Article

# Time Series Analysis with R

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## Abstract

A brief overview of the R statistical computing and programming environment is given that explains why many time series researchers in both applied and the-oretical research may find R useful. The core features of R for basic time series analysis are outlined. Some intermediate level and advanced topics in time series analysis that are supported in R are discussed such as including state-space mod-els, structural change, generalized linear models, threshold models, neural nets, co-integration, GARCH, wavelets, and stochastic differential equations. Numer-ous examples of beautiful graphs constructed using R for time series are shown. R code for reproducing all the graphs and tables is given on my homepage.

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... Its forecasting superiority is subsequently assessed through formal SPA testing. Further details on implementing traditional statistical methods in the R environment are provided next, while more information can be found in [54,55]. ...
... Here, as in [65], STS models are automatically implemented in R by maximum likelihood through the function "StructTS" in the "stats" package. Further information on the automatically estimation and forecasting with STS models in R can be retrieved from [55]. ...
Article
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The European Union (EU) has positioned itself as a frontrunner in the worldwide battle against climate change and has set increasingly ambitious pollution mitigation targets for its members. The burden is heavier for the more vulnerable economies in Central and Eastern Europe (CEE), who must juggle meeting strict greenhouse gas emission (GHG) reduction goals, significant fossil-fuel reliance, and pressure to respond to current pandemic concerns that require an increasing share of limited public resources, while facing severe repercussions for non-compliance. Thus, the main goals of this research are: (i) to generate reliable aggregate GHG projections for CEE countries; (ii) to assess whether these economies are on track to meet their binding pollution reduction targets; (iii) to pin-point countries where more in-depth analysis using spatial inventories of GHGs at a finer resolution is further needed to uncover specific areas that should be targeted by additional measures; and (iv) to perform geo-spatial analysis for the most at-risk country, Poland. Seven statistical and machine-learning models are fitted through automated forecasting algorithms to predict the aggregate GHGs in nine CEE countries for the 2019–2050 horizon. Estimations show that CEE countries (except Romania and Bulgaria) will not meet the set pollution reduction targets for 2030 and will unanimously miss the 2050 carbon neutrality target without resorting to carbon credits or offsets. Austria and Slovenia are the least likely to meet the 2030 emissions reduction targets, whereas Poland (in absolute terms) and Slovenia (in relative terms) are the farthest from meeting the EU’s 2050 net-zero policy targets. The findings thus stress the need for additional measures that go beyond the status quo, particularly in Poland, Austria, and Slovenia. Geospatial analysis for Poland uncovers that Krakow is the city where pollution is the most concentrated with several air pollutants surpassing EU standards. Short-term projections of PM2.5 levels indicate that the air quality in Krakow will remain below EU and WHO standards, highlighting the urgency of policy interventions. Further geospatial data analysis can provide valuable insights into other geo-locations that require the most additional efforts, thereby, assisting in the achievement of EU climate goals with targeted measures and minimum socio-economic costs. The study concludes that statistical and geo-spatial data, and consequently research based on these data, complement and enhance each other. An integrated framework would consequently support sustainable development through bettering policy and decision-making processes.
... If the data are just nonlinear, they only consist of nonlinear structures; then, q can be 0 since the Box-Jenkins method is a linear model that cannot simulate nonlinear interaction. Suboptimal methods may be used in a hybrid model, but suboptimality does not change the functional characteristics of the hybrid approach [17,[46][47][48]. The interpretation of time series requires quantification of the vector dynamic response with time shifts. ...
Article
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Design: At the heart of time series forecasting, if nonlinear and nonstationary data are analyzed using traditional time series, the results will be biased. At the same time, if just using machine learning without any consideration given to input from traditional time series, not much information can be obtained from the results because the machine learning model is a black box. Purpose: In order to better study time series forecasting, we extend the combination of traditional time series and machine learning and propose a hybrid cascade neural network considering a metaheuristic optimization genetic algorithm in space–time forecasting. Finding: To further show the utility of the cascade neural network genetic algorithm, we use various scenarios for training and testing while also extending simulations by considering the activation functions SoftMax, radbas, logsig, and tribas on space–time forecasting of pollution data. During the simulation, we perform numerical metric evaluations using the root-mean-square error (RMSE), mean absolute error (MAE), and symmetric mean absolute percentage error (sMAPE) to demonstrate that our models provide high accuracy and speed up time-lapse computing.
... Infine la misurazione dello stato di salute dei pazienti al controllo dopo tre mesi ha evidenziato un notevole incremento sia del punteggio PCS (che misura la limitazione fisica, la disabilità, il benessere generale e la percezione del proprio stato di salute) e sia del punteggio MCS (che misura l'attitudine psicologica del paziente, la limitazione nelle attività sociali e personali). I valori di PCS tuttavia rimanevano inferiori al riferimento normativo per fascia di età riportati da Gandek et al [19] (49.7±7.9 vs 44.05 media presente studio), mentre erano più alti rispetto ai valori riportati da Cole et al [16] a 1 anno (media 40) in uno studio specifico sull'outcome dopo ricostruzione artroscopica della cuffia dei rotatori. I valori di MCS si sono avvicinati invece maggiormente al valore di riferimento normativo (47.5±10.3 ...
Article
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Introduzione. In Italia la ricerca delle professioni sanitarie è poco sviluppata e vi è una carenza di conoscenza della metodologia per condurla. In alcuni ospedali sedi del presente studio è stato costituito un Centro di Ricerca per supportare e formare le professioni sanitarie alla conduzione di ricerche cliniche. Lo studio vuole valutare se la sua costituzione ha portato ad un aumento della produzione scientifica in termini di protocolli approvati e articoli pubblicati, oltre a misurare il livello di conoscenze, attitudini e abilità di ricerca degli infermieri. Disegno dello studio. Multiple Interrupted Time Series e studio trasversale. Metodi: Sono stati raccolti i dati dal 2002 al 2012 in 7 ospedali, 4 in cui è stato costituito il Centro Ricerca delle professioni sanitarie e 3 no. Inoltre si è effettuata una indagine con il Nursing Research Questionnaire modificato (NRQ-IT). Risultati. Per due ospedali con il centro di ricerca si conferma un incremento statisticamente significativo dell’outcome primario (numero di protocolli approvati dal Comitato Etico, aventi come ricercatore responsabile un infermiere) a circa 2 anni dall’implementazione dell’intervento. Per gli altri due ospedali sperimentali non è possibile raggiungere conclusioni definitive per i pochi dati disponibili (post intervento). Negli ospedali controllo le osservazioni rimangono stazionarie senza alcuna produzione scientifica. Per il questionario le differenze risultano staticamente significative per “Abilità di ricerca”, “Partecipazione in attività di ricerca” e “Uso della ricerca nella pratica”. Conclusioni. Lo studio sostiene come la costituzione di una unità di supporto alla ricerca delle professioni assistenziali all’interno degli ospedali faciliti la produzione di ricerche assistenziale ed aumenti la cultura della ricerca.
... Time series forecasting(TSF) is the use of a model to predict future values based on previously observed values. This modeling approach is used primarily when little knowledge is available on the underlying data generating process or when there is no adequate informative model that relates the prediction variable to other explanatory variables [3,4]. ...
Article
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Air quality index (AQI) is a number used by government agencies to communicate to the public how polluted the air currently. It is based on several factors like SO2, NO2, O3, RSPM/PM10, and PM2.5. Several methods were developed in the past by various researchers/environmental agencies for the determination of AQI. Still, there is no universally accepted method that exists, which is appropriate for all situations. We have developed a prediction model that is confined to standard classification or regression models. These prediction models have ignored the co-relation between sub-models in different time slots. The paper focusses on a refined model for inferring air pollutants based on historical and current meteorological datasets. Also, the model is designed to forecast AQI for the coming months, quarters or years where the emphasis is on how to improve its accuracy and performance. The algorithms are used on Air Pollution Geocodes Dataset (2016-2018), and results calculated for 196 cities of India on various classifiers. Accuracy of 94%-96% achieved from Linear Robust Regression, which increases to 97.92% after application of KNN and 97.91% after SVM and 97.47 after 5th epoch of ANN. Decision Tree Classifier has given the best accuracy of 99.7%, which increases by 0.02% on the application of the Random Forest Classifier. Forecasting achieved by Moving Average Smoothing using R-ARIMA, which offers daily values for the coming 45 days or monthly data of AQI for the next year.
... Time series forecasting(TSF) is the use of a model to predict future values based on previously observed values. This modeling approach is used primarily when little knowledge is available on the underlying data generating process or when there is no adequate informative model that relates the prediction variable to other explanatory variables [3,4]. ...
Conference Paper
Full-text available
Air quality index (AQI) is a number used by government agencies to communicate to the public how polluted the air currently. It is based on several factors like SO2, NO2, O3, RSPM/PM10, and PM2.5. Several methods were developed in the past by various researchers/environmental agencies for the determination of AQI. Still, there is no universally accepted method that exists, which is appropriate for all situations. We have developed a prediction model that is confined to standard classification or regression models. These prediction models have ignored the co-relation between sub-models in different time slots. The paper focusses on a refined model for inferring air pollutants based on historical and current meteorological datasets. Also, the model is designed to forecast AQI for the coming months, quarters or years where the emphasis is on how to improve its accuracy and performance. The algorithms are used on Air Pollution Geocodes Dataset (2016-2018), and results calculated for 196 cities of India on various classifiers. Accuracy of 94%-96% achieved from Linear Robust Regression, which increases to 97.92% after application of KNN and 97.91% after SVM and 97.47 after 5th epoch of ANN. Decision Tree Classifier has given the best accuracy of 99.7%, which increases by 0.02% on the application of the Random Forest Classifier.
... @BULLET European call option price is assumed to be a stochastic process with stationary and independent increments and the risk -free interest rate is constant in accordance with stated in (Gerber and Landry, 1997) @BULLET According to Mcleod et al. (2012) many researchers use R language to perform statistical calculations. Then the simulation program of European call option on an incomplete market will be created using the R language assistance to perform calculations @BULLET This study compares the results of the calculation of European call option with a linear approximation, shifted Gamma Process and shifted Inverse Gaussian Process with Black-Scholes model, which is more often used, to see that the calculation of the linear approximation is almost close to the Black- Scholes when circumstances are made to resembles the Black-Scholes model @BULLET This study also compares the results of calculations with the original data of option prices in the market. ...
Article
Option is derivative instrument that have investment benefit and provide return for the writer and the holder. Option price determination is affected by risk factor. However in Black-Scholes model option price is determined without arbitrage risk affection so it is impossible to take return. In this study, option price formula is constructed to be more represent the condition of financial market using incomplete market concept where financial asset, that is traded, is affected by arbitrage risk so it is possible for market participants to take return. European call option is defined by Esscher Transform method and option price formula is determined by changing its form to linear approximation. The result from this study is option price formula with linear approximation has some privileges. That is easy to be applied in computation process, more representatives in getting risk indication in the financial market and can predict option price more accurately. Linear approximation formula is applied in the program that can be used by option writer or holder and is equipped with export data feature that can be possible for further research development.
... The application of Neural Network in time series prediction models [18] is expected to provide more accurate and robust results against data fluctuations [19]. One of the flexibility, of the Neural Network model as a nonparametric model is that there is no need to test model assumptions [20], so the main thing to consider is the formation of a model to get the smallest possible error [21]. ...
Article
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Air pollution is the entry or inclusion of living things, energy substances, and other components into the air. Moreover, Air pollution is the presence of one or several contaminants in the outside atmospheric air such as dust, foam, gas, fog, smoke or steam in large quantities with various properties and time intervals of the contaminants in the air resulting in disturbances to the lives of humans, plants or animals. One of the parameters measured in determining air quality is PM2.5. However, PM2.5 has a higher probability of being able to enter the lower respiratory tract because small particle diameters can potentially pass through the lower respiratory tract. In this paper, we will get two different insight. First, the probability of status change using Markov chain and second, forecasting by using VAR-NN-PSO(Vector Autoregressive, Neural Network, Particle Swarm optimization). More details we classify by three classifications no risk (1-30), medium risk (30-48), and moderate (>49) in Pingtung and Chaozhou start from January 2014 to May 2019. This data is starting from January 2014 to May 2019 so that it can be modeled with the Markov chain. At the same time, we perform Hybrid VAR-NN-PSO to forecast PM2.5 in Pingtung and Chaozhou. In this optimization, the search for solutions is carried out by a population consisting of several particles. Based on the results of the discussion, opportunities for the transition from monthly status change are obtained continuous stochastic time with a stationary probability distribution. Regarding the VAR-NN-PSO, we obtained the mean absolute percentage error (MAPE) 3.57% for PM2.5 data in Pingtung and 4.87% for PM2.5 data in Chaozhou, respectively. This model can be predicted to forecasting 180 days ahead. The population in PSO has generated randomly with the smallest value and the largest value the accuracy.
... Our R package, (McLeod et al., 2016a), for ARTFIMA, ARFIMA and ARIMA model fitting, forecasting and simulation is freely available. R, also freely available, provides many stateof-the-art and advanced functions for time series analysis ( McLeod et al., 2012), as well it provides an advanced quantitative programming environment for data science. The most important R functions in our package, artfima, are described in Table 1. ...
Article
Estimation and diagnostic checking with the tempered ARFIMA (ARTFIMA) model is discussed. The ARTFIMA model replaces the fractional difference term with a tempered fractional difference that depends on a parameter λ. When λ = 0 the model reduces to the usual ARFIMA model. This model was derived from a continuous-time model developed to describe geophysical turbulence. More generally, the ARTFIMA provides a model that includes the ARMA as well as ARFIMA. Basic properties are discussed including exact maximum likelihood estimation (MLE) and Whittle MLE and their associated asymptotic distributions. Unlike the ARMA and ARFIMA cases, it is shown that the Whittle estimator is not always first order efficient, and this finding is confirmed by a simulation experiment. The distribution of the residual autocorrelations is derived and its application to portmanteau diagnostic check discussed. An R software package, artfima, available on CRAN, implements model fitting for the ARTFIMA family of models including the ARIMA/ARFIMA special cases. It is demonstrated, with examples, that the ARTFIMA family of models may provide a more parsimonious or sparse model and applications to forecasting, simulation and spectral analysis are discussed .
... We model the data trend with an ARIMA process. The Hurst exponents and fBm models are estimated with a R-package [26][27][28]. ...
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Scrub typhus, an infectious disease caused by a bacterium transmitted by “chigger” mites, constitutes a public health problem in Thailand. Predicting epidemic peaks would allow implementing preventive measures locally. This study analyses the predictability of the time series of incidence of scrub typhus aggregated at the provincial level. After stationarizing the time series, the evaluation of the Hurst exponents indicates the provinces where the epidemiological dynamics present a long memory and are predictable. The predictive performances of ARIMA (autoregressive integrated moving average model), ARFIMA (autoregressive fractionally integrated moving average) and fractional Brownian motion models are evaluated. The results constitute the reference level for the predictability of the incidence data of this zoonosis.
... Regression models in which a time-lagged dependent variable is used as an additional predictor variable are often referred to as dynamic linear regression models-also known as autoregressive (AR) models. AR models are commonly used for the analysis and forecasting of time series data in economics (McLeod et al., 2012) and hydrology and climate (Anderson, 2011). The lagged dependent variable introduces a temporal component into the model, so that the EVI at a given time step is also a function of the EVI of the previous time step in the time series as: y t = ϕy (t−1) + βX t + ε t , t = 1, 2, 3, . . . ...
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Floodplain wetlands are valuable ecosystems for maintaining biodiversity, but are vulnerable to hydrological modification and climatic extremes. The floodplain wetlands in the middle Yangtze region are biodiversity hotspots, particularly important for wintering migratory waterbirds. In recent years, extremely low winter water level events frequently occurred in the middle Yangtze River. The hydrological droughts greatly impacted the development and distribution of the wet meadows, one of the most important ecological components in the floodplains, which is vital for the survival of many migratory waterbirds wintering in the Yangtze region. To effectively manage the wet meadows, it is critical to pinpoint the drivers for their deterioration. In this study, we assessed the effects of hydrological connectivity on the ecological stability of wet meadow in Poyang Lake for the period of 2000 to 2016. We used the time series of MODIS EVI (Enhanced Vegetation Index) as a proxy for productivity to infer the ecological stability of wet meadows in terms of resistance and resilience. Our results showed that (1) the wet meadows developed in freely connected lakes had significantly higher resilience; (2) wet meadows colonizing controlled lakes had higher resistance to water level anomalies; (3) there was no difference in the resistance to rainfall anomaly between the two types of lakes; (4) the wet meadow in freely connected lakes might approach a tipping point and a regime shift might be imminent. Our findings suggest that adaptive management at regional- (i.e., operation of Three Gorges Dam) and site-scale (e.g., regulating sand mining) are needed to safeguard the long-term ecological stability of the system, which in term has strong implications for local, regional and global biodiversity conservation.
Chapter
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Graphics is an important component of data analysis workflows, especially in interactive systems such as R. This chapter gives an overview of R's static graphics facilities. In addition to commonly used functions, we describe the underlying plotting model and how it can be exploited to customize default output. We also give a brief overview of the relatively recent Grid graphics, and the lattice and ggplot2 packages which use it to implement general purpose high-level systems.
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It is shown that the limiting distribution of the augmented Dickey-Fuller (ADF) test under the null hypothesis of a unit root is valid under a very general set of assumptions that goes far beyond the linear AR(∞) process assumption typically imposed. In essence, all that is required is that the error process driving the random walk possesses a continuous spectral density that is strictly positive. Furthermore, under the same weak assumptions, the limiting distribution of the ADF test is derived under the alternative of stationarity, and a theoretical explanation is given for the well-known empirical fact that the test's power is a decreasing function of the chosen autoregressive order p. The intuitive reason for the reduced power of the ADF test is that, as p tends to infinity, the p regressors become asymptotically collinear.
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The most general form of a nonlinear strictly stationary process is that referred to as a Volterra expansion; this is to a linear process what a polynomial is to a linear function. Because of this similarity, an analogue of Tukey's one degree of freedom for nonadditivity test is constructed as a test for linearity versus a second-order Volterra expansion.
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The increasing popularity of R is leading to an increase in its use in undergraduate courses at universities (R Development Core Team 2008). One of the strengths of R is the flexible graphics provided in its base package. However, students often run up against its limitations, or they find the amount of effort to create an interesting plot may be excessive. The grid package (Murrell 2005) has a wealth of graphical tools which are more accessible to such R users than many people may realize. The purpose of this paper is to highlight the main features of this package and to provide some examples to illustrate how students can have fun with this different form of plotting and to see that it can be used directly in the visualization of data.
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Statistical Methods for Long Term Memory Processes covers the diverse statistical methods and applications for data with long-range dependence. Presenting material that previously appeared only in journals, the author provides a concise and effective overview of probabilistic foundations, statistical methods, and applications. The material emphasizes basic principles and practical applications and provides an integrated perspective of both theory and practice. This book explores data sets from a wide range of disciplines, such as hydrology, climatology, telecommunications engineering, and high-precision physical measurement. The data sets are conveniently compiled in the index, and this allows readers to view statistical approaches in a practical context. Statistical Methods for Long Term Memory Processes also supplies S-PLUS programs for the major methods discussed. This feature allows the practitioner to apply long memory processes in daily data analysis. For newcomers to the area, the first three chapters provide the basic knowledge necessary for understanding the remainder of the material. To promote selective reading, the author presents the chapters independently. Combining essential methodologies with real-life applications, this outstanding volume is and indispensable reference for statisticians and scientists who analyze data with long-range dependence.
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Book
Book
Reveals How HMMs Can Be Used as General-Purpose Time Series Models Implements all methods in RHidden Markov Models for Time Series: An Introduction Using R applies hidden Markov models (HMMs) to a wide range of time series types, from continuous-valued, circular, and multivariate series to binary data, bounded and unbounded counts, and categorical observations. It also discusses how to employ the freely available computing environment R to carry out computations for parameter estimation, model selection and checking, decoding, and forecasting. Illustrates the methodology in actionAfter presenting the simple Poisson HMM, the book covers estimation, forecasting, decoding, prediction, model selection, and Bayesian inference. Through examples and applications, the authors describe how to extend and generalize the basic model so it can be applied in a rich variety of situations. They also provide R code for some of the examples, enabling the use of the codes in similar applications. Effectively interpret data using HMMs This book illustrates the wonderful flexibility of HMMs as general-purpose models for time series data. It provides a broad understanding of the models and their uses.
Book
The first edition of this book has established itself as one of the leading references on generalized additive models (GAMs), and the only book on the topic to be introductory in nature with a wealth of practical examples and software implementation. It is self-contained, providing the necessary background in linear models, linear mixed models, and generalized linear models (GLMs), before presenting a balanced treatment of the theory and applications of GAMs and related models. The author bases his approach on a framework of penalized regression splines, and while firmly focused on the practical aspects of GAMs, discussions include fairly full explanations of the theory underlying the methods. Use of R software helps explain the theory and illustrates the practical application of the methodology. Each chapter contains an extensive set of exercises, with solutions in an appendix or in the book’s R data package gamair, to enable use as a course text or for self-study.
Chapter
Once we have identified any trend and seasonal effects, we can deseasonalise the time series and remove the trend. If we use the additive decomposition method of §1.5, we first calculate the seasonally adjusted time series and then remove the trend by subtraction. This leaves the random component, but the random component is not necessarily well modelled by independent random variables. In many cases, consecutive variables will be correlated. If we identify such correlations, we can improve our forecasts, quite dramatically if the correlations are high. We also need to estimate correlations if we are to generate realistic time series for simulations. The correlation structure of a time series model is defined by the correlation function, and we estimate this from the observed time series.
Book
Thanks to its data handling and modeling capabilities and its flexibility, R is becoming the most widely used software in bioinformatics. R Programming for Bioinformatics builds the programming skills needed to use R for solving bioinformatics and computational biology problems. Drawing on the author's experiences as an R expert, the book begins with coverage on the general properties of the R language, several unique programming aspects of R, and object-oriented programming in R. It presents methods for data input and output as well as database interactions. The author also examines different facets of string handling and manipulations, discusses the interfacing of R with other languages, and describes how to write software packages. He concludes with a discussion on the debugging and profiling of R code.
Book
This is the first book on applied econometrics using the R system for statistical computing and graphics. It presents hands-on examples for a wide range of econometric models, from classical linear regression models for cross-section, time series or panel data and the common non-linear models of microeconometrics such as logit, probit and tobit models, to recent semiparametric extensions. In addition, it provides a chapter on programming, including simulations, optimization, and an introduction to R tools enabling reproducible econometric research. An R package accompanying this book, AER, is available from the Comprehensive R Archive Network (CRAN). It contains some 100 data sets taken from a wide variety of sources, the full source code for all examples used in the text plus further worked examples, e.g., from popular textbooks. The data sets are suitable for illustrating, among other things, the fitting of wage equations, growth regressions, hedonic regressions, dynamic regressions and time series models as well as models of labor force participation or the demand for health care. The goal of this book is to provide a guide to R for users with a background in economics or the social sciences. Readers are assumed to have a background in basic statistics and econometrics at the undergraduate level. A large number of examples should make the book of interest to graduate students, researchers and practitioners alike.
Article
Time series econometrics is used for predicting future developments of variabls of interest such as economic growth, stock market volatility or interest rates. A model has to be constructed, accordingly, to describe the data generation process and to estimate its parameters. Modern tools to accomplish these tasks are provided in this volume, which also demonstrates by example how the tools can be applied. © Cambridge University Press 2004 and Cambridge University Press, 2009.
Article
1. Introduction to wavelets 2. Review of Fourier theory and filters 3. Orthonormal transforms of time series 4. The discrete wavelet transform 5. The maximal overlap discrete wavelet transform 6. The discrete wavelet packet transform 7. Random variables and stochastic processes 8. The wavelet variance 9. Analysis and synthesis of long memory processes 10. Wavelet-based signal estimation 11. Wavelet analysis of finite energy signals Appendix. Answers to embedded exercises References Author index Subject index.
Book
The analysis of integrated and co-integrated time series can be considered as the main methodology employed in applied econometrics. This book not only introduces the reader to this topic but enables him to conduct the various unit root tests and co-integration methods on his own by utilizing the free statistical programming environment R. The book encompasses seasonal unit roots, fractional integration, coping with structural breaks, and multivariate time series models. The book is enriched by numerous programming examples to artificial and real data so that it is ideally suited as an accompanying text book to computer lab classes. The second edition adds a discussion of vector auto-regressive, structural vector auto-regressive, and structural vector error-correction models. To analyze the interactions between the investigated variables, further impulse response function and forecast error variance decompositions are introduced as well as forecasting. The author explains how these model types relate to each other.
Article
Wavelet methods have recently undergone a rapid period of development with important implications for a number of disciplines including statistics. This book has three main objectives: (i) providing an introduction to wavelets and their uses in statistics; (ii) acting as a quick and broad reference to many developments in the area; (iii) interspersing R code that enables the reader to learn the methods, to carry out their own analyses, and further develop their own ideas. The book code is designed to work with the freeware R package WaveThresh4, but the book can be read independently of R. The book introduces the wavelet transform by starting with the simple Haar wavelet transform, and then builds to consider more general wavelets, complex-valued wavelets, non-decimated transforms, multidimensional wavelets, multiple wavelets, wavelet packets, boundary handling, and initialization. Later chapters consider a variety of wavelet-based nonparametric regression methods for different noise models and designs including density estimation, hazard rate estimation, and inverse problems; the use of wavelets for stationary and non-stationary time series analysis; and how wavelets might be used for variance estimation and intensity estimation for non-Gaussian sequences. The book is aimed both at Masters/Ph.D. students in a numerate discipline (such as statistics, mathematics, economics, engineering, computer science, and physics) and postdoctoral researchers/users interested in statistical wavelet methods.
Article
The most general form of a nonlinear strictly stationary process is that referred to as a Volterra expansion; this is to a linear process what a polynomial is to a linear function. Because of this similarity, an analogue of Tukey's one degree of freedom for non-additivity test is constructed as a test for linearity versus a second-order Volterra expansion.
Article
With time series data, there is often the issue of finding accurate approximations for the variance of such quantities as the sample autocovariance function or spectral estimate. Smith and Field (J. Time. Ser. Anal 14: 381–395, 1993) proposed a variance estimate motivated by resampling in the frequency domain. In this paper we present some results on the cumulants of this and other frequency domain estimates obtained via symbolic computation. The statistics of interest are linear combinations of products of discrete Fourier transforms. We describe an operator which calculates the joint cumulants of such statistics, and use the operator to deepen our understanding of the behaviour of the resampling based variance estimate. The operator acts as a filter for a general purpose operator described in Andrews and Stafford (J.R. Statist. Soc. B55, 613–627).
Conference Paper
Suppose that a forecasting model is available for the process Xt but that interest centres on the instantaneous transformation Yt = T(Xt). On the assumption that Xt is Gaussian and stationary, or can be reduced to stationarity by differencing, this paper examines the autocovariance structure of and methods for forecasting the transformed series. The development employs the Hermite polynomial expansion, thus allowing results to be derived for a very general class of instantaneous transformations.
Book
Ripley brings together two crucial ideas in pattern recognition: statistical methods and machine learning via neural networks. He brings unifying principles to the fore, and reviews the state of the subject. Ripley also includes many examples to illustrate real problems in pattern recognition and how to overcome them.
Article
The shape parameter of a two-variable graph is the ratio of the horizontal and vertical distances spanned by the data. For at least 70 years this parameter has received much attention in writings on data display, because it is a critical factor on two-variable graphs that show how one variable depends on the other. But despite the attention, there has been little systematic study. In this article the shape parameter and its effect on the visual decoding of slope information are studied through historical, empirical, theoretical, and experimental investigations. These investigations lead to a method for choosing the shape that maximizes the accuracy of slope judgments.
Article
New fractal parameters, the dimension of minimum covers and the related index of fractality has been introduced. The limiting value of dimension coincides with the usual fractal dimension D. Numerical calculations carried out for stock price series have shown that the application of minimal covers leads to rapid convergence to a power-law asymptotic behavior of the function with respect to δ. This makes it possible to treat the index as a local characteristic and to introduce the function which is an indicator of local stability of the time series, the greater m, the more stable the series. It has been shown, using a very rich empirical data array, that the index of fractality, in essence, defines a natural way of integrating over all possible price trajectories (starting from the shortest). It turns out that trajectories corresponding to random walk have the greatest weight.
Article
Acknowledgments I would like to thank Pierre Duguay, Stephen Poloz, and David Delchamps for helpful comments. ISSN 1192-5434 ISBN 0-662-20494-8 Printed in Canada on recycled paper iii Contents