This PhD thesis focuses on using time series models for counts in modelling and forecasting a special type of count series called intermittent series. An intermittent series is a series of non-negative integer values with some zero values. Such series occur in many areas including inventory control of spare parts. Various methods have been developed for intermittent demand forecasting with Croston’s method being the most widely used. Some studies focus on finding a model underlying Croston’s method. With none of these studies being successful in demonstrating an underlying model for which Croston’s method is optimal, the focus should now shift towards stationary models for intermittent demand forecasting. This thesis explores the application of a class of models for count data called the Integer Autoregressive Moving Average (INARMA) models. INARMA models have had applications in different areas such as medical science and economics, but this is the first attempt to use such a model-based method to forecast intermittent demand. In this PhD research, we first fill some gaps in the INARMA literature by finding the unconditional variance and the autocorrelation function of the general INARMA(p,q) model. The conditional expected value of the aggregated process over lead time is also obtained to be used as a lead time forecast. The accuracy of h-step-ahead and lead time INARMA forecasts are then compared to those obtained by benchmark methods of Croston, Syntetos-Boylan Approximation (SBA) and Shale-Boylan-Johnston (SBJ). The results of the simulation suggest that in the presence of a high autocorrelation in data, INARMA yields much more accurate one-step ahead forecasts than benchmark methods. The degree of improvement increases for longer data histories. It has been shown that instead of identification of the autoregressive and moving average order of the INARMA model, the most general model among the possible models can be used for forecasting. This is especially useful for short history and high autocorrelation in data. The findings of the thesis have been tested on two real data sets: (i) Royal Air Force (RAF) demand history of 16,000 SKUs and (ii) 3,000 series of intermittent demand from the automotive industry. The results show that for sparse data with long history, there is a substantial improvement in using INARMA over the benchmarks in terms of Mean Square Error (MSE) and Mean Absolute Scaled Error (MASE) for the one-step ahead forecasts. However, for series with short history the improvement is narrower. The improvement is greater for h-step ahead forecasts. The results also confirm the superiority of INARMA over the benchmark methods for lead time forecasts.

El presente trabajo de investigación tiene como propósito analizar una propuesta de indicadores macroeconómicos y financieros para un sistema de alerta temprana en la tasa de morosidad de las Cajas Municipales de Ahorro y Crédito del sistema financiero peruano, durante el periodo 2006-2017. El objetivo principal de este estudio es demostrar la influencia de las variables seleccionadas con respecto a la tasa de morosidad y determinar el efecto producido por cada una sobre la variable dependiente como un sistema de alerta o prevención. Las variables escogidas para el análisis son PBI sector comercio, tasa de desempleo, ratio de solvencia, ratio de liquidez, número de agencias, créditos directos y créditos directos por empleado. Para este caso, la información estadística se analizará a través del modelo econométrico vector autorregresivo (VAR) para determinar los efectos que presentan las variables sobre la tasa de morosidad y el modelo vector autorregresivo estructural (VARS) para analizarlo de forma estructural de largo plazo. Así mismo, se determina los efectos dinámicos de las variables macroeconómicas y financieras con respecto a la tasa de morosidad. Dentro de los resultados obtenidos tenemos que las variables macroeconómicas y financieras estudiadas sí influyen en la tasa de morosidad, lo cual corroboran nuestras hipótesis y funcionan como un sistema de alerta temprana para las Cajas Municipales. Con respecto al efecto de las variables, se observa que el efecto de cada una varía o se mantiene en la fase corta y en la fase permanente. / The purpose of this research is to analyze a proposal of macroeconomic and financial factors for an early warning system for the default rate of Municipal Savings and Credit of the Peruvian financial system, during the period 2006-2017. The objective of this study is to demonstrate the influence of selected variables on the default rate and also, as a complement, know the effect produced by each one as a prevention system. The variables chosen for the analysis are GDP trade sector, unemployment rate, solvency rate, liquidity, number of agencies, direct credits and direct credits per employee. For this, the statistical information will be analyzed through the autoregressive vector (VAR), an econometric model that determine the effects of the variables on the default rate and the structural autoregressive vector model (VARS) to analyze it in a long-term structural manner. Additionally, the dynamic effects of the macroeconomic and financial variables are determined in relation to the default rate. The results of this study are that macroeconomic and financial factors have an influence in the default rate, which are in order with our hypotheses and it works as an early warning for Municipal Savings. About the effect of each variable, there are cases that it changes or remains in the short term and long term. / Tesis

<p>For random waves the free surface elevation can be described by a number of individual wave parameters. The main objective of this work has been to study the statistical properties of individual parameters in successive waves; the wave crest height, the wave height and the wave period.</p><p>In severe sea states the wave crest heights exhibit a nonlinear behavior, which must be reflected in the models. An existing marginal distribution that uses second order Stokes-type nonlinearity is transformed to a two-dimensional distribution by use of the two–dimensional Rayleigh distribution. This model only includes sum frequency effects. A two-dimensional distribution is also established by transforming a second order model including both sum and different frequency effects. Both models are based on the narrow-band assumption, and the effect of finite water depth is included. A parametric wave crest height distribution proposed by Forristall (2000) has been extended to two dimensions by transformation of the two-dimensional Weibull distribution. </p><p>Two successive wave heights are modeled by a Gaussian copula, which is referred to as the Nataf model. Results with two initial distributions for the transformation are presented, the Næss (1985) model and a two-parameter Weibull distribution, where the latter is in best agreement with data. The results are compared with existing models. The Nataf model has also been used for modeling three successive wave heights. Results show that the Nataf transformation of three successive wave heights can be approximated by a first order autoregression model. This means that the distribution of the wave height given the previous wave height is independent of the wave heights prior to the previous wave height. The simulation of successive wave heights can be done directly without simulating the time series of the complete surface elevation. </p><p>Successive wave periods are modeled with the Nataf transformation by using a two-parameter Weibull distribution and a generalized Gamma distribution as the initial distribution, where the latter is in best agreement with data. Results for the marginal and two-dimensional distributions are compared with existing models. In practical applications, it is often of interest to consider successive wave periods with corresponding wave heights exceeding a certain threshold. Results show that the distribution for successive wave periods when the corresponding wave heights exceed the root-mean-square value of the wave heights can be approximated by a multivariate Gaussian distribution. When comparing the results with data, a long time series is needed in order to obtain enough data cases. Results for three successive wave periods are also presented. </p><p>The models are compared with field data from the Draupner field and the Japan Sea, and with laboratory data from experiments at HR Wallingford. In addition, data from numerical simulations based on second order wave theory, including both sum and frequency effects, are included.</p>

<p>A brain-computer interface, BCI, is a technical system that allows a person to control the external world without relying on muscle activity. This thesis presents an EEG based BCI designed for automatic classification of two dimensional hand movements. The long-term goal of the project is to build an intuitive communication system for operation by people with severe motor impairments. If successful, such system could for example be used by a paralyzed patient to control a word processor or a wheelchair.</p><p>The developed BCI was tested in an offine pilot study. In response to an external cue, a test subject moved a joystick in one of four directions. During the movement, EEG was recorded from seven electrodes mounted on the subject's scalp. An autoregressive model was fitted to the data, and the extracted coefficients were used as input features to a neural network based classifier. The classifier was trained to recognize the direction of the movements. During the first half of the experiment, real physical movements were performed. In the second half, subjects were instructed just to imagine the hand moving the joystick, but to avoid any muscle activity.</p><p>The results of the experiment indicate that the EEG signals do in fact contain extractable and classifiable information about the performed movements, during both physical and imagined movements.</p>

For random waves the free surface elevation can be described by a number of individual wave parameters. The main objective of this work has been to study the statistical properties of individual parameters in successive waves; the wave crest height, the wave height and the wave period. In severe sea states the wave crest heights exhibit a nonlinear behavior, which must be reflected in the models. An existing marginal distribution that uses second order Stokes-type nonlinearity is transformed to a two-dimensional distribution by use of the two–dimensional Rayleigh distribution. This model only includes sum frequency effects. A two-dimensional distribution is also established by transforming a second order model including both sum and different frequency effects. Both models are based on the narrow-band assumption, and the effect of finite water depth is included. A parametric wave crest height distribution proposed by Forristall (2000) has been extended to two dimensions by transformation of the two-dimensional Weibull distribution. Two successive wave heights are modeled by a Gaussian copula, which is referred to as the Nataf model. Results with two initial distributions for the transformation are presented, the Næss (1985) model and a two-parameter Weibull distribution, where the latter is in best agreement with data. The results are compared with existing models. The Nataf model has also been used for modeling three successive wave heights. Results show that the Nataf transformation of three successive wave heights can be approximated by a first order autoregression model. This means that the distribution of the wave height given the previous wave height is independent of the wave heights prior to the previous wave height. The simulation of successive wave heights can be done directly without simulating the time series of the complete surface elevation. Successive wave periods are modeled with the Nataf transformation by using a two-parameter Weibull distribution and a generalized Gamma distribution as the initial distribution, where the latter is in best agreement with data. Results for the marginal and two-dimensional distributions are compared with existing models. In practical applications, it is often of interest to consider successive wave periods with corresponding wave heights exceeding a certain threshold. Results show that the distribution for successive wave periods when the corresponding wave heights exceed the root-mean-square value of the wave heights can be approximated by a multivariate Gaussian distribution. When comparing the results with data, a long time series is needed in order to obtain enough data cases. Results for three successive wave periods are also presented. The models are compared with field data from the Draupner field and the Japan Sea, and with laboratory data from experiments at HR Wallingford. In addition, data from numerical simulations based on second order wave theory, including both sum and frequency effects, are included.

This paper examines the forecast accuracy of an unrestricted Vector Autoregressive (VAR) model for GDP, relative to a comparable Vector Error Correction (VEC) model that recognizes that the data is characterized by co-integration. In addition, an alternative forecast method, Intercept Correction (IC), is considered for further comparison. Recursive out-of-sample forecasts are generated for both models and forecast techniques. The generated forecasts for each model are objectively evaluated by a selection of evaluation measures and equal accuracy tests. The result shows that the VEC models consistently outperform the VAR models. Further, IC enhances the forecast accuracy when applied to the VEC model, while there is no such indication when applied to the VAR model. For certain forecast horizons there is a significant difference in forecast ability between the VEC IC model compared to the VAR model.

In applications, the true underlying model of an observed time series is typically unknown or has a complicated structure. A common approach is to approximate the true model by autoregressive (AR) equation whose orders are chosen by information criterions such as AIC, BIC and Parsen's CAT and whose parameters are estimated by the least square (LS), the Yule Walker (YW) or other methods. However, as sample size increases, it often implies that the model order has to be refined and the parameters need to be recalculated. In order to avoid such shortcomings, we propose the Regularized AR (RAR) approximation and illustrate its applications in frequency detection and long memory process forecasting. The idea of the RAR approximation is to utilize a “long" AR model whose order significantly exceeds the model order suggested by information criterions, and to estimate AR parameters by Regularized LS (RLS) method, which enables to estimate AR parameters with different level of accuracy and the number of estimated parameters can grow linearly with the sample size. Therefore, the repeated model selection and parameter estimation are avoided as the observed sample increases. We apply the RAR approach to estimate the unknown frequencies in periodic processes by approximating their generalized spectral densities, which significantly reduces the computational burden and improves accuracy of estimates. Our theoretical findings indicate that the RAR estimates of unknown frequency are strongly consistent and normally distributed. In practice, we may encounter spurious frequency estimates due to the high model order. Therefore, we further propose the robust trimming algorithm (RTA) of RAR frequency estimation. Our simulation studies indicate that the RTA can effectively eliminate the spurious roots and outliers, and therefore noticeably increase the accuracy. Another application we discuss in this thesis is modeling and forecasting of long memory processes using the RAR approximation. We demonstration that the RAR is useful in long-range prediction of general ARFIMA(p,d,q) processes with p > 1 and q > 1 via simulation studies.

A brain-computer interface, BCI, is a technical system that allows a person to control the external world without relying on muscle activity. This thesis presents an EEG based BCI designed for automatic classification of two dimensional hand movements. The long-term goal of the project is to build an intuitive communication system for operation by people with severe motor impairments. If successful, such system could for example be used by a paralyzed patient to control a word processor or a wheelchair. The developed BCI was tested in an offine pilot study. In response to an external cue, a test subject moved a joystick in one of four directions. During the movement, EEG was recorded from seven electrodes mounted on the subject's scalp. An autoregressive model was fitted to the data, and the extracted coefficients were used as input features to a neural network based classifier. The classifier was trained to recognize the direction of the movements. During the first half of the experiment, real physical movements were performed. In the second half, subjects were instructed just to imagine the hand moving the joystick, but to avoid any muscle activity. The results of the experiment indicate that the EEG signals do in fact contain extractable and classifiable information about the performed movements, during both physical and imagined movements.

This paper analyzes empirically the effect of crude oil price change on the economic growth of Indian-Subcontinent (India, Pakistan and Bangladesh). We use a multivariate Vector Autoregressive analysis followed by Wald Granger causality test and Impulse Response Function (IRF). Wald Granger causality test results show that only India’s economic growth is significantly affected when crude oil price decreases. Impact of crude oil price increase is insignificantly negative for all three countries during first year. In second year, impact is negative but smaller than first year for India, negative but larger for Bangladesh and positive for Pakistan.

In applications, the true underlying model of an observed time series is typically unknown or has a complicated structure. A common approach is to approximate the true model by autoregressive (AR) equation whose orders are chosen by information criterions such as AIC, BIC and Parsen's CAT and whose parameters are estimated by the least square (LS), the Yule Walker (YW) or other methods. However, as sample size increases, it often implies that the model order has to be refined and the parameters need to be recalculated. In order to avoid such shortcomings, we propose the Regularized AR (RAR) approximation and illustrate its applications in frequency detection and long memory process forecasting. The idea of the RAR approximation is to utilize a “long" AR model whose order significantly exceeds the model order suggested by information criterions, and to estimate AR parameters by Regularized LS (RLS) method, which enables to estimate AR parameters with different level of accuracy and the number of estimated parameters can grow linearly with the sample size. Therefore, the repeated model selection and parameter estimation are avoided as the observed sample increases. We apply the RAR approach to estimate the unknown frequencies in periodic processes by approximating their generalized spectral densities, which significantly reduces the computational burden and improves accuracy of estimates. Our theoretical findings indicate that the RAR estimates of unknown frequency are strongly consistent and normally distributed. In practice, we may encounter spurious frequency estimates due to the high model order. Therefore, we further propose the robust trimming algorithm (RTA) of RAR frequency estimation. Our simulation studies indicate that the RTA can effectively eliminate the spurious roots and outliers, and therefore noticeably increase the accuracy. Another application we discuss in this thesis is modeling and forecasting of long memory processes using the RAR approximation. We demonstration that the RAR is useful in long-range prediction of general ARFIMA(p,d,q) processes with p > 1 and q > 1 via simulation studies.