forecasting-macroeconomic-variables-under-model-instability
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forecasting-macroeconomic-variables-under-model-instability
Forecasting Macroeconomic Variables Under Model InstabilityDavide Pettenuzzo Allan TimmermannBrandeis University* * ƯCSD, CEPR, and CREATES142133Abstr forecasting-macroeconomic-variables-under-model-instabilityractWc compare different approaches to accounting for parameter instability in the context of macroeconomic forecasting models that assume cither small, frequent changes versus models whose parameters exhibit large, rare changes. An empirical out-of-sample forecasting exercise for U.S. GDP growt h a forecasting-macroeconomic-variables-under-model-instabilitynd inflation suggests that models that allow for parameter instability generate more accurate density forecasts than constant-parameter models althougforecasting-macroeconomic-variables-under-model-instability
h they fail to produce bettor point forecasts. Model combinations deliver similar gains in predictive performance although they fail to improve on theForecasting Macroeconomic Variables Under Model InstabilityDavide Pettenuzzo Allan TimmermannBrandeis University* * ƯCSD, CEPR, and CREATES142133Abstr forecasting-macroeconomic-variables-under-model-instabilityime-varying parameters; regime switching: change point models; stochastic volatility: GDP growth forecasts; inflation forecasts.JEL classification: C22, C53’Brandeis University, Sachar International Center, 115 South St, Waltham, MA, Tel: (7S1) 736-2834. Email: dpettcnirỉỊbrandeis.edu.* University o forecasting-macroeconomic-variables-under-model-instabilityf California, San Diego, 9500 Gilman Drive, MC 0553, La Jolla CA 92093. Tel: (858) 534-0891. Email: atimmennXtucsd.edu.11 IntroductionParameter instabforecasting-macroeconomic-variables-under-model-instability
ility is pervasive, affecting models used to predict many commonly studied macroeconomic variables (Stock and Watson, 1996; Rossi, 2013). Although manForecasting Macroeconomic Variables Under Model InstabilityDavide Pettenuzzo Allan TimmermannBrandeis University* * ƯCSD, CEPR, and CREATES142133Abstr forecasting-macroeconomic-variables-under-model-instabilitynce of instability into the model specification in order to improve on forecasting models that assume constant parameters.Since many different methods exist, for addressing model instability it. is part icularly important to address if (and how) the assumed form of instability affects the models' ab forecasting-macroeconomic-variables-under-model-instabilityility to generate accurate forecasts. A key question is whether it. is best to assume frequent., but small changes to model parameters or, conversely,forecasting-macroeconomic-variables-under-model-instability
to allow for rare, but large, shifts. The familiar time-varying parameter (TVP) model of Cooley and Prescott (1973) assumes that, the parameters arc Forecasting Macroeconomic Variables Under Model InstabilityDavide Pettenuzzo Allan TimmermannBrandeis University* * ƯCSD, CEPR, and CREATES142133Abstr forecasting-macroeconomic-variables-under-model-instabilityss). The Markov switching (MS) model of Hamilton (1989) assumes that, model parameters switch between a small set of repeated values (states). Detectable regime switches are typically Luge but do not occur every period. The change point (CP) model of Chib (1998) also allows for regime switches but d forecasting-macroeconomic-variables-under-model-instabilityispenses with the assumption that regimes repeal, instead allowing the parameters within each regime to bo unique.Evaluating t he impact of parameterforecasting-macroeconomic-variables-under-model-instability
instability on forecasting performance is important in part because it is difficult to accurately determine the nature of such instability. As pointedForecasting Macroeconomic Variables Under Model InstabilityDavide Pettenuzzo Allan TimmermannBrandeis University* * ƯCSD, CEPR, and CREATES142133Abstr forecasting-macroeconomic-variables-under-model-instabilityejection of the null of stable parameters, which type of model instability (e.g., drifting parameters versus regime switching) characterizes a particular variable. However, whether one faces multiple small breaks versus occasional large breaks could potent ially have Luge consequences for many econo forecasting-macroeconomic-variables-under-model-instabilitymic decisions. For example, the effect on economic welfare of a government 's policy decisions may depend on whether shifts in the underlying GDP growforecasting-macroeconomic-variables-under-model-instability
t h rate occur suddenly or more gradually t hrough t ime.This paper evaluates the mi|M>rlancc for predictive performance of how parameter instability Forecasting Macroeconomic Variables Under Model InstabilityDavide Pettenuzzo Allan TimmermannBrandeis University* * ƯCSD, CEPR, and CREATES142133Abstr forecasting-macroeconomic-variables-under-model-instabilityrly inflation and real GDP growth in the U.S. Both of these series have l>een widely studied; see Chauvet and Potter (2013) ami Faust and Wright (2013) for recent reviews. Wo consider a TVP-stochastic volatility (TVP-SV) model along with MS models with two or three regimes and CP models with up to f forecasting-macroeconomic-variables-under-model-instabilityour different regimes. Using a mean squared error2loss function. we find modest evidence that models that allow for parameter instability can produceforecasting-macroeconomic-variables-under-model-instability
better out-of-sample point forecasts of inflat ion while they do not seem to generate notable gains for the real GDP series. In contrast, we find stroForecasting Macroeconomic Variables Under Model InstabilityDavide Pettenuzzo Allan TimmermannBrandeis University* * ƯCSD, CEPR, and CREATES142133Abstr forecasting-macroeconomic-variables-under-model-instabilityt., homoskedastic model. Moreover, this improvement is mainly due to the ability of time-varying parameter models to generate more accurate density forecasts hl the post 1984 Great Moderation sample. The best performance is observed for the models with stochastic volatility followed by MS and CP mod forecasting-macroeconomic-variables-under-model-instabilityels with three states. Moreover, decompositions of the TVP-SV model’s performance into separate TVP and SV components suggest that it is the ability oforecasting-macroeconomic-variables-under-model-instability
f the models to account for time varying volatility dynamics that leads to the improvements over the linear, homoskedastic benchmark.In a recursive coForecasting Macroeconomic Variables Under Model InstabilityDavide Pettenuzzo Allan TimmermannBrandeis University* * ƯCSD, CEPR, and CREATES142133Abstr forecasting-macroeconomic-variables-under-model-instabilityimal prediction pool of Geweke and Amisano (2011) produce density forecasts that are superior to those generated by the benchmark linear models. However, the model combinations do not perform as well as t he TVP-SV model. Plots of t he recursively computed combinat ion weights tell a clear story. Pr forecasting-macroeconomic-variables-under-model-instabilityior IO 1985, t he linear and CP models receive most of the weights in the combination. TheTVP-SV model rapidly increases in importance after the emergforecasting-macroeconomic-variables-under-model-instability
ence of the Great Moderation, however, and receives a weight above 80% towards the end of t he sample for both the inflation and real GDP series. ThesForecasting Macroeconomic Variables Under Model InstabilityDavide Pettenuzzo Allan TimmermannBrandeis University* * ƯCSD, CEPR, and CREATES142133Abstr forecasting-macroeconomic-variables-under-model-instabilityht the importance of allowing for time-varying volatility.Ot her papers have studied the effect of structural breaks on predictability of macroeconomic t ime series. Bauwens Ct. al. (201 1) provide a comprehensive analysis of the forecasting performance of t wo types of change point models for a ran forecasting-macroeconomic-variables-under-model-instabilityge of macroeconomic series but do not compare TVP, MS and CP models as we do here. Giacomim and Rossi (2009) analyze the detection and prediction of bforecasting-macroeconomic-variables-under-model-instability
reakdowns in forecasting models, whereas Rossi and Sekhposyan (2011) propose now regression-based tests for forecast optimality under model instabilitForecasting Macroeconomic Variables Under Model InstabilityDavide Pettenuzzo Allan TimmermannBrandeis University* * ƯCSD, CEPR, and CREATES142133Abstr forecasting-macroeconomic-variables-under-model-instabilityeeds as follows. Section 2 introduces the benchmark (constant coefficient). TVP-SV. MS and CP models considered in our study and explains how we est imate the models. Sect ion 3 introduces the data on inflation and real GDP growth and presents empirical results for the out of sample forecasting expe forecasting-macroeconomic-variables-under-model-instabilityriment. Section 4 discusses different model combination schemes while Section 5 concludes.32 ModelsThis section introduces the different model specififorecasting-macroeconomic-variables-under-model-instability
cations considered in our study and explains how they are estimated and used to generate forecasts.Our benchmark specification is a linear model with Forecasting Macroeconomic Variables Under Model InstabilityDavide Pettenuzzo Allan TimmermannBrandeis University* * ƯCSD, CEPR, and CREATES142133Abstr forecasting-macroeconomic-variables-under-model-instabilityeters and stochastic volatility (TVP-SV); (ii) a Markov switching (MS) model; and (iii) a change point (CP) model. These specifications are all common ways t o account for parameter inst ability and represent very different ways to approach the problem. Whereas the TVP-SV model lets the parameters o forecasting-macroeconomic-variables-under-model-instabilityf both the first and second moments change every period, the MS and CP models typically identify discrete shifts in the parameters which occur infrequforecasting-macroeconomic-variables-under-model-instability
ently. The MS model assumes (hat a small number of regimes repeat whereas t he CP model assumes t hat the regimes are historically unique. Bot h of thForecasting Macroeconomic Variables Under Model InstabilityDavide Pettenuzzo Allan TimmermannBrandeis University* * ƯCSD, CEPR, and CREATES142133Abstr forecasting-macroeconomic-variables-under-model-instabilityodels will perform best as their performance depends on the nature of any instabilities in the data generat ing process.2.1 Linear modelSuppose we are interested in predicting a univariate variable, Ị/Í+1, given a set of predictors known at time /. xt. As the benchmark specification, we consider a s forecasting-macroeconomic-variables-under-model-instabilitytandard linear forecasting model with constant regression coefficients and constant volatility:.’/?+! =/‘ + 0'Xr +£r+l, £f+l ~JV(0,<7*), T-1-1Here 3 aforecasting-macroeconomic-variables-under-model-instability
nd xr arc k * 1 vectors of regression coefficients and predictors t hat are specific to each empirical application.We assume that the parameters of (1Gọi ngay
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