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on Econometric Time Series |
| By: | Pierre Perron (Boston University); Mototsugu Shintaniz (The University of Tokyo); Tomoyoshi Yabu (Keio University) |
| Abstract: | We propose a new procedure to select the unknown frequencies of a trigonometric function, a problem Örst investigated by Anderson (1971) under the assumption of serially uncorrelated noise. We extend the analysis to general linear processes without the prior knowledge of a stationary or integrated model allowing the frequencies to be unknown. We provide a consistent model selection procedure. We Örst show that if we estimate a model with fewer frequencies than those in the correct model, the estimates converge to a subset of the frequencies in the correct model. This opens the way to a consistent model selection strategy based on a speciÖc to general procedure that tests whether additional frequencies are needed. This is achieved using tests based on the feasible ísuper e¢ cientî(under unit root noise) Generalized Least Squares estimator of Perron, Shintani and Yabu (2017) who assumed the frequencies to be known. We show that the limiting distributions of our test statistics are the same for both cases about the noise function. Simulation results conÖrm that our frequency selection procedure works well with sample sizes typically available in practice. We illustrate the usefulness of our method via applications to unemployment rates and global temperature series. |
| Keywords: | Cyclical trends, median-unbiased estimator, nonlinear trends, supere¢ cient estimator, unit root |
| JEL: | C22 |
| Date: | 2020–01 |
| URL: | http://d.repec.org/n?u=RePEc:bos:wpaper:wp2020-012&r=all |
| By: | Mohitosh Kejriwal (Purdue University); Xuewen Yu (Purdue University); Pierre Perron (Boston University) |
| Abstract: | This paper proposes new bootstrap procedures for detecting multiple persistence shifts in a time series driven by nonstationary volatility. The assumed volatility process can accommodate discrete breaks, smooth transition variation as well as trending volatility. We develop wild bootstrap sup-Wald tests of the null hypothesis that the process is either stationary [I(0)] or has a unit root [I(1)] throughout the sample. We also propose a sequential procedure to estimate the number of persistence breaks based on ordering the regime-speciÖc bootstrap p-values. The asymptotic validity of the advocated procedures is established both under the null of stability and a variety of persistence change alternatives. A comparison with existing tests that assume homoskedasticity illustrates the finite sample improvements offered by our methods. An application to OECD ináation rates highlights the empirical relevance of the proposed approach and weakens the case for persistence change relative to existing procedures. |
| Keywords: | heteroskedasticity, multiple structural changes, sequential procedure, unit root, Wald tests, wild bootstrap |
| JEL: | C22 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:bos:wpaper:wp2020-009&r=all |
| By: | Alessandro Casini (University of Rome Tor Vergata); Pierre Perron (Boston University) |
| Abstract: | For a partial structural change in a linear regression model with a single break, we develop a continuous record asymptotic framework to build inference methods for the break date. We have T observations with a sampling frequency h over a fixed time horizon [0, N] , and let T → ∞ with h ↓ 0 while keeping the time span N fixed. We impose very mild regularity conditions on an underlying continuous-time model assumed to generate the data. We consider the least-squares estimate of the break date and establish consistency and convergence rate. We provide a limit theory for shrinking magnitudes of shifts and locally increasing variances. The asymptotic distribution corresponds to the location of the extremum of a function of the quadratic variation of the regressors and of a Gaussian centered martingale process over a certain time interval. We can account for the asymmetric informational content provided by the pre- and post-break regimes and show how the location of the break and shift magnitude are key ingredients in shaping the distribution. We consider a feasible version based on plug-in estimates, which provides a very good approximation to the finite sample distribution. We use the concept of Highest Density Region to construct confidence sets. Overall, our method is reliable and delivers accurate coverage probabilities and relatively short average length of the confidence sets. Importantly, it does so irrespective of the size of the break. |
| Keywords: | Asymptotic distribution, break date, change-point, highest density region, semimartingale |
| JEL: | C10 C12 C22 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:bos:wpaper:wp2020-013&r=all |
| By: | Alessandra Amendola; Vincenzo Candila; Fabrizio Cipollini; Giampiero M. Gallo |
| Abstract: | We suggest the Doubly Multiplicative Error class of models (DMEM) for modeling and forecasting realized volatility, which combines two components accommodating low-, respectively, high-frequency features in the data. We derive the theoretical properties of the Maximum Likelihood and Generalized Method of Moments estimators. Two such models are then proposed, the Component-MEM, which uses daily data for both components, and the MEM-MIDAS, which exploits the logic of MIxed-DAta Sampling (MIDAS). The empirical application involves the S&P 500, NASDAQ, FTSE 100 and Hang Seng indices: irrespective of the market, both DMEM's outperform the HAR and other relevant GARCH-type models. |
| Date: | 2020–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2006.03458&r=all |
| By: | Mohitosh Kejriwal (Purdue University); Pierre Perron (Boston University); Xuewen Yu (Purdue University) |
| Abstract: | Kejriwal and Perron (2010, KP) provided a comprehensive treatment for the problem of testing multiple structural changes in cointegrated regression models. A variety of models were considered depending on whether all regression coefficients are allowed to change (pure structural change) or a subset of the coefficients is held Öxed (partial structural change). In this note, we Örst show that the limit distributions of the test statistics in the latter case are not invariant to changes in the coe¢ cients not being tested; in fact, they diverge as the sample size increases. To address this issue, we propose a simple two step procedure to test for partial parameter stability. The Örst entails the application of a joint test of stability for all coe¢ cients as in KP. Upon a rejection, the second conducts a stability test on the subset of coe¢ cients of interest while allowing the other coe¢ cients to change at the estimated breakpoints. Its limit distribution is standard chi-square. The relevant asymptotic theory is provided along with simulations that illustrates the usefulness of the procedure in finite samples. |
| Keywords: | cointegration, partial structural change, break date, sup-Wald tests, joint hypothesis testing |
| JEL: | C22 |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:bos:wpaper:wp2020-011&r=all |
| By: | Rustam Ibragimov; Rasmus Pedersen; Anton Skrobotov |
| Abstract: | Many key variables in finance, economics and risk management, including financial returns and foreign exchange rates, exhibit nonlinear dependence, heterogeneity and heavy-tailedness of some usually largely unknown type. The presence of non-linear dependence (usually modelled using GARCH-type dynamics) and heavy-tailedness may make problematic the analysis of (non-)efficiency, volatility clustering and predictive regressions in economic and financial markets using traditional approaches that appeal to asymptotic normality of sample autocorrelation functions (ACFs) of returns and their squares. The paper presents several new approaches to deal with the above problems. We provide the results that motivate the use of measures of market (non-)efficiency, volatility clustering and nonlinear dependence based on (small) powers of absolute returns and their signed versions. The paper provides asymptotic theory for sample analogues of the above measures in the case of general time series, including GARCH-type processes. It further develops new approaches to robust inference on them in the case of general GARCH-type processes exhibiting heavy-tailedness properties. The approaches are based on robust inference methods exploiting conservativeness properties of t-statistics Ibragimov and Muller (2010,2016) and several new results on their applicability in the settings considered. In the approaches, estimates of parameters of interest are computed for groups of data and the inference is based on t-statistics in resulting group estimates. This results in valid robust inference under a wide range of heterogeneity and dependence assumptions satisfied in financial and economic markets. Numerical results and empirical applications confirm advantages of the new approaches over existing ones and their wide applicability. |
| Date: | 2020–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2006.01212&r=all |
| By: | Sander Barendse; Andrew J. Patton |
| Abstract: | We develop tests for out-of-sample forecast comparisons based on loss functions that contain shape parameters. Examples include comparisons using average utility across a range of values for the level of risk aversion, comparisons of forecast accuracy using characteristics of a portfolio return across a range of values for the portfolio weight vector, and comparisons using a recently-proposed “Murphy diagrams†for classes of consistent scoring rules. An extensive Monte Carlo study verifies that our tests have good size and power properties in realistic sample sizes, particularly when compared with existing methods which break down when then number of values considered for the shape parameter grows. We present three empirical illustrations of the new test. |
| Keywords: | Forecasting, model selection, out-of-sample testing, nuisance parameters |
| JEL: | C53 C52 C12 |
| Date: | 2020–05–27 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:909&r=all |