Filters, Waves and Spectra

Pollock, D.S.G.

doi:10.3390/econometrics6030035

Cited by 5 publications

(4 citation statements)

References 32 publications

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“…This result, which may seem remarkable, was demonstrated by Pollock (2018). As n increases, the attenuation of the high frequency elements of the data increases, and the profile of frequency response of the binomial filter, defined over the interval [−π, π], converges to the profile of a normal distribution.…”

Section: Time Domain Filters For Extracting the Trend-cycle Functionmentioning

confidence: 79%

Enhanced Methods of Seasonal Adjustment

Pollock¹

2021

Econometrics

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The effect of the conventional model-based methods of seasonal adjustment is to nullify the elements of the data that reside at the seasonal frequencies and to attenuate the elements at the adjacent frequencies. It may be desirable to nullify some of the adjacent elements instead of merely attenuating them. For this purpose, two alternative sets of procedures are presented that have been implemented in a computer program named SEASCAPE. In the first set of procedures, a basic seasonal adjustment filter is augmented by additional filters that are targeted at the adjacent frequencies. In the second set of procedures, a Fourier transform of the data is exploited to allow the elements in the vicinities of the seasonal frequencies to be eliminated or attenuated at will. The question is raised of whether an estimated trend-cycle trajectory that is devoid of high-frequency noise can serve in place of the seasonally adjusted data.

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Section: Time Domain Filters For Extracting the Trend-cycle Functionmentioning

confidence: 79%

Enhanced Methods of Seasonal Adjustment

Pollock¹

2021

Econometrics

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“…Filter model. Pollock (2018) opined that filter should be designed with reference to their frequency responses where they should be implemented in the frequency domain in which data should be free of trend that will be able to alleviate the end -of-sample problems. Schuler (2018) applied Hamilton filter in the credit to GDP gap in USA taking data of GDP from Fred during 1947Q1-2017Q1 and data of credit GDP ratio from BIS during 1952Q1-2016Q4 which produced more robust cycle estimates than H.P.…”

Section: Some Important Researchesmentioning

confidence: 99%

Trends, Cycles and Seasonal Variations of Ukrainian Gross Domestic Product

Bhowmik

2020

FMIR

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The article attempts to study trends, seasonal variations and cyclical fluctuations of Ukraine’s quarterly GDP at current prices. The period of the study is from the first quarter of 2010 to the first quarter of 2020. The methodological support of the study includes an approach based on the Hamilton regression filter, the Hodrick-Prescott filter and the asymmetric filter model of Cristiano and Fitzgerald. Based on the use of a Hamilton regression filter, which clearly gives one complete cycle with a peak and a depression, the study substantiates that the seasonally adjusted series of GDP has a slight difference with the remainder, but its seasonal fluctuations are homogeneous and have the shape of the letter V, which allowed us to draw the following conclusions: seasonal fluctuations in GDP are confirmed by the ACF and PACF models during the study period; the filter is very different from the Hamilton filter in terms of trend and cycle, but has common features in the context of asymmetry in time with the random walk filter of Cristiano and Fitzgerald. The paper substantiates the conclusions about stable and stationary series of GDP by volatility (leading to a decrease) of cyclical fluctuations based on the used forecast model ARIMA (4,0,4) for 2020-2030, which passed through the Hamilton regression filter. Based on the results of the study, the author provides recommendations on the need to introduce a new monetary and fiscal policy, including reform measures, which should be balanced with current trends in the functioning and development of international financial institutions and organizations. Such changes will be a motivating lever for the growth of the share of agriculture and related activities, production, transport, real estate, capital formation and other macroeconomic indicators of Ukraine’s economy, respectively, during the period of GDP decline. Keywords: Gross Domestic Product, decomposition, trends, cyclical fluctuations, seasonal variations, Hamilton Filter, Hodrick-Prescott Filter.

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“…Sections 2 and 3 rely on the Fourier transforms of discrete and continuous functions. An account of these, which includes the matters of sampling and aliasing, which can affect functions in both the time domain and the frequency domain, has been provided by Pollock (2018). in an appendix to the paper.…”

Section: Introductionmentioning

confidence: 99%

Linear Stochastic Models in Discrete and Continuous Time

Pollock¹

2020

Econometrics

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The econometric data to which autoregressive moving-average models are commonly applied are liable to contain elements from a limited range of frequencies. If the data do not cover the full Nyquist frequency range of [0,π] radians, then severe biases can occur in estimating their parameters. The recourse should be to reconstitute the underlying continuous data trajectory and to resample it at an appropriate lesser rate. The trajectory can be derived by associating sinc fuction kernels to the data points. This suggests a model for the underlying processes. The paper describes frequency-limited linear stochastic differential equations that conform to such a model, and it compares them with equations of a model that is assumed to be driven by a white-noise process of unbounded frequencies. The means of estimating models of both varieties are described.

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Filters, Waves and Spectra

Cited by 5 publications

References 32 publications

Enhanced Methods of Seasonal Adjustment

Enhanced Methods of Seasonal Adjustment

Trends, Cycles and Seasonal Variations of Ukrainian Gross Domestic Product

Linear Stochastic Models in Discrete and Continuous Time

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