Identifying the time‐effect factors of multiple time series

The Peña–Box model is considered for finding the time‐effect factors of a multiple time series. This paper first establishes the connection between the Peña–Box model and the vector ARMA model. According to the Peña–Box model, some series can be ignored while modelling the vector ARMA model. A consistent estimator is then proposed to identify the model for nonlinear and nonstationary time series. Finally, the finite‐sample behaviour of the estimator is illustrated via simulations. Copyright © 2005 John Wiley & Sons, Ltd.     

Multiple time-series modelling: Another look at the canadian money and income data

The practice of modelling the components of a vector time series to arrive at a joint model for the vector is considered. It is shown that in some cases this is not unreasonable. A vector ARMA model is used to model the Canadian money and income data. We also use these data to discuss the issue of differencing a multiple time series. Finally, models based on first and second differences are compared using forecasts.     

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.     

Time series forecasts and extra-model information

Often a forecaster has supplementary information (e.g. field reports or forecasts from another source) that cannot be included directly in a time series model. Especially interesting are cases where this information is given at time intervals that are different from those of the time series model forecasts. Previous authors have considered a numerical and a model-based statistical method for combining extra-model information of this type with ARIMA model forecasts. This paper extends both methods to vector ARMA model forecasts and dynamic regression (transfer function) model forecasts. It is also shown that a Lagrange multiplier numerical procedure arises as a special case of the model-based procedure. An empirical example is given.     

Forecasting economic time series that require a power transformation: Case of state tax receipts

In this study, time series analysis is applied to the problem of forecasting state income tax receipts. The data series is of special interest since it exhibits a strong trend with a high multiplicative seasonal component. An appropriate model is identified by simultaneous estimation of the parameters of the power transformation and the ARMA model using the Schwarz (1978) Bayesian information criterion. The forecasting performance of the time series model obtained from this procedure is compared with alternative time series and regression models. The study illustrates how an information criterion can be employed for identifying time series models that require a power transformation, as exemplified by state tax receipts. It also establishes time series analysis as a viable technique for forecasting state tax receipts.     

Updating ARMA predictions for temporal aggregates

This article develops and extends previous investigations on the temporal aggregation of ARMA predications. Given a basic ARMA model for disaggregated data, two sets of predictors may be constructed for future temporal aggregates: predictions based on models utilizing aggregated data or on models constructed from disaggregated data for which forecasts are updated as soon as the new information becomes available. We show that considerable gains in efficiency based on mean‐square‐error‐type criteria can be obtained for short‐term predications when using models based on updated disaggregated data. However, as the prediction horizon increases, the gain in using updated disaggregated data diminishes substantially. In addition to theoretical results associated with forecast efficiency of ARMA models, we also illustrate our findings with two well‐known time series. Copyright © 2004 John Wiley & Sons, Ltd.     

ARMA Models and the Box–Jenkins Methodology

The purpose of this paper is to apply the Box–Jenkins methodology to ARIMA models and determine the reasons why in empirical tests it is found that the post-sample forecasting the accuracy of such models is generally worse than much simpler time series methods. The paper concludes that the major problem is the way of making the series stationary in its mean (i.e. the method of differencing) that has been proposed by Box and Jenkins. If alternative approaches are utilized to remove and extrapolate the trend in the data, ARMA models outperform the models selected through Box–Jenkins methodology. In addition, it is shown that using ARMA models to seasonally adjusted data slightly improves post-sample accuracies while simplifying the use of ARMA models. It is also confirmed that transformations slightly improve post-sample forecasting accuracy, particularly for long forecasting horizons. Finally, it is demonstrated that AR(1), AR(2) and ARMA(1,1) models can produce more accurate post-sample forecasts than those found through the application of Box–Jenkins methodology.© 1997 John Wiley & Sons, Ltd.     

Long‐memory dynamic Tobit models

We introduce a long‐memory dynamic Tobit model, defining it as a censored version of a fractionally integrated Gaussian ARMA model, which may include seasonal components and/or additional regression variables. Parameter estimation for such a model using standard techniques is typically infeasible, since the model is not Markovian, cannot be expressed in a finite‐dimensional state‐space form, and includes censored observations. Furthermore, the long‐memory property renders a standard Gibbs sampling scheme impractical. Therefore we introduce a new Markov chain Monte Carlo sampling scheme, which is orders of magnitude more efficient than the standard Gibbs sampler. The method is inherently capable of handling missing observations. In case studies, the model is fit to two time series: one consisting of volumes of requests to a hard disk over time, and the other consisting of hourly rainfall measurements in Edinburgh over a 2‐year period. The resulting posterior distributions for the fractional differencing parameter demonstrate, for these two time series, the importance of the long‐memory structure in the models. Copyright © 2006 John Wiley & Sons, Ltd.     

Model‐based forecast adjustment: With an illustration to inflation

This paper introduces the idea of adjusting forecasts from a linear time series model where the adjustment relies on the assumption that this linear model is an approximation of a nonlinear time series model. This way of creating forecasts could be convenient when inference for a nonlinear model is impossible, complicated or unreliable in small samples. The size of the forecast adjustment can be based on the estimation results for the linear model and on other data properties such as the first few moments or autocorrelations. An illustration is given for a first‐order diagonal bilinear time series model, which in certain properties can be approximated by a linear ARMA(1, 1) model. For this case, the forecast adjustment is easy to derive, which is convenient as the particular bilinear model is indeed cumbersome to analyze in practice. An application to a range of inflation series for low‐income countries shows that such adjustment can lead to some improved forecasts, although the gain is small for this particular bilinear time series model.     

Real‐time or current vintage: does the type of data matter for forecasting and model selection?

In this paper we investigate the impact of data revisions on forecasting and model selection procedures. A linear ARMA model and nonlinear SETAR model are considered in this study. Two Canadian macroeconomic time series have been analyzed: the real‐time monetary aggregate M3 (1977–2000) and residential mortgage credit (1975–1998). The forecasting method we use is multi‐step‐ahead non‐adaptive forecasting. Copyright © 2008 John Wiley & Sons, Ltd.     

Modelling and Trading the English and German Stock Markets with Novelty Optimization Techniques

The motivation for this paper was the introduction of novel short‐term models to trade the FTSE 100 and DAX 30 exchange‐traded funds (ETF) indices. There are major contributions in this paper which include the introduction of an input selection criterion when utilizing an expansive universe of inputs, a hybrid combination of partial swarm optimizer (PSO) with radial basis function (RBF) neural networks, the application of a PSO algorithm to a traditional autoregressive moving model (ARMA), the application of a PSO algorithm to a higher‐order neural network and, finally, the introduction of a multi‐objective algorithm to optimize statistical and trading performance when trading an index. All the machine learning‐based methodologies and the conventional models are adapted and optimized to model the index. A PSO algorithm is used to optimize the weights in a traditional RBF neural network, in a higher‐order neural network (HONN) and the AR and MA terms of an ARMA model. In terms of checking the statistical and empirical accuracy of the novel models, we benchmark them with a traditional HONN, with an ARMA, with a moving average convergence/divergence model (MACD) and with a naïve strategy. More specifically, the trading and statistical performance of all models is investigated in a forecast simulation of the FTSE 100 and DAX 30 ETF time series over the period January 2004 to December 2015 using the last 3 years for out‐of‐sample testing. Finally, the empirical and statistical results indicate that the PSO‐RBF model outperforms all other examined models in terms of trading accuracy and profitability, even with mixed inputs and with only autoregressive inputs. Copyright © 2016 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.     

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.     

A bootstrap simulation study in ARMA (p,q) structures

In 1979 Efron proposed a new general statistical procedure known as ‘Bootstrap’, a computer-intensive method used when finite-sample theory is impossible or difficult to derive, or when only asymptotic theory is available. It is recommended in the estimation of measures of both location and scale for any statistical model without making any distributional assumptions about the data. This technique has been successfully used in various applied statistical problems, although not many applications have been reported in the area of time series. In this paper we present a new application of Bootstrap to time series. We consider a simulation study where artificial time series corresponding to AR(1), AR(2), MA(1), MA(2) and ARMA(1, 1) structures were generated, covering important regions of the parameter space of each one of them. The conventional Box-Jenkins parametric estimators of the parameters are compared with the corresponding non-parametric Bootstrap estimators, obtained by 500 Bootstrap repetitions for each series.     

Simultaneous transfer functions versus vector arma models

This work compares two classes of multiple time series models which have been developed in past decades and are usually believed to be equivalent: the vector ARMA model and the system of simultaneous transfer functions (STF). The first part analyzes the mathematical structure of the two schemes; their properties of stability, structural identification and realization. In the second, algorithms of order identification and parameter estimation are derived, following the approach of stochastic approximation. The proposed solutions are easily implementable on standard statistical software and in an extended empirical example their performance is checked. The superiority of the STF model will be well established.     

Assessing inefficiency in the s&p 500 futures market

We analyse the price movement of the S&P 500 futures market for violations of the efficient market hypothesis on a short-term basis. To assess market inefficiency we construct a model and find that the returns, i.e. the difference in the logarithm of closing prices on consecutive days, exhibit the usual conditional heteroscedasticity behaviour typical of long series of financial data. To account for this non-linear behaviour we scale the returns by a volatility factor which depends on the daily high, low, and closing price. The rescaled series, which may be interpreted as the trend-countertrend component of the time series, is modelled using Box and Jenkins techniques. The resulting model is an ARMA(1,1). The scale factors are assumed to form a time series and are modelled using a semi-non-parametric method which avoids the restrictive assumptions of most ARCH or GARCH models. Using the combined model we perform 1000 simulations of market data, each simulation comprising 250 days (approximately one year). We then formulate a naive trading strategy which is based on the ratio of the one-day-ahead expected return to its one-day-ahead expected conditional standard deviation. The trading strategy has four adjustable parameters which are set to maximize profits for the simulation data. Next, we apply the trading strategy to one year of recent out-of-sample data. Our conclusion is that the S&P 500 futures market exhibits only slight inefficiencies, but that there exist, in principle, better trading strategies which take account of risk than the benchmark strategy of buy-and-hold. We have also constructed a linear model for the return series. Using the linear model, we have simulated returns and determined the optimum values for the adjustable parameters of the trading strategy. In this case, the optimum trading strategy is the same as the benchmark strategy, buy-and-hold. Finally, we have compared the profitability of the optimized trading strategy, based on the non-linear model, to three ad hoc trading strategies using the out-of-sample data. The three ad hoc strategies are more profitable than the optimized strategy.     

On multistep prediction error methods for time series models

Multistep prediction error methods for linear time series models are considered from both a theoretical and a practical standpoint. The emphasis is on autoregressive moving-average (ARMA) models for which a multistep prediction error estimation method (PEM) is developed. The results of a Monte Carlo simulation study aimed at establishing the possible merits of the multistep PEM are presented.     

On Selecting a Power Transformation in Time-Series Analysis

The primary aim of this paper is to select an appropriate power transformation when we use ARMA models for a given time series. We propose a Bayesian procedure for estimating the power transformation as well as other parameters in time series models. The posterior distributions of interest are obtained utilizing the Gibbs sampler, a Markov Chain Monte Carlo (MCMC) method. The proposed methodology is illustrated with two real data sets. The performance of the proposed procedure is compared with other competing procedures. © 1997 John Wiley & Sons, Ltd.     

Forecasting high‐frequency financial data with the ARFIMA–ARCH model

Financial data series are often described as exhibiting two non‐standard time series features. First, variance often changes over time, with alternating phases of high and low volatility. Such behaviour is well captured by ARCH models. Second, long memory may cause a slower decay of the autocorrelation function than would be implied by ARMA models. Fractionally integrated models have been offered as explanations. Recently, the ARFIMA–ARCH model class has been suggested as a way of coping with both phenomena simultaneously. For estimation we implement the bias correction of Cox and Reid ( 1987 ). For daily data on the Swiss 1‐month Euromarket interest rate during the period 1986–1989, the ARFIMA–ARCH (5,d,2/4) model with non‐integer d is selected by AIC. Model‐based out‐of‐sample forecasts for the mean are better than predictions based on conditionally homoscedastic white noise only for longer horizons (τ > 40). Regarding volatility forecasts, however, the selected ARFIMA–ARCH models dominate. Copyright © 2001 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.