged dependent variables and autocorrelated errors

An asymptotically efficient method of estimating the parameters of seemingly urnelated regression equations with lagged dependent variables and autocorrelated errors is presented. The procedure is an adaptation of the two-step Gauss Newtton method of estimating distributed lag models. The procedure is applicable to both vector and simple autoregressive processes. The estimator and two competitors are compared in a Monte Carlo study. The suggested procedure performs relatively well and is clearly superior for the estimation of the autocorrelation coefficients