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[D] Complexity of Time Series Models: ARIMA vs. LSTM

#artificialintelligence

Does this concept of VC Dimension carry over to models in time series analysis? Is it possible to show that LSTM's have a higher VC dimension compared to ARIMA style models? Supposedly, neural network based time series models were developed because modeols like ARIMA was unable to provide reliable estimates for bigger and complex datasets. Mathematically speaking, what allows a LSTM to capture more variation and complexity in a dataset compared to ARIMA? Just as a general question: in what instances would it be better to use a CNN for time series forecasting compared to an LSTM?


Optimizing Convergence for Iterative Learning of ARIMA for Stationary Time Series

arXiv.org Machine Learning

Forecasting of time series in continuous systems becomes an increasingly relevant task due to recent developments in IoT and 5G. The popular forecasting model ARIMA is applied to a large variety of applications for decades. An online variant of ARIMA applies the Online Newton Step in order to learn the underlying process of the time series. This optimization method has pitfalls concerning the computational complexity and convergence. Thus, this work focuses on the computational less expensive Online Gradient Descent optimization method, which became popular for learning of neural networks in recent years. For the iterative training of such models, we propose a new approach combining different Online Gradient Descent learners (such as Adam, AMSGrad, Adagrad, Nesterov) to achieve fast convergence. The evaluation on synthetic data and experimental datasets show that the proposed approach outperforms the existing methods resulting in an overall lower prediction error.


Demand Forecasting for Platelet Usage: from Univariate Time Series to Multivariate Models

arXiv.org Machine Learning

Platelet products are both expensive and have very short shelf lives. As usage rates for platelets are highly variable, the effective management of platelet demand and supply is very important yet challenging. The primary goal of this paper is to present an efficient forecasting model for platelet demand at Canadian Blood Services (CBS). To accomplish this goal, four different demand forecasting methods, ARIMA (Auto Regressive Moving Average), Prophet, lasso regression (least absolute shrinkage and selection operator) and LSTM (Long Short-Term Memory) networks are utilized and evaluated. We use a large clinical dataset for a centralized blood distribution centre for four hospitals in Hamilton, Ontario, spanning from 2010 to 2018 and consisting of daily platelet transfusions along with information such as the product specifications, the recipients' characteristics, and the recipients' laboratory test results. This study is the first to utilize different methods from statistical time series models to data-driven regression and a machine learning technique for platelet transfusion using clinical predictors and with different amounts of data. We find that the multivariate approaches have the highest accuracy in general, however, if sufficient data are available, a simpler time series approach such as ARIMA appears to be sufficient. We also comment on the approach to choose clinical indicators (inputs) for the multivariate models.


Webinars – Axcel

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Demand forecasting is critical to the success of a company. It drives the decision-making from supply chain management to marketing campaigns. In this webinar, we discuss time series elements including trend, seasonality, and random parts. We explain how to design, implement, and validate a demand forecasting model in Excel. We also present how you can level up your analysis with Axcel AI by running advanced decomposition and time series models such as autoregressive integrated moving average (ARIMA) and visualize the results with a single function in Excel.


Top 5 Best Articles on R for Business [November 2020]

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Register for our blog to get the Top Articles every month. Making multiple ARIMA Time Series models in R used to be difficult. But, with the purrr nest() function and modeltime, forecasting has never been easier. Learn how to make many ARIMA models in this tutorial.This article was written by Business Science's very own Matt Dancho. In this post, we load our cleaned up big MT Cars data set in order to be able to refer directly to the variable without a short code or the f function from our datatable.


Greenhouse Gas Emission Prediction on Road Network using Deep Sequence Learning

arXiv.org Machine Learning

Mitigating the substantial undesirable impact of transportation systems on the environment is paramount. Thus, predicting Greenhouse Gas (GHG) emissions is one of the profound topics, especially with the emergence of intelligent transportation systems (ITS). We develop a deep learning framework to predict link-level GHG emission rate (ER) (in CO2eq gram/second) based on the most representative predictors, such as speed, density, and the GHG ER of previous time steps. In particular, various specifications of the long-short term memory (LSTM) networks with exogenous variables are examined and compared with clustering and the autoregressive integrated moving average (ARIMA) model with exogenous variables. The downtown Toronto road network is used as the case study and highly detailed data are synthesized using a calibrated traffic microsimulation and MOVES. It is found that LSTM specification with speed, density, GHG ER, and in-links speed from three previous minutes performs the best while adopting 2 hidden layers and when the hyper-parameters are systematically tuned. Adopting a 30 second updating interval improves slightly the correlation between true and predicted GHG ERs, but contributes negatively to the prediction accuracy as reflected on the increased root mean square error (RMSE) value. Efficiently predicting GHG emissions at a higher frequency with lower data requirements will pave the way to non-myopic eco-routing on large-scale road networks {to alleviate the adverse impact on the global warming


Reinforced Deep Markov Models With Applications in Automatic Trading

arXiv.org Machine Learning

Inspired by the developments in deep generative models, we propose a model-based RL approach, coined Reinforced Deep Markov Model (RDMM), designed to integrate desirable properties of a reinforcement learning algorithm acting as an automatic trading system. The network architecture allows for the possibility that market dynamics are partially visible and are potentially modified by the agent's actions. The RDMM filters incomplete and noisy data, to create better-behaved input data for RL planning. The policy search optimisation also properly accounts for state uncertainty. Due to the complexity of the RKDF model architecture, we performed ablation studies to understand the contributions of individual components of the approach better. To test the financial performance of the RDMM we implement policies using variants of Q-Learning, DynaQ-ARIMA and DynaQ-LSTM algorithms. The experiments show that the RDMM is data-efficient and provides financial gains compared to the benchmarks in the optimal execution problem. The performance improvement becomes more pronounced when price dynamics are more complex, and this has been demonstrated using real data sets from the limit order book of Facebook, Intel, Vodafone and Microsoft.


Comparison between ARIMA and Deep Learning Models for Temperature Forecasting

arXiv.org Artificial Intelligence

II. RELATED WORK Weather forecasting is essential for us to know unforeseeable information that will aid us when carrying daily tasks. For According to a study conducted by Mark Hallstrom, Dylan example farmers could use this futuristic information to Liu and Christopher Vo to exert machine learning to predict cultivate crops on time. Further, Air lines could schedule weather [2]. The illustrated method in this study uses data flights safely and accurately. Other than that, these predictions collected from Weather Underground. The collected data set could use to notify people when imminent dangers such as includes minimum temperature, maximum temperature and tsunamis, hurricanes are near. This information helps us to mean pressure of the atmosphere, mean humidity and daily make important daily decisions. Weather forecasting is a weather condition during the years of 2011 - 2015 in Stanford.


Comparison of ARIMA, ETS, NNAR and hybrid models to forecast the second wave of COVID-19 hospitalizations in Italy

arXiv.org Machine Learning

Coronavirus disease (COVID-19) is a severe ongoing novel pandemic that has emerged in Wuhan, China, in December 2019. As of October 13, the outbreak has spread rapidly across the world, affecting over 38 million people, and causing over 1 million deaths. In this article, I analysed several time series forecasting methods to predict the spread of COVID-19 second wave in Italy, over the period after October 13, 2020. I used an autoregressive model (ARIMA), an exponential smoothing state space model (ETS), a neural network autoregression model (NNAR), and the following hybrid combinations of them: ARIMA-ETS, ARIMA-NNAR, ETS-NNAR, and ARIMA-ETS-NNAR. About the data, I forecasted the number of patients hospitalized with mild symptoms, and in intensive care units (ICU). The data refer to the period February 21, 2020-October 13, 2020 and are extracted from the website of the Italian Ministry of Health (www.salute.gov.it). The results show that i) the hybrid models, except for ARIMA-ETS, are better at capturing the linear and non-linear epidemic patterns, by outperforming the respective single models; and ii) the number of COVID-19-related hospitalized with mild symptoms and in ICU will rapidly increase in the next weeks, by reaching the peak in about 50-60 days, i.e. in mid-December 2020, at least. To tackle the upcoming COVID-19 second wave, on one hand, it is necessary to hire healthcare workers and implement sufficient hospital facilities, protective equipment, and ordinary and intensive care beds; and on the other hand, it may be useful to enhance social distancing by improving public transport and adopting the double-shifts schooling system, for example.


Asset Price Forecasting using Recurrent Neural Networks

arXiv.org Machine Learning

This thesis serves three primary purposes, first of which is to forecast two stocks, i.e. Goldman Sachs (GS) and General Electric (GE). In order to forecast stock prices, we used a long short-term memory (LSTM) model in which we inputted the prices of two other stocks that lie in rather close correlation with GS. Other models such as ARIMA were used as benchmark. Empirical results manifest the practical challenges when using LSTM for forecasting stocks. One of the main upheavals was a recurring lag which we called "forecasting lag". The second purpose is to develop a more general and objective perspective on the task of time series forecasting so that it could be applied to assist in an arbitrary that of forecasting by ANNs. Thus, attempts are made for distinguishing previous works by certain criteria (introduced by a review paper written by Ahmed Tealab) so as to summarise those including effective information. The summarised information is then unified and expressed through a common terminology that can be applied to different steps of a time series forecasting task. The last but not least purpose of this thesis is to elaborate on a mathematical framework on which ANNs are based. We are going to use the framework introduced in the book "Neural Networks in Mathematical Framework" by Anthony L. Caterini in which the structure of a generic neural network is introduced and the gradient descent algorithm (which incorporates backpropagation) is introduced in terms of their described framework. In the end, we use this framework for a specific architecture, which is recurrent neural networks on which we concentrated and our implementations are based. The book proves its theorems mostly for classification case. Instead, we proved theorems for regression case, which is the case of our problem.