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on Econometric Time Series |
| By: | Guy Melard |
| Abstract: | In this paper, we establish, in an indirect way, strong consistency and asymptotic normality of a Gaussian quasi-maximum likelihood estimator for the parameters of a causal, invertible, and identifiable vector autoregressive-moving average (VARMA) model. The proof is based on similar results for a much wider class of VARMA models with time-dependent coefficients, thus in the context of non-stationary and non-homoscedastic time series. For that reason, the proof is characterized by avoidanceof spectral analysis arguments and does not make use of ergodicity. The paperis of course also applicable to ARMA models. |
| Keywords: | non-stationary process; multivariate time series; time-varying models; identifiability; ARMA models |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/304272&r=all |
| By: | Bhandari, Avishek |
| Abstract: | This paper seeks to understand the long memory behaviour of global equity returns using novel methods from wavelet analysis. We implement the wavelet based multivariate long memory approach, which possibly is the first application of wavelet based multivariate long memory technique in finance and economics. In doing so, long-run correlation structures among global equity returns are captured within the framework of wavelet-multivariate long memory methods, enabling one to analyze the long-run correlation among several markets exhibiting both similar and dissimilar fractal structures. |
| Keywords: | Long memory, Fractal connectivity, Wavelets, Hurst exponent |
| JEL: | C13 C14 C22 C32 G15 |
| Date: | 2020–04–15 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:99653&r=all |
| By: | Travis J. Berge |
| Abstract: | What is the output gap and when do we know it? A factor stochastic volatility model estimates the common component to forecasts of the output gap produced by the staff of the Federal Reserve, its time-varying volatility, and time-varying, horizon-specific forecast uncertainty. The common factor to these forecasts is highly procyclical, and unexpected increases to the common factor are associated with persistent responses in other macroeconomic variables. However, output gap estimates are very uncertain, even well after the fact. Output gap uncertainty increases around business cycle turning points. Lastly, increased macroeconomic uncertainty, as measured by the output gap's time-varying volatility, produces pronounced negative responses to other macroeconomic variables. |
| Keywords: | Output gap; Unobserved variables; Real-time data; Factor model; Stochastic volatility; Macroeconomic uncertainty |
| JEL: | C53 E32 |
| Date: | 2020–02–03 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgfe:2020-12&r=all |
| By: | Jennifer Castle; Jurgen Doornik; David Hendry |
| Abstract: | Abstract: Seeking substantive relationships among vast numbers of spurious connections when modelling Big Data requires an appropriate approach. Big Data are useful if they can increase the probability that the data generation process is nested in the postulated model, increase the power of specification and mis-specification tests, and yet do not raise the chances of adventitious significance. Simply choosing the best-fitting equation or trying hundreds of empirical fits and selecting a preferred one–perhaps contradicted by others that go unreported–is not going to lead to a useful outcome. Wide-sense non-stationarity (including both distributional shifts and integrated data) must be taken into account. The paper discusses the use of principal components analysis to identify cointegrating relations as a route to handling that aspect of non-stationary big data, along with saturation to handle distributional shifts, and models the monthly UK unemployment rate, using both macroeconomic and Google Trends data, searching over 3000 explanatory variables and yet identifying a parsimonious, well-specified and theoretically interpretable model specification. |
| Keywords: | Cointegration; Big Data; Model Selection; Outliers; Indicator Saturation; Autometrics |
| JEL: | C51 Q54 |
| Date: | 2020–04–15 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:905&r=all |
| By: | André Klein; Guy Melard |
| Abstract: | In this paper the invertibility condition of the asymptotic Fisher information matrix of a controlled vector autoregressive moving average stationary process, VARMAX, is displayed in a theorem. It is shown that the Fisher information matrix of a VARMAX process becomes invertible if the VARMAX matrix polynomials have no common eigenvalue. Contrarily to what was mentioned previously in a VARMA framework, the reciprocal property is untrue. We make use of tensor Sylvester matrices since checking equality of the eigenvalues of matrix polynomials is most easily done in that way. A tensor Sylvester matrix is a block Sylvester matrix with blocks obtained by Kronecker products of the polynomial coefficients by an identity matrix, on the left for one polynomial and on the right for the other one. The results are illustrated by numerical computations. |
| Keywords: | Tensor Sylvester matrix; Matrix polynomial; Common eigenvalues; Fisher in- formation matrix; Stationary VARMAX process |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/304274&r=all |
| By: | Oezer Karagedikli (South East Asian Central Banks (SEACEN)); Ole Rummel (South East Asian Central Banks (SEACEN)) |
| Abstract: | It has been argued that credit-to-GDP gaps (credit gap) are useful early warning indicators for banking crises. In addition, the Basel Committee on Banking Supervision has also advocated using these gaps - estimated using a one-sided Hodrick-Prescott filter with a smoothing parameter of 400,000 - to inform policy on the appropriate counter-cyclical capital buffer. We use the weighted average representation of the same filter and show that it attaches high weights to observations from the past, including the distant past: up to 40 lags (10 years) of past data are used in the calculation of the one-sided trend/permanent component of the credit-to-GDP ratio. We show how past data that belongs to the ‘old-regime’ prior to the crises continue to influence the estimates of the trend for years to come. By using narrative evidence from a number of countries that experienced deep financial crises, we show that this leads to some undesirable influence on the trend estimates that is at odds with the post-crisis environment. |
| JEL: | J31 J64 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:mar:magkse:202022&r=all |
| By: | Elma Hasanovic (Central Bank of Bosnia and Herzegovina) |
| Abstract: | The purpose of this paper is to evaluate the performance of some leading univariate and multivariate models: ARIMA, the standard OLS VAR and Bayesian VAR models, in forecasting inflation in Bosnia and Herzegovina. Although the presented models are small and highly aggregated, they provide a convenient framework to illustrate practical forecast issues. Furthermore, they are a good starting point in the process of the forecast development. The empirical part of this paper estimates the domestic and international transmission effects on inflation and tries to find good predictors of the inflation. A variety of inflation indicators included in the VAR models are assessed as potential predictors of inflation. They have been suggested by economic theory and existing research. A pseudo out-of-sample forecast approach is employed to assess the models’ performance at different horizons using a recursive strategy. The study then evaluates the relative forecast performance of univariate model and various alternative specifications of the VAR models and offers conclusions. The results confirm the significant improvement in forecasting performance at all forecast horizons when Bayesian techniques, which incorporate information from the likelihood function and some informative prior distributions, are used. |
| Keywords: | Bayesian VAR, model selection, inflation forecasting |
| Date: | 2020–02–25 |
| URL: | http://d.repec.org/n?u=RePEc:gii:giihei:heidwp07-2020&r=all |