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State-Space Models with Regime Switching | Department of Economics | University of Washington
Publications, Books. Both state-space models and Markov switching models have been highly productive paths for empirical research in macroeconomics and finance. This book presents recent advances in econometric methods that make feasible the estimation of models that have both features. One approach, in the classical framework, approximates the likelihood function; the other, in the . PDF | On Jan 1, , Yoosoon Chang and others published State Space Models With Endogenous Regime Switching | Find, read and cite all the research you need on ResearchGate. State Space Models with Endogenous Regime Switching Author: Yoosoon Chang, Junior Maih and Fei Tan Series: Working Paper Number: 12/ Working Paper 12/ (pdf) This article studies the estimation of state space models whose parameters are switching endogenously between two regimes, depending on whether an autoregressive latent factor.
State-space models with regime switching pdf download
To browse Academia. Skip to main content. Log In Sign Up. Regime switching state-space models applied to psychological processes: handling missing data and making inferences. Raoul Grasman. Ellen Hamaker. Download Free PDF. Free PDF. Download PDF Package. Premium PDF Package. This paper. A short summary of this paper. We model these processes with the regime switching state-space model proposed by Kim J.
However, the current algorithm cannot handle missing data, which limits its appli- cability to psychological data. Moreover, the performance of standard errors for the purpose of making inferences about the parameter estimates is yet unknown. Finally, we apply the regime switching state-space model to the three empirical data sets described above. Key words: Kalman filter, regime switching, state-space model, missing data.
Regime switching is an important phenomenon in many psychological processes. In some cases, regime switching is part of a developmental process and occurs only once, when the tran- sition is made from one developmental stage to another cf.
Other psychological processes are characterized by recurrent switches, such that a person repeatedly alternates between two ore more states or regimes. The sleep-wake cycle is a prominent example of this, state-space models with regime switching pdf download, as are the different stages of sleep.
Moreover, diverse psychological disorders are characterized by switches between distinct psy- chological states, such as mania and depression in bipolar disorder, and avoidance and intrusion in posttraumatic stress disorder. Furthermore, in experimental psychology regime switching can occur when the participant changes strategies, for instance, by switching between being fast at the cost of making more mistakes, and being accurate at the cost of being slower, state-space models with regime switching pdf download.
The study of such processes at the level of the individual requires the use of a regime switching model in which it is assumed that the observation at occasion t state-space models with regime switching pdf download from one of a limited number of distributions, state-space models with regime switching pdf download.
These distributions—which we refer to as the regimes or states—differ from each other with respect to their parameters e. In econometrics, there has always been a specific interest in regime switching models, es- pecially to model phases of economic growth versus phases of recession, state-space models with regime switching pdf download.
Recently, Yang and Chow Requests for reprints should be sent to E. E-mail: e, state-space models with regime switching pdf download. Despite the obvious potential of this approach for the study of psychological processes, there are a number of unresolved issues that may keep this approach from being more widely used.
The purpose of this paper is to consider two of these is- sues, that is, how to handle missing data, and the quality of inferences about parameter estimates when dealing with relatively short time series. This paper is organized as follows. We begin by motivating the necessity of these devel- opments by introducing three empirical applications that may be of interest to psychological researchers.
In the fourth section we present the results from several simulations we performed to investigate the performance of the algorithm in the case of complete data and in cases of dif- ferent kinds of missing data in relatively short time series i. We focus on the mean point estimates and on the coverage rates of the confidence intervals in order to evaluate the performance. In the fifth section we return to the applications and present the re- sults we obtain from analyzing these data with the regime switching state-space model.
We end this paper with a discussion in which we evaluate the findings of this paper, and comment on the suitability and the practical feasibility of regime switching state-space modeling for the study of psychological processes, state-space models with regime switching pdf download. Psychological Applications We consider three applications in this paper, two of which fall in the domain of clinical psychology, and one concerning sports psychology. In this section we introduce these three ap- plications and argue why regime switching is of interest in these applications.
Application 1: Premenstrual Syndrome Premenstrual syndrome PMS is characterized by a broad class of state-space models with regime switching pdf download, behavioral and physical symptoms that occur for several days state-space models with regime switching pdf download weeks before menses and subside following the menstrual period Freeman, While the diagnosis of PMDD or PMS is typically based on retrospective measures, the in- clusion of some prospective approach, such as keeping a symptom chart, is considered essential in order to rule out differential diagnoses such as other mood disorders American Psychiatric Association, We propose a more sophisticated approach to prospective data using a regime switching model.
The data in this application come from a female in her early twenties, who indicated retrospectively to suffer from PMDD related symptoms at a subclinical level. The measurements were taken in the evening using a palm pilot and the questions were referring to the entire day. Moreover, the question is whether this latter regime is typically encountered prior to and elevates after the start of menses, thus conforming to a PMS pattern.
In addition, increased irritability—such as persistent anger, a tendency to respond to events with angry outbursts or blaming others, or an exaggerated sense of frustration over minor matters—is also quite common American Psychiatric Associa- tion, The data in our second application come from a female in her mid thirties who was diagnosed with MDE. She indicated a long history of feeling depressed, but her main reason for seeking professional help were frequent outbursts of extreme irritation bordering rage.
The data in this application consist of affective measurements on two dimensions, that is, a pleasure—displeasure state-space models with regime switching pdf download and an activation—deactivation dimension Russell, A paper and pencil version was used, rather than an electronic device, in order to avoid too large an intru- sion on daily life.
The participant indicated the time of responding on each rating: These were within a 20 minutes interval around the whole hour i. Note that such data will necessarily contain a considerable portion of missing observations due to both occasionally missed measurements during the day, and strings of missing observations during the night. A total of 16 days were covered, resulting in hours of which were observed i. We are interested in whether the subjectively reported outbursts of irritation by this par- ticipant are best understood as a separate, qualitative distinct psychological state that exists in addition to a calmer, depressed state, or that it is simply part of the same continuum that under- lies the affective ratings reported by this client.
Moreover, state-space models with regime switching pdf download, if these prove to be distinct affective states, we are interested in the amount of time spent in each state, and how likely this participant is to switch from one state to the other. To investigate whether Johnson actually had a hot hand, Berkhof, Van Mechelen, and Hoijtink analyzed the data from the — season to the — season.
Berkhof et al. In contrast to Berkhof et al. This way, the series span a total of days of which Johnson played days i. We want to investigate whether the fluctuations are part of a continuum, in that Vinnie John- son performed better in some games than in others, or that there are qualitatively distinct states that are associated with different performance, both in his eagerness to attack and his success.
Summary The three applications discussed above represent different scenarios in which researchers may be interested in the possibility that a regime switching mechanism underlies the fluctuations in the data, resulting in qualitatively different states that the subject can be in.
In all three cases there are missing data which need to be handled in the modeling procedure. Furthermore, to be able to make inferences based on the estimated model, standard errors for the model parameters are essential. For more details, the reader is referred to Kim and Nelson Since the introduction of the Markov-switching autoregressive MSAR model Hamilton, over twenty years ago, there have been hundreds of applications of this model in econo- metrics. The MSAR model is based on a switching process that forms a discrete-valued hidden Markov model, while the observed data are modeled through an autoregressive AR process.
Kim generalized this approach to the state-space model, such that a wide range of time series models can be extended with Markov switching. Then we discuss the estimation of the latent variables in this model, which is based on combining the well-known Kalman filter cf.
Hamilton, This is followed by a brief discussion of how to obtain parameter estimates for a regime switching state- space model based on by-products of the Kalman filter and the Hamilton filter.
Regime Switching State-Space Model Let yt represent a p-variate vector with observations at occasion t. The residuals in the p-variate vector et are uncorrelated over time, and are uncorrelated with at and xtbut may be correlated with each other at the same occasion using RSt. The vector at is often referred to as the state at occasion t. The r-variate vector cSt contains the intercepts. The residuals in the r-variate vector ut are uncorrelated over time, state-space models with regime switching pdf download, and are also uncorrelated with the residuals from the measurement equation i.
From Equations 1 and 2 it is clear that the model parameters i. This variable St can take on discrete values between 1 and M, and it follows a discrete-valued Markov process. Estimating the Latent Variables at in a Regime Switching State-Space Model The Kalman filter was first proposed in as an online procedure to estimate the latent variables of a state-space model as well as to predict its future values, under the assumption that the model parameters are known Kalman, In the first step, which is referred to as the prediction step, a prediction is made for at based on all information available up to the previous occasion.
In the third step, which is referred to as the update step, the estimate of at is updated in the light of the actual observations at occasion t to obtain at t. These three steps are repeated for each occasion. In the case of a regime switching state-space model the procedure is more complicated, because one does not know in which regime the system is at any given occasion and thus does 2 As in the linear state-space model, the latent variables in the regime switching state-space model are modeled as a VAR 1 process.
This does not mean that the state-space model is restricted to first-order autoregressive relationships: For instance, it is well known that an VAR process of order p can be rewritten as an VAR 1 process e. Below, the three steps of the Kalman filter as outlined above are discussed in case of a regime switching state-space model, state-space models with regime switching pdf download.
It will be shown that this results in an M-fold increase of possibilities at each time point which would make the filter inoperable as the length of the series increases. This solution requires the use of the Hamilton filter, which is discussed at the end. If no particular action is taken, this implies that for a series of length n, there will be M n possible latent trajectories, such state-space models with regime switching pdf download the filter will quickly become inoperable.
These are then used in the prediction equations for the next oc- casion in the Kalman filter i. This probability is obtained using the Hamilton filter Hamilton, ; Kim,which is discussed below. This results in M 2 predicted estimates i,j at t. Next, the Hamilton filter equations for the probabilities are run i. Finally, the collapsed equations are run i. After this, the algorithm moves on to the next occasion. However, in prac- tice, one typically wants to estimate these.
In the case of the linear Kalman filter, state-space models with regime switching pdf download algorithm produces by-products that can be used to obtain maximum likelihood estimates of the model pa- rameters cf. Similarly, by-products of the procedure described above can be used to obtain maximum likelihood estimates for the model parameters of a regime switching state-space model.
Handling Missing Values It is not uncommon to have missing observations in psychological time series, especially state-space models with regime switching pdf download these concern diary data. Harvey discusses how to handle missing data in the linear Kalman filter i. In short, this procedure can be described as fol- lows. This has two consequences.
M7a - State-Space Models (Theory) - CIV6540E
, time: 2:09:04State-space models with regime switching pdf download
State Space Models with Endogenous Regime Switching Author: Yoosoon Chang, Junior Maih and Fei Tan Series: Working Paper Number: 12/ Working Paper 12/ (pdf) This article studies the estimation of state space models whose parameters are switching endogenously between two regimes, depending on whether an autoregressive latent factor. the regime probabilities will be calculated using the probability filter. A comprehensive treatment of state-space and Markov switching models is given by Kim and Nelson (). The aim of this work is to evaluate the maximum likelihood method to state space Markov switching models with time varying transition proba-bilities using the EM. 6/17/ · [PDF] State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with. Report. Browse more videos. Playing next. [PDF Download] Finite Mixture and Markov Switching Models (Springer Series in Statistics) [PDF] Khaled Touq. Released on: June 16,
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