Estimation of structural changes in nonlinear time series models by using particle filters and genetic programming. (English) Zbl 1348.93257
Summary: Several works have demonstrated detection of changes of state equations (called structural changes) based on statistical measures but have given no suggestions regarding the functional forms of the state equations after changes. This paper deals with the estimation of structural changes in nonlinear time series models by using particle filters, Genetic Programming (GP), and its applications. We consider the problems of state estimation from the observed time series that are generated based on nonlinear state equations. It is assumed that structural changes can be detected by some measure of likelihood and that the state equation after changes is modified from its current functional form. Individuals corresponding to functional forms in the GP pool are generated at random, and we apply the crossover operation between the current functional form and the individuals by giving possible multiple functional forms. Then, we have the optimal functional form among the possible functional forms generated by GP from the current form. As an application, we show the estimation of structural change for an artificially generated time series and also discuss the estimation of functional forms for a real economic time series before and after structural changes.
MSC:
| 93E11 | Filtering in stochastic control theory |
| 93E10 | Estimation and detection in stochastic control theory |
| 93C10 | Nonlinear systems in control theory |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 90C59 | Approximation methods and heuristics in mathematical programming |
Keywords:
structural changes; particle filters; genetic programming; state estimation; nonlinear time series modelingReferences:
| [1] | DoucetA, GordonNJ, KrishnamurthyV. Particle filters for state estimation of jump Markov linear systems. IEEE Transactions on Signal Processing2001; 49(3):613-624. |
| [2] | DoucetA, De FreitasN, GordonN. Sequential Monte Carlo Methods in Practice. Splinger Verlag: New York, 2001. |
| [3] | GustafssonF, GunnarssonF, BergmanN, ForssellU, JanssonJ, KarlssonR, NordlundPJ. Particle filters for positioning, navigation, and tracking. IEEE Transactions on Signal Processing2002; 50(2):425-437. |
| [4] | KotechaJH, DjuricPM. Gaussian sum particle filtering. IEEE Transactions on Signal Processing2003; 51(10):2602-2612. · Zbl 1369.94196 |
| [5] | SchonT, GustafssonF, NordlundPJ. Marginalized particle filters for mixed linear/nonlinear state-space models. IEEE Transactions on Signal Processing2005; 53(7):2279-2289. · Zbl 1370.94229 |
| [6] | BayardDS, SchumitzkyA. Implicit dual control based on particle filtering and forward dynamic programming. International Journal of Adaptive Control and Signal Processing2010; 24(3):155-177. · Zbl 1298.93353 |
| [7] | GarattiS, BittantiS. A new paradigm for parameter estimation in system modeling. International Journal of Adaptive Control and Signal Processing2013; 27(8):667-687. · Zbl 1284.93225 |
| [8] | XuT, JianH, JianZ, PingW. A sigma point‐based resampling algorithm in particle filter. International Journal of Adaptive Control and Signal Processing2012; 26(11):1013-1023. · Zbl 1276.93077 |
| [9] | ZiaA, KirubarajanT, ReillyJP, YeeD, PunithakumarK, ShiraniS. An EM algorithm for nonlinear state estimation with model uncertainties. IEEE Transactions on Signal Processing2008; 56(3):921-936. · Zbl 1390.94516 |
| [10] | TokinagaS, TanK. State estimation from time series by using particle filters based on equation approximations with the genetic programming and its applications to suppression of fluctuations (in Japanese). IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences (Japanese Edition)2010; J93‐A(11):739-755. |
| [11] | ChowGC. Tests of equality between sets of coefficients in 2 linear regressions. Econometrica1960; 28(3):591-605. · Zbl 0099.14304 |
| [12] | VaswaniN. Additive change detection in nonlinear systems with unknown change parameters. IEEE Transactions on Signal Processing2007; 55(3):859-872. · Zbl 1391.94557 |
| [13] | VaswaniN, Roy‐ChowdhuryAK, ChellappaR. Shape activity: a continuous‐state HMM for moving/deforming shapes with application to abnormal activity detection. IEEE Transactions on Image Processing2005; 14(10):1603-1616. |
| [14] | AndrieuC, DoucetA, SinghSS, TadicVB. Particle methods for change detection, system identification, and control. Proceedings of the IEEE2004; 92(3):423-438. |
| [15] | KadirkamanathanV, LiP, JawardMH, FabriSG. Particle filtering‐based fault detection in non‐linear stochastic systems. International Journal of Systems Science2002; 33(4):259-265. · Zbl 1012.93064 |
| [16] | LiP, KadirkamanathanV. Particle filtering based likelihood ratio approach to fault diagnosis in nonlinear stochastic systems. IEEE Transactions on Systems Man and Cybernetics Part C‐Applications and Reviews2001; 31(3):337-343. |
| [17] | HammouriH, KinnaertM, El YaagoubiEH. Observer‐based approach to fault detection and isolation for nonlinear systems. IEEE Transactions on Automatic Control1999; 44(10):1879-1884. · Zbl 0956.93005 |
| [18] | KozaJR. Genetic Programming. MIT Press: Cambridge, Massachusetts, 1992. |
| [19] | IkedaY, TokinagaS, LuJ. Estimation of link delay distribution based on the genetic programming and network delay tomography and its applications(in Japanese). Journal of the Information Processing Society of Japan2006; 47(SIG1(TOM 14)):12-18. |
| [20] | LuJ, TokinagaS, IkedaY. Explanatory rule extraction based on the trained neural network and the genetic programming. Journal of the Operations Research Society of Japan2006; 49(1):66-82. · Zbl 1111.90325 |
| [21] | LuJ, KishikawaY, TokinagaS. Realization of feature description systems for clusters by rule generation based on genetic programming and its applications. Electronics and Communications in Japan Part Ii‐Electronics2007; 90(9):87-97. |
| [22] | TokinagaS, IkedaY. Chaoticity and multifractality analysis of signal patterns generated through behaviors of agents located on a plane and affected by local interactions (in Japanese). Transactions of the Institute of Electronics, Information and Communication Engineers A2011; J94‐A(6):389-404. |
| [23] | LuJ, TokinagaS. Analysis of cluster formations on planer cells based on genetic programming. Computational and Mathematical Organization Theory2013; 19(4):426-445. |
| [24] | LuJ, TokinagaS. Estimation of state changes in system descriptions for dynamic Bayesian networks by using a genetic procedure and particle filters. Economic Modelling2014; 39:138-145. |
| [25] | MingyiH, BugalloMF, DjuricPM. Joint model selection and parameter estimation by population Monte Carlo simulation. IEEE Journal of Selected Topics in Signal Processing2010; 4(3):526-539. |
| [26] | AndrieuC, DjuricPM, DoucetA. Model selection by MCMC computation. Signal Processing2001; 81(1):19-37. · Zbl 1098.94514 |
| [27] | LarocqueJR, ReillyJP. Reversible jump MCMC for joint detection and estimation of sources in colored noise. IEEE Transactions on Signal Processing2002; 50(2):231-240. |
| [28] | FoxE, SudderthEB, JordanMI, WillskyAS. Bayesian nonparametric inference of switching dynamic linear models. IEEE Transactions on Signal Processing2011; 59(4):1569-1585. |
| [29] | CaronF, DavyM, DoucetA, DuflosE, VanheegheP. Bayesian inference for linear dynamic models with Dirichlet process mixtures. IEEE Transactions on Signal Processing2008; 56(1):71-84. · Zbl 1391.62144 |
| [30] | ParkJ, SandbergIW. Universal approximation using radial‐basis‐function networks. Neural Computation1991; 3(2):246-257. |
| [31] | SchwenkerF, KestlerHA, PalmG. Three learning phases for radial‐basis‐function networks. Neural Networks2001; 14(4‐5):439-458. |
| [32] | LeeHL, PadmanabhanV, WhangSJ. Information distortion in a supply chain: the bullwhip effect. Management Science1997; 43(4):546-558. · Zbl 0888.90047 |
| [33] | LeeHL, SoKC, TangCS. The value of information sharing in a two‐level supply chain. Management Science2000; 46(5):626-643. · Zbl 1231.90044 |
| [34] | SugiharaT. Economic Time Series Analysis with Adaptive Models (Tekiōtekimoderuniyorukeizaijikeiretsubunseki) (in Japanese). Kougakutosho: Tokyo, 1994. |
| [35] | MertensE. Structural shocks and the comovements between output and interest rates. Journal of Economic Dynamics & Control2010; 34(6):1171-1186. · Zbl 1230.91111 |
| [36] | GordonNJ, SalmondDJ, SmithAFM. Novel‐approach to nonlinear non‐Gaussian Bayesian state estimation. IEEE Proceedings‐F Radar and Signal Processing1993; 140(2):107-113. |
| [37] | KarlssonR, GustafssonF. Recursive Bayesian estimation: bearings‐only applications. IEEE Proceedings‐Radar Sonar and Navigation2005; 152(5):305-313. |
| [38] | RenZJ, CohenMA, HoTH, TerwieschC. Information sharing in a long‐term supply chain relationship: the role of customer review strategy. Operations Research2010; 58(1):81-93. · Zbl 1233.90071 |
| [39] | Ministry of Economy Trade and Industry of Japan. Survey of Service Industries in Japan, 2012. |
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