Spectral Analysis Of Time Series Research Articles

Daily lake-level time series spectral analysis using EMD, VMD, EWT, and EFD

ABSTRACT This study investigates the dynamics of daily Urmia Lake level (ULL) changes using spectral analysis tools to discover fluctuating patterns in the ULL series. Therefore, in the present research, the empirical mode decomposition (EMD), variational mode decomposition (VMD), empirical wavelet transform (EWT), and empirical Fourier decomposition (EFD) were used to analyze the ULL signal. ULL series were decomposed into subseries, and the optimized outcome was used. All methods concluded that the ULL series has a steep downward trend. Signal reconstruction was performed, and it was inferred that EFD could not estimate the ULL series appropriately and had root-mean-square error (RMSE) = 12.26. Different from EFD, other methods performed better signal construction according to RMSE and error analysis. The mode-mixing issue was the last step in verifying the capabilities of signal-analyzing methods. Based on the power spectral density (PSD), it was seen that EMDs had mode-mixing problems and limitations in signal decomposition, whereas VMD and EWT did not have these issues. Results demonstrated that the present study has some limitations. Overall, it was concluded that VMD performed better in terms of RMSE, error analysis, reconstruction, mode-mixing problems, and PSD analysis while decomposing and extracting features from the ULL signal.

Testing the record of climate-related cyclicity in microbial lamination: An example from Miocene oncolites in the Ebro Basin, Spain

This work tests the relationship between quasi-periodic climate-linked parameters and cyclicity recorded through microbial lamination using spectral analysis of time series based on lamina thickness and luminance, as well as C and O stable isotope data. Three oncolites of the Ebro Basin were used: specimens C4-1 and C4-31 from a lacustrine bed dated at 13.8 My, and specimen VD-13 from a fluvial bed whose age is younger than 12 My. Lamination consists of alternating light and dark calcite laminae, which correspond to crystal size and porosity variations. Composite light and dark laminae can be seen by the naked eye. Spectral analysis based on the thickness and luminance measurements of simple light–dark lamina couplet successions revealed that the three specimens had recurrent periods of 2.5, 3 and 10–13. On the hypothesis that each simple light–dark lamina couplet represents a 1-year duration, the 2.5 and 10–13 periods can be related to the 2.5-year quasi-biennial oscillation and the 11-year Schwabe sunspot cycle, respectively. Other less frequent periods present around 5 and 7, together with period 3, could be related to the most typical modes of the North Atlantic Oscillation and/or El Niño Southern Oscillation. The periods at 19–23, present in specimen C4-31, can be correlated with the 22-year Hale sunspot cycle. The 10–13 and 19–23 periods were also detected using the δ13C and δ18O values of successive laminae in specimen C4-31. These data suggest that solar irradiance variations influenced the characteristics of the oncolite laminae, through temperature and precipitation. Although the studied oncolites do not present an optimal thickness lamination pattern for spectral analysis, their lamination is capable of registering periodic climatic variations, and these results provide further evidence that microbial laminations can serve as high-resolution records of climate and climate-linked cycles over different time scales.

On the Validation of the Rotation Procedure from HEE to MEMFA Reference Frame in the Presence of Alfvén Waves in the Interplanetary Medium

Alfvén waves play an important role in the stability, heating, and transport of magnetized plasmas. They are found to be ubiquitous in solar winds (SW), which mainly propagate outward from the Sun, especially in high-speed streams that originate from coronal holes. When high-speed streams impinge on the Earth’s magnetosphere, the impact of Alfvénic fluctuations can cause magnetic reconnections between the intermittent southward Interplanetary Magnetic Field (IMF) and the geomagnetic field, resulting in energy injection from the SW into the Earth’s magnetosphere. In this work, we tested a rotation procedure from the Heliocentric Earth Ecliptic (HEE) to the Mean ElectroMagnetic Fields Aligned (MEMFA) reference frame. This is achieved by means of the Empirical Mode Decomposition (EMD) method for both the SW velocity and IMF at 1 AU. Our aim is to check the reliability of the method and its limitations in identifying Alfvénic fluctuations through the spectral analysis of time series in the MEMFA coordinate system. With this procedure, we studied the fluctuations in the main-field-aligned direction and those in the orthogonal plane to the main field. To highlight the peculiarities of each case of study and be able to better identify Alfvén waves when applying this procedure to real data, we reproduced the magnetic and velocity fields of a typical corotating high-speed stream. We tested the procedure in several cases by varying the amplitude of Alfvén waves and noise .We performed the spectral analysis of the Mean Field Aligned (MFA) component of both the magnetic and velocity fields to define the power related to the two main directions: the one aligned to the ambient magnetic field and the one orthogonal to it. The efficiency of the procedure and the results’ reliability are supported by Monte Carlo (MC) tests. The method is also applied to a real case that is represented by a selected corotating SW stream that occurred during August 2008, which fell in the solar minimum of solar cycle 23. The results are also compared with those obtained by using Elsässer variables to analyze the Alfvénicity of fluctuations via the normalized cross helicity and the normalized residual energy.

Линии CaII в спокойной области на Солнце. I. Динамические процессы в солнечной атмосфере

We have studied oscillation processes in the quiet Sun outside a coronal hole at different levels of the solar chromosphere. The study was based on spectroscopic observations of ionized calcium lines (K, H, and 849.8 nm) obtained by the Sayan Solar Observatory’s Automated Solar Telescope (AST). Spectral analysis of time series for some parameters of the lines has been carried out. We have compared the results of this work with the results of our study of oscillation processes in quiet regions located at the base of a coronal hole. The oscillation power was found to be higher in the region of the quiet Sun outside a coronal hole. At the same time, for the regions under study there is a common tendency for the oscillation power to decrease with height for all frequency ranges, except for the low-frequency one, in most chromospheric structures. In structures with a weak magnetic field, the power increases with height to the lower chromosphere and decreases somewhat to the upper chromosphere.

CAII lines in a quiet region on the Sun I. Dynamic processes in the solar atmosphere

We have studied oscillation processes in the quiet Sun outside a coronal hole at different levels of the solar chromosphere. The study was based on spectroscopic observations of ionized calcium lines (K, H, and 849.8 nm) obtained by the Sayan Solar Observatory’s Automated Solar Telescope (AST). Spectral analysis of time series for some parameters of the lines has been carried out. We have compared the results of this work with the results of our study of oscillation processes in quiet regions located at the base of a coronal hole. The oscillation power was found to be higher in the region of the quiet Sun outside a coronal hole. At the same time, for the regions under study there is a common tendency for the oscillation power to decrease with height for all frequency ranges, except for the low-frequency one, in most chromospheric structures. In structures with a weak magnetic field, the power increases with height to the lower chromosphere and decreases somewhat to the upper chromosphere.

On the Combination of Harmonics and Polynoms in Econometric Modeling of RUB/AZN Exchange Rate

Conducting a combinational polynomial and spectral analysis of time series formed on the basis of daily observations of changes in the RUB/AZN exchange rate with pronounced fluctuations for the period 11.05.2017- 02.11.2018 based on computer econometric modeling.The purpose of the research. The possibility of describing the global rate dynamics by approximation with a combination of a nonlinear polynomial trend and harmonic oscillations of various frequencies relative to this curve; the ability to calculate amplitudes and phases, which can be used to estimate the power spectrum of the Fourier approximation; the ability to develop a high-precision algorithm for predicting exchange rate changes in RUB/AZN.Materials and methodology. The official statistics of the State Statistics Committee of Azerbaijan were used; classical methods of mathematical analysis and economic analysis; methods of econometrics, harmonic (Fourier) analysis, statistical spectral analysis, “Fourier analysis” of the MS Excel add-in, tools of the Eviews 8 application package with the standard deviation and average approximation error being taken into account, the necessary statistical procedures required for identifying and estimating the parameters of the model and checking its adequacy and accuracy.Results. By breaking up the empirical analysis of given time series into time-scale polynomial and time-frequency components. Combinations of the optimal degree of variants of polynomials up to the 11th degree and the number of harmonics of sines and cosines of all possible discrete frequencies were revealed.Conclusion. This result allows us to reconsider the asymmetric impact of RUB/AZN exchange rate pressure on the foreign trade balance between Russia and Azerbaijan. An increase/decrease in exchange rate pressure affects the likelihood of a ruble-manat crisis, while this phenomenon may negatively/positively affect the foreign trade balance and may make it difficult/easier to import resources, goods and services between countries. This, in turn, adds significance to the task of further detailed structuring and analysis of exchange rate changes in RUB/AZN in the face of increased sanction pressures against Russia, thereby actualizing the development of the retrospective part of the study.

Influence of spatial resolution in mesoscale modeling to reproduce wind power production in southern Mexico

Understanding near-surface wind variability is crucial to support wind power penetration on national electrical grids. High-resolution numerical simulations are often proposed as the best solution to study the fluctuation of wind resources. We compare Weather Research and Forecasting (WRF) and Modern-Era Retrospective Analysis for Research and Applications version 2 (MERRA-2) bias-corrected wind speeds at hub height at different spatial resolutions and transform them to wind power production using a logistic power curve fitted to wind power measurements; the comparisons are based on error statistics and time series spectral analysis. The results show that numerical models reproduce observed wind speeds with correlations higher than 0.9 for WRF and 0.8 for MERRA-2. Moreover, annual observed wind power is reproduced with a maximum difference from observations of 0.011. However, each resolution reproduces the magnitudes of high-resolution periodicities differently so that there is a clear relationship between grid size and signal variance at high frequencies, as variance is indirectly proportional to frequency. This relationship is expected for wind speed, but based on results, it can be associated also for capacity factor sampled at hourly intervals. Therefore, the main benefit of high spatial resolution lies in the added variance in frequencies at sub-daily time scales. The study of the added value of high-resolution simulations in this region contributes to current efforts to develop reliable forecasting tools and strategies to support the development of wind power as a reliable energy source.

Особенности возбуждения сейш в акватории вблизи Поронайска (о. Сахалин)

The results of studying potential sources of seiche excitation energy in the water area near Poronaisk (Sakhalin Island) using natural measurement data in 2008–2009 are presented. Time series data with a duration of about three months were collected by two autonomous sea-level recorders at one-second sample rate. Spectral analyses of time series made possible to conclude that wave processes with periods from 2 to 7 hours can be classified as seiches. Possible seiche periods calculated by numerical methods are very close to the periods of seiches detected in the Terpeniya Bay. The calculated envelopes of wave processes showed a good coincidence of the peaks of seiches with a period of 7 hours and wind waves, which confirms the transfer of energy from atmospheric disturbances to the seven-hour seiche. Seiche period of 3.5 hours is shown to be equal to the period of tidal harmonic 4M7. Thus, the resonance pass of energy transmission from tidal harmonic to seiche was revealed taking into account high for marine waters q-factor equal to 11.9 at the period of 3.5 hours. The highest seiches at a period of 2.7 hours are observed on the 6-8 day after maximum of daily tide with a period of 24.68 hours, which is close to the period of lunar tide harmonic M1. The analyses of excitation factors of seiches with 2-hour period showed that the excitation energy, or at least a part of it, is provided by atmospheric disturbances. Thus, the increasing of seiche height occurs during the winds of southern directions in the Terpeniya Bay.

Weekly patterns of motivation in students in higher education: a time series spectral analysis

Student motivation in higher education is a popular topic, though there is virtually nothing known about how motivation changes over the week. Based on observations of student behaviour in the classroom and considering popularly used expressions in everyday life (e.g. TGIF, Motivation Monday), we investigated how motivation changed over the week and patterns that repeated weekly. Data were collected from undergraduate students over 56 consecutive days to allow detection of motivation cycles and fit trigonometric functions to the data via spectral analysis. We also examined how mood and motivation covaried over the week. Our results indicated (a) motivation follows a cosine function with a weekly cycle – motivation begins to increase on Sunday and is relatively high early-week, tapers off on Friday, and is lowest on Saturday, (b) weekly cycles of mood, and (c) cyclical covariation between mood and motivation. Implications for research, students, and universities are discussed.

Forecasting based on spectral time series analysis: prediction of the Aurubis stock price

The attempt to predict stock price movements has occupied investors ever since. Reliable forecasts are a basis for investment management, and improved forecasting results lead to enhanced portfolio performance and sound risk management. While forecasting using the Wiener process has received great attention in the literature, spectral time series analysis has been disregarded in this respect. The paper’s main objective is to evaluate whether spectral time series analysis can produce reliable forecasts of the Aurubis stock price. Aurubis poses a suitable candidate for an investor’s portfolio due to its sound economic and financial situation and the steady dividend policy. Additionally, reliable management contributes to making Aurubis an investment opportunity. To judge if the achieved forecast results can be considered satisfactory, they are compared against the simulation results of a Wiener process. After de-trending the time series using an Augmented Dickey-Fuller test, the residuals were compartmentalized into sine and cosine functions. The frequencies, amplitude, and phase were obtained using the Fast Fourier transform. The mean absolute percentage error measured the accuracy of the stock price prediction, and the results showed that the spectral analysis was able to deliver superior results when comparing the simulation using a Wiener process. Hence, spectral time series can enhance stock price forecasts and consequently improve risk management.

Periodic Changes in the Abundance of Laxmann’s Shrew (Sorex caecutiens, Eulipotyphla) and Factors of Its Population Dynamics in the Foothill Taiga of the Northern Urals

Long-term data on fluctuations in the abundance of Laxmann’s shrew (Sorex caecutiens Laxmann) in the foothill taiga of the Northern Urals (Pechora-Ilych State Biosphere Reserve) have been evaluated using spectral analysis of time series. Periodic components in the population dynamics of the species have been revealed, including a statistically significant component that had a period of 3 years but was not highly regular. Analysis of factors accounting for variation in abundance parameters has shown that the population dynamics of S. caecutiens are influenced by both weather conditions and mechanisms of density-dependent regulation.

Forecasting Daily Graphs Active Energy Consumption of a Megapolis Taking Into Account Forecast Data of Daylight Illumination

The results are presented of the analysis of the daily average values graphs for the time series of active power, air temperature, natural illumination, cloudiness and precipitation for Moscow. The method of one-dimensional singular spectral analysis were obtained the results of the dependence of active power on air temperature and natural illumination and the dependence of active power on cloudiness, precipitation and illumination. Mathematical model was proposed of one-dimensional singular spectral analysis of time series of natural illumination, cloudiness and precipitation is proposed to improve the results of forecasting active power. The results are presented of the decomposition of active power and meteorological factors for 2019 year. To implement the mathematical model of one-dimensional singular spectral analysis of time series of active power and meteorological factors was used the developed algorithm in the R- software Studio in language R. Forecasts daily graphs of active power were made using predictive data of natural illumination obtained using a forecast model based on a neural network during February 2019.The proposed version of the one-dimensional singular spectral decomposition allows finding the relationship between the selected harmonic components of power consumption and natural illumination and power consumption and air temperature. For analyzing and transforming the time series of meteorological factors were used the data of the meteorological hardware-software complex PAC "Meteo".

ОСОБЕННОСТИ ЛЕТНЕГО МЕТЕОРОЛОГИЧЕСКОГО РЕЖИМА ЗАПАДНОГО ПЛАТО ЭЛЬБРУСА

The results of meteorological observations, carried out in the framework of the international project Ice Memory on the Western plateau of the Elbrus Mountain during the Second drilling expedition (24.06–17.07.2018), are analyzed. The analysis of the field data made together with the assessment of the large-scale meteorological fields from the NCEP/NCAR reanalysis did show that, on the whole, the observed meteorological conditions corresponded to the background state of the atmosphere in the Greater Caucasus in the summer season (with the exception of the anomalous high moisture content). The Western plateau is characterized by a high frequency of storm winds ( > 20 m/s) with low drifting snow and intensive snowfalls: the precipitation sum for the expedition period is approximately estimated as 150 mm. Spectral analysis of time series allowed establishing the significant role of the mountain and valley circulation in the formation of the meteorological regime. It is shown that the melting of snow in high-mountain conditions is determined by the incoming short-wave radiation, while turbulent flows of heat and moisture mainly transport energy from the surface. For 20 days of the observations, approximately 49 mm of snow (in the water equivalent) melted, and about 25% of this volume evaporated. The rest of the moisture diffused into the snow cover, and thus, remained in the accumulation layer. During the expedition, deviations of meteorological values from the norm were relatively small, so it can be assumed that the obtained value of the evaporated liquid on the Western plateau during the ablation period was close to the climatic mean.

Prolongation of Tick-Borne Encephalitis Cycles in Warmer Climatic Conditions.

Tick-borne encephalitis exhibits profound inter-annual fluctuations in incidence. Previous studies showed that three-fifths of the variation can be explained in terms of four superimposed oscillations: a quasi-biennial, triennial, pentennial, and a decadal cycle. This study was conducted to determine how these cycles could be influenced by climate change. Epidemiological data, spanning from the 1970s to the present, and originating from six regions/countries bridging Scandinavia and the Mediterranean, represented a temporal/latitudinal gradient. Spectral analysis of time series was used to determine variation in the cycles’ length/amplitude with respect to these gradients. The analysis showed that—whereas the lengths of the shorter cycles do not vary substantially—cycles in the decadal band tend to be longer southwards. When comparing the disease’s oscillations before- and after the mid-1990s, a shift towards longer oscillations was detected in the pentennial–decadal band, but not in the biennial– triennial band. Simultaneously, oscillations in the latter band increased in intensity whereas the decadal oscillations weakened. In summary, the rhythm of the cycles has been altered by climate change. Lengthened cycles may be explained by prolonged survival of some animal hosts, and consequently greater inertia in herd immunity changes, slowing down a feedback loop between the herd immunity and amount of virus circulating in nature.

Modeling the Gas price data Using Periodogram and Fourier Series Analysis

هذه الورقة تأخذ في الاعتبار تطبيق شكل الدورة Periodogram وتحليل سلسلة فورير Fourier Series Analysis وهي من الطرق اللامعلمية في التحليل في مجال الترددFrequency domain أو التحليل الطيفي spectral analysis للسلاسل الزمنية وذلك باستخدام بيانات مبيعات الغاز في الولايات المتحدة الامريكية في المدة من 1993-2014 والهدف الأساسي هو تشخيص دورة التقلبات وتقدير النموذج المناسب للبيانات وإيجاد قيم تنبؤات للمستقبل ولتحقيق هذه الأهداف تم الحصول على البيانات ومن ثم استخدمت طريقة شكل الدورة وسلسلة فورير لتحليل البيانات وبناء على التحليل وجد أن دورة التقلبات خلال المدة قيد الدراسة كانت تقريبا 135 شهراً، وقد تم تقدير نموذج سلسلة فورير للبيانات ذو كفاءة Accuracy عالية يشتمل على مكونات الاتجاه والموسمية والأخطاء وقد استخدمت معايير RMSE، MASE وMAE للتأكد من كفاءة النموذج ومن ثم تم استخدام النموذج للتنبؤ بأسعار الغاز لمدة ستة أشهر وقد ظهرت جودة التنبؤ أيضا عن طريق إيجاد 90% 95% فترات ثقة للتنبؤات. إضافة إلى ذلك تم تقديم تحليل في مجال الزمن لسلسلة البيانات وقد استخدمت طريقة بوكس جنكيز للحصول على نموذج ARMAالمناسب وإيجاد التنبؤات واخيرا تم إجراء مقارنة بين مقاييس الدقة لطريقتي التحليل في مجال الزمن والتحليل في مجال التردد من خلال النتائج المتحصل عليها فوجد أن طريقة مجال التردد تنافس طريقة مجال الزمن والفرق طفيف في الكفاءة.

REVELATION OF ACUTE INTESTINAL INFEKTIONS’ PERIODIC BIORYTHMS AND IDENTIFICATION OF DHE QUOLITATIVE PREVISIONS IN GYUMRI

Longtime observations show that epidemical situation in Republic of Armenia has beenand d continues to be difficult /problematic/, particularly in ters of intestinal infections. The naturesof infectious deseases as well as their epidemiological patterns have been changed.Revelation of the periodicity and the anpalysis of the peaks in frequency will help us to make possibleprevissions and insert goal-orientation into the epidemiological control.Taking into consideration etiological, clinical and epidemiological features of intestinal infections duringthe constal analysis of intestinal infection deseases /1977-2011/ over the separate infections of intestinalgroup. We use the method of spectral analysis of the group of harmony and time /variation.We have used the spectral analysis method of the time-series to clarify real epidemiological pattern and tomake predictions, and with the help of Byui-Balo's hidden frequency's revelation method we have redusedthe probability of a possible error bringing the resulted frequency close to the real, natural biorythm.Spectral analysisyears of time series, which characterize the avute intestinal infections, overoll morbidity of34 years allows us to conform /establish/ multirythmical characteristics of epidemiological dynamics. Itturns out, that there is a specific periodicity for the deseases of intestinal group with separate nozologicalgorms.Thus, theoretically, with the help of the above mentioned method, the following periodicity has beenreceived for the total group of intestinal deseases with /- (3,1+2,8) – (3,8+2,2) - 5 - 4,6 - 2,2 - 5,1 - 2,1 - 2,3–year interval, which coincides with the practice activities with - 6 - 6 - 5 - 5 - 2 - 5 - 2 - 2 – regularity.The investigated regularities predict approximate, probable periods /times/ of the risk. It is well known, thatthe periodic increase and decrease of the morbidity is different for the different germs of the infections ofintestinal group. It also has different subspecies of the germ .It should be noted that increases /peaks/ and falls have general tendency to decrease and stabilize for the allintestinal infections in terms of cumulative, namely there are on a lower level, comparate with the previousperiodicity.Biological cycle also depends on climatic factors associated with the improvement of conditions fordevelopment of the germ.Using spectral analysis of time series, risk periods of intestinal separate infections were determined forGyumri, which will be if not flashing, then probably years of high morbidity. According to previsions madeby us, the frequency of separate infections has the following schedule:Only permanent moniitoring and current and deep epidemiological research gives the opportunity to revealdistinct epidemiological regularities.Computer mapping programs, especially Arc View GIS geographical informational system gives such anopportunity. With the help of digital maps resulted from this program, it is possible to get regional andallocation of infections, prevalence of indicators. it's also possible to determine the extent of contamination,which gives the opportunity to make epidemic measures intentional and effective to save means andresources.

Cyclostratigraphic and δ13C record of the Lower Cretaceous Adriatic Platform, Croatia: Assessment of Milankovitch-forcing

The 700-m-thick Hauterivian to Albian section from the interior of the large, Adriatic Platform is exposed on Mljet and Korčula islands, Croatia. The cyclic platform consists of meter-scale parasequences, bundled into parasequence sets, superbundles and then into breccia-bounded depositional sequences. Spectral analysis of time series (cycle number vs. cycle thickness) shows peaks in the short-term eccentricity (95 to 130 kyr) bands and 160 to 200 kyr bands.Isotope samples from micrite matrix of mudstone and wackestone have δ13C values generally from −1.5 to +2‰ VPDB, and δ18O from −1 to −3.5‰ VPDB. Adriatic Platform δ13C values are shifted ~2‰ VPDB more negative than marine pelagic values. A δ13C and δ18O meteoric signal is limited to just beneath sequence boundaries, suggesting that the isotopic shift is due mainly to marine phreatic‐ and synorogenic burial diagenesis. Major excursions on the 5-point smoothed δ13C profile of the Adriatic Platform, tied biostratigraphically to δ13C curves from pelagic sections, include the oceanic anoxic events OAE1a, 1b, and 1c.Time series constructed from δ13C values (unsmoothed data) vs. stratigraphic position show peaks in the Milankovitch band, especially short-term eccentricity. Most positive peaks are near parasequence set boundaries (50 to 60%) and regressive parts of parasequences (20%). Although diagenetically shifted, the δ13C record retains a highly clipped memory of astronomically-driven global δ13C fluctuations albeit modified by platform water restriction during cyclic deposition.

PANORAMA E IMPORTÂNCIA ECONÔMICA DO CAFÉ NO MERCADO INTERNACIONAL DE COMMODITIES AGRÍCOLAS: UMA ANÁLISE ESPECTRAL

RESUMO: Este artigo procura discutir o panorama e a importância econômica do café para o Brasil ao fazer uso do instrumental empírico e analítico da análise espectral, tendo como base a série temporal dos preços do café no mercado internacional de commodities agrícolas de Nova Iorque (EUA). De fato, o café é um importante componente das exportações totais de vários países, inclusive do Brasil. Com o passar do tempo, o café acabou se tornando um produto, economicamente, importante de muitas famílias pelo mundo. Do ponto de vista metodológico, a pesquisa utilizou o arcabouço estatístico-econométrico oriundo da análise espectral de séries temporais. Os resultados obtidos dessa análise evidenciam que os choques climáticos sobre os preços do café poderão ter efeitos mais longos e que políticas agrícolas, que afetem diretamente a cadeia produtiva do café, poderão ter efeitos mais duradouros. Além disso, os resultados indicam que a tendência dos preços do café se configura numa combinação de tendências dos tipos determinística e estocástica.PALAVRAS-CHAVE: Análise Espectral, Brasil, Café, Commodities Agrícolas.

Methodology and Convergence Rates for Functional Time Series Regression

The functional linear model extends the notion of linear regression to the case where the response and covariates are iid elements of an infinite dimensional Hilbert space. The unknown to be estimated is a Hilbert-Schmidt operator, whose inverse is by definition unbounded, rendering the problem of inference ill-posed. In this paper, we consider the more general context where the sample of response/covariate pairs forms a weakly dependent stationary process in the respective product Hilbert space: simply stated, the case where we have a regression between functional time series. We consider a general framework of potentially nonlinear processes, exploiting recent advances in the spectral analysis of time series. Our main result is the establishment of the rate of convergence for the corresponding estimators of the regression coefficients, the latter forming a summable sequence in the space of Hilbert-Schmidt operators. In a sense, our main result can be seen as a generalisation of the classical functional linear model rates, to the case of time series, and rests only upon cumulant mixing conditions. While the analysis becomes considerably more involved in the dependent case, the rates are strikingly comparable to those of the i.i.d. case, but at the expense of an additional factor caused by the necessity to estimate the spectral density operator at a nonparametric rate, as opposed to the parametric rate for covariance operator estimation.

Estimation and Assessment of Temporal Stability of Periodicities of Droughts in Iran

The main objective of the present study was to identify the periodic behavior of monthly droughts in Iran. For this purpose, monthly precipitation data obtained from 41 synoptic stations for a period of 22 years (1992–2013) were used. To identify the frequency of different severities of drought, effective drought index (EDI) was calculated at monthly scale and then spectral analysis of time series of EDI was conducted for each station. Temporal stability of these periods was also estimated using the wavelet transform. The results of spectral analysis of monthly droughts in Iran showed that periodicities in time series of Iran’s droughts are very diverse and involve periods of 2 to 22 years. Assessment of temporal stability of periodicities using the wavelet transform also indicated that there is a dominant periodic interval (significant at a level of α = 0.1) only in 8 stations of Ardebil, Iranshahr, Zahedan, Bandar Lengeh, Shahroud, Khorramabad, Oroomieh, and Shahre Kord. Studying the variability of time series of EDI in 41 stations showed that the severity of wet years is declining and the severity of droughts is increasing. It was also observed that periodic intervals were shorter at the beginning but longer at the end of time series. This suggests that the probability of incidence of drought in Iran is increasing. Additionally, a reduction can be observed in interval between incidences of droughts in Iran. This means that the interval between occurrence of droughts were longer at the beginning and then shorter at the end of times series.