This paper analyses how Time Series Analysis techniques can be applied to capture movement of an exchange traded index in a stock market. Specifically, Seasonal Auto Regressive Integrated Moving Average (SARIMA) class of models is applied to capture the movement of Nifty 50 index which is one of the most actively exchange traded contracts globally [1]. A total of 729 model parameter combinations were evaluated and the most appropriate selected for making the final forecast based on AIC criteria [8]. NIFTY 50 can be used for a variety of purposes such as benchmarking fund portfolios, launching of index funds, exchange traded funds (ETFs) and structured products. The index tracks the behaviour of a portfolio of blue chip companies, the largest and most liquid Indian securities and can be regarded as a true reflection of the Indian stock market [2].
We introduce twenty four two-parameter families of advanced time series forecasting functions using a new and nonparametric approach. We also introduce the concept of powering and derive nonseasonal and seasonal models with examples in education, sales, finance and economy. We compare the performance of our twenty four models to both Holt--Winters and ARIMA models for both nonseasonal and seasonal times series. We show in particular that our models not only do not require a decomposition of a seasonal time series into trend, seasonal and random components, but leads also to substantially lower…
The monthly air traffic of a city is a time series with an obvious seasonal pattern, and is closely related to the economic situation and social environment of the city. In Hong Kong, for example, July, August, and October tend to be the peak season of traffic flow, while there is also a relatively fixed off-season. In the case of a stable social environment, a carefully identified and fitted seasonal ARIMA model can predict the traffic flow in the future months well. This work selects the air traffic data, including arrival and departure passengers of Hong Kong, after the financial crisis and…
The autoregressive moving average (ARMA) model takes the significant position in time series analysis for a wide-sense stationary time series. The difference operator and seasonal difference operator, which are bases of ARIMA and SARIMA (Seasonal ARIMA), respectively, were introduced to remove the trend and seasonal component so that the original non-stationary time series could be transformed into a wide-sense stationary one, which could then be handled by Box-Jenkins methodology. However, such difference operators are more practical experiences than exact theories by now. In this paper, we i…
Maximum likelihood methods, while widely used, may be non-robust due to disagreement between the assumptions upon which the models are based and the true density probability distribution of observed data. Because the Empirical Characteristic Function (ECF) is the Fourier transform of the empirical distribution function, it retains all the information in the sample but can overcome difficulties arising from the likelihood. This paper discusses an estimation method via the ECF for stable seasonal fractional ARIMA processes. Under some assumptions, we show that the resulting estimators are consis…
Beijing University of Posts and Telecommunications（北京邮电大学）；University College London（伦敦大学学院）；Shandong University（山东大学）；Mälardalen University（梅拉达伦大学）；Tianjin University of Commerce（天津商业大学）
Heat demand prediction is a prominent research topic in the area of intelligent energy networks. It has been well recognized that periodicity is one of the important characteristics of heat demand. Seasonal-trend decomposition based on LOESS (STL) algorithm can analyze the periodicity of a heat demand series, and decompose the series into seasonal and trend components. Then, predicting the seasonal and trend components respectively, and combining their predictions together as the heat demand prediction is a possible way to predict heat demand. In this paper, STL-ENN-ARIMA (SEA), a combined mod…
Recurrent Neural Networks (RNN) have become competitive forecasting methods, as most notably shown in the winning method of the recent M4 competition. However, established statistical models such as ETS and ARIMA gain their popularity not only from their high accuracy, but they are also suitable for non-expert users as they are robust, efficient, and automatic. In these areas, RNNs have still a long way to go. We present an extensive empirical study and an open-source software framework of existing RNN architectures for forecasting, that allow us to develop guidelines and best practices for th…
The simulation of the continuation of a given time series is useful for many practical applications. But no standard procedure for this task is suggested in the literature. It is therefore demonstrated how to use the seasonal ARIMA process to simulate the continuation of an observed time series. The R-code presented uses well-known modeling procedures for ARIMA models and conditional simulation of a SARIMA model with known parameters. A small example demonstrates the correctness and practical relevance of the new idea.
We propose a new method for decomposing seasonal data: STR (a Seasonal-Trend decomposition using Regression). Unlike other decomposition methods, STR allows for multiple seasonal and cyclic components, covariates, seasonal patterns that may have non-integer periods, and seasonality with complex topology. It can be used for time series with any regular time index including hourly, daily, weekly, monthly or quarterly data. It is competitive with existing methods when they exist, but tackles many more decomposition problem than other methods allow. STR is based on a regularized optimization, and …
Background: Seasonal influenza causes a substantial burden on healthcare services over the winter period when these systems are already under pressure. Policies during the COVID-19 pandemic supressed the transmission of season influenza, making the timing and magnitude of a potential resurgence difficult to predict. Methods: We developed a hierarchical generalised additive model (GAM) for the short-term forecasting of hospital admissions with a positive test for the influenza virus sub-regionally across England. The model incorporates a multi-level structure of spatio-temporal splines, weekly …
University of New Mexico（新墨西哥大学）；Marquette University（马凯特大学）
Predicting product sales of large retail companies is a challenging task considering volatile nature of trends, seasonalities, events as well as unknown factors such as market competitions, change in customer's preferences, or unforeseen events, e.g., COVID-19 outbreak. In this paper, we benchmark forecasting models on historical sales data from Walmart to predict their future sales. We provide a comprehensive theoretical overview and analysis of the state-of-the-art timeseries forecasting models. Then, we apply these models on the forecasting challenge dataset (M5 forecasting by Kaggle). Spec…
School of Management, Xi’an Jiaotong University（西安交通大学管理学院）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）
The accurate seasonal and trend forecasting of tourist arrivals is a very challenging task. In the view of the importance of seasonal and trend forecasting of tourist arrivals, and limited research work paid attention to these previously. In this study, a new adaptive multiscale ensemble (AME) learning approach incorporating variational mode decomposition (VMD) and least square support vector regression (LSSVR) is developed for short-, medium-, and long-term seasonal and trend forecasting of tourist arrivals. In the formulation of our developed AME learning approach, the original tourist arriv…
Time series forecasting plays an increasingly important role in modern business decisions. In today's data-rich environment, people often aim to choose the optimal forecasting model for their data. However, identifying the optimal model requires professional knowledge and experience, making accurate forecasting a challenging task. To mitigate the importance of model selection, we propose a simple and reliable algorithm to improve the forecasting performance. Specifically, we construct multiple time series with different sub-seasons from the original time series. These derived series highlight …
Innovation ARIMA models application to predict pressure variations in water supply networks with open-loop control. Case study in Noja (Cantabria, Spain)
Observations in data which are significantly different from its neighbouring points but cannot be classified as noise are known as anomalies or outliers. These anomalies are a cause of concern and a timely warning about their presence could be valuable. In this paper, we have evaluated and compared the performance of popular algorithms from domains of Machine Learning and Statistics in detecting anomalies on both offline data as well as real time data. Our aim is to come up with an algorithm which can handle all types of seasonal and non-seasonal data effectively and is fast enough to be of pr…
In this article, we introduce the R package portes with extensive illustrative applications. The asymptotic distributions and the Monte Carlo procedures of the most popular univariate and multivariate portmanteau test statistics, including a new generalized variance statistic, for time series models using the powerful parallel computing framework facility, are implemented in this package. The proposed package has a general mechanism where the user can compute the test statistic for the diagnostic checking of any time series models. This package is also useful for simulating univariate and mult…
Emergent and unscheduled cardiology admissions from cardiac catheterization laboratory add complexity to the management of Cardiology and in-patient department. In this article, we sought to study the behavior of cardiology admissions from Catheterization laboratory using time series models. Our research involves retrospective cardiology admission data from March 1, 2012, to November 3, 2016, retrieved from a hospital in Iowa. Autoregressive integrated moving average (ARIMA), Holts method, mean method, naïve method, seasonal naïve, exponential smoothing, and drift method were implemented to fo…
Combining forecast from different models has shown to perform better than single forecast in most time series. To improve the quality of forecast we can go for combining forecast. We study the effect of decomposing a series into multiple components and performing forecasts on each component separately... The original series is decomposed into trend, seasonality and an irregular component for each series. The statistical methods such as ARIMA, Holt-Winter have been used to forecast these components. In this paper we focus on how the best models of one series can be applied to similar frequency …
The need to forecast solar irradiation at a specific location over short-time horizons has acquired immense importance. In this paper, we report on analyses results involving statistical and machine learning techniques to predict hourly horizontal solar irradiation at one-hour ahead horizon using data sets from three different cities in the U.S. with different climatic conditions. A simple forecast approach that assumes consecutive days are identical serves as a baseline model against which to compare competing forecast alternatives. One approach is to use seasonal ARIMA models. Surprisingly, …
Pattern similarity-based methods are widely used in classification and regression problems. Repeated, similar-shaped cycles observed in seasonal time series encourage to apply these methods for forecasting. In this paper we use the pattern similarity-based methods for forecasting monthly electricity demand expressing annual seasonality. An integral part of the models is the time series representation using patterns of time series sequences. Pattern representation ensures the input and output data unification through trend filtering and variance equalization. Consequently, pattern representatio…
Czestochowa University of Technology（琴斯托霍瓦理工大学）；Uber Technologies（优步科技公司）
This work presents a hybrid and hierarchical deep learning model for mid-term load forecasting. The model combines exponential smoothing (ETS), advanced Long Short-Term Memory (LSTM) and ensembling. ETS extracts dynamically the main components of each individual time series and enables the model to learn their representation. Multi-layer LSTM is equipped with dilated recurrent skip connections and a spatial shortcut path from lower layers to allow the model to better capture long-term seasonal relationships and ensure more efficient training. A common learning procedure for LSTM and ETS, with …
Developing statistical models for seismic noise is an exercise of high value in seismic data analysis since these models play a critical role in detecting the onset of seismic events. A majority of these models are usually built on certain critical assumptions, namely, stationarity, linearity, and Gaussianity. Despite their criticality, very little reported literature exists on validating these assumptions on real seismic data. The objectives of this work are (i) to critically study these long-held assumptions and (ii) to propose a systematic procedure for developing appropriate time-series mo…
Time series modeling has entered an era of unprecedented growth in the size and complexity of data which require new modeling approaches. While many new general purpose machine learning approaches have emerged, they remain poorly understand and irreconcilable with more traditional statistical modeling approaches. We present a general class of exponential smoothed recurrent neural networks (RNNs) which are well suited to modeling non-stationary dynamical systems arising in industrial applications. In particular, we analyze their capacity to characterize the non-linear partial autocorrelation st…
This work presents a Long Short-Term Memory (LSTM) network for forecasting a monthly electricity demand time series with a one-year horizon. The novelty of this work is the use of pattern representation of the seasonal time series as an alternative to decomposition. Pattern representation simplifies the complex nonlinear and nonstationary time series, filtering out the trend and equalizing variance. Two types of patterns are defined: x-pattern and y-pattern. The former requires additional forecasting for the coding variables. The latter determines the coding variables from the process history.…
Managing the quality of water for present and future generations of coastal regions should be a central concern of both citizens and public officials. Remote sensing can contribute to the management and monitoring of coastal water and pollutants. Algal blooms are a coastal pollutant that is a cause of concern. Many satellite data, such as MODIS, have been used to generate water-quality products to detect the blooms such as chlorophyll a (Chl-a), a photosynthesis index called fluorescence line height (FLH), and sea surface temperature (SST). It is important to characterize the spatial and tempo…
Global Forecasting Models (GFM) that are trained across a set of multiple time series have shown superior results in many forecasting competitions and real-world applications compared with univariate forecasting approaches. One aspect of the popularity of statistical forecasting models such as ETS and ARIMA is their relative simplicity and interpretability (in terms of relevant lags, trend, seasonality, and others), while GFMs typically lack interpretability, especially towards particular time series. This reduces the trust and confidence of the stakeholders when making decisions based on the …
The recurrent thread of dengue incidence in Sri Lanka is still abundant and it creates a huge burden to the country. Hence, the National Dengue Control Unit of Sri Lanka propose a national action plan to prevent and control the dengue incidence. To implement the necessary actions for short and long terms the proposed plan operates under three levels:country-level, province-level, and district levels. In order to optimize resource allocation, the health officers require the forecasts for country, province and district levels, which preserves the aggregate consistency associated with the distric…
