We show through elementary means that the covariance functions of second-order stationary vector Markov regime switching time series models have vector ARMA(p; q) representations, where the upper bounds for p and q are elementary functions of the number of regimes. This applies in general to vector Markov regime switching processes with both mean-variance and autoregressive switching. This result yields an easily computed method for setting a lower bound on the number of underlying Markov regimes from an estimated autocovariance function.
|
262
|
Time Series: Theory and Methods
– Brockwell, Davis
- 1998
|
|
194
|
A New Approach to the Economic Analysis of Nonstationary Time
– Hamilton
- 1989
|
|
117
|
Introduction to Multiple Time Series Analysis
– Lütkepohl
- 1993
|
|
81
|
Stochastic models for heterogeneous DNA sequences
– Churchill
- 1989
|
|
81
|
Multiple time series
– Hannan
- 1970
|
|
62
|
Analysis of Time Series Subject to Changes in Regime
– Hamilton
- 1990
|
|
45
|
Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test”, Review of financial Studies
– Lo, MacKinlay
- 1988
|
|
44
|
The Likelihood Ratio Test Under Nonstandard Conditions: Testing the Markov Switching Model of GNP
– Hansen
- 1992
|
|
44
|
Hidden markov models for speech recognition
– Juang, Rabiner
- 1991
|
|
24
|
A Survey of Matrix Theory
– MARCUS, MINC
- 1964
|
|
21
|
Long Swings in the Dollar: Are they in the Data and Do Markets know it
– Engle, Hamilton
- 1990
|
|
19
|
Specification Testing in Markov-Switching Time-Series Models
– Hamilton
- 1996
|
|
18
|
One-sided inference about functionals of a density
– Donoho
- 1988
|
|
17
|
Characterization of single channel currents using digital signal processing techniques based on hidden Markov models
– Chung, Moore, et al.
- 1990
|
|
13
|
Maximum-penalized-likelihood estimation for independent and Markov-dependent mixture models
– Leroux, Puterman
- 1992
|
|
10
|
A Survey of Matrix Theory and Matrix Inequalities. Allyn and
– Marcus, Minc
- 1964
|
|
8
|
A Check on the Robustness of Hamilton's Markov Switching Model Approach to the Economic Analysis of the Business Cycle
– Boldin
- 1996
|
|
8
|
Recursive Estimation in Switching Autoregressions with a Markov Regime
– Holst, Lindgren, et al.
- 1994
|
|
7
|
Estimating the order of hidden Markov models
– Ryden
- 1995
|
|
6
|
Bayesian restoration of single channel patch clamp recordings
– Fredkin, Rice
- 1992
|
|
6
|
Stationary random processes
– unknown authors
- 1967
|
|
3
|
A Markov model of heteroscedasticity
– Turner, Startz, et al.
- 1990
|
|
3
|
Speci cation Testing in Markov-Switching Time-Series Models
– Hamilton
- 1996
|
|
2
|
Markov chain models, time series analysis and extreme value theory
– Poskitt, Chung
- 1996
|
|
2
|
Maximum-penalized- likelihood estimation for independent and Markov-dependent mixture models
– Leroux, Puterman
- 1992
|
|
1
|
A time series model with suddenly changing parameters
– Andel
- 1992
|
|
1
|
On the structure of moving average processes
– Ansley, Spivey, et al.
- 1977
|
|
1
|
Identification of a mixed autoregressive-moving average process: The corner method", Time series
– Beguin, Gourierous, et al.
- 1980
|
|
1
|
Testing under non-standard conditions in frequency domain: with applications to Markov regime switching models of exchange rates and federal fund rates", Working paper
– Gong, Mariano
- 1995
|
|
1
|
A new approach to ARMA modelling
– Gray, Kelley, et al.
- 1978
|
|
1
|
Doubly stochastic vector AR(1) processes
– Karlsen
- 1990
|
|
1
|
Introduction to multiple time series analysis
– Lukepohl
- 1994
|
|
1
|
On a measure of fit in time series models
– Ljung, Box
- 1978
|
|
1
|
Hidden Markov chains can be hard to train", Paper presented at 230th IMS Meeting
– Nadas, Mercer
- 1994
|
|
1
|
Identi cation of a mixed autoregressive-moving average process: the corner method", Time Series
– Beguin, Gourierous, et al.
- 1980
|
|
1
|
ARMA Model Identi cation
– Choi
- 1992
|
|
1
|
On a measure of t in time series models
– Ljung, Box
- 1978
|
|
