Long Memory of Financial Time Series and Hidden Markov Models with Time‐Varying Parameters

Hidden Markov models are often used to model daily returns and to infer the hidden state of financial markets. Previous studies have found that the estimated models change over time, but the implications of the time‐varying behavior have not been thoroughly examined. This paper presents an adaptive estimation approach that allows for the parameters of the estimated models to be time varying. It is shown that a two‐state Gaussian hidden Markov model with time‐varying parameters is able to reproduce the long memory of squared daily returns that was previously believed to be the most difficult fact to reproduce with a hidden Markov model. Capturing the time‐varying behavior of the parameters also leads to improved one‐step density forecasts. Finally, it is shown that the forecasting performance of the estimated models can be further improved using local smoothing to forecast the parameter variations. Copyright © 2016 John Wiley & Sons, Ltd.     

A wavelet approach for factor‐augmented forecasting

It has been acknowledged that wavelets can constitute a useful tool for forecasting in economics. Through a wavelet multi‐resolution analysis, a time series can be decomposed into different timescale components and a model can be fitted to each component to improve the forecast accuracy of the series as a whole. Up to now, the literature on forecasting with wavelets has mainly focused on univariate modelling. On the other hand, in a context of growing data availability, a line of research has emerged on forecasting with large datasets. In particular, the use of factor‐augmented models have become quite widespread in the literature and among practitioners. The aim of this paper is to bridge the two strands of the literature. A wavelet approach for factor‐augmented forecasting is proposed and put to test for forecasting GDP growth for the major euro area countries. The results show that the forecasting performance is enhanced when wavelets and factor‐augmented models are used together. Copyright © 2010 John Wiley & Sons, Ltd.     

On forecasting counts

Forecasting for a time series of low counts, such as forecasting the number of patents to be awarded to an industry, is an important research topic in socio‐economic sectors. Recently (2004), Freeland and McCabe introduced a Gaussian type stationary correlation model‐based forecasting which appears to work well for the stationary time series of low counts. In practice, however, it may happen that the time series of counts will be non‐stationary and also the series may contain over‐dispersed counts. To develop the forecasting functions for this type of non‐stationary over‐dispersed data, the paper provides an extension of the stationary correlation models for Poisson counts to the non‐stationary correlation models for negative binomial counts. The forecasting methodology appears to work well, for example, for a US time series of polio counts, whereas the existing Bayesian methods of forecasting appear to encounter serious convergence problems. Further, a simulation study is conducted to examine the performance of the proposed forecasting functions, which appear to work well irrespective of whether the time series contains small or large counts. Copyright © 2008 John Wiley & Sons, Ltd.     

A non‐linear dynamic model for multiplicative seasonal‐trend decomposition

A non‐linear dynamic model is introduced for multiplicative seasonal time series that follows and extends the X‐11 paradigm where the observed time series is a product of trend, seasonal and irregular factors. A selection of standard seasonal and trend component models used in additive dynamic time series models are adapted for the multiplicative framework and a non‐linear filtering procedure is proposed. The results are illustrated and compared to X‐11 and log‐additive models using real data. In particular it is shown that the new procedures do not suffer from the trend bias present in log‐additive models. Copyright © 2002 John Wiley & Sons, Ltd.     

Empirical analysis and forecasting of volatility dynamics in high‐frequency returns with time‐varying components

We study intraday return volatility dynamics using a time‐varying components approach, and the method is applied to analyze IBM intraday returns. Empirical evidence indicates that with three additive components—a time‐varying mean of absolute returns and two cosine components with time‐varying amplitudes—together they capture very well the pronounced periodicity and persistence behaviors exhibited in the empirical autocorrelation pattern of IBM returns. We find that the long‐run volatility persistence is driven predominantly by daily level shifts in mean absolute returns. After adjusting for these intradaily components, the filtered returns behave much like a Gaussian noise, suggesting that the three‐components structure is adequately specified. Furthermore, a new volatility measure (TCV) can be constructed from these components. Results from extensive out‐of‐sample rolling forecast experiments suggest that TCV fares well in predicting future volatility against alternative methods, including GARCH model, realized volatility and realized absolute value. Copyright © 2009 John Wiley & Sons, Ltd.     

Short‐term forecasting of industrial electricity consumption in Brazil

This paper presents short‐term forecasting methods applied to electricity consumption in Brazil. The focus is on comparing the results obtained after using two distinct approaches: dynamic non‐linear models and econometric models. The first method, that we propose, is based on structural statistical models for multiple time series analysis and forecasting. It involves non‐observable components of locally linear trends for each individual series and a shared multiplicative seasonal component described by dynamic harmonics. The second method, adopted by the electricity power utilities in Brazil, consists of extrapolation of the past data and is based on statistical relations of simple or multiple regression type. To illustrate the proposed methodology, a numerical application is considered with real data. The data represents the monthly industrial electricity consumption in Brazil from the three main power utilities: Eletropaulo, Cemig and Light, situated at the major energy‐consuming states, Sao Paulo, Rio de Janeiro and Minas Gerais, respectively, in the Brazilian Southeast region. The chosen time period, January 1990 to September 1994, corresponds to an economically unstable period just before the beginning of the Brazilian Privatization Program. Implementation of the algorithms considered in this work was made via the statistical software S‐PLUS. Copyright © 1999 John Wiley & Sons, Ltd.     

Forecasting Simultaneously High‐Dimensional Time Series: A Robust Model‐Based Clustering Approach

This paper considers the problem of forecasting high‐dimensional time series. It employs a robust clustering approach to perform classification of the component series. Each series within a cluster is assumed to follow the same model and the data are then pooled for estimation. The classification is model‐based and robust to outlier contamination. The robustness is achieved by using the intrinsic mode functions of the Hilbert–Huang transform at lower frequencies. These functions are found to be robust to outlier contamination. The paper also compares out‐of‐sample forecast performance of the proposed method with several methods available in the literature. The other forecasting methods considered include vector autoregressive models with ∕ without LASSO, group LASSO, principal component regression, and partial least squares. The proposed method is found to perform well in out‐of‐sample forecasting of the monthly unemployment rates of 50 US states. Copyright © 2013 John Wiley & Sons, Ltd.     

Modelling time series with season‐dependent autocorrelation structure

Time series with season‐dependent autocorrelation structure are commonly modelled using periodic autoregressive moving average (PARMA) processes. In most applications, the moving average terms are excluded for ease of estimation. We propose a new class of periodic unobserved component models (PUCM). Parameter estimates for PUCM are readily interpreted; the estimated coefficients correspond to variances of the measurement noise and of the error terms in unobserved components. We show that PUCM have correlation structure equivalent to that of a periodic integrated moving average (PIMA) process. Results from practical applications indicate that our models provide a natural framework for series with periodic autocorrelation structure both in terms of interpretability and forecasting accuracy. Copyright © 2008 John Wiley & Sons, Ltd.     

Factor forecasts for the UK

Data are now readily available for a very large number of macroeconomic variables that are potentially useful when forecasting. We argue that recent developments in the theory of dynamic factor models enable such large data sets to be summarized by relatively few estimated factors, which can then be used to improve forecast accuracy. In this paper we construct a large macroeconomic data set for the UK, with about 80 variables, model it using a dynamic factor model, and compare the resulting forecasts with those from a set of standard time‐series models. We find that just six factors are sufficient to explain 50% of the variability of all the variables in the data set. These factors, which can be shown to be related to key variables in the economy, and their use leads to considerable improvements upon standard time‐series benchmarks in terms of forecasting performance. Copyright © 2005 John Wiley & Sons, Ltd.     

Forecasting regional house price inflation: a comparison between dynamic factor models and vector autoregressive models

This paper uses the dynamic factor model framework, which accommodates a large cross‐section of macroeconomic time series, for forecasting regional house price inflation. In this study, we forecast house price inflation for five metropolitan areas of South Africa using principal components obtained from 282 quarterly macroeconomic time series in the period 1980:1 to 2006:4. The results, based on the root mean square errors of one to four quarters ahead out‐of‐sample forecasts over the period 2001:1 to 2006:4 indicate that, in the majority of the cases, the Dynamic Factor Model statistically outperforms the vector autoregressive models, using both the classical and the Bayesian treatments. We also consider spatial and non‐spatial specifications. Our results indicate that macroeconomic fundamentals in forecasting house price inflation are important. Copyright © 2010 John Wiley & Sons, Ltd.     

Building neural network models for time series: a statistical approach

This paper is concerned with modelling time series by single hidden layer feedforward neural network models. A coherent modelling strategy based on statistical inference is presented. Variable selection is carried out using simple existing techniques. The problem of selecting the number of hidden units is solved by sequentially applying Lagrange multiplier type tests, with the aim of avoiding the estimation of unidentified models. Misspecification tests are derived for evaluating an estimated neural network model. All the tests are entirely based on auxiliary regressions and are easily implemented. A small‐sample simulation experiment is carried out to show how the proposed modelling strategy works and how the misspecification tests behave in small samples. Two applications to real time series, one univariate and the other multivariate, are considered as well. Sets of one‐step‐ahead forecasts are constructed and forecast accuracy is compared with that of other nonlinear models applied to the same series. Copyright © 2006 John Wiley & Sons, Ltd.     

Forecasting real‐time data allowing for data revisions

A modeling approach to real‐time forecasting that allows for data revisions is shown. In this approach, an observed time series is decomposed into stochastic trend, data revision, and observation noise in real time. It is assumed that the stochastic trend is defined such that its first difference is specified as an AR model, and that the data revision, obtained only for the latest part of the time series, is also specified as an AR model. The proposed method is applicable to the data set with one vintage. Empirical applications to real‐time forecasting of quarterly time series of US real GDP and its eight components are shown to illustrate the usefulness of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Modelling and forecasting time series sampled at different frequencies

This paper discusses how to specify an observable high‐frequency model for a vector of time series sampled at high and low frequencies. To this end we first study how aggregation over time affects both the dynamic components of a time series and their observability, in a multivariate linear framework. We find that the basic dynamic components remain unchanged but some of them, mainly those related to the seasonal structure, become unobservable. Building on these results, we propose a structured specification method built on the idea that the models relating the variables in high and low sampling frequencies should be mutually consistent. After specifying a consistent and observable high‐frequency model, standard state‐space techniques provide an adequate framework for estimation, diagnostic checking, data interpolation and forecasting. An example using national accounting data illustrates the practical application of this method. Copyright © 2008 John Wiley & Sons, Ltd.     

An intelligent model selection and forecasting system

In this paper we present an intelligent decision‐support system based on neural network technology for model selection and forecasting. While most of the literature on the application of neural networks in forecasting addresses the use of neural network technology as an alternative forecasting tool, limited research has focused on its use for selection of forecasting methods based on time‐series characteristics. In this research, a neural network‐based decision support system is presented as a method for forecast model selection. The neural network approach provides a framework for directly incorporating time‐series characteristics into the model‐selection phase. Using a neural network, a forecasting group is initially selected for a given data set, based on a set of time‐series characteristics. Then, using an additional neural network, a specific forecasting method is selected from a pool of three candidate methods. The results of training and testing of the networks are presented along with conclusions. Copyright © 1999 John Wiley & Sons, Ltd.     

Adaptive modelling and forecasting of offshore wind power fluctuations with Markov‐switching autoregressive models

Wind power production data at temporal resolutions of a few minutes exhibit successive periods with fluctuations of various dynamic nature and magnitude, which cannot be explained (so far) by the evolution of some explanatory variable. Our proposal is to capture this regime‐switching behaviour with an approach relying on Markov‐switching autoregressive (MSAR) models. An appropriate parameterization of the model coefficients is introduced, along with an adaptive estimation method allowing accommodation of long‐term variations in the process characteristics. The objective criterion to be recursively optimized is based on penalized maximum likelihood, with exponential forgetting of past observations. MSAR models are then employed for one‐step‐ahead point forecasting of 10 min resolution time series of wind power at two large offshore wind farms. They are favourably compared against persistence and autoregressive models. It is finally shown that the main interest of MSAR models lies in their ability to generate interval/density forecasts of significantly higher skill. Copyright © 2010 John Wiley & Sons, Ltd.     

Forecasting US Recessions with a Large Set of Predictors

In this paper, I use a large set of macroeconomic and financial predictors to forecast US recession periods. I adopt Bayesian methodology with shrinkage in the parameters of the probit model for the binary time series tracking the state of the economy. The in‐sample and out‐of‐sample results show that utilizing a large cross‐section of indicators yields superior US recession forecasts in comparison to a number of parsimonious benchmark models. Moreover, the data‐rich probit model gives similar accuracy to the factor‐based model for the 1‐month‐ahead forecasts, while it provides superior performance for 1‐year‐ahead predictions. Finally, in a pseudo‐real‐time application for the Great Recession, I find that the large probit model with shrinkage is able to pick up the recession signals in a timely fashion and does well in comparison to the more parsimonious specification and to nonparametric alternatives. Copyright © 2016 John Wiley & Sons, Ltd.     

Bias‐corrected bootstrap prediction intervals for autoregressive model: new alternatives with applications to tourism forecasting

This paper proposes the use of the bias‐corrected bootstrap for interval forecasting of an autoregressive time series with an arbitrary number of deterministic components. We use the bias‐corrected bootstrap based on two alternative bias‐correction methods: the bootstrap and an analytic formula based on asymptotic expansion. We also propose a new stationarity‐correction method, based on stable spectral factorization, as an alternative to Kilian's method exclusively used in past studies. A Monte Carlo experiment is conducted to compare small‐sample properties of prediction intervals. The results show that the bias‐corrected bootstrap prediction intervals proposed in this paper exhibit desirable small‐sample properties. It is also found that the bootstrap bias‐corrected prediction intervals based on stable spectral factorization are tighter and more stable than those based on Kilian's stationarity‐correction. The proposed methods are applied to interval forecasting for the number of tourist arrivals in Hong Kong. Copyright © 2010 John Wiley & Sons, Ltd.     

Forecasting with missing data: application to coastal wave heights

This paper presents a comparative analysis of linear and mixed models for short‐term forecasting of a real data series with a high percentage of missing data. Data are the series of significant wave heights registered at regular periods of three hours by a buoy placed in the Bay of Biscay. The series is interpolated with a linear predictor which minimizes the forecast mean square error. The linear models are seasonal ARIMA models and the mixed models have a linear component and a non‐linear seasonal component. The non‐linear component is estimated by a non‐parametric regression of data versus time. Short‐term forecasts, no more than two days ahead, are of interest because they can be used by the port authorities to notify the fleet. Several models are fitted and compared by their forecasting behaviour. Copyright © 1999 John Wiley & Sons, Ltd.     

Average conditional correlation and tree structures for multivariate GARCH models

We propose a simple class of multivariate GARCH models, allowing for time‐varying conditional correlations. Estimates for time‐varying conditional correlations are constructed by means of a convex combination of averaged correlations (across all series) and dynamic realized (historical) correlations. Our model is very parsimonious. Estimation is computationally feasible in very large dimensions without resorting to any variance reduction technique. We back‐test the models on a six‐dimensional exchange‐rate time series using different goodness‐of‐fit criteria and statistical tests. We collect empirical evidence of their strong predictive power, also in comparison to alternative benchmark procedures. Copyright © 2006 John Wiley & Sons, Ltd.     

Is forecasting with large models informative? Assessing the role of judgement in macroeconomic forecasts

We evaluate residual projection strategies in the context of a large‐scale macro model of the euro area and smaller benchmark time‐series models. The exercises attempt to measure the accuracy of model‐based forecasts simulated both out‐of‐sample and in‐sample. Both exercises incorporate alternative residual‐projection methods, to assess the importance of unaccounted‐for breaks in forecast accuracy and off‐model judgement. Conclusions reached are that simple mechanical residual adjustments have a significant impact on forecasting accuracy irrespective of the model in use, likely due to the presence of breaks in trends in the data. The testing procedure and conclusions are applicable to a wide class of models and of general interest. Copyright © 2010 John Wiley & Sons, Ltd.