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on Econometric Time Series |
| By: | Joshua C.C. Chan |
| Abstract: | Time-varying parameter VARs with stochastic volatility are routinely used for structural analysis and forecasting in settings involving a few macroeconomic variables. Applying these models to high-dimensional datasets has proved to be challenging due to intensive computations and over-parameterization concerns. We develop an efficient Bayesian sparsification method for a class of models we call hybrid TVP-VARs - VARs with time-varying parameters in some equations but constant coefficients in others. Specifically, for each equation, the new method automatically decides (i) whether the VAR coefficients are constant or time-varying, and (ii) whether the error variance is constant or has a stochastic volatility specification. Using US datasets of various dimensions, we find evidence that the VAR coefficients and error variances in some, but not all, equations are time varying. These large hybrid TVP-VARs also forecast better than standard benchmarks. |
| Keywords: | large vector autoregression, time-varying parameter, stochastic volatility, trend output growth, macroeconomic forecasting |
| JEL: | C11 C52 E37 E47 |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2019-77&r=all |
| By: | Atefeh Zamani; Hossein Haghbin; Maryam Hashemi; Rob J Hyndman |
| Abstract: | Functional autoregressive models are popular for functional time series analysis, but the standard formulation fails to address seasonal behaviour in functional time series data. To overcome this shortcoming, we introduce seasonal functional autoregressive time series models. For the model of order one, we derive sufficient stationarity conditions and limiting behavior, and provide estimation and prediction methods. Some properties of the general order P model are also presented. The merits of these models are demonstrated using simulation studies and via an application to real data. |
| Keywords: | functional time series analysis, seasonal functional autoregressive model, central limit theorem, prediction, estimation |
| JEL: | C32 C14 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2019-16&r=all |
| By: | Beaumont, Paul; Smallwood, Aaron |
| Abstract: | Despite a recent proliferation of research using cyclical long memory, surprisingly little is known regarding the asymptotic properties of likelihood-based methods. Estimators have been studied in both the time and frequency domains for the Gegenbauer autoregressive moving average process (GARMA). However, a full set of asymptotic results for all parameters has only been proposed by Chung (1996a,b), who present somewhat tenuous results without an initial consistency proof. In this paper, we review the GARMA process and the properties of frequency and time domain likelihood-based estimators using Monte Carlo analysis. The results demonstrate the strong efficacy of both estimators and generally sup- port the proposed theory of Chung for the parameter governing the cycle length. Important caveats await. The results show that asymptotic confidence bands can be unreliable in very small samples under weak long memory, and the distribution theory under the null of an infinitely long cycle appears to be unusable. Possible solutions are proposed, including the use of narrower confidence bands and the application of theory under the alternative of finite cycles. |
| Keywords: | long memory, GARMA, CSS estimator, Whittle estimator |
| JEL: | C22 C4 C40 C5 |
| Date: | 2019–09–30 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:96313&r=all |
| By: | Hecq, Alain; Issler, João Victor; Telg, Sean |
| Abstract: | The mixed causal-noncausal autoregressive (MAR) model has been proposed to estimate time series processes involving explosive roots in the autoregressive part, as it allows for stationary forward and backward solutions. Possible exogenous variables are substituted into the error term to ensure the univariate MAR structure of the variable of interest. To study the impact of fundamental exogenous variables directly, we instead consider a MARX representation which allows for the inclusion of exogenous regressors. We argue that, contrary to MAR models, MARX models might be identified using second-order properties. The asymptotic distribution of the MARX parameters is derived assuming a class of nonGaussian densities. We assume a Student’s t-likelihood to derive closed form solutions of the corresponding standard errors. By means of Monte Carlo simulations, we evaluate the accuracy of MARX model selection based on information criteria. We examine the influence of the U.S. exchange rate and industrial production index on several commodity prices. |
| Date: | 2019–10–10 |
| URL: | http://d.repec.org/n?u=RePEc:fgv:epgewp:810&r=all |
| By: | D.S.G. Pollock |
| Abstract: | Econometric analysis requires filtering techniques that are adapted to cater to data sequences that are short and that have strong trends. Whereas the economists have tended to conduct their analyses in the time domain, the engineers have emphasised the frequency domain. This paper places its emphasis in the frequency domain; and it shows how the frequency-domain methods can be adapted to cater to short trended sequences. Working in the frequency domain allows an unrestricted choice to be made of the frequency response of a filter. It also requires that the data should be free of trends. Methods for extracting the trends prior to filtering and for restoring them thereafter are described. |
| Keywords: | Time Series, Fourier Analysis, Sampling, Filtering |
| URL: | http://d.repec.org/n?u=RePEc:lec:leecon:19/08&r=all |
| By: | D.S.G. Pollock |
| Abstract: | The relationship between autoregressive moving-average (ARMA) models in discrete time and the corresponding models in continuous time is examined in this paper. The linear stochastic models that are commonly regarded as the counterparts of the ARMA models are driven by a forcing function that consists of the increments of a Wiener Process. This function is unbounded in frequency. In cases where the periodogram of the data indicates that there is a clear upper bound to its frequency content, we propose an alternative frequency- limited white-noise forcing function. Then, there is a straightforward translation from the ARMA model to a differential equation, which is based of the principle of impulse invariance. Whenever there is no perceptible limit to the frequency content, the translation must be based on a principle of autocovariance equivalence. On the website of the author, there is a computer program that effects both of these discrete-to-continuous translations. |
| URL: | http://d.repec.org/n?u=RePEc:lec:leecon:19/07&r=all |
| By: | Julio-Román, Juan Manuel; Gamboa-Estrada, Fredy Alejandro |
| Abstract: | We study the relationship between daily oil prices and nominal exchange rates between 1995 and 2019 in Colombia through a Time-Varying Vector Auto-Regressions with residual Stochastic Volatility, TV-VAR-SV, model. For this task we also employ co-integration, Univariate Auto-Regressions with residual Stochastic Volatility, UAR-SVTV, and De-trended Cross Correlation, DCC analyses. We found that a stable lon-grun relationship between the two processes is lacking. We also found significant time variation in residual volatility and co-volatility. More specifically, we found that both periods of time, the international financial crisis and the oil price drop of 2015, behave conspicuously different from other “more normal” times. These results are consistent with a shift in the features of the DCC at the start of the crisis. Before the crises the DCCs are positive but weak for different windows sizes, turning negative and significant after it. The latter DCCs and their significance increase with the window size. These results are concurrent, also, with two clearly differentiated periods of time; one when oil production was not financially feasible, and thus production, exports and oil related currency inflows were small, and the other when oil production became feasible because of the price increase, which led to a boom in exploration, production, exports and oil related currency inflows. |
| Keywords: | Nominal Exchange Rate; Oil prices; Small Open Economy; Co-Volatility |
| JEL: | C22 C51 F31 F41 G15 |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:rie:riecdt:22&r=all |