A robust functional time series forecasting method

Univariate time series often take the form of a collection of curves observed sequentially over time. Examples of these include hourly ground-level ozone concentration curves. These curves can be viewed as a time series of functions observed at equally spaced intervals over a dense grid. Since functional time series may contain various types of outliers, we introduce a robust functional time series forecasting method to down-weigh the influence of outliers in forecasting. Through a robust principal component analysis based on projection pursuit, a time series of functions can be decomposed into a set of robust dynamic functional principal components and their associated scores. Conditioning on the estimated functional principal components, the crux of the curve-forecasting problem lies in modelling and forecasting principal component scores, through a robust vector autoregressive forecasting method. Via a simulation study and an empirical study on forecasting ground-level ozone concentration, the robust method demonstrates the superior forecast accuracy that dynamic functional principal component regression entails. The robust method also shows the superior estimation accuracy of the parameters in the vector autoregressive models for modelling and forecasting principal component scores, and thus improves curve forecast accuracy.     

Functional time series approach for forecasting very short-term electricity demand

This empirical paper presents a number of functional modelling and forecasting methods for predicting very short-term (such as minute-by-minute) electricity demand. The proposed functional methods slice a seasonal univariate time series (TS) into a TS of curves; reduce the dimensionality of curves by applying functional principal component analysis before using a univariate TS forecasting method and regression techniques. As data points in the daily electricity demand are sequentially observed, a forecast updating method can greatly improve the accuracy of point forecasts. Moreover, we present a non-parametric bootstrap approach to construct and update prediction intervals, and compare the point and interval forecast accuracy with some naive benchmark methods. The proposed methods are illustrated by the half-hourly electricity demand from Monday to Sunday in South Australia.     

Forecasting functional time series using weighted likelihood methodology

Functional time series whose sample elements are recorded sequentially over time are frequently encountered with increasing technology. Recent studies have shown that analyzing and forecasting of functional time series can be performed easily using functional principal component analysis and existing univariate/multivariate time series models. However, the forecasting performance of such functional time series models may be affected by the presence of outlying observations which are very common in many scientific fields. Outliers may distort the functional time series model structure, and thus, the underlying model may produce high forecast errors. We introduce a robust forecasting technique based on weighted likelihood methodology to obtain point and interval forecasts in functional time series in the presence of outliers. The finite sample performance of the proposed method is illustrated by Monte Carlo simulations and four real-data examples. Numerical results reveal that the proposed method exhibits superior performance compared with the existing method(s).     

Forecasting Study of Shanghai’s and Shenzhen’s Stock Markets Using a Hybrid Forecast Method

In this article, a novel hybrid method to forecast stock price is proposed. This hybrid method is based on wavelet transform, wavelet denoising, linear models (autoregressive integrated moving average (ARIMA) model and exponential smoothing (ES) model), and nonlinear models (BP Neural Network and RBF Neural Network). The wavelet transform provides a set of better-behaved constitutive series than stock series for prediction. Wavelet denoising is used to eliminate some slight random fluctuations of stock series. ARIMA model and ES model are used to forecast the linear component of denoised stock series, and then BP Neural Network and RBF Neural Network are developed as tools for nonlinear pattern recognition to correct the estimation error of the prediction of linear models. The proposed method is examined in the stock market of Shanghai and Shenzhen and the results are compared with some of the most recent stock price forecast methods. The results show that the proposed hybrid method can provide a considerable improvement for the forecasting accuracy. Meanwhile, this proposed method can also be applied to analysis and forecast reliability of products or systems and improve the accuracy of reliability engineering.     

Forecasting before,during, and after recession with singular spectrum analysis

The aim of this research is to apply the singular spectrum analysis (SSA) technique, which is a relatively new and powerful technique in time series analysis and forecasting, to forecast the 2008 UK recession, using eight economic time series. These time series were selected as they represent the most important economic indicators in the UK. The ability to understand the underlying structure of these series and to quickly identify turning points such as the on-set of the recent recession is of key interest to users. In recent years, the SSA technique has been further developed and applied to many practical problems. Hence, these series will provide an ideal practical test of the potential benefits from SSA during one of the most challenging periods for econometric analyses of recent years. The results are compared with those obtained using the ARIMA and Holt–Winters models as these methods are currently used as standard forecasting methods in the Office for National Statistics in the UK.     

变权重组合预测模型的局部加权最小二乘解法

随着科学技术的不断进步，预测方法也得到了很大的发展，常见的预测方法就有数十种之多。而组合预测是将不同的预测方法组合起来，综合利用各个方法所提供的信息，其效果往往优于单一的预测方法，故得到了广泛的应用。而基于变系数模型的思想研究了组合预测模型，将变权重的求取转化为变系数模型中系数函数的估计问题，从而可以基于局部加权最小二乘方法求解，利用交叉证实法选取光滑参数。其结果表明所提方法预测精度很高，效果优于其他方法。     

Forecast efficiency of systematically sampled time series

In this paper we consider the effect of the sampling interval in systematically sampled time series on the forecast efficiency. We find that for sufficientlv long sampled series the loss in forecasting accuracy by using the sampled instead of the original series is small     

Bayesian Forecasting of Many Count-Valued Time Series

Abstract

We develop and exemplify application of new classes of dynamic models for time series of nonnegative counts. Our novel univariate models combine dynamic generalized linear models for binary and conditionally Poisson time series, with dynamic random effects for over-dispersion. These models estimate dynamic regression coefficients in both binary and nonzero count components. Sequential Bayesian analysis allows fast, parallel analysis of sets of decoupled time series. New multivariate models then enable information sharing in contexts when data at a more highly aggregated level provide more incisive inferences on shared patterns such as trends and seasonality. A novel multiscale approach—one new example of the concept of decouple/recouple in time series—enables information sharing across series. This incorporates cross-series linkages while insulating parallel estimation of univariate models, and hence enables scalability in the number of series. The major motivating context is supermarket sales forecasting. Detailed examples drawn from a case study in multistep forecasting of sales of a number of related items showcase forecasting of multiple series, with discussion of forecast accuracy metrics, comparisons with existing methods, and broader questions of probabilistic forecast assessment.     

Forecasting Contemporaneously Aggregated Vector ARMA Processes

Given a multiple time series that is generated by a multivariate ARMA process and assuming the objective is to forecast a weighted sum of the individual variables, then under a mean squared error measure of forecasting precision, it is preferable to forecast the disaggregated multiple time series and aggregate the forecasts, rather than forecast the aggregated series directly, if the involved processes are known. This result fails to hold if the processes used for forecasting are estimated from a given set of time series data. The implications of these results for empirical research are investigated using different sets of economic data.     

The relationship between the length of the base period and population forecast errors

"The base period of a population forecast is the time period from which historical data are collected for the purpose of forecasting future population values. The length of the base period is one of the fundamental decisions made in preparing population forecasts, yet very few studies have investigated the effects of this decision on population forecast errors. In this article the relationship between the length of the base period and population forecast errors is analyzed, using three simple forecasting techniques and data from 1900 to 1980 for states in the United States. It is found that increasing the length of the base period up to 10 years improves forecast accuracy, but that further increases generally have little additional effect. The only exception to this finding is long-range forecasts of rapidly growing states, in which a longer base period substantially improves forecast accuracy for two of the forecasting techniques."     

基于一种贴近度的IOWA算子的优性组合预测模型

传统的组合预测模型中每一种单项预测方法在各个时点具有相同的加权系数,但实际上同一种单项预测方法在各个时点的预测精度有高有低,为了克服单项预测方法取固定权系数的缺陷,构建了基于一种贴近度的IOWA算子的变权系数的组合预测模型,并探讨模型的非劣性组合预测、优性组合预测存在性的充分条件,实例分析结果表明：该模型在预测效果评价指标体系中明显优于传统的组合预测方法。     

Combination forecasting for directional accuracy: An application to survey interest rate forecasts

Using published interest rates forecasts issued by professional economists, two combination forecasts designed to improve the directional accuracy of interest rate forecasting are constructed. The first combination forecast takes a weighted average of the individual forecasters' predictions. The more successful the forecaster was in past forecasts at predicting the direction of change in interest rates, the greater is the weight given to his/her current forecast. The second combination forecast is simply the forecast issued by the forecaster who had the greatest success rate at predicting the direction of change in interest rates in previous forecasts. In cases where two or more forecasters tie for best historic directional accuracy track record, the arithmetic mean of these forecasters is used. The study finds that neither combination forecasting method performs better than coin-flipping at predicting the direction of change in interest rates. Nor does either method beat the simple arithmetic mean of the predictions of all the forecasters surveyed at predicting the direction of change in interest rates.     

Automatic specification of piecewise linear additive models: application to forecasting natural gas demand

When facing any forecasting problem not only is accuracy on the predictions sought. Also, useful information about the underlying physics of the process and about the relevance of the forecasting variables is very much appreciated. In this paper, it is presented an automatic specification procedure for models that are based on additivity assumptions and piecewise linear regression. This procedure allows the analyst to gain insight about the problem by examining the automatically selected model, thus easily checking the validity of the forecast. Monte Carlo simulations have been run to ensure that the model selection procedure behaves correctly under weakly dependent data. Moreover, comparison over other well-known methodologies has been done to evaluate its accuracy performance, both in simulated data and in the context of short-term natural gas demand forecasting. Empirical results show that the accuracy of the proposed model is competitive against more complex methods such as neural networks.     

Univariate ARIMA Forecasts of Defined Variables

Many important variables in business and economics are neither measured nor measurable but are simply defined in terms of other measured variables. For instance, the real interest rate is defined as the difference between the nominal interest rate and the inflation rate. There are two ways to forecast a defined variable: one can directly forecast the variable itself, or one can derive the forecast of the defined variable indirectly from the forecasts of the constituent variables. Using Box-Jenkins univariate time series analysis for four defined variables—real interest rate, money multiplier, real GNP, and money velocity—the forecasting accuracy of the two methods is compared. The results show that indirect forecasts tend to outperform direct methods for these defined variables.     

PREDICTION-FOCUSED MODEL SELECTION FOR AUTOREGRESSIVE MODELS

In order to make predictions of future values of a time series, one needs to specify a forecasting model. A popular choice is an autoregressive time‐series model, for which the order of the model is chosen by an information criterion. We propose an extension of the focused information criterion (FIC) for model‐order selection, with emphasis on a high predictive accuracy (i.e. the mean squared forecast error is low). We obtain theoretical results and illustrate by means of a simulation study and some real data examples that the FIC is a valid alternative to the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) for selection of a prediction model. We also illustrate the possibility of using the FIC for purposes other than forecasting, and explore its use in an extended model.     

Short-term forecasting with a computationally efficient nonparametric transfer function model

In this paper a semi-parametric approach is developed to model non-linear relationships in time series data using polynomial splines. Polynomial splines require very little assumption about the functional form of the underlying relationship, so they are very flexible and can be used to model highly non-linear relationships. Polynomial splines are also computationally very efficient. The serial correlation in the data is accounted for by modelling the noise as an autoregressive integrated moving average (ARIMA) process, by doing so, the efficiency in nonparametric estimation is improved and correct inferences can be obtained. The explicit structure of the ARIMA model allows the correlation information to be used to improve forecasting performance. An algorithm is developed to automatically select and estimate the polynomial spline model and the ARIMA model through backfitting. This method is applied on a real-life data set to forecast hourly electricity usage. The non-linear effect of temperature on hourly electricity usage is allowed to be different at different hours of the day and days of the week. The forecasting performance of the developed method is evaluated in post-sample forecasting and compared with several well-accepted models. The results show the performance of the proposed model is comparable with a long short-term memory deep learning model.     

Multistep ahead forecasting of vector time series

This article develops the theory of multistep ahead forecasting for vector time series that exhibit temporal nonstationarity and co-integration. We treat the case of a semi-infinite past by developing the forecast filters and the forecast error filters explicitly. We also provide formulas for forecasting from a finite data sample. This latter application can be accomplished by using large matrices, which remains practicable when the total sample size is moderate. Expressions for the mean square error of forecasts are also derived and can be implemented readily. The flexibility and generality of these formulas are illustrated by four diverse applications: forecasting euro area macroeconomic aggregates; backcasting fertility rates by racial category; forecasting long memory inflation data; and forecasting regional housing starts using a seasonally co-integrated model.     

Forecasting the spot price of gold:combined forecast approaches versus a composite forecast approach

The fluctuation of the gold price has significant impact on the economic and social aspects of a society. In the literature, most authors have employed fundamental analysis approach in forecast model building. The basic principle underlying this approach is that it is the supply and the demand which simultaneously determines the gold price. However, due to the lack of data of quantity supplied and quantity demanded, simultaneous econometric approach seems unsuccessful. In this paper, combined and composite time series forecasting techniques are proposed. The effects of various economic factors towards spot price of gold are also examined. Among the combined forecasting models, it seems that the odds-matrix method of assigning weights provides the most accurate forecasts of spot price of gold. For the economic factors considered, the futures price of gold and and the exchange rate seem to be most informative in forecasting the spot price of gold.     

Nonparametric forecasting: a comparison of three kernel-based methods

In this paper the use of three kernel-based nonparametric forecasting methods - the conditional mean, the conditional median, and the conditional mode -is explored in detail. Several issues related to the estimation of these methods are discussed, including the choice of the bandwidth and the type of kernel function. The out-of-sample forecasting performance of the three nonparametric methods is investigated using 60 real time series. We find that there is no superior forecast method for series having approximately less than 100 observations. However, when a time series is long or when its conditional density is bimodal there is quite a difference between the forecasting performance of the three kernel-based forecasting methods.     

Specific-to-general predictor selection in approximate autoregressions—Monte Carlo evidence and a large scale performance assessment with real data

This paper describes the performance of specific-to-general composition of forecasting models that accord with (approximate) linear autoregressions. Monte Carlo experiments are complemented with ex-ante forecasting results for 97 macroeconomic time series collected for the G7 economies in Stock and Watson (J. Forecast. 23:405–430, 2004). In small samples, the specific-to-general strategy is superior in terms of ex-ante forecasting performance in comparison with a commonly applied strategy of successive model reduction according to weakest parameter significance. Applied to real data, the specific-to-general approach turns out to be preferable. In comparison with successive model reduction, the successive model expansion is less likely to involve overly large losses in forecast accuracy and is particularly recommended if the diagnosed prediction schemes are characterized by a medium to large number of predictors.