Exponential Smoothing Procedure Research Articles

Robust day-ahead solar forecasting with endogenous data and sliding windows

Renewable energy forecasting services comprise various modules for intra-day and day-ahead forecasts. This work specifically addresses day-ahead forecasts, utilizing specifications based on endogenous, historical measurements. These specifications are designed to be computationally efficient, requiring fewer input variables and less training data. Such weather-independent specifications serve as benchmarks against the more computationally demanding forecasts based on numerical weather predictions. A series of experiments, designed to simulate the real-world application of an online system, were conducted on sliding windows of back-contact photovoltaic (installed at KAUST, Saudi Arabia) output series, solar irradiance recorded in Hawaii, and simulated data. Our analysis evaluated 24 specifications, which are variants of (i) functional time series models (including two novel shrinkage procedures); (ii) time series nearest neighbor schemes; (iii) exponential smoothing procedures; (iv) autoregressive integrated moving average processes; (v) automatic techniques based on time series decomposition; and (vi) the persistence model. In addition to employing outlier-robust accuracy metrics, such as mean absolute error, our evaluation also prioritized prediction-interval accuracy, quantified by the mean scaled interval score. Our findings suggest that practitioners can achieve significant improvements over the persistence model by forecasting daily profiles using adaptive nonparametric or functional data analysis-based procedures. Moreover, applying shrinkage to nearest neighbor (NN) forecasts toward smooth, average daily profiles significantly enhances NN performance. Conversely, some popular, computationally intensive models fail to perform adequately to justify their additional cost.

Forecasting Hourly Intermittent Rainfall by Deep Belief Networks with Simple Exponential Smoothing

Accurate rainfall forecasting is essential in planning and managing water resource systems efficiently. However, intermittent rainfall patterns increase the difficulty of accurately forecasting rainfall values. Deep learning techniques have recently been popular and powerful in forecasting. Thus, this study employed deep belief networks with a simple exponential smoothing procedure (DBNSES) to forecast hourly intermittent rainfall values in Taiwan. Weather factors were used as independent variables to forecast rainfall volume. The simple exponential smoothing data preprocessing procedure was used to deal with the intermittent data patterns. The other three forecasting models, namely the least squares support vector regression (LSSVR), the generalized regression neural network (GRNN), and the backpropagation neural network (BPNN), were employed to forecast rainfall using the same data sets. In addition, genetic algorithms were utilized to determine the parameters of four forecasting models. The empirical results indicate that the developed DBNSES models are superior to the other forecasting models in terms of forecasting accuracy. In addition, the DBNSES can obtain smaller values of RMSE than those in the previous studies. Therefore, the DBNSES model is a suitable and effective way of forecasting rainfall with intermittent data patterns.

Multiple day biclustering of high‐frequency financial time series

With recent technological advances, high‐frequency transaction‐by‐transaction data are widely available to investors and researchers. To explore the microstructure of variability of stock prices on transaction‐level intra‐day data and to dynamically study patterns of comovement over multiple trading days, we propose a multiple day time series biclustering algorithm (CC‐MDTSB) that extends the time series biclustering algorithm (CC‐TSB). For identifying biclusters within each trading day, our algorithm provides a faster alternative to the random replacement method in the CC‐TSB algorithm. Moreover, our algorithm does not require prespecification of the number of biclusters for each trading day. Instead, we set a threshold on the number of stocks within the biclusters to yield an adaptive stopping criterion for multiple day analysis. An analysis of the biclusters determined over multiple trading days enables us to study the dynamic behaviour of stocks over time. We effectively estimate the comovement probability of each m‐tuple of stocks conditional on the other stocks within the dynamic biclusters and propose a method to forecast comovement days using a nonparametric double exponential smoothing procedure. Copyright © 2018 John Wiley & Sons, Ltd.

АДАПТИВНАЯ МОДЕЛЬ БИНАРНОГО ВЫБОРА И ВОЗМОЖНОСТИ ЕЕ ПРАКТИЧЕСКОГО ИСПОЛЬЗОВАНИЯ

Цель: построение адаптивной модели бинарного выбора на основе нового подхода к реализации адаптивных принципов. Обсуждение: принципы адаптации, перекочевав из живой природы в науку, технику, теорию и практику управления, показывают абсолютную универсальность. Трудно назвать область человеческой деятельности, в которой эти принципы нельзя было бы использовать. Особое место они занимают в моделировании экономических процессов. Механизм, с помощью которого осуществляется практическая реализация принципов адаптации, основан на экспоненциальном сглаживании. Процедура экспоненциального сглаживания оказалась столь удачной, что ее использовали даже при объяснении смысла гипотезы адаптивных ожиданий. В результате применения этой процедуры происходит затухание более ранних тенденций и закономерностей, что естественным образом обеспечивает доминирование закономерностей, демонстрируемых последними наблюдениями. Возникает закономерный вопрос: действительно ли процедура экспоненциального сглаживания представляет собой единственный способ, с помощью которого удается осуществить плавную замену старых тенденций новыми. В исследовании предлагается не затухание более ранних тенденций, а усиление вновь нарождающихся. Понятно, что усиление новых тенденций автоматически приводит к относительному снижению значимости старых. Фактически достигается тот же самый эффект. Результаты: предлагаемый способ построения адаптивного механизма назван степенным сглаживанием, что, по мнению авторов, подчеркивает аналогичность его предназначенности с экспоненциальным сглаживанием. Но в отличие от экспоненциального сглаживания степенное сглаживание применяется для построения нелинейных регрессионных моделей, коэффициенты которых оцениваются с помощью метода максимального правдоподобия, специфика которого учитывается экспоненциальным сглаживанием. Изложены детали применения этого подхода дял построения адаптивной модели бинарного выбора.

Brown’s Weighted Exponential Moving Average Implementation in Forex Forecasting

In 2016, a time series forecasting technique which combined the weighting factor calculation formula found in weighted moving average with Brown’s double exponential smoothing procedures had been introduced. The technique is known as Brown’s weighted exponential moving average (B-WEMA), as a new variant of double exponential smoothing method which does the exponential filter processes twice. In this research, we will try to implement the new method to forecast some foreign exchange, or known as forex data, including EUR/USD, AUD/USD, GBP/USD, USD/JPY, and EUR/JPY data. The time series data forecasting results using B-WEMA then be compared with other conventional and hybrid moving average methods, such as weighted moving average (WMA), exponential moving average (EMA), and Brown’s double exponential smoothing (B-DES). The comparison results show that B-WEMA has a better accuracy level than other forecasting methods used in this research.

A Functional Wavelet–Kernel Approach for Time Series Prediction

SummaryWe consider the prediction problem of a time series on a whole time interval in terms of its past. The approach that we adopt is based on functional kernel nonparametric regression estimation techniques where observations are discrete recordings of segments of an underlying stochastic process considered as curves. These curves are assumed to lie within the space of continuous functions, and the discretized time series data set consists of a relatively small, compared with the number of segments, number of measurements made at regular times. We estimate conditional expectations by using appropriate wavelet decompositions of the segmented sample paths. A notion of similarity, based on wavelet decompositions, is used to calibrate the prediction. Asymptotic properties when the number of segments grows to ∞ are investigated under mild conditions, and a nonparametric resampling procedure is used to generate, in a flexible way, valid asymptotic pointwise prediction intervals for the trajectories predicted. We illustrate the usefulness of the proposed functional wavelet–kernel methodology in finite sample situations by means of a simulated example and two real life data sets, and we compare the resulting predictions with those obtained by three other methods in the literature, in particular with a smoothing spline method, with an exponential smoothing procedure and with a seasonal autoregressive integrated moving average model.

Generalized adaptive exponential smoothing of observations from an ergodic hidden Markov model

We consider a sequence of observations which is generated by a so-called hidden Markov model. An exponential smoothing procedure applied to such an observation sequence generates an inhomogeneous Markov process as a sequence of smoothed values. If the state sequence of the underlying hidden Markov model is moreover ergodic, then for two classes of smoothing functions the strong ergodicity of the sequence of smoothed values is proved. As a consequence a central limit theorem and a law of large numbers hold true for the smoothed values. The proof uses general results for so-called convergent inhomogeneous Markov processes. The procedure proposed by the author can be applied to some time series discussed in the literature.

Generalized adaptive exponential smoothing of observations from an ergodic hidden Markov model

We consider a sequence of observations which is generated by a so-called hidden Markov model. An exponential smoothing procedure applied to such an observation sequence generates an inhomogeneous Markov process as a sequence of smoothed values. If the state sequence of the underlying hidden Markov model is moreover ergodic, then for two classes of smoothing functions the strong ergodicity of the sequence of smoothed values is proved. As a consequence a central limit theorem and a law of large numbers hold true for the smoothed values. The proof uses general results for so-called convergent inhomogeneous Markov processes. The procedure proposed by the author can be applied to some time series discussed in the literature.

Identification of demand patterns for selective processing: a case study

A basic function in the proper management of repair part inventories is the anticipation of demand. The US Navy maintains a database of univariate demand data for its repair part inventories using a quarterly time interval and a limited number of periods. Historically, the exponential smoothing procedure has been used for demand forecasting. This method is simple and robust, but it does not make use of any characteristics of the entire time series such as trend, cycles, presence of outliers or demand clustering. Sharper information may be available with the use of the Box–Jenkins system. Not all repair parts can capitalize on this and there is a problem in identifying those that do. Moreover the number of parts is quite large and the speed of identification is an issue. This paper addresses this problem. The research begins with the development of several simple, robust and dimensionless time series features. These are used to predict the suitability of Box–Jenkins (ARIMA) modeling. Two predictive models are considered: classical regression and a modern expert-system statistical package, ModelQuest™. Their strengths and weaknesses are compared. The result of either is a computationally simple means for determining which repair parts time series may benefit from the Box–Jenkins methodology for purposes of inventory management.

The use of protocols to select exponential smoothing procedures: A reconsideration of forecasting competitions

Forecasting competitions have evaluated the accuracy of extrapolative methods unselectively; that is, by applying each method to an entire batch of time series without asking whether the method is appropriate for each individual series. For example, simple exponential smoothing was applied to trended as well as untrended time series. In consequence, the calculated error measures do not unambiguously portray the accuracy one can expect in using a given procedure selectively. In this study, we employ three different protocols for selecting appropriate exponential smoothing procedures. Then, based on 132 time series from previous forecasting competitions, we compare forecasting accuracy in cases for which the procedures are designated (by each protocol) as appropriate with accuracy achieved in applications designated as inappropriate. The selection protocols are a variance analysis proposed by Gardner and McKenzie, a set of visual rules adapted from Collopy and Armstrong's rule-based forecasting system, and a method-switching procedure developed by Goodrich. We found the selection protocols to be effective in selecting appropriate applications of strong-trend (linear and exponential trend) procedures. For example, when the Holt (linear trend) procedure is applied selectively, its forecasting accuracy is much superior to that suggested by the forecasting competitions. On the other hand, the protocols are not effectively distinguishing appropriate from inappropriate applications of damped and no-trend procedures. Further, our results reveal considerable disagreement among the protocols themselves, making it apparent that much work remains to be done to improve the state of the art in forecasting-method selection.

Generalized adaptive exponential smoothing procedures

The classical exponential smoothing procedure to be applied to a sequence of observations is modified into some adaptive variants and also generalized to the recursive schemeThis means that given the history of observations and smoothed values up to time n, the updated smoothed value Wn +1 is given by a function u of Wn and Xn, which satisfies only certain structural properties. We study these procedures within the framework of random systems with complete connections and exploit results from Markov process theory to study the sequence . A broad class of ‘smoothing functions' u, which induce sequences with nice statistical properties, is presented. A method to estimate the limit of the expected smoothed values is also developed.,

Generalized adaptive exponential smoothing procedures

The classical exponential smoothing procedure to be applied to a sequence of observations is modified into some adaptive variants and also generalized to the recursive scheme This means that given the history of observations and smoothed values up to time n, the updated smoothed value Wn + 1 is given by a function u of Wn and Xn , which satisfies only certain structural properties. We study these procedures within the framework of random systems with complete connections and exploit results from Markov process theory to study the sequence . A broad class of ‘smoothing functions' u, which induce sequences with nice statistical properties, is presented. A method to estimate the limit of the expected smoothed values is also developed.,

Multivariate exponential smoothing: Method and practice

A multivariate extension of the familiar exponential smoothing procedure for forecasting univariate time series composed of level, seasonality and irregularity is presented. The updated estimates of the level, trend and seasonal effects of each of the component series are obtained as weighted averages of estimates derived by a univariate smoothing procedure and correction factors based on information gained from the other series. The forecasts are shown to be asymptotically optimal under particular state space models. The performance of the procedure is illustrated and compared to that of other univariate and multivariate forecasting procedures using two actual bivariate time series. The results are encouraging for the use of the procedure in practice.

A Simulation of Techniques for Forecasting Shipments Using Firm Orders-to-Date

Many companies use firm orders-to-date to make forecasts of units to be shipped at a future time t that is j periods away, j = 1, 2,..., h. A number of methods for making these forecasts were developed and evaluated using simulation. The time series for bookings was decomposed into a shipment time series and a time series for factors representing the fraction of shipments booked j periods ahead. Separate techniques were used for the shipments series (namely, naive, exponential smoothing and Bayesian procedures) and for the factors (naive and exponential smoothing procedures). The accuracy of these approaches, as well as an ARIMA model that ignored orders-to-date, was evaluated by using several simulated patterns of bookings. No approach was dominant, but one of the simplest approaches (naive/smoothing) did comparatively well.

A Simulation of Techniques for Forecasting Shipments Using Firm Orders-to-Date

Many companies use firm orders-to-date to make forecasts of units to be shipped at a future time t that is j periods away, j = 1, 2,..., h. A number of methods for making these forecasts were developed and evaluated using simulation. The time series for bookings was decomposed into a shipment time series and a time series for factors representing the fraction of shipments booked j periods ahead. Separate techniques were used for the shipments series (namely, naive, exponential smoothing and Bayesian procedures) and for the factors (naive and exponential smoothing procedures). The accuracy of these approaches, as well as an ARIMA model that ignored orders-to-date, was evaluated by using several simulated patterns of bookings. No approach was dominant, but one of the simplest approaches (naive/smoothing) did comparatively well.

Evaluation of the average of patients: application to endocrine assays

Recent work (Cembrowski et al, Am J Clin Pathol 1984;81:492–499) has shown that the average of selected patient data can theoretically be used to demonstrate systematic errors. We formerly demonstrate that the sensitivity or power of the ‘average of patients’ (AOP) is related to the index ( N p ∗S w 2)/S p 2 where N p is the number of patient results averaged, S W the within-run component of the standard deviation of the analytical method and S P the standard deviation of the trimmed population. The utility of the AOP can therefore be assessed rapidly without power function curves or the calculation of the daily AOP itself. The index showed that, for 12 radioimmunoassays done in our laboratory, the power of the AOP was greatest for T3 uptake, then FTI, then T4. Daily AOP were followed for these tests with control results on parallel Shewhart plots. We also applied an exponential smoothing procedure on the AOP and control results to improve trend detection. These analyses demonstrated that the AOP can improve the detection of systematic errors and the differentiation of true errors from errors affecting only control specimens.

Conditions for the optimality of exponential smoothing forecast procedures

Exponential smoothing procedures, in particular those recommended byBrown [1962] are used extensively in many areas of economics, business and engineering. It is shown in this paper that: i) Brown's forecasting procedures are optimal in terms of achieving minimum mean square error forecasts only if the underlying stochastic process is included in a limited subclass of ARIMA (p, d, q) processes. Hence, it is shown what assumptions are made when using these procedures. ii) The implication of point (i) is that the users ofBrown's procedures tacitly assume that the stochastic processes which occur in the real world are from the particular restricted subclass of ARIMA (p, d, q) processes. No reason can be found why these particular models should occur more frequently than others. iii) It is further shown that even if a stochastic process which would lead toBrown's model occurred, the actual methods used for making the forecasts are clumsy and much simpler procedures can be employed.

The Use of Time Series Analysis Techniques in Forecasting Meteorological Drought

Using an exponential smoothing procedure and an autoregressive-moving average process; forecasts for the monthly Palmer Drought Severity Index were calculated. The autocorrelation and partial autocorrelation functions of severity index values were used as a starting point for the autoregressive-moving average model selection process. Of the many possible autoregressive-moving average models, the one that was selected provided the best forecasts based on the mean square error. Monthly data for the period 1929–1969 were utilized in a nonlinear least-squares computer routine to arrive at estimated parameter values for the autoregressive-moving average model. Monthly forecasts with a lead time of one month were generated using the exponential smoothing and autoregressive-moving average procedures for the period 1970–1972. These forecasts were compared with the myopic (persistence) forecasts, Xt+1=Xt. The mean square errors of the forecasts were 0.63 for the autoregressive-moving average model, 0.65 for the myopic model, and 0.79 for the exponential smoothing model. From the mean-square-error calculations, it appears that there is no statistically significant difference between the forecasts given by the Box-Jenkins and myopic models; however, the 95% confidence intervals for these two models overlap only slightly during the first part of the forecast period indicating that there may be some advantage to using the Box-Jenkins model instead of the myopic model. Both of these models are superior to the exponential smoothing model. These results demonstrate the usefulness of the relatively new autoregressive-moving average time series analysis procedures.