Method For Time Series Forecasting Research Articles

Rethinking self-supervised learning for time series forecasting: A temporal perspective

Self-supervised learning has garnered significant attention for its ability to learn meaningful representations. Recent advancements have introduced self-supervised methods for time series forecasting. However, these efforts have faced limitations due to two primary drawbacks. Firstly, these approaches often borrow techniques from vision and language domains without adequately addressing the unique temporal dependencies inherent in time series data. Secondly, time series often show that the distribution shifts over time, which makes accurate forecasting challenging. In response to these issues, we propose TempSSL, a self-supervised learning framework designed for time series forecasting. TempSSL divides the time series data into context (history data) and target (future data), employing two pre-training strategies: (1) Temporal Masked Modeling (TMM) designed to capture temporal dependencies by reconstructing future time series based on historical context; (2) Temporal Contrastive Learning (TCL) employs context and target as positive samples to enhance discriminative representations and mitigate distribution shifts within the time series. TempSSL’s innovation lies in two key aspects. Firstly, it underscores the importance of temporal dependencies for time series forecasting by designing specific pre-training tasks. Secondly, it effectively integrates contrastive learning and masked modeling, leveraging their respective strengths to develop time series representation with strong instance discriminability and local perceptibility. Extensive experiments across seven widely used benchmark datasets demonstrate that TempSSL consistently outperforms existing self-supervised and end-to-end forecasting methods, achieving improvements ranging from 1.92% ∼ 78.12%. Additionally, TempSSL’s practical effectiveness is further demonstrated through successful application in natural gas demand forecasting.

DETERMINATION AND APPLICATION OF FORECASTING METHOD FOR MEDICINE CONSUMPTION IN HEALTHCARE ORGANIZATION

The aim of this research is to estimate the consumption of a selected medicine in a public hospital for the next 1-year period by choosing the most appropriate fore casting method. Kaptoril 5-mg tablets from January 2018 to December 2022 were examined. In this research, time series methods were applied to the existing data using the Minitab 18 program. Moving average, exponentials moothing, and Holt-Winters fore casting methods were used in this study. Error measures such as mean absolute error, mean absolute percent age error, and mean squared error were used to compare the methods. For Kaptoril 5 mg, the most appropriatedem and fore casting method according to error measures is the Multiplicative Holt-Winters Method. According to this method, the mean absolute percent age error is 37.23. According to the multiplic ative Holt-Winters model, the total medicine consumption in 2023 was found to be 145 tablets. This research shows that time series fore casting methods can be applied to help reliable decision making in stock management of medicines by making a sample application on a selected medicine in a public hospital.

A study and development of high‐order fuzzy time series forecasting methods for air quality index forecasting

AbstractThe endless adverse effects of air pollution incidents have raised significant public concerns in the past few decades. The measure of air pollution, that is, the air quality index (AQI), is highly volatile and associated with different kinds of uncertainties. Following this, the study and development of accurate fuzzy time series forecasting (TSF) methods for predicting the AQI have a significant role in air pollution control and management. Motivated by this, in this paper, a systematic study is made to evaluate the true potential of fuzzy TSF methods employing traditional fuzzy set (TFS), intuitionistic fuzzy set (IFS), hesitant fuzzy set (HFS), and neutrosophic fuzzy set (NFS) in forecasting the AQI. Two novel high‐order fuzzy TSF methods, TFS‐multilayer perceptron (MLP) and HFS‐MLP, are proposed employing TFS and HFS in which ratio trend variation of AQI data is used instead of original AQI, MLP is used to model the fuzzy logical relationships (FLRs), and none/mean of aggregated membership values are used while modeling the FLRs using MLP. The results from the proposed fuzzy TSF methods are compared with recently proposed fuzzy TSF methods employing TFS, IFS, and NFS and six popular machine learning models, including MLP, support vector regression (SVR), Bagging Regressors, XGBoost, long‐short term memory (LSTM), and convolutional neural network (CNN). The “Wilcoxon Signed‐Rank test” and “Friedman and Nemenyi hypothesis test” are applied to the results obtained by employing different ratios in the train‐validation‐test to draw decisive conclusions reliably. The simulation results show the statistical dominance of the proposed TFS‐MLP method over all other crisp and fuzzy TSF methods employed in this paper.

TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods

Time series are generated in diverse domains such as economic, traffic, health, and energy, where forecasting of future values has numerous important applications. Not surprisingly, many forecasting methods are being proposed. To ensure progress, it is essential to be able to study and compare such methods empirically in a comprehensive and reliable manner. To achieve this, we propose TFB, an automated benchmark for Time Series Forecasting (TSF) methods. TFB advances the state-of-the-art by addressing shortcomings related to datasets, comparison methods, and evaluation pipelines: 1) insufficient coverage of data domains, 2) stereotype bias against traditional methods, and 3) inconsistent and inflexible pipelines. To achieve better domain coverage, we include datasets from 10 different domains : traffic, electricity, energy, the environment, nature, economic, stock markets, banking, health, and the web. We also provide a time series characterization to ensure that the selected datasets are comprehensive. To remove biases against some methods, we include a diverse range of methods, including statistical learning, machine learning, and deep learning methods, and we also support a variety of evaluation strategies and metrics to ensure a more comprehensive evaluations of different methods. To support the integration of different methods into the benchmark and enable fair comparisons, TFB features a flexible and scalable pipeline that eliminates biases. Next, we employ TFB to perform a thorough evaluation of 21 Univariate Time Series Forecasting (UTSF) methods on 8,068 univariate time series and 14 Multivariate Time Series Forecasting (MTSF) methods on 25 datasets. The results offer a deeper understanding of the forecasting methods, allowing us to better select the ones that are most suitable for particular datasets and settings. Overall, TFB and this evaluation provide researchers with improved means of designing new TSF methods.

Performance analysis of ARIMA Model for wind speed forecasting in Jerusalem, Palestine

Palestine lacks sufficient conventional energy sources that meet the daily needs of the Palestinian people, and consequently, it heavily relies on neighboring countries for its supply with energy compensations. Wind energy is recognized as an abundant, effective, and eco-friendly power source, but it poses several challenges in harnessing due to the inherent variability of wind characteristics. The main objective of this research study is to delve into the wind energy landscape in Palestine, and to offer some insights into the feasibility of wind speed forecasting for implementing sustainable energy solutions, with a special focus on ARIMA; a widely used statistical method for time series forecasting. It specifically explores the potential of using ARIMA models to forecast wind speed using a data captured from a meteorological station located in east Jerusalem, Palestine for a duration of 2 years—January 1, 2021 to December 31, 2022. To find the optimal values of ARIMA parameters (p, d, q) for the considered study site, a set of experiments were conducted and the model's forecasting accuracy was evaluated using three metrics: RMSE, MAE, and the coefficient of determination (R2). The results have shown that ARIMA (21,2) emerges as the most accurate structure with an input period that demonstrates superior estimation with minimal RMSE (1.74), minimal MAE (1.58) and higher R2 (0.76) values. This means that the optimal estimation is achieved when an autoregressive process is based on the previous two lagged observations and the moving average process incorporates the dependency between the observation and the residual error from a second-order moving average applied to the lagged observations. These findings give valuable insights into the feasibility and precision of wind speed forecasting models for sustainable energy solutions, and emphasize the potential for harnessing wind energy in the region as clarified by ARIMA forecasting accuracy.

Long-Term Forecasting Using MAMTF: A Matrix Attention Model Based on the Time and Frequency Domains

There are many time series forecasting methods, but there are few research methods for long-term multivariate time series forecasting, which are mainly dominated by a series of forecasting models developed on the basis of a transformer. The aim of this study is to perform forecasting for multivariate time series data and to improve the forecasting accuracy of the model. In the recent past, it has appeared that the prediction effect of linear models surpasses that of the family of self-attention mechanism models, which encourages us to look for new methods to solve the problem of long-term multivariate time series forecasting. In order to overcome the problem that the temporal order of information is easily broken in the self-attention family and that it is difficult to capture information on long-distance data using recurrent neural network models, we propose a matrix attention mechanism, which is able to weight each previous data point equally without breaking the temporal order of the data, so that the overall data information can be fully utilized. We used the matrix attention mechanism as the basic module to construct the frequency domain block and time domain block. Since complex and variable seasonal component features are difficult to capture in the time domain, mapping them to the frequency domain reduces the complexity of the seasonal components themselves and facilitates data feature extraction. Therefore, we use the frequency domain block to extract the seasonal information with high randomness and poor regularity to help the model capture the local dynamics. The time domain block is used to extract the smooth floating trend component information to help the model capture long-term change patterns. This also improves the overall prediction performance of the model. It is experimentally demonstrated that our model achieves the best prediction results on three public datasets and one private dataset.

SALES PREDICTION BASED ON SARIMAX TIME SERIES ALGORITHM

Businesses must perform time-series forecasting of seasonal item sales because it enables them to predict future demand and modify their inventory accordingly. This investigation compares the performance of three well-known machine learning methods for time-series forecasting of seasonal item sales: Support Vector Machine (SVM), Seasonal Autoregressive Integrated Moving Average with Exogenous Variables (SARIMAX), and Multi-layer Perception (MLP). A dataset of historical sales data is used to evaluate the algorithms. The data is split into training and testing sets, and measures like Mean Absolute Error (MAE), Relative Absolute Error (RAE), and Root Mean Squared Error (RMSE) are used to assess each algorithm's performance. The analysis's findings support the assertion that SARIMA- X provides greater accuracy than other methods incalculating the seasonal sales of the historical data. Keywords—, Time-series forecasting, SARIMAX, ARIMA, Machine Learning

Racial Disparities in Telemedicine Uptake during the COVID-19 Pandemic among Patients with Hematologic Malignancies in the United States

Background: The COVID-19 pandemic impacted healthcare visit trends, transitioning care to utilize telemedicine. We aimed to investigate if the uptake in telemedicine during pandemic was equitable across racial groups for patients with hematologic malignancies. Methods: Using the nationwide Flatiron Health electronic health record (EHR)-derived de-identified database we analyzed patients with diagnosis of acute myelogenous leukemia (AML), diffuse large B-cell lymphoma (DLBCL), follicular lymphoma (FL), mantle cell lymphoma (MCL), chronic lymphocytic leukemia (CLL) or multiple myeloma (MM). Patients were categorized into treatment types within lines of therapy: outpatient (oral therapy and outpatient infusions combined with oral therapy) vs. inpatient treatments (chemotherapy, cellular therapy). Monthly visit rates were calculated as the number of visits (telemedicine or in-person [in-clinic treatment administration, vitals, and/or labs]) per active patient per 30-day standardized month. We used time-series forecasting methods on pre-pandemic monthly visit rate data (March 2016 - February 2020) to estimate projected counterfactual monthly visit rates between March 2020 - February 2021.Telemedicine uptake was descriptively analyzed over time (t). Results: We included 18,924 active patients (2,394 Black and 16,530 White) and 884,504 visits (117,673 Black and 766,831 White). 4,053 AML, 3,468 diffuse large B cell lymphoma, 1,943 follicular lymphoma, 2,151 mantle cell lymphoma, 5,926 chronic lymphocytic leukemia and 7,752 myeloma patients. Black patients had no significant reductions in in-person visit rates throughout the pandemic period compared to the projected rates. Conversely, White patients experienced an 18% (95% PI 9.9% - 25%) lower rate of in-person visits for outpatient therapy during the early pandemic (March - May 2020) (actual monthly visit rate 1.61; projected visit rate 2.0 [95% CI 1.8-2.2]). Telemedicine uptake was significantly higher for White patients compared with Black patients for all diseases and treatment categories between March 2020-February 2021 (t = 9.5, p < 0.01), AML inpatient (t = 2.4, p = 0.04), MM outpatient (Figure 3C) (t = 6.0, p < 0.01) and MM inpatient treatment categories (Figure 3D) (t = 2.3, p = 0.04). Conclusions: White patients had significantly higher telemedicine uptake compared with Black patients for all treatment categories. These findings challenge healthcare systems to direct efforts toward reducing the gap in healthcare access.

A Comparative Study of Future Stock Price Prediction Through Artificial Neural Network and ARIMA Modelling

Stock price estimation and prediction have been the popular topics for ages for various market participants, including investors, traders, financial analysts and researchers. Understanding the expected direction of stock prices can provide insights into broader market trends and sentiments. Different methods have been tried to find out future predictions with the least degree of error. Autoregressive integrated moving average (ARIMA) and artificial neural networks (ANN) are two popular methods for time series forecasting, including stock price prediction. This paper attempts to forecast stock prices with more accuracy by using ARIMA and ANN tool modelling with secondary data NIFTY 50 of the National Stock Exchange from December 2005 to July 2019. Stock price prediction through ARIMA and ANN was calculated and compared. Results obtained revealed that the ANN method of forecasting stock prices has more accuracy as compared to ARIMA modelling. Future studies can be based on different sector-based data across different sectors and stock markets.

Do psychological factors exert greater influence on investment decisions than physiological factors? Evidence from Borsa Istanbul

We investigate the impact of Ramadan, the Holy month of fasting, on the phenomenon of post-earnings announcement drift (PEAD) in Borsa Istanbul. Utilizing quarterly earnings announcements and employing both the analyst forecast method and time series forecast method as surprise measures, our study spans the earnings period from the first quarter of 2007 to the last quarter of 2018. Our objective is to bridge the gap between studies highlighting the negative impacts of physiological factors and the positive impacts of psychological factors on economic decision-making. Given the anticipated opposing effects of physiological and psychological factors on PEAD during Ramadan, our findings offer a unique opportunity to compare the influences of physiology and psychology on investment decisions. Contrary to the expected positive impact resulting from physiological factors causing attention deficit, our research reveals that earnings announcements made during Ramadan exhibit, on average, a 16–25% lower drift in the subsequent 60-day period, depending on the method used. We attribute this unexpected outcome to the dominance of psychological factors, such as heightened sentiment, self-awareness, and spirituality, over physiological factors. This finding holds significance for policymakers, as activities that may seem to have a harmful impact on the economy due to visible physiological or physical factors can unexpectedly yield positive effects due to less tangible psychological factors. Additionally, our results hold importance for investors, as a hedge strategy using earnings surprises results in a negative return if the announcements are made during Ramadan. Our findings remain robust across different measures of PEAD and various intensities of physiological factors.

Application of Time Series for Casting Using Machine Learn Method

Time series forecasting plays a vital role in optimizing processes through many industries, and the casting for the domain is no exception. Casting processes suddenly require exact predictions to shine product quality, low waste, and optimize resource allocations. This paper discovers the application of machine learning methods for time series forecasting. It starts with an exact review of existing research, enjoying the critical role of correct forecasting in this field. The research leverages device learning techniques, adding autoregressive integrated walking average (ARIMA), Long Short-Term Memory (LSTM) networks and XGBoost, to model & guess time series data related to casting processes. A different and unique dataset is collected, again processed and used for experimentation. The results shows the ability and control of these machine learning methods in forecasting many possibilities of casting processes. Through a serious talk of the results and their real implications, these paper implies to the increasing body of memory in the space of time series forecasting for casting. The discovery offer insights into a feasibility of using machine learning to shows casting operations, improve product quality and optimize resource use. This research no only shows the potential of machine learning in the casting field but also shows as a foundation for further Discovery and application of advanced forecasting techniques in this domain.

A deep implicit memory Gaussian network for time series forecasting

In recent years, significant achievements have been made in time series forecasting using deep learning methods, particularly the Long Short-Term Memory Network (LSTM). However, time series often exhibit complex patterns and relationships like trends, seasonal patterns and irregularities, and LSTM networks fail to effectively strengthen long-term dependence in time series data, which may lead to inaccurate forecasting effect or performance degradation. Therefore, building a model to explore the temporal dependence within the time series data completely still remains a challenge. In this paper, we propose a novel Deep Implicit Memory Gaussian (DIMG) Network based on bidirectional deep memory kernel process and the implicit features enhancement method for time series forecasting. We first use the implicit features enhancement method to obtain the hidden features of the data according to the nonlinear mapping characteristics of encoder. Then, a new deep learning process called bidirectional deep memory kernel has been developed, which merges the structural properties of deep learning with the adaptability of kernel methods to capture intricate information and memory structures in sequential data. This process fully encapsulates the structure of Bi-LSTM and Gaussian process regression (GPR). Finally, the performance of the proposed model is evaluated on two real-world datasets. The experimental results verify that our model outperforms other reported methods in terms of prediction accuracy.

Flight trajectory prediction enabled by time-frequency wavelet transform

Accurate flight trajectory prediction is a crucial and challenging task in air traffic control, especially for maneuver operations. Modern data-driven methods are typically formulated as a time series forecasting task and fail to retain high accuracy. Meantime, as the primary modeling method for time series forecasting, frequency-domain analysis is underutilized in the flight trajectory prediction task. In this work, an innovative wavelet transform-based framework is proposed to perform time-frequency analysis of flight patterns to support trajectory forecasting. An encoder-decoder neural architecture is developed to estimate wavelet components, focusing on the effective modeling of global flight trends and local motion details. A real-world dataset is constructed to validate the proposed approach, and the experimental results demonstrate that the proposed framework exhibits higher accuracy than other comparative baselines, obtaining improved prediction performance in terms of four measurements, especially in the climb and descent phase with maneuver control. Most importantly, the time-frequency analysis is confirmed to be effective to achieve the flight trajectory prediction task.

The COVID-19 Pandemic and In-Person Visit Rate Disruptions Among Patients With Hematologic Neoplasms in the US in 2020 to 2021

The COVID-19 pandemic has led to a reduction in routine in-person medical care; however, it is unknown whether there have been any changes in visit rates among patients with hematologic neoplasms. To examine associations between the COVID-19 pandemic and in-person visits and telemedicine use among patients undergoing active treatment for hematologic neoplasms. Data for this retrospective observational cohort study were obtained from a nationwide electronic health record-derived, deidentified database. Data for patients with hematologic neoplasms who had received at least 1 systemic line of therapy between March 1, 2016, and February 28, 2021, were included. Treatments were categorized into 3 types: oral therapy, outpatient infusions, and inpatient infusions. The data cutoff date was April 30, 2021, when study analyses were conducted. Monthly visit rates were calculated as the number of documented visits (telemedicine or in-person) per active patient per 30-day period. We used time-series forecasting methods on prepandemic data (March 2016 to February 2020) to estimate expected rates between March 1, 2020, and February 28, 2021 (if the pandemic had not occurred). This study included data for 24 261 patients, with a median age of 68 years (IQR, 60-75 years). A total of 6737 patients received oral therapy, 15 314 received outpatient infusions, and 8316 received inpatient infusions. More than half of patients were men (14 370 [58%]) and non-Hispanic White (16 309 [66%]). Early pandemic months (March to May 2020) demonstrated a significant 21% reduction (95% prediction interval [PI], 12%-27%) in in-person visit rates averaged across oral therapy and outpatient infusions. Reductions in in-person visit rates were also significant for all treatment types for multiple myeloma (oral therapy: 29% reduction; 95% PI, 21%-36%; P = .001; outpatient infusions: 11% reduction; 95% PI, 4%-17%; P = .002; inpatient infusions: 55% reduction; 95% PI, 27%-67%; P = .005), for oral therapy for chronic lymphocytic leukemia (28% reduction; 95% PI, 12%-39%; P = .003), and for outpatient infusions for mantle cell lymphoma (38% reduction; 95% PI, 6%-54%; P = .003) and chronic lymphocytic leukemia (20% reduction; 95% PI, 6%-31%; P = .002). Telemedicine visit rates were highest for patients receiving oral therapy, with greater use in the early pandemic months and a subsequent decrease in later months. In this cohort study of patients with hematologic neoplasms, documented in-person visit rates for those receiving oral therapy and outpatient infusions significantly decreased during the early pandemic months but returned to close to projected rates in the later half of 2020. There were no statistically significant reductions in the overall in-person visit rate for patients receiving inpatient infusions. There was higher telemedicine use in the early pandemic months, followed by a decline, but use was persistent in the later half of 2020. Further studies are needed to ascertain associations between the COVID-19 pandemic and subsequent cancer outcomes and the evolution of telemedicine use for care delivery.

Forecasting Palm Oil Production Using Fuzzy Time Forecasting Two-Factor Cross Associations with Frequency Density Partitions

Economic decisions have many determining factors based on estimates of macroeconomic variables. The accuracy of decision estimates can have an important impact. Forecasting is a method to reducing uncertainty about the future, because of economic decisions have multi-factor problems, the high order fuzzy time series forecast method is more suitable than the first order fuzzy time series forecast. Predictions are made for main factors by taking influence from both factors. FLR reflects the relationship between the premise and consequence. In this paper will be discussed fuzzy time series forecasting multi-factor one order cross association based on frequency density partition as a forecasting method to forecast palm oil production with influenced by large of the area. The results of the estimates show that the proposed method has a high forecast performance, with AFER value is according to the AFER criteria table 10%, it can be concluded that the forecast has very good criteria

Time Series Forecasting of Motor Bearing Vibration Based on Informer.

Electric energy, as an economical and clean energy, plays a significant role in the development of science and technology and the economy. The motor is the core equipment of the power station; therefore, monitoring the motor vibration and predicting time series of the bearing vibration can effectively avoid hazards such as bearing heating and reduce energy consumption. Time series forecasting methods of motor bearing vibration based on sliding window forecasting, such as CNN, LSTM, etc., have the problem of error accumulation, and the longer the time-series forecasting, the larger the error. In order to solve the problem of error accumulation caused by the conventional methods of time series forecasting of motor bearing vibration, this paper innovatively introduces Informer into time series forecasting of motor bearing vibration. Based on Transformer, Informer introduces ProbSparse self-attention and self-attention distilling, and applies random search to optimize the model parameters to reduce the error accumulation in forecasting, achieve the optimization of time and space complexity and improve the model forecasting. Comparing the forecasting results of Informer and those of other forecasting models in three publicly available datasets, it is verified that Informer has excellent performance in time series forecasting of motor bearing vibration and the forecasting results reach ∼.

Optimized Artificial Neural network models to time series

Artificial Neural networks (ANN) are powerful and effective tools in time-series applications. The first aim of this paper is to diagnose better and more efficient ANN models (Back Propagation, Radial Basis Function Neural networks (RBF), and Recurrent neural networks) in solving the linear and nonlinear time-series behavior. The second aim is dealing with finding accurate estimators as the convergence sometimes is stack in the local minima. It is one of the problems that can bias the test of the robustness of the ANN in time series forecasting. To determine the best or the optimal ANN models, forecast Skill (SS) employed to measure the efficiency of the performance of ANN models. The mean square error and the absolute mean square error were also used to measure the accuracy of the estimation for methods used. The important result obtained in this paper is that the optimal neural network was the Backpropagation (BP) and Recurrent neural networks (RNN) to solve time series, whether linear, semilinear, or non-linear. Besides, the result proved that the inefficiency and inaccuracy (failure) of RBF in solving nonlinear time series. However, RBF shows good efficiency in the case of linear or semi-linear time series only. It overcomes the problem of local minimum. The results showed improvements in the modern methods for time series forecasting.

MODELING AND FORECASTING USING ARIMA: An Empirical Study of GDP in Sri Lanka.

An autoregressive integrated moving average (ARIMA) model is useful to analyze time-series data either for better understanding or for forecasting future points in the series. This paper aims to model and forecast the GDP of Sri Lanka based on the Box-Jenkins approach based on the annual data from 1971 to 2021. Box ? Jenkins technique is a relatively advanced time series forecast method it is applied in this paper to forecast GDP at the million US$ in Sri Lanka. The study attempt to study and model to forecast the GDP of Sri Lanka using an appropriate forecasting model. After testing the stationarity of the data, the series were stationary at the first difference after calculating the logarithm of the data. From the Correlogram of ACF, we determined the appropriate ARIMA model which is ARIMA (1,1,1) to forecast GDP. The ARIMA (1, 1, 1) model was seen as a superior fit model for estimating Sri Lanka?s GDP at a million US$. According to the values predicted, Sri Lankan GDP shows a higher growth trend in the next few years from 2022 to 2030 at million US$. However, the forecasting result of this model is only a predicted value.

Advances in Time Series Forecasting Development for Power Systems’ Operation with MLOps

Forecast developers predominantly assess residuals and error statistics when tuning the targeted model’s quality. With that, eventual cost or rewards of the underlying business application are typically not considered in the model development phase. The analysis of the power system wholesale market allows us to translate a time series forecast method’s quality to its respective business value. For instance, near real-time capacity procurement takes place in the wholesale market, which is subject to complex interrelations of system operators’ grid activities and balancing parties’ scheduling behavior. Such forecasting tasks can hardly be solved with model-driven approaches because of the large solution space and non-convexity of the optimization problem. Thus, we generate load forecasts by means of a data-driven based forecasting tool ProLoaF, which we benchmark with state-of-the-art baseline models and the auto-machine learning models auto.arima and Facebook Prophet.

A case study comparing machine learning with statistical methods for time series forecasting: size matters

A case study comparing machine learning with statistical methods for time series forecasting: size matters