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Modeling US historical time-series prices and inflation using alternative long-memory approaches

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Abstract

We consider two important features of the historical US price data (1774–2015), namely the data’s persistence and cyclical structure. We first consider the persistence of the series and focus on standard long-memory models that incorporate a peak at the zero frequency. We examine different models with respect to the deterministic terms, including nonlinear deterministic trends of the Chebyshev form. Then, we investigate a more general model that includes both persistence and cyclicality of the series and, thus, includes two fractional integration parameters, one at the zero (long-run) frequency and the other at the nonzero (cyclical) frequency. We model the cyclical structure as a Gegenbauer process. This specification outperforms the standard long-memory specifications. We find that the order of integration at the zero frequency is about 0.5, and the one at the cyclical frequency is about 0.2 with cycles repeating approximately every 6 years, producing mean-reverting long-memory effects at both the zero and cyclical frequencies. Fitting the values to this model, however, we discover the presence of a break that, according to the methods employed, takes place at around 1940–1941. The results indicate the prevalence of the long-run or zero component with a much higher degree of persistence during the second post-1940–1941 subsample, suggesting important implications for monetary policy.

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Notes

  1. As the existing literature frequently notes, inflation persistence plays an important role in the conduct of monetary policy as well as the development of the underlying macroeconomic theories. Inflation persistence measures the speed with which the inflation rate returns to its equilibrium level after an inflationary shock. If the inflation rate returns to its equilibrium level quickly (i.e., the inflation rate exhibits less persistence) after a shock, then the monetary authorities can more effectively reduce inflation fluctuations, all else equal (Fuhrer 1995). High inflation persistence, on the other hand, causes shocks to exert long-lasting effects and may require a strong policy response to affect the dynamics of inflation and bring it under control. In the worst case, inflation may follow a random-walk I(1) process, making it impossible for central banks to control inflation. In the best case, inflation may follow a stationary I(0) process, implying that it reverts to its equilibrium level rapidly after a random shock. In this latter case, the response to the inflationary shock may not require an active monetary policy. Thus, the optimal timing and size of monetary policy crucially depend on not only knowledge of how shocks affect the dynamics of inflation but also on the degree of persistence that identifies the inflation process. In this regard, we note that inflation persistence plays an important role in the current debate on inflation targeting. When a central bank successfully anchors inflationary expectations by its inflation targeting policy, it reduces or eliminates inflation persistence, since well-anchored inflationary expectations depend less on past inflation.

  2. Hassler et al. (2009) propose a similar procedure based on a LM test in the time domain to detect general forms of fractional integration at the long-run and/or the cyclical component of a time series.

  3. These regularity conditions are rather mild, involving the behavior of \( u_{t} \) and specific technical assumptions on the two polynomials in Eq. (2).

  4. See Hamming (1973) and Smyth (1998) for a detailed description of these polynomials.

  5. See Cuestas and Gil-Alana (2016) for further details on the choice of m.

  6. One can download the data from: http://liberalarts.oregonstate.edu/spp/polisci/research/inflation-conversion-factors.

  7. For the exponential spectral model of Bloomfield (1973), we tried different orders from 1 to 3. The results were similar in the three cases. Thus, we report the results only with m = 1.

  8. Similar to the nonlinear case above, expressing the two equations in (8) in a single equation produces I(0) errors, implying that t values apply.

  9. Using other types of nonlinear deterministic terms such as Hermite polynomials does not produce any evidence of nonlinearities in the data.

  10. In particular, we perform tests of no serial correlation, functional form, normality, and homoscedasticity using Microfit 5.0. For serial correlation, we use a Lagrange Multiplier test of residuals serial correlation (Godfrey 1978a, b): test statistic, 0.356; for the functional form, the Ramsey’s (1969) RESET test using powers of the fitted values: test statistic, 1.145 and 1.177 with squared and cubic terms, respectively; for normality, a test based on skewness and kurtosis of residuals, (Bera and Jarque 1981): test statistic, 3.490; and for homoscedasticity, we use Koenker (1981) modified LM test of Breusch and Pagan (1979): test statistic, 1.906.

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Acknowledgements

We gratefully acknowledge the comments from the Editor and two anonymous reviewers. Luis A. Gil-Alana gratefully acknowledges financial support from the Ministerio de Economía y Competitividad (ECO2017-85503-R).

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Authors and Affiliations

  1. Department of Economics, University of Nevada, Las Vegas, 4505 S. Maryland Parkway, Las Vegas, NV, USA

    Giorgio Canarella & Stephen M. Miller

  2. Faculty of Economics, University of Navarra, Pamplona, Spain

    Luis A. Gil-Alana

  3. University of Pretoria, Pretoria, South Africa

    Rangan Gupta

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  1. Giorgio Canarella
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  2. Luis A. Gil-Alana
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  3. Rangan Gupta
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  4. Stephen M. Miller
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Correspondence to Stephen M. Miller.

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Canarella, G., Gil-Alana, L.A., Gupta, R. et al. Modeling US historical time-series prices and inflation using alternative long-memory approaches. Empir Econ 58, 1491–1511 (2020). https://doi.org/10.1007/s00181-018-1597-2

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