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Econometrics for Finance - S5 - Univariate Time Series - Modeling and Forecasting

Yearly municipal budget data. Yearly in-sample. Downs and Rocke Monthly accounting data. Hillmer, Larcker, and Schroeder Judgmental methods, univariate. Monthly truck sales. Heuts and Bronckers Monthly hospital patient movements. Lin Quarterly unemployment rate. Transfer function. Edlund and Karlsson Comparisons with exponential smoothing The exponential smoothing state space models are all non-stationary. Models with seasonality or non-damped trend or both have two unit roots; all other models—that is, non-seasonal models with either no trend or damped trend—have one unit root.

It is possible to define a stationary model with similar characteristics to exponential smoothing, but this is not normally done. The philosophy of exponential smoothing is that the world is non-stationary. One advantage of the exponential smoothing models is that they can be non-linear. So time series that exhibit non-linear characteristics including heteroscedasticity may be better modelled using exponential smoothing state space models.

For seasonal data, there are many more ARIMA models than the 30 possible models in the exponential smoothing. The larger model space of ARIMA models actually harms forecasting performance because it introduces additional uncertainty. The smaller exponential smoothing class is sufficiently rich to capture the dynamics of almost all real business and economic time series. This is not true. The two classes of models overlap. Thus, the two model classes overlap and are complimentary; each has its strengths and weaknesses.

1. Introduction

State space models provide a unifying framework in which any linear time series model can be written. The key forecasting contribution of Kalman was to give a recursive algorithm known as the Kalman filter for computing forecasts. Statisticians became interested in state space models when Schweppe showed that the Kalman filter provides an efficient algorithm for computing the one-step-ahead prediction errors and associated variances needed to produce the likelihood function.

Shumway and Stoffer combined the EM algorithm with the Kalman filter to give a general approach to forecasting time series using state space models, including allowing for missing observations. Fildes compared the forecasts obtained using Harrison and Stevens method with those from simpler methods such as exponential smoothing, and concluded that the additional complexity did not lead to improved forecasting performance.

The modelling and estimation approach of Harrison and Stevens was further developed by West, Harrison, and Migon and West and Harrison Harvey , extended the class of models and followed a non-Bayesian approach to estimation. Harvey provides a comprehensive review and introduction to this class of models including continuous-time and non-Gaussian variations. These models bear many similarities with exponential smoothing methods, but have multiple sources of random error. Ray discussed convergence rates for the linear growth structural model and showed that the initial states usually chosen subjectively have a nonnegligible impact on forecasts.

Harvey and Snyder proposed some continuous-time structural models for use in forecasting lead time demand for inventory control. Proietti discussed several variations on the BSM, compared their properties and evaluated the resulting forecasts. Non-Gaussian structural models have been the subject of a large number of papers, beginning with the power steady model of Smith with further development by West et al. Mittnik provided a survey of this class of models, and Vinod and Basu obtained forecasts of consumption, income, and interest rates using balanced state space models.

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These models have only one source of random error and subsume various other time series models including ARMAX models, ARMA models, and rational distributed lag models. Time series prediction is a very challenging signal processing problem as in real situations it is typically a function of a large number of factors most of which are unknown or inaccessible at the time of prediction. Although such time series appear as very noisy, non-stationary and non-linear signals, its history carries a significant evidence that can be used to build the predictive model.

Although linearity is a useful assumption and a powerful tool in many areas, it became increasingly clear in the late s and early s that linear models are insufficient in many real applications. For example, sustained animal population size cycles the well-known Canadian lynx data , sustained solar cycles annual sunspot numbers , energy flow, and amplitude—frequency relations were found not to be suitable for linear models.

Functional-coefficient model A functional coefficient AR FCAR or FAR model is an AR model in which the AR coefficients are allowed to vary as a measurable smooth function of another variable, such as a lagged value of the time series itself or an exogenous variable. Chen and Tsay proposed a modeling procedure using ideas from both parametric and nonparametric statistics.

The approach assumes little prior information on model structure without suffering from the bcurse of dimensionalityQ; see also Cai, Fan, and Yao Harvill and Ray presented multi-step-ahead forecasting results using univariate and multivariate functional coefficient V FCAR models.

These authors restricted their comparison to three forecasting methods: the naive plug-in predictor, the bootstrap predictor, and the multi-stage predictor. Both simulation and empirical results indicate that the bootstrap method appears to give slightly more accurate forecast results. A potentially useful area of future research is whether the forecasting power of VFCAR models can be enhanced by using exogenous variables.

Neural nets An artificial neural network ANN can be useful for nonlinear processes that have an unknown functional relationship and as a result are difficult to fit. The main idea with ANNs is that inputs, or dependent variables, get filtered through one or more hidden layers each of which consist of hidden units, or nodes, before they reach the output variable.

The intermediate output is related to the final output. Numerous studies have documented the successes of ANNs in forecasting financial data. However, in two editorials in this Journal, Chatfield , questioned whether ANNs had been oversold as a miracle forecasting technique. If parsimony is considered to be really important, then it is interesting to compare the out-of sample forecasting performance of linear versus nonlinear models, using a wide variety of different model selection criteria.

This issue was considered in quite some depth by Swanson and White However, in contrast to Swanson and White, Heravi, Osborn, and Birchenhall found that linear models produce more accurate forecasts of monthly seasonally unadjusted European industrial production series than ANN models.

Times change, and it is fair to say that the risk of over-parametrization and overfitting is now recognized by many authors; see, e. Nevertheless, the question of whether or not an ANN is over-parametrized still remains unanswered. Evolutionary Algorithm An evolutionary algorithm EA uses a collection of heuristic rules to modify a population of trial solutions in such a way that each generation of trial values tends to be, on average, better than its predecessor.

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In statistical applications, the fitness is a function of the summary statistic being optimized e. Genetic algorithm is the most popular type of EA inspired by the basic principles of biological evolution and natural selection. It is stochastic search algorithm which simulate the evolution of living organisms, where the fittest individuals dominate over the weaker ones, by mimicking the biological mechanisms of evolution, such as selection, crossover and mutation.

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Sloan, Raymond W. Sluss have described genetic algorithm to forecast the long term quarterly sales of product in telecommunication technology sector. This has been used widely available economic indicators such as disposable personal income and new housing starts as independent variables. Authors have used individual chromosomes to indicate inclusion and dis-inclusion of specific economic variable as well as operational rules for combining the variables.

Lucasius, M. Blommers, L. Buydens, and G. It is a development of a genetic algorithm for determining the structure of a sample of DNA based on spectrometric data about the sample. Levertijd We doen er alles aan om dit artikel op tijd te bezorgen. Het is echter in een enkel geval mogelijk dat door omstandigheden de bezorging vertraagd is. Bezorgopties We bieden verschillende opties aan voor het bezorgen of ophalen van je bestelling.

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Welke opties voor jouw bestelling beschikbaar zijn, zie je bij het afronden van de bestelling. Schrijf een review. E-mail deze pagina. Auteur: Wayne A. Woodward Henry L. Co-auteur: Alan C. Samenvatting Virtually any random process developing chronologically can be viewed as a time series.


In economics closing prices of stocks, the cost of money, the jobless rate, and retail sales are just a few examples of many. Developed from course notes and extensively classroom-tested, Applied Time Series Analysis with R, Second Edition includes examples across a variety of fields, develops theory, and provides an R-based software package to aid in addressing time series problems in a broad spectrum of fields.

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The material is organized in an optimal format for graduate students in statistics as well as in the natural and social sciences to learn to use and understand the tools of applied time series analysis. Extensive help regarding the use of tswge functions is provided in appendices and on an associated website.

Time series models. Regression Models for Time Series Analysis. Regression models for time series analysis. Spectral Analysis and Time Series. Volume 1: Univariate Series. Time Series Models: 2nd Edition. Time series and dynamic models. Nonlinear time series models in empirical finance. Linear model theory.