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on Econometric Time Series |
| By: | Marian Gidea; Yuri Katz |
| Abstract: | We explore the evolution of daily returns of four major US stock market indices during the technology crash of 2000, and the financial crisis of 2007-2009. Our methodology is based on topological data analysis (TDA). We use persistence homology to detect and quantify topological patterns that appear in multidimensional time series. Using a sliding window, we extract time-dependent point cloud data sets, to which we associate a topological space. We detect transient loops that appear in this space, and we measure their persistence. This is encoded in real-valued functions referred to as a 'persistence landscapes'. We quantify the temporal changes in persistence landscapes via their $L^p$-norms. We test this procedure on multidimensional time series generated by various non-linear and non-equilibrium models. We find that, in the vicinity of financial meltdowns, the $L^p$-norms exhibit strong growth prior to the primary peak, which ascends during a crash. Remarkably, the average spectral density at low frequencies of the time series of $L^p$-norms of the persistence landscapes demonstrates a strong rising trend for 250 trading days prior to either dotcom crash on 03/10/2000, or to the Lehman bankruptcy on 09/15/2008. Our study suggests that TDA provides a new type of econometric analysis, which goes beyond the standard statistical measures. The method can be used to detect early warning signals of imminent market crashes. We believe that this approach can be used beyond the analysis of financial time series presented here. |
| Date: | 2017–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1703.04385&r=ets |
| By: | Delle Monache, Davide (Bank of Italy); Petrella, Ivan (WBS and CEPR) |
| Abstract: | This paper introduces an adaptive algorithm for time-varying autoregressive models in the presence of heavy tails. The evolution of the parameters is determined by the score of the conditional distribution, the resulting model is observation-driven and is estimated by classical methods. In particular, we consider time variation in both coeficients and volatility, emphasizing how the two interact with each other. Meaningful restrictions are imposed on the model parameters so as to attain local stationarity and bounded mean values. The model is applied to the analysis of in ation dynamics with the following results: allowing for heavy tails leads to signi cant improvements in terms of it and forecast, and the adoption of the Student-t distribution proves to be crucial in order to obtain well calibrated density forecasts. These results are obtained using the US CPI infl ation rate and are confirmed by other in ation indicators, as well as for CPI infl ation of the other G7 countries. |
| Keywords: | adaptive algorithm ; in flation ; score-driven models ; student-t ; timevarying parameters JEL Classification Numbers: C22 ; C51 C53 E31 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:wrkemf:13&r=ets |
| By: | Andrea Carriero (Queen Mary University of London); Galvao, Ana Beatriz (University of Warwick); Kapetanios, George (Kings College London) |
| Abstract: | This paper contributes to the academic literature and the practice of macroeconomic forecasting. Our evaluation compares the performance of four classes of state-of-art forecasting models : Factor-Augmented Distributed Lag (FADL) Models, Mixed Data Sampling (MIDAS) Models, Bayesian Vector Autoregressive (BVAR) Models and a medium-sized Dynamic Stochastic General Equilibrium Model (DSGE). We look at these models to predict output growth and ination with datasets from the US, UK, Euro Area, Germany, France, Italy and Japan. We evaluate the accuracy of point and density forecasts, and compare models with a large set of predictors with models that employ a medium-sized dataset. Our empirical results shed light on how the predictive ability of economic indicators for output growth and ination changes with horizon, on the impact of dataset size on the calibration of density forecasts, and how the choice of the multivariate forecasting model depends on the forecasting horizon. |
| Keywords: | factor models ; BVAR models ; MIDAS models ; DSGE models ; density forecasts JEL Classification Numbers: C53 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:wrkemf:10&r=ets |
| By: | Mitchell, James (Warwick Business School, University of Warwick); Robertson, Donald (Faculty of Economics, University of Cambridge); Wright, Stephen (Department of Economics, Maths & Statistics Birkbeck College, University of London) |
| Abstract: | A longstanding puzzle in macroeconomic forecasting has been that a wide variety of multivariate models have struggled to out-predict univariate representations. We seek an explanation for this puzzle in terms of population properties. We show that if we just know the univariate properties of a time-series, yt, this can tell us a lot about the dimensions and the predictive power of the true (but unobservable) multivariate macroeconomic model that generated yt. We illustrate using data on U.S. inflation. We find that, especially in recent years, the univariate properties of inflation dictate that even the true multivariate model for inflation would struggle to out-predict a univariate model. Furthermore, predictions of changes in ination from the true model would either need to be IID or have persistence properties quite unlike those of most current macroeconomic models. |
| Keywords: | Forecasting ; Macroeconomic Models ; Autoregressive Moving Average Representations ; Predictive Regressions ; Nonfundamental Representations ; Inflation Forecasts JEL Classification Numbers: C22 ; C32 ; C53 ; E37 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:wrkemf:08&r=ets |
| By: | Sermin Gungor; Richard Luger |
| Abstract: | We develop a simulation-based procedure to test for stock return predictability with multiple regressors. The process governing the regressors is left completely free and the test procedure remains valid in small samples even in the presence of non-normalities and GARCH-type effects in the stock returns. The usefulness of the new procedure is demonstrated both in a simulation study and by examining the ability of a group of financial variables to predict excess stock returns. We find robust evidence of predictability during the period 1948–2014, driven entirely by the term spread. This empirical evidence, however, is much weaker over subsamples. |
| Keywords: | Asset Pricing, Econometric and statistical methods, Financial markets |
| JEL: | C12 C32 G14 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:bca:bocawp:17-10&r=ets |
| By: | Zhou, Peng (Cardiff Business School) |
| Abstract: | This paper proposes a new filter technique to separate trend and cycle based on stylised economic properties of trend and cycle, rather than relying on ad hoc statistical proper-ties such as frequency. Given the theoretical separation between economic growth and business cycle literature, it is necessary to make the measures of trend and cycle match what the respective theories intend to explain. The proposed filter is applied to the long macroeconomic data collected by the Bank of England (1700-2015). |
| Keywords: | Filter, Trend, Cycle |
| JEL: | C32 |
| Date: | 2017–01 |
| URL: | http://d.repec.org/n?u=RePEc:cdf:wpaper:2017/1&r=ets |
| By: | Christian Bayer; Peter K. Friz; Archil Gulisashvili; Blanka Horvath; Benjamin Stemper |
| Abstract: | We consider rough stochastic volatility models where the driving noise of volatility has fractional scaling, in the "rough" regime of Hurst parameter $H |
| Date: | 2017–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1703.05132&r=ets |