Diebold, F. X. and M. Nerlove (1989). The dynamics of exchange rate volatility: a multivariate latent factor ARCH model. Journal of Applied Econometrics 4, 1--21.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....with independent Gaussian error. So we have y t # t # N(# t , # 2 ) # t 1 # t # N(0, # 0 # 1 # 2 t ) This model is exactly adaptable. It has received a great deal of attention in the econometric literature as it has some attractive multivariate generalizations: see the work by Diebold and Nerlove (1989), Harvey, Ruiz, and Sentana (1992) and King, Sentana, and Wadhwani (1994) As far as we know no likelihood methods exist in the literature for the analysis of this type of model (and its various generalizations) although a number of very good approximations have been suggested. Extended example: ....

Diebold, F. X. and M. Nerlove (1989). The dynamics of exchange rate volatility: a multivariate latent factor ARCH model. J. Appl. Econometrics 4, 1--21.

....of K orthogonal linear combinations of y t ; 31] suggested a simple two stage estimation procedure for this model; 11] gave conditions for covariance stationarity of the K factor GARCH models and showed how multivariate IGARCH models allow for the possibility of co persistence in variance. [25] proposed a latent factor model in which the common movements in volatility are represented by a single unobserved latent factor subject to ARCH e ect; later, 49] replaced the ARCH process with an SV process. 47] discussed using MCMC methods on the factor volatility model in which both the ....

F X Diebold and M Nerlove. The dynamics of exchange rate volatility: A multivariate latent ARCH model. Journal of Applied Econometrics, 4:1-21, 1989. 125

....A major aim of this paper is to overcome these problems and demonstrate a unified fitting and inference framework for truly high dimensional models of stochastic volatility. Previous work on multivariate models of volatility has been reported by Bollerslev, Engle, and Wooldridge (1988) Diebold and Nerlove (1989), Bollerslev (1990) Engle, Ng, and Rothschild (1990) Lin (1992) King, Sentana, and Wadhwani (1994) Engle and Kroner (1995) Braun, Nelson, and Sunier (1995) within the ARCH GARCH tradition, and by Harvey, Ruiz, and Shephard (1994) Jacquier, Polson, and Rossi (1995) Pitt and Shephard (1999b) ....

....5. Goto step 2 and repeat. Stochastic Volatility in Factor (SVF) model. Under this model, y t jB; f t N p (Bf t ; V ) f t jh t N k (0; D t ) h jt Gamma j = OE j (h jt Gamma1 Gamma j ) oe j j jt ; j k where the variances of the y t are constant. This model is similar to that of Diebold and Nerlove (1989) where an ARCH process was specified to generate volatility clustering. It has also been studied by Jacquier, Polson, and Rossi (1995) and at more length by Aguilar and West (1998) Under this simplified model, if k p then it becomes possible to find linear combinations (portfolios in financial ....

Diebold, F. X. and M. Nerlove (1989). The dynamics of exchange rate volatility: a multivariate latent factor ARCH model. J. Applied Econometrics 4, 1--21.

....not the pound. Engle Bollerslev (1986, p. 24) note slow decay in the correlation structure of the Swiss franc US dollar exchange rate. They attribute the phenomenon to persistence in the ARCH process. That is, shocks to the variance tend to have lingering effects over time. 18 See for example Diebold Nerlove (1985) Engle Bollerslev (1986), and Baillie Bollerslev (July 1987) 54 54 3.4. Estimation by ARCH In Mean Solutions to the maximum likelihood functions of the ARCH in Mean models for the three countries are found by making use of the Berndt, Hall, Hall, Hausman (1974) algorithm. 19 The results are shown in Table 3.5. The ....

Diebold, Francis X. and Marc Nerlove. The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor ARCH Model. Special Studies Paper of the Federal Reserve Board; November 1986; Z.11(255).

....results for the general multivariate GARCH(p; q) process in vector speci cation. This speci cation nests all popular linear speci cations such as the BEKK speci cation of Engle and Kroner (1995) the constant conditional correlation model of Bollerslev (1990) and the factor GARCH models of Diebold and Nerlove (1989) and Engle, Ng and Rothschild (1990) In Section 2, we provide explicit results for the case of Gaussian innovations. In Section 3, we discuss the relationship between the (co )kurtosis and measures for conditional heteroskedasticity. Furthermore, impulse response functions are de ned for the ....

Diebold, F.X. & M. Nerlove (1989) The dynamics of exchange rate volatility: a multivariate latent factor ARCH model. Journal of Applied Econometrics 4, 1-21.

....It constitutes a factor style model with a common, but differently scaled, stochastic volatility model and individual stochastic volatility models for each series. It generalizes straightforwardly to allow for two or more factors. This style of model is in keeping with the latent factor models of Diebold and Nerlove (1989), King, Sentana, and Wadhwani (1994) Pitt and Shephard (1999b) and Chib, Nardari, and Shephard (1999) Its motivation is that in financial assets it is often the case that returns move together, with a few common driving mechanisms. The common factors allow us to pick this up in a straightforward ....

Diebold, F. X. and M. Nerlove (1989). The dynamics of exchange rate volatility: a multivariate latent factor ARCH model. J. Applied Econometrics 4, 1--21.

....model. While such studies can yield interesting insights, they hardly constitute a theoretical explanation of ARCH. There have been several hypotheses put forth to explain ARCH effects. One such hypothesis holds that serially correlated news arrival drives increases in variance (see, for example, Diebold and Nerlove [1989] or Gallant, Hsieh and Tauchen [1989] for details) While this is plausible on its face, is poses the obvious question as to why the information arrival process should be serially correlated. Other researchers (Stock [1987, 1988] have examined time deformations that can occur when calendar time ....

Diebold, F. X. and M. Nerlove, The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor ARCH Model. Journal of Applied Econometrics, 4 (1989), 1-21.

.... This conditional heteroscedastic structure is well adapted to reproduce the alternating periods of volatility and smoothness characterizing excess returns behavior (Bollerslev; Chou; and Kroner 1992) and is more parsimonious than alternative commonly used large scale multivariate specifications (Diebold and Nerlove 1989; Engle; Ng; and Rothschild 1990; Ng; Engle; and Rothschild 1992; Normandin and St Amour 1998) Furthermore; as will be explained below; the explicit account of conditional heteroscedastic behavior is crucial for the statistical identification of domestic and foreign risk prices; which are ....

Diebold; F.X.; and M. Nerlove (1989); "The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor ARCH Model;" Journal of Applied Econometrics 4; pp. 1--21.

....introduce some constraints in order to make this number smaller. A natural approach, compatible with the needs of financial theory and with some features of financial series which often have common evolution in the volatilities, leads to the introduction of unobserved factors (Diebold and Nerlove [7], Engle, Ng and Rothschild [12] For simplicity and identifiability reasons, the original representation (30) is reduced to: y t = 1 fiy 2 t Gamma1 ) 1=2 t t N(0; 1) y t = ay t t t N p (0; oe 2 I p ) 43) and the dimension of y t is p = 2. As far as the ....

....reasons, the original representation (30) is reduced to: y t = 1 fiy 2 t Gamma1 ) 1=2 t t N(0; 1) y t = ay t t t N p (0; oe 2 I p ) 43) and the dimension of y t is p = 2. As far as the estimation of this model is concerned Diebold and Nerlove [7] propose to apply the extended Kalman filter, which leads to some approximations, while Gouri eroux, Monfort and Renault [21] suggest the indirect inference approach. The implementation of the Metropolis Hastings simulation from f(y T jy T ; exp ( Gamma T X t=1 jjy t Gamma ay ....

Diebold, D. and Nerlove, M., The dynamic of exchange rate volatility: a multivariate latent factor ARCH model, Journal of Applied Econometrics, 4, 1-22, 1989.

....modeling and forecasting of realized volatility may prove useful, as factor structure is central to both empirical and theoretical financial economics. Previous research on factor volatility models has typically relied on complex procedures involving a latent volatility factor, as for example in Diebold and Nerlove (1989), Engle, Ng and Rothschild (1990) and King, Sentana and Wadhwani (1994) In contrast, factor analysis of realized volatility should be relatively straightforward, even in highdimensional environments. Moreover, the identification of explicit volatility factors, and associated market wide ....

Diebold, F.X. and M. Nerlove (1989), "The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor ARCH Model," Journal of Applied Econometrics, 4, 1-22.

....Qcov kj (t) the integrated covariance. As a special case of this framework, one may assign a few of the orthogonal Wiener components to be common factors and the remaining as pure idiosyncratic error terms. This produces a continuous time analogue to the discrete time factor volatility models of Diebold and Nerlove (1989) and King, Sentana and Wadhwani (1994) Within this pure diffusion setting, one may obtain stronger results. Foster and Nelson (1996) construct a volatility filter based on a weighted average of past squared returns, which extracts the instantaneous volatility perfectly in the continuous record ....

....of Figure 2, clearly indicate a strong positive association between the two exchange rate volatilities. Thus, not only do the two exchange rates tend to move together, as indicated by the positive means for cov t and corr t , but so too do their volatilities. This suggests factor structure, as in Diebold and Nerlove (1989) and Bollerslev and Engle (1993) The cor relations in the fir st panel of T able 2 and the corr t lstdd t and corr lstdy t scatterplots in t he second and third panels of Figure 2 also indicate positive association between correlation and volatility. Whereas some nonlinea rity may be operat ....

Diebold, F.X., and Nerlove, M. (1989), "The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor ARCH Model," Journal of Applied Econometrics, 4, 1-22.

....concept, while F kj, t) t) is denoted the integrated covariance. As a special case, one may dedicate a few orthogonal Wiener components to be common factors while others serve as idiosyncratic error terms, providing a continuoustime analogue to the discrete time latent factor volatility model in Diebold and Nerlove (1989). Of course, integrated volatilities are inherently unobservable. Gallant, Hsu and Tauchen (1999) propose an intriguing reprojection method for estimating the distribution of F k 2 , h) t) see also Chernov and Ghysels, 1998) but it relies on specific parametric assumptions. Motivated by (11) ....

....volatilities. Thus, not only do the two exchange rates tend to move together, as indicated by the positive means for cov t and corr t , but their volatilities are also closely linked. This provides empirical justification for the use of multivariate volatility models with a factor structure, as in Diebold and Nerlove (1989) and Bollerslev and Engle (1993) The correlation figures in Table 2 along with the corr t lstdd t scatterplot in the second panel of Figure 2 also indicate a positive association between correlation and volatility. To quantify further this volatility effect in correlation, we show in the top ....

Diebold, F.X. and Nerlove, M. (1989), "The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor ARCH Model," Journal of Applied Econometrics, 4, 1-22.

....higher, 2) 460K of free memory for the DOS version and 100K of free memory and 1.2M of free extended memory for the 386 version, 3) 3M free hard disk space, and (4) Hercules, CGA, MCGA, EGA, VGA, or Super VGA video card. 1. Introduction and Overview Having reviewed an earlier version of STAMP (Diebold, 1989) and the underlying statistical theory (Diebold, 1992) it s a pleasure to continue the tradition with a review of STAMP version 5.0. STAMP (Structural Time Series Analyser, Modeller and Predictor) provides tools for modeling and forecasting time series using unobserved component (UC) models, in ....

....in state space form from the outset, of which 18traditional unobserved components models are only one example. Other s include stochastic volatility models (e.g. Taylor, 1986) regime switching models (e.g. Hamilton, 1989) and related multivariate models with latent factor structure (e.g. Diebold and Nerlove, 1989, and Diebold and Rudebusch, 1996) 4) As the list of models implemented in STAMP grows, so too should the list of estimation methods. In particular, the nonlinear models listed in (3) above have challenging likelihood structures, and Markov chain Monte Carlo methods are proving useful for ....

Diebold, F.X. and M. Nerlove, 1989, "The Dynamics of Exchange Rate Volatility: A Multivariate Latent-Factor ARCH Model," Journal of Applied Econometrics, 4, 1-22.

....terms of DM and Yen, i.e. DM and Yen . 6 contains the N individual square integrable mutually independent asset specific stochastic volatilities. This continuous time latent factor formulation directly parallels the idea behind the discrete time latentfactor volatility models proposed by Diebold and Nerlove (1989) and King, Sentana and Wadhwani (1994) The generalization to multiple common factors would be conceptually straightforward, but notationally more cumbersome. Other more complicated multivariate continuous time models could also be considered. However, the simple structure in equation (7) conveys ....

.... Nelson (1991) Campbell and Hentschel (1992) and Bekaert and Wu (1997) 13 volatility model in equation (7) More generally, however, the positive volatility correlation provides the empirical justification for the use of multivariate volatility models with factor structure, as suggested by Diebold and Nerlove (1989), Engle, Ng and Rothschild (1990) Bollerslev and Engle (1993) and King, Sentana and Wadhwani (1994) The correlations in Table 2 and the corr t lstdd t and corr t lstdy t scatterplots in Figure 4 also indicate positive association between correlation and volatility. Whereas some nonlinearity ....

Diebold, F.X. and M. Nerlove (1989), "The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor ARCH Model," Journal of Applied Econometrics, 4, 1-22.

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Diebold, F. X. and M. Nerlove (1989). The dynamics of exchange rate volatility: a multivariate latent factor ARCH model. Journal of Applied Econometrics 4, 1--21.

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Biometrika 81, 541#53. 18 Diebold, F. X. and M. Nerlove #1989#. The dynamics of exchange rate volatility: a multivariate latent factor ARCH model. J. Applied Econometrics 4, 1#21.

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Diebold, F.X., and Nerlove, M., "The Dynamics of Exchange Rate Volatility: A Multiva riate Latent Factor ARCH Model." Journal of Applied Econometrics, Vol. 4, pp. 1-21. Dixon, W.J. (Chief Editor), BMDP Statistical Software Manual, Vol. 2. Berkeley, California: University of California Press, 1990.

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Diebold, F. X., M. Nerlove, (1989), The Dynamics of Exchange Rate Volatility: A Multivariate Latent-Factor ARCH Model, Journal of Applied Econometrics, 4, 1-22.

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Diebold F.X and M. Nerlove (1989), The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor ARCH Model, Journal of Applied Econometrics, 4, 1-21.

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Biometrika 82, 339--50. Diebold, F. X. and M. Nerlove (1989). The dynamics of exchange rate volatility: a multivariate latent factor ARCH model. J. Appl. Econometrics 4, 1--21.

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Diebold, F.X. and Nerlove, M. (1989). The dynamics of exchange rate volatility: A multivariate latent factor ARCH model, Journal of Applied Econometrics 4, 1--21.

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