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Markov Regime Switching in Economic Time Series

Erlandsson, Ulf LU (2005) In Lund Economic Studies
Abstract (Swedish)
Popular Abstract in Swedish

Avhandlingens bidrag ligger inom området för Markov regimskiftesmodeller i tidsserieanalys. Den består av fem separata uppsatser som specifikt undersöker två statistiska frågeställningar, samt applicerar metodologin på fyra olika makroekonomiska områden. De två huvudsakliga statistiska bidragen rör (i) utvecklandet av ett flexibelt test baserat på simulering för att utröna det exakta antalet regimer i en Markov-modell, och (ii) en utvärdering av asymtotik i Markov-modeller med tidsvarierande övergångssannolikheter. Vi använder de ekonometriska resultaten på verklig data från nominella växelkurser, räntor, ekonomisk tillväxt inom ett konjunkturcykelperspektiv, samt valutakriser.

... (More)
Popular Abstract in Swedish

Avhandlingens bidrag ligger inom området för Markov regimskiftesmodeller i tidsserieanalys. Den består av fem separata uppsatser som specifikt undersöker två statistiska frågeställningar, samt applicerar metodologin på fyra olika makroekonomiska områden. De två huvudsakliga statistiska bidragen rör (i) utvecklandet av ett flexibelt test baserat på simulering för att utröna det exakta antalet regimer i en Markov-modell, och (ii) en utvärdering av asymtotik i Markov-modeller med tidsvarierande övergångssannolikheter. Vi använder de ekonometriska resultaten på verklig data från nominella växelkurser, räntor, ekonomisk tillväxt inom ett konjunkturcykelperspektiv, samt valutakriser.



Det första pappret, ?Exchange Rates and Markov Switching Dynamics,? (tillsammans med Yin-Wong Cheung) utvecklar ett Monte Carlo-baserat test för specifikation av antalet regimer i Markov-modellen. Testet är mer flexibelt än tidigare föreslagna test, samt har fördelen att det växlar nollhypotes så att inferens rörande möjligheten att överhuvudtaget dra en slutsats baserat på ett begränsat datamaterial kan erhållas. Vi utvärderar de motsägelsefulla empiriska resultaten i tidigare forskning rörande Markov-dynamik i ett antal dollardenominerade växelkurser, och kommer fram till att detta sannolikt är en effekt av att dataserier innehåller för lite information för att kunna dra en slutsats. Med ett större sample finner vi bevis för Markov-dynamik i månatlig data.



I ?Regime Switches in Swedish Interest Rates? undersöker vi en extremt letpokurtisk tidsserie, nämligen svenska interbankräntor under 1987-2002 på veckobasis. Genom våra specifikationstest erhåller vi resultatet att en tre-regims modell bäst beskriver ränteserien. Modellen lyckas uppnå betingad normalitet i residualerna, vilket inte varit möjligt med mer traditionella ansatser såsom GARCH modeller. I en jämförelse med ett antal andra modeller visar sig tre-regims modellen vara det bästa valet för att prognostisera volatilitet i serien, på de undersökta prognoshorisonterna (1-8 veckor).



Det tredje uppsatsen, ?Constructing Early-Warning Systems: A Modified Markov Switching Approach?, behandlar användningen av övergångssannolikheter i Markov-modellen i syfte att generera prognoser av regimskiften på medellång till lång sikt. Vi visar att det finns en korttidsbias i standardmodellen som gör den direkt olämplig för de prognoser vi eftersöker och visar sedemera hur denna bias kan reduceras med hjälp av en modifierad maximum-likelihood estimator av modellen. I en empirisk applikation på den amerikanska konjunkturcykeln så finner vi starkt stöd för den modifierade estimatorn när bättre prognosförmåga på 4-12 kvartal eftersöks.



I papper nummer fyra, ?Transition Variables in the Markov Switching Model: Some Small Sample Properties,? studerar vi statistiska egenskaper för regresserorer i övergångsekvationer för modellen när antalet regimskiften i datan är litet, vilket ofta är fallet i empiriska applikationer. Det visar sig att likelihood ratio-statistiken har en tydlig tendens att överskatta signifikansnivån hos regressorerna när antalet skiften är lågt. Våra kalibreringar indikerar att detta torde vara ett reellt problem i många hittillsvarande applikationer. I en egen applikation på prediktorer av recessioner i USA finner vi att signifikansnivåns bör skiftas ner till mellan 1.5-2% för att motsvara en 95 procentig konfidensnivå.



Tillsammans med Guillaume Arias applicerar jag Markov modellen i syfte att studera prediktorer av valutakriser i pappret ?Regime Switching as an Alternative Early-Warning System of Currency Crises: An Application to South-East Asia.? Vi sammanfattar forskningsfronten i olika metodologier för att prediktera valutakriser. Baserat på detta samlar vi in data för tidigare föreslagna variabler, och använder en Markov-modeller baserad på volatilitetsregimer för utvärdera dessa variabler användbarhet i prognos- och förklaringssyfte. Med hjälp av den modifierade Markov-modellen föreslagen i det tredje pappret i denna avhandling så bygger vi sedan ett prognossystem för valutakriser som har bra egenskaper relativt tidigare föreslagna system. (Less)
Abstract
This dissertation studies statistical properties and applications of the Markov switching models for economic time series in five separate papers. The two main statistical themes are (i) the task of choosing the number of states to use in the model, and (ii) inference on time-varying transition probabilities. Our empirical applications span a wide array of topics in international finance and macroeconomics. Specifically, we study the dynamics of nominal exchange rates, interest rates, the business cycle and currency crises.



In the first paper, ?Exchange Rates and Markov Switching Dynamics (joint work with Yin-Wong Cheung), we develop a simulation procedure to construct a two-sided test for testing hypotheses regarding... (More)
This dissertation studies statistical properties and applications of the Markov switching models for economic time series in five separate papers. The two main statistical themes are (i) the task of choosing the number of states to use in the model, and (ii) inference on time-varying transition probabilities. Our empirical applications span a wide array of topics in international finance and macroeconomics. Specifically, we study the dynamics of nominal exchange rates, interest rates, the business cycle and currency crises.



In the first paper, ?Exchange Rates and Markov Switching Dynamics (joint work with Yin-Wong Cheung), we develop a simulation procedure to construct a two-sided test for testing hypotheses regarding the number of states in an empirical data-set. We use the test to resolve conflicting results regarding the existence of Markov switching dynamics in three dollar-denominated exchange rates. Our test shows that some of the earlier data-sets were not informative enough to draw a conclusion upon, with the result of previous tests sometimes contradicting each other. In data spanning 1973-1998 and on the monthly and higher frequency, we do, however, find conclusive evidence of Markov switching dynamics.



The second paper, ?Regime Switches in Swedish Interest Rates?, uses a similar simulation approach to arrive at the conclusion of three states in a set of weekly data on Swedish interbank offered interest rates. A short-lived and highly volatile states pin-point the repeated speculative attacks on the Swedish krona in the early 90s. With the states in place, we are able to obtain conditional normality even in this extremely leptokurtic time-series. Furthermore, we show that the specification is quite apt at forecasting interest rate volatility, and the evidence in favor of the model versus a number of competing alternatives is strong for all the forecast horizons we have applied.



Turning to the dynamics of Markov models with time-varying transitions probabilities, the third paper, ?Constructing Early-Warning Systems: A Modified Markov Switching Approach? sets out to investigate the relatively infrequent use of this intuitive extension to the original model. It is shown in a simple theoretical setting, and in several simulation exercises, that the maximum likelihood estimator overemphasizes the short-run effects of predictors of transition probabilities in modestly sized samples. This leads to extreme parameter estimates and projected transition probabilities with too abrupt behavior. We introduce a penalized estimator, which is able to reduce parameter estimates toward their true magnitudes, and also increases correlation between the projected and true transition probabilities, and offer some suggestions on how to choose the magnitude of the penalty. In an application to the U.S. business cycle, we show that the penalized estimator yields a more parsimonious model with better forecasting properties in the medium to long term compared to its non-penalized counterpart.



In the fourth paper, ?Transition Variables in the Markov Switching Model: Some Small Sample Properties?, we offer a note of caution in terms of using time-varying transition probabilities. We argue that rather than the nominal sample size, as measured by the total number of observations in the time-series, the number of regime switches should be considered instead when making inference on variable significance in the transition equations. By simulation, it is shown that for many cases the likelihood ratio statistic is over-sized, leading to too many transition variables being deemed significant. The size-distortion is not only dependent upon the number of switches in the data, but also the degree of uncertainty inherent in it and the persistence in the regressed variable. We suggest a straightforward, but computationally intensive approach to obtaining statistics with proper size. Looking at a number of business cycle predictors, we show that their statistics must be adjusted by a considerable magnitude to reflect true confidence levels. For model specification, this consequently has marked effect.



The last paper (which is joint work with Guillaume Arias), ?Regime Switching as an Alternative Early-Warning System of Currency Crises: An Application to South-East Asia? is devoted to inferring indicators predicting the on-set of the South-East Asian currency crises in 1997. We survey the current literature in the area, and based on this, derive a number of possible determinants of currency crises. In a framework based on the Markov switching model with time-varying transition probabilities, we evaluate these determinants and specify models for forecasting of oncoming crises in the medium to long term. We show that the model is quite efficient in describing the underlying data and that it possesses relatively good forecasting properties. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Professor Haldrup, Niels, Department of Economics, University of Aarhus
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Nationalekonomi, ekonometri, ekonomisk teori, ekonomiska system, ekonomisk politik, forecasting, Markov switching, exchange rates, interest rates, business cycle, economic policy, economic systems, economic theory, econometrics, Economics, currency crisis
in
Lund Economic Studies
pages
126 pages
publisher
Department of Economics, Lund Universtiy
defense location
EC3:210, Holger Crafoords Ekonomicentrum, Tycho Brahes väg 1, Lund
defense date
2005-06-09 13:15
ISSN
0460-0029
language
English
LU publication?
yes
id
164bffd0-d5c7-4123-9f85-47ae86ed016e (old id 545023)
date added to LUP
2007-09-27 11:19:05
date last changed
2016-09-19 08:44:58
@phdthesis{164bffd0-d5c7-4123-9f85-47ae86ed016e,
  abstract     = {This dissertation studies statistical properties and applications of the Markov switching models for economic time series in five separate papers. The two main statistical themes are (i) the task of choosing the number of states to use in the model, and (ii) inference on time-varying transition probabilities. Our empirical applications span a wide array of topics in international finance and macroeconomics. Specifically, we study the dynamics of nominal exchange rates, interest rates, the business cycle and currency crises.<br/><br>
<br/><br>
In the first paper, ?Exchange Rates and Markov Switching Dynamics (joint work with Yin-Wong Cheung), we develop a simulation procedure to construct a two-sided test for testing hypotheses regarding the number of states in an empirical data-set. We use the test to resolve conflicting results regarding the existence of Markov switching dynamics in three dollar-denominated exchange rates. Our test shows that some of the earlier data-sets were not informative enough to draw a conclusion upon, with the result of previous tests sometimes contradicting each other. In data spanning 1973-1998 and on the monthly and higher frequency, we do, however, find conclusive evidence of Markov switching dynamics.<br/><br>
<br/><br>
The second paper, ?Regime Switches in Swedish Interest Rates?, uses a similar simulation approach to arrive at the conclusion of three states in a set of weekly data on Swedish interbank offered interest rates. A short-lived and highly volatile states pin-point the repeated speculative attacks on the Swedish krona in the early 90s. With the states in place, we are able to obtain conditional normality even in this extremely leptokurtic time-series. Furthermore, we show that the specification is quite apt at forecasting interest rate volatility, and the evidence in favor of the model versus a number of competing alternatives is strong for all the forecast horizons we have applied.<br/><br>
<br/><br>
Turning to the dynamics of Markov models with time-varying transitions probabilities, the third paper, ?Constructing Early-Warning Systems: A Modified Markov Switching Approach? sets out to investigate the relatively infrequent use of this intuitive extension to the original model. It is shown in a simple theoretical setting, and in several simulation exercises, that the maximum likelihood estimator overemphasizes the short-run effects of predictors of transition probabilities in modestly sized samples. This leads to extreme parameter estimates and projected transition probabilities with too abrupt behavior. We introduce a penalized estimator, which is able to reduce parameter estimates toward their true magnitudes, and also increases correlation between the projected and true transition probabilities, and offer some suggestions on how to choose the magnitude of the penalty. In an application to the U.S. business cycle, we show that the penalized estimator yields a more parsimonious model with better forecasting properties in the medium to long term compared to its non-penalized counterpart.<br/><br>
<br/><br>
In the fourth paper, ?Transition Variables in the Markov Switching Model: Some Small Sample Properties?, we offer a note of caution in terms of using time-varying transition probabilities. We argue that rather than the nominal sample size, as measured by the total number of observations in the time-series, the number of regime switches should be considered instead when making inference on variable significance in the transition equations. By simulation, it is shown that for many cases the likelihood ratio statistic is over-sized, leading to too many transition variables being deemed significant. The size-distortion is not only dependent upon the number of switches in the data, but also the degree of uncertainty inherent in it and the persistence in the regressed variable. We suggest a straightforward, but computationally intensive approach to obtaining statistics with proper size. Looking at a number of business cycle predictors, we show that their statistics must be adjusted by a considerable magnitude to reflect true confidence levels. For model specification, this consequently has marked effect.<br/><br>
<br/><br>
The last paper (which is joint work with Guillaume Arias), ?Regime Switching as an Alternative Early-Warning System of Currency Crises: An Application to South-East Asia? is devoted to inferring indicators predicting the on-set of the South-East Asian currency crises in 1997. We survey the current literature in the area, and based on this, derive a number of possible determinants of currency crises. In a framework based on the Markov switching model with time-varying transition probabilities, we evaluate these determinants and specify models for forecasting of oncoming crises in the medium to long term. We show that the model is quite efficient in describing the underlying data and that it possesses relatively good forecasting properties.},
  author       = {Erlandsson, Ulf},
  issn         = {0460-0029},
  keyword      = {Nationalekonomi,ekonometri,ekonomisk teori,ekonomiska system,ekonomisk politik,forecasting,Markov switching,exchange rates,interest rates,business cycle,economic policy,economic systems,economic theory,econometrics,Economics,currency crisis},
  language     = {eng},
  pages        = {126},
  publisher    = {Department of Economics, Lund Universtiy},
  school       = {Lund University},
  series       = {Lund Economic Studies},
  title        = {Markov Regime Switching in Economic Time Series},
  year         = {2005},
}