Abstract
We propose a new stochastic long-memory model with a time-varying fractional integration parameter, evolving non-linearly according to a Logistic Smooth Transition Autoregressive (LSTAR) specification. To estimate the time-varying fractional integration parameter, we implement a method based on the wavelet approach, using the instantaneous least squares estimator (ILSE). The empirical results show the relevance of the modeling approach and provide evidence of regime change in inflation persistence that contributes to a better understanding of the inflationary process in the US. Most importantly, these empirical findings remind us that a “one-size-fits-all” monetary policy is unlikely to work in all circumstances. The empirical results are consistent with newly developed tests of wavelet-based unit root and fractional Brownian motion.
A Appendix
Wavelet analysis is relatively new in economics and finance, although the literature on wavelets is growing rapidly. For a review on wavelet analysis from a time-series perspective, see Ramsey (1999, 2002) , Schleicher (2002), Crowley (2007), and, most importantly, Percival and Walden (2000) and Gençay, Selçuk, and Whitcher (2002). Percival and Walden (2000) provide an extensive treatment of wavelet methods for time series research with many interesting scientific applications. Crowley (2007) and Schleicher (2002) propose a guide to wavelets for economists. Gençay, Selçuk, and Whitcher (2002) follows a similar approach to wavelets as given by Percival and Walden (2000) but with an emphasis on financial and economic applications.
A sizable body of research attests to the relevant role of wavelets in time series analysis from a spectral perspective in economics and finance. The unit root test of Fan and Gençay (2010) and the serial correlation test of Gençay and Signori (2015) stem from this perspective. Xue, Gençay, and Fagan (2014) propose a framework for jump detection using wavelets and formally develops a wavelet-based jump test statistic. Gençay and Gradojevic (2011) propose a wavelet approach to estimate the parameters of a linear regression where the regress and the regressors are persistent processes and contain measurement errors. Tseng and Gençay (2016) introduce the wavelet perspective to the estimation of linear models with one time-varying parameters.
Early notable applications in economics and finance include Ramsey, Uskinov, and Zaslavsky (1995), Ramsey and Lampart (1998), and Ramsey (1999, 2002) . Multi-scaling extraction of wavelets has been applied to volatility analysis, risk hedging, portfolio allocation, seasonality, FX markets, and other financial areas. Gençay, Selçuk, and Whitcher (2001a) demonstrate the benefits of using wavelet analysis in order to evaluate variations in foreign exchange volatility across different time scales. Gençay, Selçuk, and Whitcher (2001b) propose a method to extract the intraday seasonality, which is free of model selection parameters. Nekhili, Altay-Salih, and Gençay (2002) investigate the scale properties of U.S. Dollar/Deutsche Mark returns, and find that the co-existence of short-term as well as long-term traders indicates different time scales for different market traders. Xu and Gençay (2003) find that the U.S. Dollar/ Deutsche Mark returns present scaling and multifractal properties, and demonstrate that the existence of different market traders, with multiple trading frequencies, can increase volatility persistence.
In, Kim, Gençay and Gradojevic (2011) apply wavelet analysis to portfolio allocation between value and growth stocks over various investment horizons, and explore two common alternatives, the Fama-French versus the S&P500/Barra portfolios. The results using the Fama-French portfolio show that as the investment horizon increases, the optimal mean allocation of investors tilts heavily away from growth stocks, particularly for lower and moderate levels of risk aversion. Growth and value stocks of the Fama–French portfolio are anticorrelated (antipersistent). For the S&P 500/Barra portfolio, the allocation weights between value and growth do not vary much. Growth and value stocks of the S&P 500/Barra portfolio follow the Gaussian white noise process.
Gençay et al. (2010) use wavelets with high-frequency financial data and a hidden Markov model to establish a new stylized fact about volatility – that low volatility at a long time horizon is most likely followed by low volatility at shorter time horizons – the reverse for high volatility does not seem to be the case. The authors label this phenomenon asymmetric vertical dependence. In other applications, Gençay, Selçuk, and Whitcher (2003, 2005) ) propose a wavelet approach for estimating the systematic risk (the beta of an asset) in the context of the Capital Asset Pricing Model (CAPM), and find that asset pricing models yield different results for each time scale, in particular, that there is strong evidence that the relation between the return of a portfolio and its beta becomes stronger as the wavelet scale increases. Conlon, Cotter, and Gençay (2014) study the impact of investment horizon on the realizable benefit from international diversification and find that unconditional correlation among the markets increases with scale, indicating that benefit of diversification is less evident for the long term investors.
Conlon, Cotter, and Gençay (2016) propose the wavelet framework to examine the impact of management preferences on optimal futures hedging strategy and associated performance. Their empirical results reveal substantial hedge ratio variation across distinct management preferences and suggest that hedging performance is strongly dependent on underlying preferences. In particular, hedgers with high risk aversion and short horizon reduce hedge portfolio risk but achieve inferior utility in comparison to those with low aversion.
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The online version of this article offers supplementary material (DOI:https://doi.org/10.1515/snde-2016-0130).
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