The approximation of long‐memory processes by an ARMA model

A mean square error criterion is proposed in this paper to provide a systematic approach to approximate a long‐memory time series by a short‐memory ARMA(1, 1) process. Analytic expressions are derived to assess the effect of such an approximation. These results are established not only for the pure fractional noise case, but also for a general autoregressive fractional moving average long‐memory time series. Performances of the ARMA(1,1) approximation as compared to using an ARFIMA model are illustrated by both computations and an application to the Nile river series. Results derived in this paper shed light on the forecasting issue of a long‐memory process. Copyright © 2001 John Wiley & Sons, Ltd.     

Long‐memory forecasting of US monetary indices

Several studies have tested for long‐range dependence in macroeconomic and financial time series but very few have assessed the usefulness of long‐memory models as forecast‐generating mechanisms. This study tests for fractional differencing in the US monetary indices (simple sum and divisia) and compares the out‐of‐sample fractional forecasts to benchmark forecasts. The long‐memory parameter is estimated using Robinson's Gaussian semi‐parametric and multivariate log‐periodogram methods. The evidence amply suggests that the monetary series possess a fractional order between one and two. Fractional out‐of‐sample forecasts are consistently more accurate (with the exception of the M3 series) than benchmark autoregressive forecasts but the forecasting gains are not generally statistically significant. In terms of forecast encompassing, the fractional model encompasses the autoregressive model for the divisia series but neither model encompasses the other for the simple sum series. Copyright © 2006 John Wiley & Sons, Ltd.     

Forecasting the Nikkei spot index with fractional cointegration

We investigate the forecast performance of the fractionally integrated error correction model against several competing models for the prediction of the Nikkei stock average index. The competing models include the martingale model, the vector autoregressive model and the conventional error correction model. We consider models with and without conditional heteroscedasticity. For forecast horizons of over twenty days, the best forecasting performance is obtained for the model when fractional cointegration is combined with conditional heteroscedasticity. Our results reinforce the notion that cointegration and fractional cointegration are important for long‐horizon prediction. Copyright © 1999 John Wiley & Sons, Ltd.     

Predicting Bid–Ask Spreads Using Long‐Memory Autoregressive Conditional Poisson Models

We introduce a long‐memory autoregressive conditional Poisson (LMACP) model to model highly persistent time series of counts. The model is applied to forecast quoted bid–ask spreads, a key parameter in stock trading operations. It is shown that the LMACP nicely captures salient features of bid–ask spreads like the strong autocorrelation and discreteness of observations. We discuss theoretical properties of LMACP models and evaluate rolling‐window forecasts of quoted bid–ask spreads for stocks traded at NYSE and NASDAQ. We show that Poisson time series models significantly outperform forecasts from AR, ARMA, ARFIMA, ACD and FIACD models. The economic significance of our results is supported by the evaluation of a trade schedule. Scheduling trades according to spread forecasts we realize cost savings of up to 14 % of spread transaction costs. Copyright © 2013 John Wiley & Sons, Ltd.     

Realized Volatility Forecasting of Agricultural Commodity Futures Using Long Memory and Regime Switching

We investigate the dynamic properties of the realized volatility of five agricultural commodity futures by employing the high‐frequency data from Chinese markets and find that the realized volatility exhibits both long memory and regime switching. To capture these properties simultaneously, we utilize a Markov switching autoregressive fractionally integrated moving average (MS‐ARFIMA) model to forecast the realized volatility by combining the long memory process with regime switching component, and compare its forecast performances with the competing models at various horizons. The full‐sample estimation results show that the dynamics of the realized volatility of agricultural commodity futures are characterized by two levels of long memory: one associated with the low‐volatility regime and the other with the high‐volatility regime, and the probability to stay in the low‐volatility regime is higher than that in the high‐volatility regime. The out‐of‐sample volatility forecast results show that the combination of long memory with switching regimes improves the performance of realized volatility forecast, and the proposed model represents a superior out‐of‐sample realized volatility forecast to the competing models. Copyright © 2016 John Wiley & Sons, Ltd.     

A Multiplicative Error Model with Heterogeneous Components for Forecasting Realized Volatility

To forecast realized volatility, this paper introduces a multiplicative error model that incorporates heterogeneous components: weekly and monthly realized volatility measures. While the model captures the long‐memory property, estimation simply proceeds using quasi‐maximum likelihood estimation. This paper investigates its forecasting ability using the realized kernels of 34 different assets provided by the Oxford‐Man Institute's Realized Library. The model outperforms benchmark models such as ARFIMA, HAR, Log‐HAR and HEAVY‐RM in within‐sample fitting and out‐of‐sample (1‐, 10‐ and 22‐step) forecasts. It performed best in both pointwise and cumulative comparisons of multi‐step‐ahead forecasts, regardless of loss function (QLIKE or MSE). Copyright © 2015 John Wiley & Sons, Ltd.     

Local to unity,long‐horizon forecasting thresholds for model selection in the AR(1)

This article introduces a novel framework for analysing long‐horizon forecasting of the near non‐stationary AR(1) model. Using the local to unity specification of the autoregressive parameter, I derive the asymptotic distributions of long‐horizon forecast errors both for the unrestricted AR(1), estimated using an ordinary least squares (OLS) regression, and for the random walk (RW). I then identify functions, relating local to unity ‘drift’ to forecast horizon, such that OLS and RW forecasts share the same expected square error. OLS forecasts are preferred on one side of these ‘forecasting thresholds’, while RW forecasts are preferred on the other. In addition to explaining the relative performance of forecasts from these two models, these thresholds prove useful in developing model selection criteria that help a forecaster reduce error. Copyright © 2004 John Wiley & Sons, Ltd.     

Model selection and forecasting for long-range dependent processes

Fractionally integrated autoregressive moving-average (ARFIMA) models have proved useful tools in the analysis of time series with long-range dependence. However, little is known about various practical issues regarding model selection and estimation methods, and the impact of selection and estimation methods on forecasts. By means of a large-scale simulation study, we compare three different estimation procedures and three automatic model-selection criteria on the basis of their impact on forecast accuracy. Our results endorse the use of both the frequency-domain Whittle estimation procedure and the time-domain approximate MLE procedure of Haslett and Raftery in conjunction with the AIC and SIC selection criteria, but indicate that considerable care should be exercised when using ARFIMA models. In general, we find that simple ARMA models provide competitive forecasts. Only a large number of observations and a strongly persistent time series seem to justify the use of ARFIMA models for forecasting purposes.     

Modeling and forecasting the oil volatility index

The increase in oil price volatility in recent years has raised the importance of forecasting it accurately for valuing and hedging investments. The paper models and forecasts the crude oil exchange‐traded funds (ETF) volatility index, which has been used in the last years as an important alternative measure to track and analyze the volatility of future oil prices. Analysis of the oil volatility index suggests that it presents features similar to those of the daily market volatility index, such as long memory, which is modeled using well‐known heterogeneous autoregressive (HAR) specifications and new extensions that are based on net and scaled measures of oil price changes. The aim is to improve the forecasting performance of the traditional HAR models by including predictors that capture the impact of oil price changes on the economy. The performance of the new proposals and benchmarks is evaluated with the model confidence set (MCS) and the Generalized‐AutoContouR (G‐ACR) tests in terms of point forecasts and density forecasting, respectively. We find that including the leverage in the conditional mean or variance of the basic HAR model increases its predictive ability. Furthermore, when considering density forecasting, the best models are a conditional heteroskedastic HAR model that includes a scaled measure of oil price changes, and a HAR model with errors following an exponential generalized autoregressive conditional heteroskedasticity specification. In both cases, we consider a flexible distribution for the errors of the conditional heteroskedastic process.     

Modeling of frequency containment reserve prices with econometrics and artificial intelligence

The forecasting of prices for electricity balancing reserve power can essentially improve the trading positions of market participants in competitive auctions. Having identified a lack of literature related to forecasting balancing reserve prices, we deploy approaches originating from econometrics and artificial intelligence and set up a forecasting framework based on autoregressive and exogenous factors. We use SARIMAX models as well as neural networks with different structures and forecast based on a rolling one-step forecast with reestimation of the models. It turns out that the naive forecast performs reasonably well but is outperformed by the more advanced models. In addition, neural network approaches outperform the econometric approach in terms of forecast quality, whereas for the further use of the generated models the econometric approach has advantages in terms of explaining price drivers. For the present application, more advanced configurations of the neural networks are not able to further improve the forecasting performance.     

Out‐of‐sample volatility prediction: A new mixed‐frequency approach

This paper proposes a new mixed‐frequency approach to predict stock return volatilities out‐of‐sample. Based on the strategy of momentum of predictability (MoP), our mixed‐frequency approach has a model switching mechanism that switches between generalized autoregressive conditional heteroskedasticity (GARCH)‐class models that only use low‐frequency data and heterogeneous autoregressive models of realized volatility (HAR‐RV)‐type that only use high‐frequency data. The MoP model simply selects a forecast with relatively good past performance between the GARCH‐class and HAR‐RV‐type forecasts. The model confidence set (MCS) test shows that our MoP strategy significantly outperforms the competing models, which is robust to various settings. The MoP test shows that a relatively good recent past forecasting performance of the GARCH‐class or HAR‐RV‐type model is significantly associated with a relatively good current performance, supporting the success of the MoP model.     

Forecasting Temperature Indices Density with Time‐Varying Long‐Memory Models

The hedging of weather risks has become extremely relevant in recent years, promoting the diffusion of weather‐derivative contracts. The pricing of such contracts requires the development of appropriate models for the prediction of the underlying weather variables. Within this framework, a commonly used specification is the ARFIMA‐GARCH. We provide a generalization of such a model, introducing time‐varying memory coefficients. Our model satisfies the empirical evidence of the changing memory level observed in average temperature series, and provides useful improvements in the forecasting, simulation, and pricing issues related to weather derivatives. We present an application related to the forecast and simulation of a temperature index density, which is then used for the pricing of weather options. Copyright © 2011 John Wiley & Sons, Ltd.     

Evidence of long memory in short‐term interest rates

The issues of non‐stationarity and long memory of real interest rates are examined here. Autoregressive models allowing short‐term mean reversion are compared with fractional integration models in terms of their ability to explain the behaviour of the data and to forecast out‐of‐sample. The data used are weekly observations of 3‐month Eurodeposit rates for 10 countries, adjusted for inflation, for 14 years. Following Brenner, Harjes and Kroner, the volatility of these rates is shown to both exhibit GARCH effects and depend on the level of interest rates. Although relatively little support is found for the hypothesis of mean reversion, evidence of long memory in interest rate changes is found for seven countries. The out‐of‐sample forecasting performance for a year ahead of the fractional integrated models was significantly better than a no change. Copyright © 2003 John Wiley & Sons, Ltd.     

Comparing the DSGE model with the factor model: an out‐of‐sample forecasting experiment

In this paper, we put dynamic stochastic general equilibrium DSGE forecasts in competition with factor forecasts. We focus on these two models since they represent nicely the two opposing forecasting philosophies. The DSGE model on the one hand has a strong theoretical economic background; the factor model on the other hand is mainly data‐driven. We show that incorporating a large information set using factor analysis can indeed improve the short‐horizon predictive ability, as claimed by many researchers. The micro‐founded DSGE model can provide reasonable forecasts for US inflation, especially with growing forecast horizons. To a certain extent, our results are consistent with the prevailing view that simple time series models should be used in short‐horizon forecasting and structural models should be used in long‐horizon forecasting. Our paper compares both state‐of‐the‐art data‐driven and theory‐based modelling in a rigorous manner. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting Daily Variations of Stock Index Returns with a Multifractal Model of Realized Volatility

Multifractal models have recently been introduced as a new type of data‐generating process for asset returns and other financial data. Here we propose an adaptation of this model for realized volatility. We estimate this new model via generalized method of moments and perform forecasting by means of best linear forecasts derived via the Levinson–Durbin algorithm. Its out‐of‐sample performance is compared against other popular time series specifications. Using an intra‐day dataset for five major international stock market indices, we find that the the multifractal model for realized volatility improves upon forecasts of its earlier counterparts based on daily returns and of many other volatility models. While the more traditional RV‐ARFIMA model comes out as the most successful model (in terms of the number of cases in which it has the best forecasts for all combinations of forecast horizons and evaluation criteria), the new model performs often significantly better during the turbulent times of the recent financial crisis. Copyright © 2014 John Wiley & Sons, Ltd.     

Assessing the forecasting accuracy of alternative nominal exchange rate models: the case of long memory

This paper presents an autoregressive fractionally integrated moving‐average (ARFIMA) model of nominal exchange rates and compares its forecasting capability with the monetary structural models and the random walk model. Monthly observations are used for Canada, France, Germany, Italy, Japan and the United Kingdom for the period of April 1973 through December 1998. The estimation method is Sowell's (1992) exact maximum likelihood estimation. The forecasting accuracy of the long‐memory model is formally compared to the random walk and the monetary models, using the recently developed Harvey, Leybourne and Newbold (1997) test statistics. The results show that the long‐memory model is more efficient than the random walk model in steps‐ahead forecasts beyond 1 month for most currencies and more efficient than the monetary models in multi‐step‐ahead forecasts. This new finding strongly suggests that the long‐memory model of nominal exchange rates be studied as a viable alternative to the conventional models. Copyright © 2006 John Wiley & Sons, Ltd.     

ARARMA models for time series analysis and forecasting

Methods of time series forecasting are proposed which can be applied automatically. However, they are not rote formulae, since they are based on a flexible philosophy which can provide several models for consideration. In addition it provides diverse diagnostics for qualitatively and quantitatively estimating how well one can forecast a series. The models considered are called ARARMA models (or ARAR models) because the model fitted to a long memory time series (t) is based on sophisticated time series analysis of AR (or ARMA) schemes (short memory models) fitted to residuals Y(t) obtained by parsimonious‘best lag’non-stationary autoregression. Both long range and short range forecasts are provided by an ARARMA model Section 1 explains the philosophy of our approach to time series model identification. Sections 2 and 3 attempt to relate our approach to some standard approaches to forecasting; exponential smoothing methods are developed from the point of view of prediction theory (section 2) and extended (section 3). ARARMA models are introduced (section 4). Methods of ARARMA model fitting are outlined (sections 5,6). Since‘the proof of the pudding is in the eating’, the methods proposed are illustrated (section 7) using the classic example of international airline passengers.     

Tourism in the Canary Islands: forecasting using several seasonal time series models

This paper deals with the analysis of the number of tourists travelling to the Canary Islands by means of using different seasonal statistical models. Deterministic and stochastic seasonality is considered. For the latter case, we employ seasonal unit roots and seasonally fractionally integrated models. As a final approach, we also employ a model with possibly different orders of integration at zero and the seasonal frequencies. All these models are compared in terms of their forecasting ability in an out‐of‐sample experiment. The results in the paper show that a simple deterministic model with seasonal dummy variables and AR(1) disturbances produce better results than other approaches based on seasonal fractional and integer differentiation over short horizons. However, increasing the time horizon, the results cannot distinguish between the model based on seasonal dummies and another using fractional integration at zero and the seasonal frequencies. Copyright © 2008 John Wiley & Sons, Ltd.     

ARFIMA approximation and forecasting of the limiting aggregate structure of long‐memory process

This article studies Man and Tiao's (2006) low‐order autoregressive fractionally integrated moving‐average (ARFIMA) approximation to Tsai and Chan's (2005b) limiting aggregate structure of the long‐memory process. In matching the autocorrelations, we demonstrate that the approximation works well, especially for larger d values. In computing autocorrelations over long lags for larger d value, using the exact formula one might encounter numerical problems. The use of the ARFIMA(0, d, d?₁) model provides a useful alternative to compute the autocorrelations as a really close approximation. In forecasting future aggregates, we demonstrate the close performance of using the ARFIMA(0, d, d?₁) model and the exact aggregate structure. In practice, this provides a justification for the use of a low‐order ARFIMA model in predicting future aggregates of long‐memory process. Copyright © 2008 John Wiley & Sons, Ltd.     

Moving average threshold heterogeneous autoregressive (MAT-HAR) models

We propose moving average threshold heterogeneous autoregressive (MAT-HAR) models as a novel combination of heterogeneous autoregression (HAR) and threshold autoregression (TAR). The MAT-HAR has multiple groups of lags of a target series, and a threshold term can appear in each group. The threshold is a moving average of lagged target series, which guarantees time-varying thresholds and simple estimation via least squares. We show via Monte Carlo simulations that the MAT-HAR has sharp in-sample and out-of-sample performance. An empirical application on the industrial production of Japan suggests that significant threshold effects exist, and the MAT-HAR has a higher forecast accuracy than the HAR.