Hansen, B.E. "The Likelihood Ratio Test under Nonstandard Conditions: Testing the Markov Switching model of GDP." Journal of Applied Econometrics, 7 (1992), 61-82.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....based on this specification test can be directly compared across di#erent structural models to identify the best model specification. 7 It is well recognized in the literature, that tests for the absence of regime shifts against a regime shifting alternative require nonstandard approaches (see Hansen (1992) and Garcia (1992) Our approach of comparing all the considered models to a common non parametric density (the SNP density) allows us to rank order all the considered models according to the p values implied by the EMM criterion function. The advantage of using the non parametric SNP is that it ....

Hansen, Bruce E. (1992), "The Likelihood Ratio Test under Non-Standard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics, vol. 7, s61--s82.

....switching in the degrees of freedom parameters and g would be appropriate. But, the GARCH model suggests that switching in the mean cannot be taken for granted, so likelihood ratio tests cannot assume that the transition probabilities are identified under the null of no state switching in v or g. Hansen (1992) has discussed simulation methods to derive critical values for such likelihood ratio tests with nonstandard distributions. The critical values are computationally burdensome to calculate, however, so we do not pursue that strategy here. Instead, we follow Vlaar and Palm (1993) by using a ....

Hansen, B.E. (1992), "The Likelihood Ratio Test under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics 7, S61-S82.

....phase. Thus, Friedman s view is that recessions are entirely transitory deviations from trend, not movements in the trend itself. 2 Both forms of asymmetry have received substantial attention in the empirical literature, with conflicting conclusions. Using classical likelihood based tests, Hansen (1992) and Garcia (1998) both fail to reject a linear autoregressive model in favor of Hamilton s model for U.S. GNP. Kim and Nelson (1999c) reach a similar conclusion using Bayesian methods. On the other hand, both Chib (1995) and Koop and Potter (1999) find evidence in favor of Hamilton s model using ....

....is troubled by the familiar Davies (1977) problem, in which a nuisance parameter is not identified under the null hypothesis. Hamilton s original paper offers suggestive evidence that the two state Markov switching model outperforms linear models in terms of forecasts, but no statistical tests. Hansen (1992) and Garcia (1998) use classical likelihood based test procedures designed to deal with the Davies problem and find that linear autoregressive models cannot be rejected for real GNP. Kim and Nelson (1999a) confirm this result using Bayesian techniques. Also using Bayesian techniques, Chib (1995) ....

Hansen, B.E., 1992, The likelihood ratio test under nonstandard conditions: testing the Markov switching model of GNP, Journal of Applied Econometrics 7, S61-S82.

....has N Gamma 1 states. Then, under the null hypothesis, the parameters that describe the Nth state are unidentied, and hence the information matrix is singular. To overcome the identication problem, several alternatives for the LRT have been proposed, including the tests that bound the exact LR (Hansen, 1992, 1996) or approximate it by parametric bootstrap (Ryd#n et al. 1998) Also, the use of penalized likelihood methods (Leroux Puterman, 1992; Ryd#n, 1995) the Lagrange multiplier principle (Hamilton, 1996) Bayesian inference (Robert, Ryd#n, Titterington, 2000) and covariance function of a ....

Hansen, B. E. (1992). The likelihood ratio test under nonstandard conditions: testing the Markov switching model of GNP. Journal of Applied Econometrics, 7, S61S82.

....periods and a value of zero during recessions. Hamilton also provided an algorithm for estimating the probability of a recession at each time period based on a maximum likelihood approach. Since that time, several other authors have investigated modifications to the model specification (Lam, 1990; Hansen, 1992; Kim, 1994) computation of the recession probabilities (Albert and Chib, 1993) and the application of the models to various other data sources (Cecchetti et al., 1990; Hamilton and Lin, 1996) In this paper we propose a new model based on the structural time series model underlying exponential ....

Hansen B. E. (1992): "The Likelihood Ratio Test Under Nonstandard Conditions: Testing The Markov Switching Model of GNP", Journal of Applied Econometrics, V7, pp S61-S82.

...., i.e. Since the state variable is unobservable, it is usually assumed that evolves as a first order Markov chain: 1) for p ij PP9p ij R t t81 t E(R t ) 9X t 67x 1 (R t#1 8X t#1 6)7 . 7x q (R t#q 8X t#q 6) X t I i,t i 91,2, k 6 I i,t S t 9 i (x,6,P) Hansen (1990) suggests an alternative test of the model. However, this type of test involves the 3 difficult issue of unidentified parameters under the alternative and it is far more complex than the AIC model selection procedure. 3 where the form the transition probability matrix , These are the ....

Hansen, Bruce E. 1990, The Likelihood Ratio Test Under Nonstandard Conditions: Testing the Markov Switching Model of GNP, Journal of Applied Econometrics 7, S61-S82.

....the critical values and indicate the significance of the second regime. Moreover, the t statistics on the variance parameters are large, especially for the JPY and GBP, indicating that the variance is significantly different in each regime. The same cannot be said for the mean parameters. 3 See Hansen (1992) for a LR procedure that overcomes this difficulty. 10 The four regime model allows the mean and variance regimes to switch independently. This additional flexibility increases the log likelihood value for all three currencies. Again, the LR test is not formal because of the identification ....

Hansen, B.E., 1992, The likelihood ratio test under nonstandard conditions: testing the Markov switching model of GNP, Journal of Applied Econometrics 7, S61-S82.

....the estimates of unexplained long horizon predictability are all statistically insignificant at conventional levels. Testing the Markovian specification of regime switching is hindered by the failure of several assumptions of standard asymptotic distribution theory. Notably, as discussed in Hansen (1992) and Garcia (1998) the transition probabilities q and p are not identified under a null hypothesis of a constant mean and variance. Since the distribution of test statistics are model and data dependent, Hansen argues for the use of computationally intensive simulations to determine the small ....

Hansen, B.E., 1992, "The Likelihood Ratio Test Under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics 7, S61-S82.

....Thus, Friedman s view is that recessions are entirely transitory deviations from trend, not movements in the trend itself. 4 Both forms of asymmetry have received substantial amounts of attention in the empirical literature, with conflicting conclusions. Using classical likelihood based tests, Hansen (1992) and Garcia (1998) both fail to reject a linear autoregressive model in favor of Hamilton s model for U.S. GNP. Kim and Nelson (1999c) reach a similar conclusion using Bayesian methods. On the other hand, both Chib (1995) and Koop and Potter (1999) find evidence in favor of Hamilton s model using ....

....is troubled by the familiar Davies (1977) problem, in which a nuisance parameter is not identified under the null hypothesis. Hamilton s original paper offers suggestive evidence that the two state Markov switching model outperforms linear models in terms of forecasts, but no statistical tests. Hansen (1992) and Garcia (1998) use classical likelihood based test procedures designed to deal with the Davies problem and find that linear autoregressive models cannot be rejected for real GNP. Kim and Nelson (1999a) confirm this result using Bayesian techniques. Also using Bayesian techniques, Chib (1995) ....

Hansen, B.E. (1992), `The likelihood ratio test under nonstandard conditions: testing the Markov switching model of GNP', Journal of Applied Econometrics, 7, S61-S82.

....specification. Furthermore, the estimates of predictability are all statistically insignificant at conventional levels. Testing the Markovian specification of regime switching is hindered by the failure of several assumptions of standard asymptotic distribution theory. Notably, as discussed in Hansen (1992) and Garcia (1998) the transition probabilities q and p are not identified under a null hypothesis of a constant mean and variance. Since the distribution of test statistics are model and data dependent, Hansen argues for the use of computationally intensive simulations to determine the small ....

Hansen, B.E., 1992, "The Likelihood Ratio Test Under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics 7, S61-S82.

....Second, we examine whether stock market returns are predictable even after accounting for Markov switching behaviour. Third, we examine whether the transition probabilities of the Markov chain vary over time in response to changes in economic variables. Finally, our paper uses the new tests of Hansen (1992,1993) and Garcia (1992) to determine whether the evidence of switching is statistically significant. Our paper is organized as follows. Section II examines whether there are distinct regimes in stock market returns. Section III estimates diffferent specifications of switching behaviour. Section ....

....hypothesis of switching. The problem is that the transition probabilities are not identified under the null hypothesis of no switching. Under these circumstances, the asymptotic distributions of likelihood ratio, Lagrange multiplier, and Wald tests are non standard. Recent econometric work by Hansen (1992,1993) has suggested a method for calculating the non standard asymptotic distribution. Garcia (1992) shows how Hansen s work can be applied to the problem of testing for Markov switching by treating the transition probabilities as nuisance parameters. To determine whether there is switching in ....

[Article contains additional citation context not shown here]

Hansen, B. E. (1992), "The Likelihood Ratio Test Under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics, Vol. 7,S61-S82.

....show that there is strong economic evidence of asymmetries in stock returns. However, they do not prove that asymmetries are statistically signicant. In Table III we report a set of likelihood ratio tests for the existence of two states in the conditional mean and variance. As pointed out by Hansen (1992), the standard likelihood ratio test for multiple states is not appropriate in this context since the transition probability parameters are 17 not identied under the null of a single state. Thus in the test for asymmetries in the conditional mean we condition on the existence of two states in the ....

Hansen, Bruce E., 1992, The likelihood ratio test under nonstandard conditions: testing the Markov switching model of GNP, Journal of Applied Econometrics 7, S61-S82.

....the unobserved Markov switching variables. We then write the variance of each observed series as: 6 Under the null hypothesis that l i =0 for all i, the parameters associated with common transitory component x t in equation (3.9) are not identified. While such problem has received attention from Hansen (1992, 1996) and Garcia (1998) the distribution of the test statistic in the presence of nuisance parameters that exist only under the alternative hypothesis is unknown for the state space model we are dealing with. However, the individual hypothesis that l i =0 for one i does not render any ....

Hansen, B.E., " The Likelihood Ratio Test under Non-Standard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics 7 (1992), S61S82.

....after floor trading in Germany has closed at 13:30h Frankfurt time. At this point of time he knows this day s USD fixing, the closing prices of the German stock and bond markets, and yesterday s closing of the US stock market. Therefore we lag observations of the DJI once. 10 Hamilton (1996) and Hansen (1992) report similar results. 11 So far, we have not considered any further adjustments, as described for instance in Efron and Tibshirani (1986, Sec. 7) 12 cf. e.g. Kuensch (1989) Period Mean Std. Dev. Skewness Kurtosis Percentile 5 95 DAX 1987 88 0.02 1.60 0.85 10.20 2.55 1.96 1994 95 0.00 ....

Hansen, B. E. (1992): "The Likelihood Ratio Test Under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics, 7, S61--S82.

....among states can also be used to model the time dependency of regime switching. Poritz (1982) first combined hidden Markov models with linear prediction. Hamilton (1990) introduced switching models to economics and econometrics, spawning a large body of research (Engel and Hamilton 1990, Hansen 1992, Durland and McCurdy 1994, Hamilton 1994, Lahiri and Wang 1994) Most of these applications focus on point predictions but not on densities. Fraser and Dimitriadis (1994) predicting one of the data sets of the Santa Fe Competition (Weigend and Gershenfeld 1994) used a hidden Markov model and ....

Hansen, B. E. (1992). The likelihood ratio test under nonstandard conditions: Testing the Markov switching model of GNP, Journal of Applied Economics 7: s61--s82.

....in a different context by Fildes and Makridakis (1995) 2 stage are then evaluated. The MS AR model that we consider is based on the model of Hamilton (1989) which has been extensively discussed in the literature, and has been tested against a linear autoregressive model (AR model) by e.g. Hansen (1992, 1996a) The SETAR model of US GNP is similar to the models of Tiao and Tsay (1994) and Potter (1995) which have been formally tested by Hansen (1996b) The methods of model specification, estimation and forecasting for SETAR and MS AR models are briefly described in sections 3 and 4. For ....

....turning points. In contrast to the two regime model, all three regimes are reasonably persistent. We include this model in the empirical forecast comparison. 4.4 Testing for more than 1 regime: the MS AR model Results of formal tests of the MS AR model against AR models have been at best mixed. Hansen (1992, 1996a) is unable to reject an AR(4) in favour of Hamilton s model (on the Hamilton data) using a standardized LR test designed to deliver (asymptotically) valid inference. Conventional testing approaches are not applicable due to the presence of unidentified nuisance parameters under the null of ....

[Article contains additional citation context not shown here]

Hansen, B. E. (1992). The likelihood ratio test under nonstandard conditions: testing the Markov switching model of GNP. Journal of Applied Econometrics, 7, S61--S82.

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Hansen, B.E. "The Likelihood Ratio Test under Nonstandard Conditions: Testing the Markov Switching model of GDP." Journal of Applied Econometrics, 7 (1992), 61-82.

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Hansen, B.E. (1992), The likelihood ratio test under nonstandard conditions: testing the Markov Switching model of GDP, Journal of Applied Econometrics, Vol. 7, pp. 61-82.

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Hansen, B.E. (1992), "The likelihood ratio test under nonstandard conditions: testing the Markov switching model of GNP", J. App. Econometrics, 70, 127-157. 29

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Hansen, B. E., 1992, "The Likelihood Ratio Test under Nonstandard Conditions: Testing the Markov Switching Model of GNP", Journal of Applied Econometrics, 7, 61-82.

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Hansen, B. E., 1992, \The Likelihood Ratio Test Under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics, Vol. 7, S61-S82.

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Hansen, B. E., 1992, \The Likelihood Ratio Test Under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics, Vol. 7, S61-S82.

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Hansen, B. E., 1992b, \The Likelihood Ratio Test Under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics, Vol. 18 7, S61-S82.

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Hansen, B. E., 1992, "The Likelihood Ratio Test Under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics, Vol. 7, S61-S82.

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