scholarly journals Burned area prediction with semiparametric models

2016 ◽  
Vol 25 (6) ◽  
pp. 669 ◽  
Author(s):  
Miguel Boubeta ◽  
María José Lombardía ◽  
Wenceslao González-Manteiga ◽  
Manuel Francisco Marey-Pérez
Keyword(s):  
Time Series ◽  
Forest Fires ◽  
Moving Average ◽  
Semiparametric Models ◽  
Burned Area ◽  
Autoregressive Moving Average ◽  
Moving Average Process ◽  
North West ◽  
B Splines ◽  
Non Parametric

Wildfires are one of the main causes of forest destruction, especially in Galicia (north-west Spain), where the area burned by forest fires in spring and summer is quite high. This work uses two semiparametric time-series models to describe and predict the weekly burned area in a year: autoregressive moving average (ARMA) modelling after smoothing, and smoothing after ARMA modelling. These models can be described as a sum of a parametric component modelled by an autoregressive moving average process and a non-parametric one. To estimate the non-parametric component, local linear and kernel regression, B-splines and P-splines were considered. The methodology and software were applied to a real dataset of burned area in Galicia for the period 1999–2008. The burned area in Galicia increases strongly during summer periods. Forest managers are interested in predicting the burned area to manage resources more efficiently. The two semiparametric models are analysed and compared with a purely parametric model. In terms of error, the most successful results are provided by the first semiparametric time-series model.

ARMA processes have maximal entropy among time series with prescribed autocovariances and impulse responses

1985 ◽  
Vol 17 (04) ◽  
pp. 810-840 ◽  
Author(s):  
Jürgen Franke
Keyword(s):  
Time Series ◽  
Impulse Response ◽  
Moving Average ◽  
Autoregressive Process ◽  
Natural Generalization ◽  
Maximal Entropy ◽  
Autoregressive Moving Average ◽  
Moving Average Process ◽  
Arma Process ◽  
Arma Processes

The maximum-entropy approach to the estimation of the spectral density of a time series has become quite popular during the last decade. It is closely related to the fact that an autoregressive process of order p has maximal entropy among all time series sharing the same autocovariances up to lag p. We give a natural generalization of this result by proving that a mixed autoregressive-moving-average process (ARMA process) of order (p, q) has maximal entropy among all time series sharing the same autocovariances up to lag p and the same impulse response coefficients up to lag q. The latter may be estimated from a finite record of the time series, for example by using a method proposed by Bhansali (1976). By the way, we give a result on the existence of ARMA processes with prescribed autocovariances up to lag p and impulse response coefficients up to lag q.

ARMA processes have maximal entropy among time series with prescribed autocovariances and impulse responses

1985 ◽  
Vol 17 (4) ◽  
pp. 810-840 ◽  
Author(s):  
Jürgen Franke
Keyword(s):  
Time Series ◽  
Impulse Response ◽  
Moving Average ◽  
Autoregressive Process ◽  
Natural Generalization ◽  
Maximal Entropy ◽  
Autoregressive Moving Average ◽  
Moving Average Process ◽  
Arma Process ◽  
Arma Processes

The maximum-entropy approach to the estimation of the spectral density of a time series has become quite popular during the last decade. It is closely related to the fact that an autoregressive process of order p has maximal entropy among all time series sharing the same autocovariances up to lag p. We give a natural generalization of this result by proving that a mixed autoregressive-moving-average process (ARMA process) of order (p, q) has maximal entropy among all time series sharing the same autocovariances up to lag p and the same impulse response coefficients up to lag q. The latter may be estimated from a finite record of the time series, for example by using a method proposed by Bhansali (1976). By the way, we give a result on the existence of ARMA processes with prescribed autocovariances up to lag p and impulse response coefficients up to lag q.

scholarly journals Relating Spatiotemporal Patterns of Forest Fires Burned Area and Duration to Diurnal Land Surface Temperature Anomalies

2018 ◽  
Vol 10 (11) ◽  
pp. 1777 ◽  
Author(s):  
Carmine Maffei ◽  
Silvia Alfieri ◽  
Massimo Menenti
Keyword(s):  
Remote Sensing ◽  
Time Series ◽  
Surface Temperature ◽  
Land Surface Temperature ◽  
Forest Fires ◽  
Land Surface ◽  
Fire Danger ◽  
Parametric Models ◽  
Burned Area ◽  
Informative Content

Forest fires are a major source of ecosystem disturbance. Vegetation reacts to meteorological factors contributing to fire danger by reducing stomatal conductance, thus leading to an increase of canopy temperature. The latter can be detected by remote sensing measurements in the thermal infrared as a deviation of observed land surface temperature (LST) from climatological values, that is as an LST anomaly. A relationship is thus expected between LST anomalies and forest fires burned area and duration. These two characteristics are indeed controlled by a large variety of both static and dynamic factors related to topography, land cover, climate, weather (including those affecting LST) and anthropic activity. To investigate the predicting capability of remote sensing measurements, rather than constructing a comprehensive model, it would be relevant to determine whether anomalies of LST affect the probability distributions of burned area and fire duration. This research approached the outlined knowledge gap through the analysis of a dataset of forest fires in Campania (Italy) covering years 2003–2011 against estimates of LST anomaly. An LST climatology was first computed from time series of daily Aqua-MODIS LST data (product MYD11A1, collection 6) over the longest available sequence of complete annual datasets (2003–2017), through the Harmonic Analysis of Time Series (HANTS) algorithm. HANTS was also used to create individual annual models of LST data, to minimize the effect of varying observation geometry and cloud contamination on LST estimates while retaining its seasonal variation. LST anomalies where thus quantified as the difference between LST annual models and LST climatology. Fire data were intersected with LST anomaly maps to associate each fire with the LST anomaly value observed at its position on the day previous to the event. Further to this step, the closest probability distribution function describing burned area and fire duration were identified against a selection of parametric models through the maximization of the Anderson-Darling goodness-of-fit. Parameters of the identified distributions conditional to LST anomaly where then determined along their confidence intervals. Results show that in the study area log-transformed burned area is described by a normal distribution, whereas log-transformed fire duration is closer to a generalized extreme value (GEV) distribution. The parameters of these distributions conditional to LST anomaly show clear trends with increasing LST anomaly; significance of this observation was verified through a likelihood ratio test. This confirmed that LST anomaly is a covariate of both burned area and fire duration. As a consequence, it was observed that conditional probabilities of extreme events appear to increase with increasing positive deviations of LST from its climatology values. This confirms the stated hypothesis that LST anomalies affect forest fires burned area and duration and highlights the informative content of time series of LST with respect to fire danger.

scholarly journals The time series regression analysis in evaluating the economic impact of COVID-19 cases in Indonesia

2021 ◽  
Vol 16 (3) ◽  
pp. 197-210
Author(s):  
Utriweni Mukhaiyar ◽  
Devina Widyanti ◽  
Sandy Vantika
Keyword(s):  
Time Series ◽  
Exchange Rate ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Transfer Function Model ◽  
Function Model ◽  
Time Series Regression ◽  
Vector Autoregressive ◽  
Daily Data ◽  
The Impact

This study aims to determine the impact of COVID-19 cases in Indonesia on the USD/IDR exchange rate using the Transfer Function Model and Vector Autoregressive Moving-Average with Exogenous Regressors (VARMAX) Model. This paper uses daily data on the COVID-19 case in Indonesia, the USD/IDR exchange rate, and the IDX Composite period from 1 March to 29 June 2020. The analysis shows: (1) the higher the increase of the number of COVID-19 cases in Indonesia will significantly weaken the USD/IDR exchange rate, (2) an increase of 1% in the number of COVID-19 cases in Indonesia six days ago will weaken the USD/IDR exchange rate by 0.003%, (3) an increase of 1% in the number of COVID-19 cases in Indonesia seven days ago will weaken the USD/IDR exchange rate by 0.17%, and (4) an increase of 1% in the number of COVID-19 cases in Indonesia eight days ago will weaken the USD/IDR exchange rate by 0.24%.

Parametric estimators for stationary time series with missing observations

1981 ◽  
Vol 13 (01) ◽  
pp. 129-146 ◽  
Author(s):  
W. Dunsmuir ◽  
P. M. Robinson
Keyword(s):  
Unknown Parameter ◽  
Strong Consistency ◽  
Moving Average ◽  
Stationary Time Series ◽  
Autoregressive Moving Average ◽  
Missing Observations ◽  
Parameter Vector ◽  
Moving Average Process ◽  
The Third ◽  
Unknown Parameter Vector

Three related estimators are considered for the parametrized spectral density of a discrete-time process X(n), n = 1, 2, · · ·, when observations are not available for all the values n = 1(1)N. Each of the estimators is obtained by maximizing a frequency domain approximation to a Gaussian likelihood, although they do not appear to be the most efficient estimators available because they do not fully utilize the information in the process a(n) which determines whether X(n) is observed or missed. One estimator, called M3, assumes that the second-order properties of a(n) are known; another, M2, lets these be known only up to an unknown parameter vector; the third, M1, requires no model for a(n). Under representative sets of conditions, which allow for both deterministic and stochastic a(n), the strong consistency and asymptotic normality of M1, M2, and M3 are established. The conditions needed for consistency when X(n) is an autoregressive moving-average process are discussed in more detail. It is also shown that in general M1 and M3 are equally efficient asymptotically and M2 is never more efficient, and may be less efficient, than M1 and M3.

Poisson mixed models for predicting number of fires

2019 ◽  
Vol 28 (3) ◽  
pp. 237
Author(s):  
Miguel Boubeta ◽  
María José Lombardía ◽  
Manuel Marey-Pérez ◽  
Domingo Morales
Keyword(s):  
Forest Fires ◽  
Mixed Models ◽  
Mixed Model ◽  
Parametric Bootstrap ◽  
Temporal Correlation ◽  
Autoregressive Process ◽  
Burned Area ◽  
Time Effects ◽  
North West ◽  
Temporal Models

Wildfires are considered one of the main causes of forest destruction. In recent years, the number of forest fires and burned area in Mediterranean regions have increased. This problem particularly affects Galicia (north-west of Spain). Conventional modelling of the number of forest fires in small areas may have a high error. For this reason, four area-level Poisson mixed models with time effects are proposed. The first two models contain independent time effects, whereas the random effects of the other models are distributed according to an autoregressive process AR(1). A parametric bootstrap algorithm is given to measure the accuracy of the plug-in predictor of fire number under the temporal models. A significant prediction improvement is observed when using Poisson regression models with random time effects. Analysis of historical data finds significant meteorological and socioeconomic variables explaining the number of forest fires by area and reveals the presence of a temporal correlation structure captured by the area-level Poisson mixed model with AR(1) time effects.

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