Box-Jenkins Research Articles

Forecasting Malaysian overnight islamic interbank rate using the Box-Jenkins model

Modelling the overnight Islamic interbank rate (IIR) is imperative to define the IIR performance as it would help the Islamic banks to adjust its costs of funding effectively and facilitate the policy makers to regulate a comprehensive monetary policy in Malaysia. The IIR framework which has been regulated by Bank Negara Malaysia under dual banking and financial system has always been overlooked in most previous studies in modelling the financial instruments rates. Therefore, it is vital to select the appropriate model as it resembles with the features of the IIR. The study assesses the forecasting performance of overnight IIR using the Box-Jenkins model. The suggested Box-Jenkins model has been applied to the Malaysian overnight IIR (in percentage) from 02/01/2001 to 31/12/2020. The empirical results determine that ARIMA (0,1,1) is the most appropriate model in forecasting overnight IIR as the model provides the smallest Mean Absolute Error (MAE), Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE). In multistep ahead forecasting, it can be summarised that ARIMA (0,1,1) model is able to trail the actual data trend of daily Malaysian overnight IIR up to 5-day ahead within 95% prediction intervals.

Modelability across time as a signature of identity construction on YouTube

Linguistic self-representation and identity construction on social media have attracted much scholarly attention. However, relevant studies tend to overlook the temporal dimension of social media, potentially systematic patterning of linguistic behavior across time, and the attendant implications of such a temporal perspective on identity. Combining an automated lexical tool (LIWC) and the Box–Jenkins method of statistical time series analysis, this paper shows how the ‘modelability’ of linguistic choices across time can be interpreted as signatures of identity construction and complement existing frameworks for identity analysis. Two levels of modelability are discussed—the availability of a well-fitting time series model as evidence of temporal patterning, and specific parameters of that model interpreted in context. These are demonstrated with a case study of the construction of ‘amateur expertise’ over 109 consecutive makeup tutorial videos on the popular YouTube channel ‘Nikkiestutorials’. Results show that the linguistic display of ‘analytical thinking’ reflects a strategy of ‘short term momentum’, the display of ‘clout’ and ‘authenticity’ a strategy of ‘short term restoration’, while the display of ‘emotional tone’ fluctuates randomly across time. The approach is further discussed in terms of its general principles and potential applications in other contexts of identity and related research.

Machine learning based predictive modeling and control of surface roughness generation while machining micro boron carbide and carbon nanotube particle reinforced Al-Mg matrix composites

Machine learning has revolutionized the way complex problems are solved in engineering. In the current work, machine learning methodology has been applied for predictive modeling of surface roughness generation during machining of Al-Mg based metal matrix composites (MMCs) reinforced with micro boron carbide and multiwalled carbon nanotube particles. Machine learning was used for parameter estimation of modeling structures such as auto regressive with exogenous variables (ARX), auto regressive moving average with exogenous variables (ARMAX), Box Jenkins (BJ) and Output Error (OE). The identified models were validated on the basis of FIT, final prediction error (FPE) and mean squared error (MSE). The PID, fractional order PID (FOPID), complex order PID (COPID) and model predictive controllers (MPC) were employed to effectively control machined surface roughness based on the best performing predictive models. Primary results indicate that: (1) CNT MMCs generate surface roughness comparable to that due to the micro MMCs with tenfold higher reinforcement fractions (2) ARX441 and ARMAX3331 are the best performing predictive models for the nano and micro MMCs respectively (3) PID and MPC are the best controllers for micro and nano MMC systems respectively considering the peak overshoots as the foremost performance metric (safety), followed by settling time (productivity).

Malaria Temporal Variation and Modelling Using Time-Series in Sussundenga District, Mozambique.

Malaria is one of the leading causes of morbidity and mortality in Mozambique, which has the fifth highest prevalence in the world. Sussundenga District in Manica Province has documented high P. falciparum incidence at the local rural health center (RHC). This study’s objective was to analyze the P. falciparum temporal variation and model its pattern in Sussundenga District, Mozambique. Data from weekly epidemiological bulletins (BES) was collected from 2015 to 2019 and a time-series analysis was applied. For temporal modeling, a Box-Jenkins method was used with an autoregressive integrated moving average (ARIMA). Over the study period, 372,498 cases of P. falciparum were recorded in Sussundenga. There were weekly and yearly variations in incidence overall (p < 0.001). Children under five years had decreased malaria tendency, while patients over five years had an increased tendency. The ARIMA (2,2,1) (1,1,1) 52 model presented the least Root Mean Square being the most appropriate for forecasting. The goodness of fit was 68.15% for malaria patients less than five years old and 73.2% for malaria patients over five years old. The findings indicate that cases are decreasing among individuals less than five years and are increasing slightly in those older than five years. The P. falciparum case occurrence has a weekly temporal pattern peaking during the wet season. Based on the spatial and temporal distribution using ARIMA modelling, more efficient strategies that target this seasonality can be implemented to reduce the overall malaria burden in both Sussundenga District and regionally.

Sex-specific deaths in Norway and Sweden during the COVID-19 pandemic: Did mandates make a difference?

To determine whether differences between Norway's and Sweden's attempts to contain SARS-CoV-2 infection coincided with detectably different changes in their all-cause mortality sex ratios. Measuring temporal variation in the all-cause mortality sex ratio before and during the pandemic in populations exposed to different constraints on risky behavior would allow us to better anticipate changes in the ratio and to better understand its association with infection control strategies. I apply time Box-Jenkins modeling to 262 months of pre-pandemic mortality sex ratios to arrive at counterfactual values of 10 intra-pandemic ratios. I compare counterfactual to observed values to determine if intra-pandemic ratios differed detectably from those expected as well as whether the Norwegian and Swedish differences varied from each other. The male to female mortality sex ratio in both Norway and Sweden increased during the pandemic. I, however, find no evidence that the increase differed between the two countries despite their different COVID-19 containment strategies. Societal expectations of who will die during the COVID-19 pandemic will likely be wrong if they assume pre-pandemic mortality sex ratios because the intra-pandemic ratios appear, at least in Norway and Sweden, detectably higher. The contribution of differences in policies to reduce risky behavior to those higher ratios appears, however, small.

Comparison of the Performance of the SANN, SARIMA and ARIMA Models for Forecasting Quarterly GDP of Nigeria

This research aimed at modelling and forecasting the quarterly GDP of Nigeria using the Seasonal Artificial Neural Network (SANN), SARIMA and Box-Jenkins models as well as comparing their predictive performance. The three models mentioned earlier were successfully fitted to the data set. Tentative architecture for the SANN was suggested by varying the number of neurons in the hidden layer while that of the input and output layer remained constant at 4. It was observed that the best architecture was when the hidden layer had 10 neurons and thus SANN (4-10-4) was chosen as the best. In fitting the ARIMA/SARIMA models, the Augmented Dickey Fuller (ADF) test was used to check for stationarity. Variance stabilization and Stationarity were achieved after logarithm transformation and first regular differencing. The ARIMA/SARIMA model with lowest AIC, BIC and HQIC values was chosen as the best amongst the competing models and fitted to the data. The adequacy of the fitted models was confirmed observing the correlogram of the residuals and the Ljung-Box Chi-Squared test result. The SANN model performed better than the SARIMA and ARIMA models as it had a Mean Squared Error value of 0.004 while SARIMA and ARIMA had mean squared errors of 0.527 and 0.705 respectively. It was concluded that the SANN which is a non-linear model be used in modelling the quarterly GDP of Nigeria. Hybrid models which combine the strength of individual models are recommended for further research.

Expectation of Rice Pod Production in Iraq by Using Time Series

The research aims to shed light on the reality of the production of Rice pods in Iraq during the period of time (1943-2019) and its development with time, then predict the production of Rice pods based on three Models of prediction Models, which are the time regression Model on production, in addition to studying the effect of harvested area on production quantities. Then forecasting the production of the Rice pods according to the Model of the regression of the harvested area on the production, the Autoregression Model, and the integrative moving averages (Box Jenkins Models), and in the end the comparison between the expected values ​​of production through the three Models to know the best Model to represent the time series of production of the Rice pods , through the use of the statistical program (SPSS (, Based on annual secondary data represented by the quantities of Rice pods, and the size of the harvested areas of this material in Iraq for the period from 1945 until 2019 obtained from (Central Statistical Organization, Iraq, 2020)

Modeling and forecasting of principal minerals production

Although coal reserves are abundant in Pakistan, still share of gas and oil is about 65% in the energy mix. Pakistan, despite being a mineral-enriched country, is facing an alarming situation as its power generation is based on foreign exchange. The mineral sector of Pakistan is dominated by four principal minerals which are gas, oil, gypsum, and coal, while gypsum being a source of reclamation and poverty reduction. There is a strong need to analyze and forecast the production of these four principal minerals to cope up with emerging challenges. Data contains 114 observations from the period of July 2005 to December 2014, measured in terms of metric tonnes (MT). In parametric models, Box-Jenkins (B-J) methodology, a regression model with auto-regressive errors (ARAR), and Holt-Winter (HW) method are used to model. In nonparametric models, univariate singular spectrum analysis (SSA) and multivariate SSA (MSSA) modeling approach are applied. Data is split into train and test data in order to specify a suitable model for forecasting. Root Mean Square Error (RMSE), Mean Absolute Percentage Error, and Theil’s U statistic are utilized as the measure of accuracy. For gas and coal, HW model is a suitable model to forecast. For gypsum and oil, Auto-regressive Integrated Moving Average (Box Jenkins ARIMA) and MSSA provide more accurate predictions, respectively. The forecasts for gas and gypsum as compared to 2014 are expected to be approximately 11 % and 45 %, respectively, more in 2020. In 2020, the forecasts of oil are expected to be eight times more than in 2014. The production of coal in 2020 is expected to decrease 12 % than in 2014. There is a strong need to optimize the production of coal by providing incentives for exploration and mining. The stakeholders should make serious efforts to bring the production of coal at an optimum level such as by providing modern equipment and high incentives to promote coal mining and exploration.

High performance approach for water level forecasting in Yom River basin of Thailand

Analyses of average monthly water level (AMWL) time series (April 2007 - March 2020) at four water level measurement stations (Y.31, Y.20, Y.1C, Y.37) for wet and dry seasons in the Yom River basin of Thailand. Using Box-Jenkins method, eight best-fit seasonal ARIMA models for one hydrological year forecasting for wet and dry seasons of AMWL were selected; among from twenty-four possible models, by minimum values of AIC, SBIC RMSE, and MAPE. Besides, The comparisons with two benchmark models, Holt-Winters’ Seasonal additive method, and Seasonal Naive method were applied. Results indicated that: The four selected SARIMA models for wet seasons of Y.31, Y20, Y1C, and Y.37 are SARIMA(1,1,1)(1,0,0)[6], SARIMA(1,1,1)(1,0,0)[6], SARIMA(1,1,2)(1,0,0)[6], and SARIMA(1,1,1)(1,0,0)[6], respectively. While the models for dry seasons are SARIMA(0,1,1)(2,0,0)[6], SARIMA(1,1,1)(1,0,1)[6], SARIMA(1,1,1)(2,0,0)[6], and SARIMA(1,0,0)(1,0,1)[6]. The forecasting performance are the minimum values of RMSE and MAPE between SARIMA and the benchmark models. The SARIMA model is the best approach for Y.31 Station [Wet Season], Y.31 Station [Dry Season], and Y.37 Station [Dry Season], while the best method for Y.20 Station [Wet Season], Y.1C Station [Wet Season], Y.37 Station [Wet Season], Y.20 Station [Dry Season], and Y.1C Station [Dry Season] is Holt-Winters’ seasonal additive method. The upstream station (Y.31 station) has higher accuracy than the downstream station (Y.37 station) due to human activities that disturb hydrological changes. Furthermore, the dry season forecasting is more accurate than the wet season.

Development of Short-term Flood Forecast Using ARIMA

The aim of this study is to use the Box-Jenkins method to build a flood forecast model by analysing real-time flood parameters for Pengkalan Rama, Melaka river, hereafter known as Sungai Melaka. The time series was tested for stationarity using the Augmented Dickey-Fuller (ADF) and differencing method to render a non-stationary time series stationary from 1 July 2020 at 12:00am to 30th July 2020. A utocorrelation (ACF) and partial autocorrelation (PACF) functions was measured and observed using visual observation to identify the suitable model for water level time series. The parameter Akaike Information Information Criterion (AIC) and the Bayesian Information Criterion (BIC) were used to find the best ARIMA model (BIC). ARIMA (2, 1, 3) was the best ARIMA model for the Pengkalan Rama, with an AIC of 5653.7004 and a BIC of 5695.209. The ARIMA (2, 1, 3) model was used to produce a lead forecast of up to 7 hours for the time series. The model's accuracy was tested by comparing the original and forecast sequences by using Pearson r and R squared. The ARIMA model appears to be adequate for Sungai Melaka, according to the findings of this study. Finally, the ARIMA model provides an appropriate short-term water level forecast with a lead forecast of up to 7 hours. As a result, the ARIMA model is undeniably ideal for river flooding.

Forecasting outbreak of COVID-19 in Turkey; Comparison of Box–Jenkins, Brown’s exponential smoothing and long short-term memory models

The new coronavirus disease (COVID-19), which first appeared in China in December 2019, has pervaded throughout the world. Because the epidemic started later in Turkey than other European countries, it has the least number of deaths according to the current data. Outbreak management in COVID-19 is of great importance for public safety and public health. For this reason, prediction models can decide the precautionary warning to control the spread of the disease. Therefore, this study aims to develop a forecasting model, considering statistical data for Turkey. Box-Jenkins Methods (ARIMA), Brown’s Exponential Smoothing model and RNN-LSTM are employed. ARIMA was selected with the lowest AIC values (12.0342, -2.51411, 12.0253, 3.67729, -4.24405, and 3.66077) as the best fit for the number of total case, the growth rate of total cases, the number of new cases, the number of total death, the growth rate of total deaths and the number of new deaths, respectively. The forecast values of the number of each indicator are stable over time. In the near future, it will not show an increasing trend in the number of cases for Turkey. In addition, the pandemic will become a steady state and an increase in mortality rates will not be expected between 17–31 May. ARIMA models can be used in fresh outbreak situations to ensure health and safety. It is vital to make quick and accurate decisions on the precautions for epidemic preparedness and management, so corrective and preventive actions can be updated considering obtained values.

Phenology as accuracy metrics for vegetation index forecasting over Tunisian forest and cereal cover types

ABSTRACT Different studies on predicting future green cover changes exist with various success levels. Each one focuses on a different story about which model is more appropriate. Therefore, finding a suitable model remains a difficult task due to the remotely sensed data issues and the complexity of the vegetation cover change process. Despite the unicity of vegetation indices time series, the forecasting assessment relies basically on the commonly used forecast error measurements (e.g. Mean Square Error (MSE), Root MSE (RMSE), and the symmetric Mean Absolute Percentage Error (sMAPE), etc.) which may not reflect the real potential of the fitted forecasting model. Herein, the experimentation of forecasting vegetation indices employing two univariate time series models and new accuracy metrics is discussed. Box Jenkins models (Seasonal AutoRegressive Integrated Moving Average (ARIMA) model) and neural network model (nonlinear autoregressive (NAR) model) are applied individually and coupled (NAR-NAR and NAR-ARIMA) based on a multi-resolution analysis-wavelet transform. These models’ forecasting ability is evaluated using 16-days Moderate Resolution Imaging Spectroradiometer Normalized Difference Vegetation Index (NDVI) time series data of two different vegetation cover types of northwestern area in Tunisia. The major finding highlights firstly the importance of integration of the decomposition step to show off the hidden components of vegetation indices. The commonly used accuracy measures show that the coupled neural networks model outperforms other models. Then, interesting conclusions were drawn when phenological metrics are used as performance measures. Herein, Box Jenkins forecasting model generates a better NDVI curve shape than hybrid models despite their low RMSE measures. This is mainly due to good estimation of some phenological events, namely, the amplitude, the peak and the season’s length. Generally, Box Jenkin model excels at handling quick variations. By contrast, combined models show better phenological metrics’ estimation when the observations are complex or describe long time periods. Based on these findings, we suggest that the choice of the evaluation metric must be related to the future forecaster interest.

Time Series Analysis of Road Traffic Accidents in Ghana

This study uses Time Series models to predict the annual traffic accidents in Ghana. The traffic accidents data spanning from January 1990 to December 2019 was used. The Box-Jenkins model building strategy was used. The Augmented Dickey Fuller (ADF) test showed that the accident data was stationary. Three ARMA models were suggested based on the ACF and PACF plots of the differenced series, these were ARMA (0,0), ARIMA (1,0), and ARMA (2,0). The model with the smallest corrected Akaike Information Criteria (AICs) and Bayesian Information Criteria (BIC) was chosen as the best model. The Ljung-Box statistics among others were used in assessing the quality of the model. ARMA (1,0) was the best model for the Ghana annual Traffic Accident data. The results showed that, from January to July, it would be difficult to make accurate estimates of the number of road incidents for the years leading up to 2020. This was due to the fact that the white noise process values were statistically independent at various times.

Forecast and soybean production base in East Java

East Java Province as one base regions of the soybean commodity. Soybean also provides added value, when processed into tofu, tempeh, chips, soy sauce and other products. The fact is that agro-industry activities are still dependent on imported raw materials. The objectives of this study is to forecast soybean commodity production and find out soybean production base in East Java. The locations of the study are East Java Province, because it has the largest harvest area and highest production in Indonesia. The research method applies an analytical method. The data collection method uses secondary data, in which the available statistical data has been published by BPS. The data analysis method used is base and non-base sector analysis Location Quotient and Box-Jenkins Model (ARIMA) analysis. The results show that out of 38 district and city in East Java, ther are 10 district soybeans production base. The district of soybean production base is Sampang Banyuwangi, Nganjuk, Bangkalan, Lamongan, Bojonegoro, Trenggalek, Blitar, Ponorogo and Jember District. The highest LQ value of soybean base production is Sampang district of 5,49; Banyuwangi district of 2,77 and Nganjuk district of 2,00. The development of soybean production forecasting in East Java in 2018-2027 fluctuations, tends to be constant and increase.

Twinning during the pandemic: Evidence of selection in utero.

Background and objectivesThe suspicion that a population stressor as profound as the COVID-19 pandemic would increase preterm birth among cohorts in gestation at its outset has not been supported by data collected in 2020. An evolutionary perspective on this circumstance suggests that natural selection in utero, induced by the onset of the pandemic, caused pregnancies that would otherwise have produced a preterm birth to end early in gestation as spontaneous abortions. We test this possibility using the odds of a live-born twin among male births in Norway as an indicator of the depth of selection in birth cohorts.MethodologyWe apply Box–Jenkins methods to 50 pre-pandemic months to estimate counterfactuals for the nine birth cohorts in gestation in March 2020 when the first deaths attributable to SARS-CoV-2 infection occurred in Norway. We use Alwan and Roberts outlier detection methods to discover any sequence of outlying values in the odds of a live-born twin among male births in exposed birth cohorts. ResultsWe find a downward level shift of 27% in the monthly odds of a twin among male births beginning in May and persisting through the remainder of 2020.Conclusions and implicationsConsistent with evolutionary theory and selection in utero, birth cohorts exposed in utero to the onset of the COVID-19 pandemic yielded fewer male twins than expected.Lay SummaryOur finding of fewer than expected male twin births during the onset of the COVID-19 pandemic provides more evidence that evolution continues to affect the characteristics and health of contemporary populations.

Forecasting the Main Indicators of Insurance Companies

Abstract. Introduction. Econometric and adaptive models make it possible to predict financial and economic indicators in the short and long term. The most common forecasting models are linear trend models, adaptive Brown, Holt, Holt-Winters, Box-Jenkins, autoregressive and other models. It has been proved that the use of adaptive forecasting models becomes especially relevant in the context of constant changes in the external environment, instability of the economic and political situation. Purpose. The purpose of this article is to substantiate the expediency of using forecasting methods when planning the development of the insurance market and to implement the procedure for forecasting the main indicators of its development using modern methods and techniques. Results. Improving the efficiency of the insurance market is facilitated by the correct organization of its planning and the direct implementation of the planned indicators. Optimality of planning is determined by the degree to which the accuracy of the predicted level of planned indicators is achieved. The methodology and results of the forecast of insurance payments made for the near future can be taken as a basis for drawing up current and strategic plans of insurance companies. Conclusions. It has been established that one of the barriers to the effective development of the insurance market in general and insurance companies in particular is the insufficient level of planning of their activities, especially in terms of forecasting key indicators. The procedure for forecasting the receipt of insurance payments was implemented using modern forecasting methods. The effectiveness of the Brown’s adaptive model for short-term planning of insurance premiums is proved. The proposed model was tested for adequacy, on its basis, recommendations were developed for further application in the practice of insurance companies. Keywords: insurance; insurance market; planning; forecasting; econometric model; adaptive model; trend extrapolation.

Statistical modeling of monthly streamflow using time series and artificial neural network models: Hindiya Barrage as a case study

Abstract Autoregressive Integrated Moving Average (ARIMA) Box-Jenkins models combine the autoregressive and moving average models to a stationary time series after the appropriate transformation, while the nonlinear autoregressive (N.A.R.) or the autoregressive neural network (ARNN) models are of the kind of multi-layer perceptron (M.L.P.), which compose an input layer, hidden layer and an output layer. Monthly streamflow at the downstream of the Euphrates River (Hindiya Barrage) /Iraq for the period January 2000 to December 2019 was modeled utilizing ARIMA and N.A.R. time series models. The predicted Box-Jenkins model was ARIMA (1,1,0) (0,1,1), while the predicted artificial neural network (N.A.R.) model was (M.L.P. 1-3-1). The results of the study indicate that the traditional Box-Jenkins model was more accurate than the N.A.R. model in modeling the monthly streamflow of the studied case. Performing a one-step-ahead forecast during the year 2019, the forecast accuracy between the forecasted and recorded monthly streamflow for both models was as follows: the Box-Jenkins model gave root mean squared error (RMSE = 48.7) and the coefficient of determination = 0.801), while the (NAR) model gave (RMSE = 93.4) and = 0.269). Future projection of the monthly stream flow through the year 2025, utilizing the Box-Jenkins model, indicated the existence of long-term periodicity.

The Immediate Impact of Covid19 on Tourism Employment in Spain: Debunking the Myth of Job Precariousness?

ABSTRACT This note explores the immediate impact that the COVID-19 crisis has had on tourist and non-tourist employment in Spain as a result of the state of alarm and period of confinement decreed from March 14th. The employment and self-employment series drawn from the Social Security affiliation data corresponding to the period between January 2017 and April 2020 are examined using the classical Box–Jenkins method (ARIMA) and the more recent Bayesian Structural Time-Series Models.

Predicting the detection of leprosy in a hyperendemic area of Brazil: Using time series analysis.

Brazil has the second highest prevalence of leprosy worldwide. Autoregressive integrated moving average models are useful tools in surveillance systems because they provide reliable forecasts from epidemiological time series. To evaluate the temporal patterns of leprosy detection from 2001 to 2015 and forecast for 2020 in a hyperendemic area in northeastern Brazil. A cross-sectional study was conducted using monthly leprosy detection from the Brazil information system for notifiable diseases. The Box-Jenkins method was applied to fit a seasonal autoregressive integrated moving average model. Forecasting models (95% prediction interval) were developed to predict leprosy detection for 2020. A total of 44,578 cases were registered with a mean of 247.7 cases per month. The best-fitted model to make forecasts was the seasonal autoregressive integrated moving average ((1,1,1); (1,1,1)). It was predicted 0.32 cases/100,000 inhabitants to January of 2016 and 0.38 cases/100,000 inhabitants to December of 2020. This study used secondary data from Brazil information system for notifiable diseases; hence, leprosy data may be underreported. The forecast for leprosy detection rate for December 2020 was < 1 case/100,000 inhabitants. Seasonal autoregressive integrated moving average model has been shown to be appropriate and could be used to forecast leprosy detection rates. Thus, this strategy can be used to facilitate prevention and elimination programmes.

Statistical modeling of sea ice concentration in the northwest region of the Antarctic Peninsula

Sea ice is one of the main components of the cryosphere that modifies the exchange of heat and moisture between the ocean and atmosphere, regulating the global climate. In this sense, it is important to identify the concentration of sea ice in different regions of Antarctica in order to measure the impact of environmental changes on the region's ecosystem. The objective of this study was to evaluate the performance of the multiple linear regression and Box-Jenkins methods for predicting the concentration of sea ice along the northwest coast of the Antarctic Peninsula. Sea ice concentration data from May to November for the period 1979-2018 were extracted from passive remote sensors including a scanning multichannel microwave radiometer, special sensor microwave imager, and special sensor microwave imager/sounder. Meteorological variables from the atmospheric reanalysis model ERA5 of the European Center for Medium-Range Weather Forecasts were used as predictor variables, and the leave-one-out cross-validation technique was used to calibrate and validate the models. It was found that both statistical models have similar performance when analyzing residual analysis results, root mean square error of cross-validation, and final accuracy and residual standard deviation, these responses being related to the regionalization of the study area and to the Box-Jenkins presents strong, homogeneous, and stable correlations in the time series modeled for each pixel.