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on Econometric Time Series |
| By: | Richard T. Baillie (Queen Mary, University of London); George Kapetanios (Queen Mary, University of London) |
| Abstract: | This paper constructs tests for the presence of nonlinearity of unknown form in addition to a fractionally integrated, long memory component in a time series process. The tests are based on artificial neural network structures and do not restrict the parametric form of the nonlinearity. The tests only require a consistent estimate of the long memory parameter. Some theoretical results for the new tests are obtained and detailed simulation evidence is also presented on the power of the tests. The new methodology is then applied to a wide variety of economic and financial time series. |
| Keywords: | Long memory, Non-linearity, Artificial neural networks, Realized volatility, Absolute returns, Real exchange rates, Unemployment. |
| JEL: | C22 C12 F31 |
| Date: | 2005–04 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp528&r=ets |
| By: | Stephen Pollock (Queen Mary, University of London); Iolanda Lo Cascio (Queen Mary, University of London) |
| Abstract: | The conventional dyadic multiresolution analysis constructs a succession of frequency intervals in the form of (<i>π</i> / 2<sup><i> j</i></sup>, <i>π</i> / 2<sup><i> j</i>-1</sup>); <i>j</i> = 1, 2, . . . , <i>n</i> of which the bandwidths are halved repeatedly in the descent from high frequencies to low frequencies. Whereas this scheme provides an excellent framework for encoding and transmitting signals with a high degree of data compression, it is less appropriate to the purposes of statistical data analysis.<br> A non-dyadic mixed-radix wavelet analysis is described that allows the wave bands to be defined more flexibly than in the case of a conventional dyadic analysis. The wavelets that form the basis vectors for the wave bands are derived from the Fourier transforms of a variety of functions that specify the frequency responses of the filters corresponding to the sequences of wavelet coefficients. |
| Keywords: | Wavelets, Non-dyadic analysis, Fourier analysis. |
| JEL: | C22 |
| Date: | 2005–05 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp529&r=ets |
| By: | Stephen Pollock (Queen Mary, University of London) |
| Abstract: | The Wiener–Kolmogorov signal extraction filters, which are widely used in econometric analysis, are constructed on the basis of statistical models of the processes generating the data. In this paper, such models are used mainly as heuristic devices that are to be specified in whichever ways are appropriate to ensure that the filters have the desired characteristics. The digital Butterworth filters, which are described and illustrated in the paper, are specified in this way. The components of an econometric time series often give rise to spectral structures that fall within well-defined frequency bands that are isolated from each other by spectral dead spaces. We find that the finite-sample Wiener–Kolmogorov formulation lends itself readily to a specialisation that is appropriate for dealing with band-limited components. |
| Keywords: | Signal extraction, Linear filtering, Frequency-domain analysis, Trend estimation. |
| JEL: | C22 |
| Date: | 2005–05 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp530&r=ets |
| By: | Chi-Young Choi (University of New Hampshire); Ling Hu (Ohio State University); Masao Ogaki (Ohio State University) |
| Abstract: | This paper proposes two estimators based on asymptotic theory to estimate structural parameters with spurious regressions involving unit-root nonstationary variables. This approach motivates a Hausman-type test for the null hypothesis of cointegration for dynamic Ordinary Least Squares estimation using one of our estimators for spurious regressions. We apply our estimation and testing methods to four applications: (i) long-run money demand in the U.S.; (ii) long-run implications of the consumption-leisure choice; (iii) output convergence among industrial and developing countries; (iv) Purchasing Power Parity for traded and non-traded goods. |
| Keywords: | Spurious regression, GLS correction method, Dynamic regression, Test for cointegration. |
| JEL: | C10 C15 |
| Date: | 2005–05 |
| URL: | http://d.repec.org/n?u=RePEc:roc:rocher:517&r=ets |
| By: | Alastair R. Hall (North Carolina State University); Atsushi Inoue (North Carolina State University) |
| Abstract: | This paper presents the limiting distribution theory for the GMM estimator when the estimation is based on a population moment condition which is subject to non--local (or fixed) misspecification. It is shown that if the parameter vector is overidentified then the weighting matrix plays a far more fundamental role than it does in the corresponding analysis for correctly specified models. Specifically, the rate of convergence of the estimator depends on the rate of convergence of the weighting matrix to its probability limit. The analysis is presented for four particular choices of weighting matrix which are commonly used in practice. In each case the limiting distribution theory is different, and also different from the limiting distribution in a correctly specified model. Statistics are proposed which allow the researcher to test hypotheses about the parameters in misspecified models. |
| Keywords: | Misspecification, Generalized Method of Moments, Asymptotic Distribution Theory |
| JEL: | C10 C32 |
| Date: | 2005–05–10 |
| URL: | http://d.repec.org/n?u=RePEc:wpa:wuwpem:0505002&r=ets |
| By: | Andrea Beltratti; Claudio Morana (SEMEQ Department - Faculty of Economics - University of Eastern Piedmont) |
| Abstract: | In the paper we study the relationship between macroeconomic and stock market volatility, using S&P500 data for the period 1970- 2001. We find evidence of both long memory and structural change in volatility and a twofold linkage between stock market and macroeconomic volatility. In terms of the break processes, our results show that there are frequent cases where the break in the volatility of stock returns is associated within few months with breaks in the volatility of the Federal funds rate and M1 growth. After accounting for the structural breaks, there remain interesting relations among the breakfree series. Fractional cointegration analysis points to the existence of three long-run relationships linking stock market, money growth, inflation, the Federal funds rate, and output growth volatility, and two common long memory factors mainly associated with output and inflation volatility. We find that stock market volatility dynamics, both persistent and non persistent, are associated in a causal way with macroeoconomic volatility shocks, particularly to output growth volatility. The stock market idiosyncratic shock, which accounts for the bulk of the overall dynamics, also affects macroeconomic volatility. Yet the evidence suggests that the causality direction is stronger from macroeconomic to stock market volatility than the other way around. |
| JEL: | C32 F30 G10 |
| Date: | 2004–05 |
| URL: | http://d.repec.org/n?u=RePEc:upo:upopwp:20&r=ets |
| By: | Claudio Morana (SEMEQ Department - Faculty of Economics - University of Eastern Piedmont) |
| Abstract: | In this paper we study the zero frequency spectral properties of fractionally cointegrated long memory processes and introduce a new frequency domain principal components estimator of the cointegration space and the factor loading matrix for the long memory factors. We find that for fractionally di?erenced (fractionally) cointegrated processes the squared multiple coherence at the zero frequency is equal to one, the spectral density matrix at the zero frequency is singular, and the factor loading and cointegrating matrices can be obtained from the eigenvectors of the spectral matrix at the zero frequency, associated with the positive and zero roots, respectively. A Monte Carlo simulation reveals that the proposed principal components estimator has already good properties with relatively small sample sizes. |
| Keywords: | cointegration, long memory, frequency domain analysis |
| JEL: | C22 |
| Date: | 2004–03 |
| URL: | http://d.repec.org/n?u=RePEc:upo:upopwp:44&r=ets |
| By: | Claudio Morana (SEMEQ Department - Faculty of Economics - University of Eastern Piedmont) |
| Abstract: | In the paper we propose a new methodological approach to core in- flation estimation, based on a frequency domain principal components estimator, suited to estimate systems of fractionally cointegrated processes. The proposed core inflation measure is the scaled common persistent factor in inflation and excess nominal money growth and bears the interpretation of monetary inflation. The proposed measure is characterised by all the properties that an “ideal” core inflation process should show, providing also a superior forecasting performance relative to other available measures. |
| Keywords: | long memory, common factors, fractional cointegration, Markov switching, core inflation, euro area. |
| JEL: | C22 E31 E52 |
| Date: | 2004–02 |
| URL: | http://d.repec.org/n?u=RePEc:upo:upopwp:54&r=ets |