abstract: Threshold regression is used to model regime switching dynamics where the effects of the explanatory variables in predicting the response variable depend on whether a certain threshold has been crossed. When regime-switching dynamics are present, new estimation problems arise related to estimating the value of the threshold. Conventional methods utilize an iterative search procedure, seeking to minimize the sum of squares criterion. However, when unnecessary variables are included in the model or certain variables drop out of the model depending on the regime, this method may have high variability. This paper proposes Lasso-type methods as an alternative to ordinary least squares. By incorporating an L_{1} penalty term, Lasso methods perform variable selection, thus potentially reducing some of the variance in estimating the threshold parameter. This paper discusses the results of a study in which two different underlying model structures were simulated. The first is a regression model with correlated predictors, whereas the second is a self-exciting threshold autoregressive model. Finally the proposed Lasso-type methods are compared to conventional methods in an application to urban traffic data. / Dissertation/Thesis / Masters Thesis Industrial Engineering 2015

Esta tesis se centra en el estudio de la serie temporal de volatilidades asociada a la rentabilidad de las acciones a partir de un modelo no lineal, el modelo SETAR "Self-Exciting Threshold AutoRegressive model". El modelo SETAR, a pesar de presentar buenas propiedades y resultados plausibles, ha sido poco utilizado debido a que la implementación de los procesos de identificación y estimación no es sencilla y tampoco está completa, lo que lleva a un proceso de modelización poco ágil. Por este motivo uno de los principales objetivos de la investigación es mejorar la automatización de estos procesos obteniendo e implementando un esquema algorítmico que permita estimar los órdenes de los procesos autoregresivos que componen el modelo, a la vez que determine para cada uno de los procesos autoregresivos cuales son los retardos significativos. El algoritmo propuesto, a diferencia del de Thanoon (1990), debe permitir trabajar con modelos de más de dos regímenes y no presentar limitaciones sobre el número de variables regresoras en cada proceso autoregresivo.En esta tesis se propone una nueva metodología que hemos denominado MIEC "Metodología para la Identificación y Estimación de Coeficientes" basada en un proceso algorítmico que permite la selección de los regresores de forma automática, así como la estimación del orden de los procesos autoregresivos. El diseño de nuestro algoritmo surge del análisis de las características de los algoritmos involucrados en las metodologías propuestas por Tong, Tsay y Thanoon para la identificación y estimación de modelos SETAR. El estudio de las propiedades de algunos criterios de información (AIC, BIC, AICc) permite demostrar que dichos criterios alcanzan el valor mínimo en modelos cuyos regresores tienen retardos consecutivos, esta propiedad es generalizable a todos los modelos SETAR. En nuestra metodología MIEC, el nuevo algoritmo se integrará con el test de linealidad TAR-F de Tsay y, si consideramos modelos SETAR con dos regímenes, con un proceso algorítmico que estima de forma automática el valor umbral.La metodología propuesta en la tesis se ha aplicado al estudio de la volatilidad asociada a la rentabilidad del IBEX-35 en el período 1990-2000. Como la volatilidad no es directamente observable y en el campo financiero no tiene una medida única, es necesario definir el concepto de volatilidad en nuestro marco de estudio y obtener en este contexto un estimador de la volatilidad. En la tesis hemos elegido como estimador de la volatilidad mensual la desviación absoluta respecto a la media del exceso de rentabilidad. Una vez obtenida la serie de volatilidades {wt}, se analizan sus características: la no estacionariedad de la serie se elimina a partir de una transformación conocida como "tasa de variación natural" yt = ln (wt) que permite interpretar yt como una medida del cambio relativo entre un período y el anterior Las características de la serie {yt} justifican la elección de un modelo SETAR y, en consecuencia, aplicamos la metodología MIEC para identificar y estimar los parámetros que caracterizan el modelo. El resultado es un SETAR (2; 2,8) con el que se explica el comportamiento histórico de la serie, y también permite realizar acertadas predicciones sobre los cambios de tendencia de la volatilidad. / This thesis is focused on the study of the volatility of the IBEX-35 returns with a non-linear model the self-exciting threshold autoregressive SETAR models; and on the improvement of the identification process.The SETAR model has certain features, that cannot be captured by a linear time series models, nevertheless this model has not been widely used in applications because the implementation of the estimation and identification process is complex, incomplete and hard. The main goal of this research is to improve the algorithm for the estimation of orders of autoregressive process and for the selecttion of significant lags.We propose, in this thesis, a new metodology - MIEC "Identification and Estimation of Coeficients Methodology"- based on an algorithmic process for the automatic selection of the regressors, and the estimation of autoregressive process orders. The analysis of Tong's methodology, Tsay's algorithm and Thanoon's algorithm has helped us to design our proposal. We have proved that the AIC (Akaike's Information Criteria), the BIC (Bayesian Information Criteria) and the AICc (Corrected Akaike's Information Criteria) are minimun if the model has regressors with consecutive lags; this feature is true in SETAR models. MIEC methodology builds an algorithm which incorporates a linearity test, the TAR-F test of Tsay, and to permits the automatic estimation of threshold in SETAR models with two regimes.We have applied our methodology to the study of the volatility of IBEX 35 returns from 1990 to 2000. As volatility is not observable, we need to construct a volatility measure, but first, it is necessary to clarify the concept of volatility, because this term is used in practice in different ways. In this thesis, we have used the absolute value of monthly excess return minus its mean as the estimator of volatility. The study of the new series gives a SETAR model to explain the behaviour of the volatility time series. The application of the MIEC procedure to the volatility of IBEX 35 returns estimates a SETAR (2; 2 ,8) model. This model explains the historical behaviour of the time series, and is able to forecast the volatility trend's changes.

Disertacijoje nagrinėjamos šalies pagrindinių ekonominių indikatorių modeliavimo galimybės, analizuojamos teorinės bei praktinės vertinimo prielaidos, šalies ūkio ypatumų sąlygojami apribojimai, tiriama Lietuvos bei užsienio šalių ekonominių modelių struktūra, šiuose modeliuose naudojamų ekonominių indikatorių rinkiniai bei pasirinkti metodai. Norint gauti patikimus rezultatus, darbe atlikta ekonominio modeliavimo metodų lyginamoji analizė. Disertacijos tyrimų objektas – makroekonominių, verslo bei socialinių indikatorių laiko eilutės. Pagrindinis disertacijoje keliamas darbo tikslas – sukurti pagrindinių šalies ekonomikos pokyčius matuojančių indikatorių dinamikos modelį, kurį naudojant galima kompleksiškai vertinti susiformavusių ekonominių indikatorių adekvatumą, jų suderinamumą bei tarpusavio sąveiką, tirti esamą šalies ekonominę būklę bei jos tvarumą, analizuoti atskirų ekonominių indikatorių pokyčių pasekmes ekonominei būsenai, kurti skirtingus ekonominius scenarijus bei įvertinti šalies ūkio ekonominę perspektyvą. Darbe sprendžiami pagrindinai uždaviniai: kuriamo šalies ekonomikos indikatorių dinamikos modelio struktūros bei teorinio pagrindimo nustatymas, tinkamų kompleksinio modeliavimo metodų parinkimas, modelio bei prognozių tikslumo ir stabilumo tyrimas, programinių priemonių sukūrimas. Atlikus esamų ekonominio modeliavimo metodų analizę, disertacijos užsibrėžtiems tikslams pasiekti ir uždaviniams įgyvendinti, buvo nuspręsta kurti naują šalies ekonominės būsenos... [toliau žr. visą tekstą] / The doctoral thesis investigates the opportunities for the modelling of leading county‘s economic indicators, analyses the theoretical and practical assumptions, the limitations conditioned by the country’s economic features, studies the structure of economic models existing in Lithuania and foreign countries, the set of economic indicators used and selected methods of modelling. A comparative analysis of economic modelling methods was also carried out. The object of this research is the time series of macroeconomic, business and social indicators. The goal of the work – to create the model of indicators that measure the country‘s economic dynamics, which enables the comprehensive assessment of the adequacy, coherence and interoperability of available economic indicators, the investigation and analysis of the current economic situation and its sustainability, the evaluation of the consequences of changes in certain economic indicators for the economic situation, the development of different economic scenarios, and the assessment of the country’s economic prospects. The main tasks solved in the work: determination of the structure and theoretical validity of the model of county‘s economic indicators dynamics, selection of appropriate comprehensive modelling methods, investigation of the accuracy and stability of the model and forecasts, development of software. After an analysis of existing economic modelling methods, in order to achieve the objectives and goals of the thesis... [to full text]

"As a part of an effective SETAR (self-exciting threshold autoregressive) mod- eling methodology, it is important to identify processes exhibiting SETAR-type non- linearity. A number of tests of nonlinearity have been developed in the literature, including those of Keenan (1985), Petruccelli and Davies (1986), Tsay (1986, 1989), Luukkonen (1988), and Chan and Tong (1990). However, it has recently been shown that all these tests perform poorly for SETAR-type nonlinearity detection in the presence of outliers. In this project we develop an improved test for SETAR-type nonlinearity in time series. The test is an outlier-robust variant of the Petruccelli and Davies (1986) test based on the cumulative sums of ordered weighted residuals from generalized maximum likelihood fits (which we call CUSUM-GM). The properties of the proposed CUSUM-GM test are illustrated by means of Monte Carlo simulations. The merits, in terms of size and power, of the proposed test are evaluated relative to the test based on ordered residuals from the ordinary least squares fit (which we call CUSUM-LS) and also to that of other tests for nonlinearity developed in literature. The simulations are run for uncontaminated data and for data contaminated with additive and innovational outliers. The simulation study strongly supports the validity of the proposed robust CUSUM-GM test, particularly in situations in which outliers might be a problem."

The aim of this thesis is to analyze the performance of nonlinear threshold models in forecasting the exchange rate of Czech koruna against EUR. Data for this study were obtained from Statistical Data Warehouse of European Central Bank (ECB) website, from Czech National Bank (CNB) Board decisions minutes and from the press releases of Governing Council of ECB. The data set was split into two periods - from 1999 until November, 2013 when CNB started to use interventions and from November, 2013 until April, 2016. Models used in the thesis are Self-Exciting Threshold Auto Regressive (SETAR) models with one and two thresholds and two Threshold Auto Regres- sive (TAR) models with different threshold variables - meetings of CNB Board as dummy variable and average volatility over recent periods. The forecasting results indicate that SETAR models did not outperform Random Walk in any period. TAR models offered promising results in the period before interventions and surprisingly failed in the period during interventions. This study supports the general belief of exchange rates being difficult to forecast and that it holds in case of Czech koruna as well. JEL Classification F12, F21, F23 H25, H71, H87 Keywords forecasting, exchange rate, time series, nonlin- earity, SETAR, TAR Author's e-mail zaka.one@gmail.com...

In recent years, many research works such as Tiao and Tsay (1994), Stock and Watson (1999), Chen et al. (2001), Clements and Jeremy (2001), Marcellino (2002), Laurini and Vieira (2005) and others have described the dynamic features of many macroeconomic variables as nonlinear. Using the approach of Keenan (1985) and Tsay (1989) this study shown that Ghana inflation rates from January 1980 to December 2009 follow a threshold nonlinear process.  In order to take into account the nonlinearity in the inflation rates we then apply a two regime nonlinear SETAR model to the inflation rates and then study both in-sample and out-of-sample forecast performance of this model by comparing it with the linear SARIMA model. Based on the in-sample forecast assessment from the linear SARIMA and the nonlinear SETAR models, the forecast measure MAE and RMSE suggest that the nonlinear SETAR model outperform the linear SARIMA model. Also using multi-step-ahead forecast method we predicted and compared the out-of-sample forecast of the linear SARIMA and the nonlinear SETAR models over the forecast horizon of 12 months during the period of 2010:1 to 2010:12. From the results as suggested by MAE and RMSE, the forecast performance of the nonlinear SETAR models is superior to that of the linear SARIMA model in forecasting Ghana inflation rates. Thought the nonlinear SETAR model is superior to the SARIMA model according to MAE and RMSE measure but using Diebold-Mariano test, we found no significant difference in their forecast accuracy for both in-sample and out-of-sample.