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In this study, monthly particulate matter (PM 10) values in Ankara (39.9334° N, 32.8597° E) from January 1993 to December 2017 are examined. The PM 10 are those thoracic particles whose aerodynamic diameter is less than 10 μm (micrometers), and it is of critical health importance due to the penetrability to the lower airways. As an alternative to classical unit root tests, a unit root test primarily based on periodograms is introduced owing to its advantages over alternatives. After examining the stationarity of the series through periodogram-based test as well as its standard rivals, periodic components in the series are examined and it is observed that the series has both periodic and seasonal components. These components are modeled, using the inherent dynamics of a time series alone, within a trigonometric harmonic regression setup, eventually yielding the forecast values for 2018 that turns out to be superior to those obtained by means of ARIMA (autoregressive integrated moving average). This is a striking result since the modeling framework requires no assumptions, no parameter estimations except for the variance of the white noise series, no simulations of the power of tests, no adjustments of test statistics with respect to sample size and no preliminary work as to independent variable which is simply time, i.e., the period of forecast.

pollution. The method we use successfully captures and accounts for the periodicities, which could otherwise be mixed with seasonality under an alternative methodology. Upon the unit root test based on periodograms, it is revealed that the investigated data has periodicities of 1 year and 20 years, so harmonic regression is utilized as an alternative to Box-Jenkins methodology. As the harmonic regression displayed a better performance both in and out-of-sample forecasts, it can be considered as a powerful alternative to model and forecast time series with a periodic structure.

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