"Non UBC"@en . "DSpace"@en . "Haukaas, T. (Ed.) (2015). Proceedings of the 12th International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP12), Vancouver, Canada, July 12-15."@en . "International Conference on Applications of Statistics and Probability (12th : 2015 : Vancouver, B.C.)"@en . "Gallo, Iv\u00E1n C\u00E1rdenas"@en . "S\u00E1nchez-Silva, Mauricio"@en . "Akhavan-Tabatabaei, Raha"@en . "Bastidas-Arteaga, Emilio"@en . "2015-05-22T15:07:42Z"@en . "2015-07"@en . "The El Ni\u00C3\u00B1o-Southern Oscillation (ENSO) is an ocean \u00E2\u0080\u0093 atmosphere phenomenon that involves sustained sea surface temperature fluctuations in the Pacific Ocean. This causes disruption in the behavior of the ocean and the atmosphere having important consequences on the global weather. This paper develops a stochastic model to describe El Ni\u00C3\u00B1o-Southern Oscillation patterns. A Markov Switching Autoregressive model (MS-AR) was implemented to fit the Southern Oscillation Index (SOI), a variable that explains the phenomenon. The model consists of two autoregressive processes describing the time evolution of SOI, each of which associated with a specific phase of ENSO (El Ni\u00C3\u00B1o and la Ni\u00C3\u00B1a). The switching between these two models is governed by a discrete time Markov chain. We study the advantages of incorporating time-varying transition probabilities between them and show that the fitted model provides an adequate description of the time series, and demonstrate its utility in analysis and evaluation of the phenomenon."@en . "https://circle.library.ubc.ca/rest/handle/2429/53365?expand=metadata"@en . "12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015 1 A Markov Regime-Switching Framework Application for Describing El Ni\u00C3\u00B1o Southern Oscillation (ENSO) Patterns Iv\u00C3\u00A1n C\u00C3\u00A1rdenas Gallo Graduate Student, Dept. of Civil and Industrial Engineering, Univ. of Los Andes, Bogot\u00C3\u00A1, Colombia Mauricio S\u00C3\u00A1nchez-Silva Professor, Dept. of Civil Engineering, Univ. of Los Andes, Bogot\u00C3\u00A1, Colombia Raha Akhavan-Tabatabaei Professor, Dept. of Industrial Engineering, Univ. of Los Andes, Bogot\u00C3\u00A1, Colombia Emilio Bastidas-Arteaga Professor, Dept. de Physique, Universit\u00C3\u00A9 de Nantes, Nantes, France ABSTRACT: The El Ni\u00C3\u00B1o-Southern Oscillation (ENSO) is an ocean \u00E2\u0080\u0093 atmosphere phenomenon that involves sustained sea surface temperature fluctuations in the Pacific Ocean. This causes disruption in the behavior of the ocean and the atmosphere having important consequences on the global weather. This paper develops a stochastic model to describe El Ni\u00C3\u00B1o-Southern Oscillation patterns. A Markov Switching Autoregressive model (MS-AR) was implemented to fit the Southern Oscillation Index (SOI), a variable that explains the phenomenon. The model consists of two autoregressive processes describing the time evolution of SOI, each of which associated with a specific phase of ENSO (El Ni\u00C3\u00B1o and la Ni\u00C3\u00B1a). The switching between these two models is governed by a discrete time Markov chain. We study the advantages of incorporating time-varying transition probabilities between them and show that the fitted model provides an adequate description of the time series, and demonstrate its utility in analysis and evaluation of the phenomenon 1. INTRODUCTION The El Ni\u00C3\u00B1o-Southern Oscillation (ENSO) is an ocean-atmosphere event that involves sustained sea surface temperature fluctuations in the Pacific Ocean. This causes disruption in the behavior of the ocean and the atmosphere, having important consequences for the global weather (National Oceanic and Atmospheric Administration, 2010). This phenomenon is not completely predictable because of the complexity that results from the relationships between ocean currents, atmospheric circulation and winds in the Pacific. ENSO involves two cyclic phases; El Ni\u00C3\u00B1o and La Ni\u00C3\u00B1a. El Ni\u00C3\u00B1o represents the warm phase of the ENSO. During this phase, the sea surface temperatures rise along the North-West coast of tropical South America. The impacts of El Ni\u00C3\u00B1o episodes depend on the geographical location. For example, in Colombia El Ni\u00C3\u00B1o results in long periods of droughts leading to problems in the agriculture sector, hydroelectric generation and water supply for vulnerable populations. El Ni\u00C3\u00B1o is only one phase of the phenomenon. An episode of La Ni\u00C3\u00B1a is followed most of the times by the El Ni\u00C3\u00B1o episode. La Ni\u00C3\u00B1a represents the cool phase of the ENSO and is associated with the cooling of ocean waters of the coast of Peru and Ecuador. Its impacts are completely opposite to those of El Ni\u00C3\u00B1o. During La Ni\u00C3\u00B1a conditions in Colombia, the amount of precipitations increases leading to floods, landslides and damages to civil infrastructure. The importance of the phenomenon lies in its effect on the global climate. Although ENSO events are characterized by a fluctuation in ocean temperatures in the equatorial Pacific, they are 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015 2 also associated with changes in wind, pressure, and rainfall patterns. This set of climate changes cause a significant impact across the tropical Pacific region and areas away from it. As mentioned above, during El Ni\u00C3\u00B1o and La Ni\u00C3\u00B1a the usual precipitation patterns can be greatly disrupted by either excessively wet or dry conditions (International Research Institute for Climate and Society, 2008) that may impact the global weather. Therefore, the ability to describe El Ni\u00C3\u00B1o and La Ni\u00C3\u00B1a events is extremely important for risk mitigation measures. There are several indicators that provide information about the state of ENSO at a given time. One of them is the Southern Oscillation Index (SOI), which is calculated from the monthly fluctuations in the air pressure difference between Tahiti and Darwin. Sustained negative values of the SOI indicate El Ni\u00C3\u00B1o episodes, while sustained positive values of the SOI indicate La Ni\u00C3\u00B1a episodes. Another indicator of ENSO is the Multivariate ENSO Index (MEI). It is a monthly measure based on the six main observed variables over the tropical Pacific. MEI contains information of the sea level pressure, surface wind (East - West), surface wind (North - South), sea surface temperature, surface air temperature and total cloudiness of the sky. In this case, sustained negative values of the MEI indicate La Ni\u00C3\u00B1a episodes, and sustained positive values of the MEI indicate El Ni\u00C3\u00B1o episodes. In Figure 1, we can observe the SOI and MEI from 1990 to 2000. In this decade, it is possible to observe two strong episodes of El Ni\u00C3\u00B1o. The first occurred from July-1993 to December-1993, and the second from April-1997 to March-1998. Poveda et al. (2010) reviewed the hydro-climatic variability of the Colombian Andes associated with El Ni\u00C3\u00B1o-Southern Oscillation (ENSO) using records of rainfall, river discharges, soil moisture and a vegetation index (NDVI). Their conclusions point to define ENSO as the main forcing mechanism of interannual climate variability. Given the indexes that were described previously (SOI and MEI), they quantify the anomalies in the sea surface temperature in terms of their sign, timing and magnitude. These studies indicate that ENSO indexes become important and valuable tools to describe several hydro-climatological variables in the region. Figure 1: SOI and MEI (1990-2000). Over time, several models have been developed to describe the behavior of the phenomenon. This effort has resulted in the atmospheric general circulation models (ACGMs). ACGMs base their forecasts of sea level temperature on the behavior of the atmosphere. It develops global coupled ocean-atmosphere general circulation models (Meehl,1990). Given the implicit complexity to model the weather physically, this kind of approach becomes accessible only for national institutions that have the technology and equipment needed. Another alternative that has been used to describe the behavior of the phenomenon is related to statistical models. Thus, predictions are based on the behavior of climate variables during the last years. This approach aims to identify correlations in order to establish patterns in the behavior of the relevant variables. Most statistical models that have been developed for climatic variables are based on the Box-Jenkins methodology (BoxJenkins,1976). These models can represent the basic structure of the time series, but they fail to reproduce the nonstationary behavior that exists in climatic variables. A source of non stationarity is the existence of cyclic patterns that determine the 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015 3 behavior of the weather. For example, El Ni\u00C3\u00B1o-Southern Oscillation (ENSO) is a cyclical process composed of a warm phase (El Ni\u00C3\u00B1o) and a cool phase (La Ni\u00C3\u00B1a). Given the existence of cyclical processes, several models have been developed to include the fact of various changing regimes over time. For example, Ubilava et al. (2013) adopted a smooth transition autoregressive modelling framework to explain the sea surface temperature in order to forecast ENSO; they argued the advantage of nonlinear models to represent dynamic processes such ENSO. In order to model the weather, the introduction of a variable that represents the weather type (regime) can be seen in Zucchini et al. (2009) where Hidden Markov Models (HMM) were proposed for modeling the space-time evolution of daily rainfall. Furthermore, James Hamilton (1989) proposes econometric time series which are composed of a Hidden Markov Model (HMM) and autoregressive models. In MS-AR models, several autoregressive models are used to describe the time evolution of the series and the switching between these different models is controlled by a Hidden Markov chain which represents the possible regimes. MS-AR models were extended by Andrew Filardo (1994) who incorporated time-varying transition probabilities (TVTP) between regimes. Since its publication, several applications of the model have been implemented. Ailliot et al. (2012) propose a Markov-Switching Autoregressive model to describe the behavior of wind time series obtaining a good fit to the data. Souza et al. (2010) used a Hidden Markov Model (HMM) to predict future crude oil price movements. Their results indicate that the proposed model might be a useful decision support tool. Walid et al. (2011) proposed a Markov Switching model to investigate the exchange rates for four emerging countries over the period 1994-2009. Yuan (2011) presents an exchange rate forecasting model which combines the multi-state Markov Switching model with smoothing techniques. Guo et al. (2010) focus on detecting hot and cold IPO (Initial Public Offering) cycles in the Chinese A-share market using a Markov regime switching model. The hot and cold periods and their turning points are detected clearly (A hot period is related to positive market conditions). Fallahi et al. (2014) used Markov Switching models to identify and analyze the cycles in the unemployment rate and four different types of criminal activities in the US. Finally, Liu et al. (2006) developed a Markov regime Switching model with two regimes representing expansion and contraction to catch the cyclical behavior of the semiconductor business. The main objective of this paper is to propose an MS-AR, in order to evaluate the pattern changes of ENSO along the time. This model contributes to the prediction of hydro-climatic variables, with significant practical implications for agriculture, hydropower generation, fluvial transport, natural hazards and disasters, and human health. Section 2 describes the proposed model analysing its advantages and shortcomings. Section 3 presents the steps followed for the model implementation. Finally, several concluding remarks are given in the last section. 2. THE PROPOSED \u00E2\u0080\u0093 MARKOV SWITCHING AUTOREGRESSIVE MODELS (MS-AR) ENSO is a cyclical phenomenon in which it is possible to identify two regimes over time (La Ni\u00C3\u00B1a and El Ni\u00C3\u00B1o). The behavior patterns during each of the two phases are opposite and differentiable. On the other hand, the duration and the change between regimes is variable over time. Also, there is uncertainty about the length of episodes or phase transitions. This group of characteristics are properly evaluated by the Markov Switching Autoregressive Model (MSAR) proposed by Hamilton (1989) and improved by Filardo (1994). In this section we present the model, its application and relevant considerations for its implementation. Certain variables undergo episodes in which the behavior of the series seem to change quite 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015 4 dramatically according to a set of regimes. The Markov Switching Autoregressive Model proposes a very tractable approach to model changes in regime. In order to develop a model that allows a given variable to follow a different time series process over time (\u00F0\u009D\u0091\u00A6\u00F0\u009D\u0091\u00A1), consider a first-order autoregression in which the constant term \u00F0\u009D\u0091\u0090 and the autoregressive coefficient \u00F0\u009D\u009E\u008D might be different for each regime \u00F0\u009D\u0091\u00A0\u00F0\u009D\u0091\u00A1 proposed: \u00F0\u009D\u0091\u00A6\u00F0\u009D\u0091\u00A1 = \u00F0\u009D\u0091\u0090\u00F0\u009D\u0091\u00A0\u00F0\u009D\u0091\u00A1 + \u00F0\u009D\u009C\u0099\u00F0\u009D\u0091\u00A0\u00F0\u009D\u0091\u00A1 \u00F0\u009D\u0091\u00A6\u00F0\u009D\u0091\u00A1\u00E2\u0088\u00921 + \u00F0\u009D\u009C\u0096\u00F0\u009D\u0091\u00A1 (1) where \u00F0\u009D\u009C\u0096\u00F0\u009D\u0091\u00A1 \u00E2\u0088\u00BC i.i.d N(0, \u00F0\u009D\u009C\u008E2). In order to model the change in regime over the time we use a Discrete Time Markov Chain (DTMC). Then, we define \u00F0\u009D\u0091\u00A0\u00F0\u009D\u0091\u00A1 as a random variable that can assume values according to a state-space {1,2, . . . , \u00F0\u009D\u0091\u0081}. Also, the probability that \u00F0\u009D\u0091\u00A0\u00F0\u009D\u0091\u00A1+1equals some particular value \u00F0\u009D\u0091\u0097 depends on the past only through the most recent value \u00F0\u009D\u0091\u00A0\u00F0\u009D\u0091\u00A1: \u00F0\u009D\u0091\u0083 {\u00F0\u009D\u0091\u00A0\u00F0\u009D\u0091\u00A1+1 = \u00F0\u009D\u0091\u0097 \u00E2\u008E\u00B8\u00F0\u009D\u0091\u00A0\u00F0\u009D\u0091\u00A1 = \u00F0\u009D\u0091\u0096 , \u00F0\u009D\u0091\u00A0\u00F0\u009D\u0091\u00A1\u00E2\u0088\u00921 = \u00F0\u009D\u0091\u0098\u00E2\u0080\u00A6 } = \u00F0\u009D\u0091\u0083 {\u00F0\u009D\u0091\u00A0\u00F0\u009D\u0091\u00A1+1 = \u00F0\u009D\u0091\u0097 \u00E2\u008E\u00B8\u00F0\u009D\u0091\u00A0\u00F0\u009D\u0091\u00A1 = \u00F0\u009D\u0091\u0096 } = \u00F0\u009D\u0091\u009D\u00F0\u009D\u0091\u0096\u00F0\u009D\u0091\u0097 (2) The transition probability \u00F0\u009D\u0091\u009D\u00F0\u009D\u0091\u0096\u00F0\u009D\u0091\u0097 gives the probability that state \u00F0\u009D\u0091\u0096 will be followed by state \u00F0\u009D\u0091\u0097 in a one-step transition. It is often convenient to collect the transition probabilities in an (\u00F0\u009D\u0091\u0081 \u00E2\u00A8\u00AF \u00F0\u009D\u0091\u0081) matrix \u00F0\u009D\u0091\u0083 known as the transition probability matrix. In this way, a MS-AR process is a discrete-time process with two components {\u00F0\u009D\u0091\u0086\u00F0\u009D\u0091\u00A1, \u00F0\u009D\u0091\u008C\u00F0\u009D\u0091\u00A1}, for our case, \u00F0\u009D\u0091\u008C\u00F0\u009D\u0091\u00A1 denotes the monthly index of SOI with values in (\u00E2\u0088\u0092\u00E2\u0088\u009E,\u00E2\u0088\u009E) and \u00F0\u009D\u0091\u0086\u00F0\u009D\u0091\u00A1 \u00E2\u0088\u0088 {Ni\u00C3\u00B1o (1), Ni\u00C3\u00B1a (2)} represents the regime at month \u00F0\u009D\u0091\u00A1. A MS-AR process is characterized by the following two conditional independence assumptions: - The conditional distribution of \u00F0\u009D\u0091\u0086\u00F0\u009D\u0091\u00A1 given the values of {\u00F0\u009D\u0091\u0086\u00F0\u009D\u0091\u00A1\u00E2\u0080\u00B2}t\u00E2\u0080\u00B2