On the Autoregressive Time Series Model Using Real and Complex Analysis

Forecasting ◽  
2021 ◽  
Vol 3 (4) ◽  
pp. 716-728
Author(s):  
Torsten Ullrich
Keyword(s):  
Time Series ◽  
Model Selection ◽  
Closed Form ◽  
Autoregressive Model ◽  
Complex Analysis ◽  
Time Series Data ◽  
Selection Process ◽  
Global Structure ◽  
Series Data ◽  
Time Step

The autoregressive model is a tool used in time series analysis to describe and model time series data. Its main structure is a linear equation using the previous values to compute the next time step; i.e., the short time relationship is the core component of the autoregressive model. Therefore, short-term effects can be modeled in an easy way, but the global structure of the model is not obvious. However, this global structure is a crucial aid in the model selection process in data analysis. If the global properties are not reflected in the data, a corresponding model is not compatible. This helpful knowledge avoids unsuccessful modeling attempts. This article analyzes the global structure of the autoregressive model through the derivation of a closed form. In detail, the closed form of an autoregressive model consists of the basis functions of a fundamental system of an ordinary differential equation with constant coefficients; i.e., it consists of a combination of polynomial factors with sinusoidal, cosinusoidal, and exponential functions. This new insight supports the model selection process.

scholarly journals Time Series Modeling on Monthly Data of Tourist Arrivals in Nepal: An Alternative Approach

2017 ◽  
Vol 1 ◽  
pp. 41-54 ◽  
Author(s):  
Amrit Subedi
Keyword(s):  
Time Series ◽  
Autoregressive Model ◽  
Time Series Data ◽  
Polynomial Function ◽  
Seasonal Fluctuation ◽  
Ar Model ◽  
Series Data ◽  
Monthly Data ◽  
Annual Trend ◽  
Alternative Approach

Background: There are various approaches of modeling on time series data. Most of the studies conducted regarding time series data are based on annual trend whereas very few concerned with data having monthly fluctuation. The data of tourist arrivals is an example of time series data with monthly fluctuation which reveals that there is higher number of tourist arrivals in some months/seasons whereas others have less number. Starting from January, it makes a complete cycle in every 12 months with 3 bends indicating that it can be captured by biquadratic function.Objective: To provide an alternative approach of modeling i.e. combination of Autoregressive model with polynomial (biquadratic) function on time series data with monthly/seasonal fluctuation and compare its adequacy with widely used cyclic autoregressive model i.e. AR (12).Materials and Methods: This study is based on monthly data of tourist arrivals in Nepal. Firstly, usual time series model AR (12) has been adopted and an alternative approach of modeling has been attempted combining AR and biquadratic function. The first part of the model i.e. AR represents annual trend whereas biquadratic part does for monthly fluctuation.Results: The fitted cyclic autoregressive model on monthly data of tourist arrivals is Est. Ym = 3614.33 + 0.9509Ym-12, (R2=0.80); Est. Ym indicates predicted tourist arrivals for mth month and Ym-12 indicates observed tourist arrivals in (m-12)th month and the combined model of AR and biquadratic function is Est. Yt(m) = -46464.6 + 1.000Yt-1 + 52911.56m - 17177m2 + 2043.95m3 - 79.43m4, (R2=0.78); Est. Yt(m) indicates predicted tourist arrivals for mth month of tth year and Yt-1 indicates average tourist arrivals in (t-1)th year. The AR model combined with polynomial function reveals normal and homoscedastic residuals more accurately compared to first one.Conclusion: The use of polynomial function combined with autoregressive model can be useful for time series data having seasonal fluctuation. It can be an alternative approach for picking up a good model for such type of data. Nepalese Journal of Statistics, 2017,  Vol. 1, 41-54

scholarly journals PERAMALAN JUMLAH PENUMPANG PESAWAT TERBANG DI PINTU KEDATANGAN BANDAR UDARA INTERNASIONAL PATTIMURA AMBON DENGAN MENGGUNAKAN METODE ARIMA BOX-JENKINS

2019 ◽  
Vol 13 (3) ◽  
pp. 135-144
Author(s):  
Sasmita Hayoto ◽  
Yopi Andry Lesnussa ◽  
Henry W. M. Patty ◽  
Ronald John Djami
Keyword(s):  
Time Series ◽  
Model Selection ◽  
Time Series Data ◽  
Moving Average ◽  
Arima Model ◽  
Series Data ◽  
Autoregressive Integrated Moving Average ◽  
Significant Parameter ◽  
International Airport ◽  
Forecast Time

The Autoregressive Integrated Moving Average (ARIMA) model is often used to forecast time series data. In the era of globalization, rapidly progressing times, one of them in the field of transportation. The aircraft is one of the transportation that the residents can use to support their activities, both in business and tourism. The objective of the research is to know the forecasting of the number of passengers of airplanes at the arrival gate of Pattimura Ambon International Airport using ARIMA Box-Jenkins method. The best model selection is ARIMA (0, 1, 3) because it has significant parameter value and MSE value is smaller.

scholarly journals Bristlecone: An F# library for model-fitting and model-selection of ecological time-series data

2019 ◽  
Author(s):  
Andrew C Martin
Keyword(s):  
Time Series ◽  
Model Selection ◽  
Tree Rings ◽  
Time Series Data ◽  
Sediment Cores ◽  
Model Fitting ◽  
Series Data ◽  
Ecological Problems ◽  
Biodiversity And Ecosystem Function

Environmental archives such as sediment cores and tree rings provide important insights on the timing and rates of change in biodiversity and ecosystem function over the long-term. Such datasets are often analysed using empirical methods, which limits their ability to address ecological questions that seek to understand underlying ecological mechanisms and processes. Top down modelling approaches – where data is confronted with simple ecological models – can be used to infer the presence, form, and strength of mechanisms of interest. To aid adoption of time-series mechanistic modelling for long-term ecology, we created a F# library, Bristlecone, that can be used to apply this approach using a Model- Fitting and Model-Selection workflow. Our objective with Bristlecone was to create a library that could be used to efficiency and effectively conduct a full MFMS analysis for long-term ecological problems. We incorporated techniques to address specific challenges with environmental archives, including uneven time steps from age-depth models (for sediment cores), and allometry and seasonality (for tree rings). We include an example analysis to demonstrate functionality of Bristlecone. Our solution presents a straightforward, repeatable, and highly parallel method for conducting inference for long- term ecological problems.

scholarly journals Time-Aware Multi-Scale RNNs for Time Series Modeling

2021 ◽  
Author(s):  
Zipeng Chen ◽  
Qianli Ma ◽  
Zhenxi Lin
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Multiple Scales ◽  
Multivariate Time Series ◽  
Human Motion ◽  
Series Data ◽  
Time Step ◽  
Multi Scale ◽  
Important Time ◽  
Time Aware

Multi-scale information is crucial for modeling time series. Although most existing methods consider multiple scales in the time-series data, they assume all kinds of scales are equally important for each sample, making them unable to capture the dynamic temporal patterns of time series. To this end, we propose Time-Aware Multi-Scale Recurrent Neural Networks (TAMS-RNNs), which disentangle representations of different scales and adaptively select the most important scale for each sample at each time step. First, the hidden state of the RNN is disentangled into multiple independently updated small hidden states, which use different update frequencies to model time-series multi-scale information. Then, at each time step, the temporal context information is used to modulate the features of different scales, selecting the most important time-series scale. Therefore, the proposed model can capture the multi-scale information for each time series at each time step adaptively. Extensive experiments demonstrate that the model outperforms state-of-the-art methods on multivariate time series classification and human motion prediction tasks. Furthermore, visualized analysis on music genre recognition verifies the effectiveness of the model.

Interpolated Mapping System Identification From Time Series Data

1993 ◽  
Author(s):  
Faruk H. Bursal ◽  
Benson H. Tongue
Keyword(s):  
Time Series ◽  
System Identification ◽  
Time Series Data ◽  
Initial Conditions ◽  
Series Data ◽  
Time Interval ◽  
Identification Algorithm ◽  
Regular Grid ◽  
Time Step ◽  
Data Set

Abstract In this paper, a system identification algorithm based on Interpolated Mapping (IM) that was introduced in a previous paper is generalized to the case of data stemming from arbitrary time series. The motivation for the new algorithm is the need to identify nonlinear dynamics in continuous time from discrete-time data. This approach has great generality and is applicable to problems arising in many areas of science and engineering. In the original formulation, a map defined on a regular grid in the state space of a dynamical system was assumed to be given. For the formulation to become practically viable, however, the requirement of initial conditions being taken from such a regular grid needs to be dropped. In particular, one would like to use time series data, where the time interval between samples is identified with the mapping time step T. This paper is concerned with the resulting complications. Various options for extending the formulation are examined, and a choice is made in favor of a pre-processing algorithm for estimating the FS map based on local fits to the data set. The suggested algorithm also has smoothing properties that are desirable from the standpoint of noise reduction.

scholarly journals Soft Computation Vector Autoregressive Neural Network (VAR-NN) GUI-Based

2018 ◽  
Vol 73 ◽  
pp. 13008 ◽  
Author(s):  
Hasbi Yasin ◽  
Budi Warsito ◽  
Rukun Santoso ◽  
Suparti
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Autoregressive Model ◽  
Stock Price ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Series Data ◽  
Percentage Error ◽  
Vector Autoregressive ◽  
Price Data

Vector autoregressive model proposed for multivariate time series data. Neural Network, including Feed Forward Neural Network (FFNN), is the powerful tool for the nonlinear model. In autoregressive model, the input layer is the past values of the same series up to certain lag and the output layers is the current value. So, VAR-NN is proposed to predict the multivariate time series data using nonlinear approach. The optimal lag time in VAR are used as aid of selecting the input in VAR-NN. In this study we develop the soft computation tools of VAR-NN based on Graphical User Interface. In each number of neurons in hidden layer, the looping process is performed several times in order to get the best result. The best one is chosen by the least of Mean Absolute Percentage Error (MAPE) criteria. In this study, the model is applied in the two series of stock price data from Indonesia Stock Exchange. Evaluation of VAR-NN performance was based on train-validation and test-validation sample approach. Based on the empirical stock price data it can be concluded that VAR-NN yields perfect performance both in in-sample and in out-sample for non-linear function approximation. This is indicated by the MAPE value that is less than 1% .

Use of Vector Autoregressive Model for Anomaly Detection in Utility Gas Turbines

2019 ◽  
Author(s):  
Vipul Goyal ◽  
Mengyu Xu ◽  
Jayanta Kapat
Keyword(s):  
Time Series ◽  
Anomaly Detection ◽  
Autoregressive Model ◽  
Gas Turbines ◽  
Time Series Data ◽  
Combined Cycle ◽  
Series Data ◽  
Vector Autoregressive Model ◽  
Vector Autoregressive ◽  
Multi Stage

Abstract This study is based on time-series data from the combined cycle utility gas turbines consisting of three-gas turbine units and one steam turbine unit. We construct a multi-stage vector autoregressive model for the nominal operation of powerplant assuming sparsity in the association among variables and use this as a basis for anomaly detection and prediction. This prediction is compared with the time-series data of the plant-operation containing anomalies. Granger causality networks, which are based on the associations between the time series streams, are learned as an important implication from the vector autoregressive modelling. Anomaly is detected by comparing the observed measurements against their predicted value.

scholarly journals A Dirichlet Autoregressive Model for the Analysis of Microbiota Time-Series Data

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
I. Creus-Martí ◽  
A. Moya ◽  
F. J. Santonja
Keyword(s):  
Time Series ◽  
Maximum Likelihood ◽  
Autoregressive Model ◽  
Time Series Data ◽  
Series Data ◽  
High Dimensional ◽  
Time Varying ◽  
Proposed Model ◽  
Time Varying Parameters

Growing interest in understanding microbiota dynamics has motivated the development of different strategies to model microbiota time series data. However, all of them must tackle the fact that the available data are high-dimensional, posing strong statistical and computational challenges. In order to address this challenge, we propose a Dirichlet autoregressive model with time-varying parameters, which can be directly adapted to explain the effect of groups of taxa, thus reducing the number of parameters estimated by maximum likelihood. A strategy has been implemented which speeds up this estimation. The usefulness of the proposed model is illustrated by application to a case study.

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