scholarly journals Fluctuations and growth in Ragnar Frisch’s rocking horse model

2021 ◽  
Author(s):  
Vincent Carret
Keyword(s):  
Time Series ◽  
Analytical Solution ◽  
Propagation Mechanism ◽  
Original Solution ◽  
Model Combining ◽  
Statistical Work ◽  
Formal Construction

Ragnar Frisch's famous "rocking horse" model has been the object of much praise and even controversy since its publication in 1933. This paper offers a new simulation of the model to show that there exists cyclical trajectories in the propagation mechanism. By building an analytical solution taking the same form as Frisch's original solution, we can provide new insights into the ideas encapsulated in his model, in particular the fact that the author constructed a model combining cycles and growth. The exploration of Frisch's formal construction of the model leads us to link his statistical work on the decomposition of time series with his economic insights on investment cycles, which both led to the 1933 model. We contrast Frisch’s approach to that of other econometricians who used similar equations, showing that their different mathematical solutions were the product of what they wanted to show with their models.

scholarly journals SHORELINE AT JETTY DUE TO CYCLIC AND RANDOM WAVES

1988 ◽  
Vol 1 (21) ◽  
pp. 141
Author(s):  
Todd L. Walton ◽  
Philip L.F. Liu ◽  
Edward B. Hands
Keyword(s):  
Time Series ◽  
Sediment Transport ◽  
Numerical Model ◽  
Analytical Solution ◽  
Numerical Models ◽  
Random Waves ◽  
Dimensionless Form ◽  
Wave Direction ◽  
Continuous Cycling ◽  
Small Wave

This paper examines the effects of random and deterministic cycling of wave direction on the updrift beach planform adjacent to a jetty. Results provided using a simplified numerical model cast in dimensionless form indicate the importance of the time series of wave direction in determining design jetty length for a given net sediment transport. Continuous cycling of • wave direction leads to the expected analytical solution. Simplications in the numerical model used restrict the applications to small wave angles, no diffraction, no reflection of waves off structure, no refraction, and no sand bypassing at jetty. The concept can be extended to more sophisticated numerical models.

A Hybrid ARIMA and Artificial Neural Networks Model to Forecast Air Quality in Urban Areas: Case of Tunisia

2012 ◽  
Vol 518-523 ◽  
pp. 2969-2979 ◽  
Author(s):  
Ayari Samia ◽  
Nouira Kaouther ◽  
Trabelsi Abdelwahed
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Artificial Neural Networks ◽  
Air Quality ◽  
Urban Areas ◽  
Moving Average ◽  
Warning System ◽  
Model Combining ◽  
Ann Models ◽  
Artificial Neural

Forecasting air quality time series represents a very difficult task since air quality contains autoregressive, linear and nonlinear patterns. Autoregressive Integrated Moving Average (ARIMA) models have been widely used in air quality time series forecasting. However, they fail to detect extreme events because of their presumed linear form of data. Artificial Neural Networks (ANN) models have proved to be promising nonlinear tools for air quality forecasting. A hybrid model combining ARIMA and ANN improved forecasting more than either of the models used independently. Experimental results with meteorological and Particulate Matter data indicated that the combined model can be used as an efficient forecasting and early warning system for providing air quality information towards the citizen, not only in Sfax Southern Suburbs but in other Tunisian regions that suffer from poor air quality conditions.

scholarly journals Propagation mechanism of phase-inversion wave in 2D lattice oscillators and their application to prediction of time-series data

2009 ◽  
Author(s):  
Hitoshi Aburatani ◽  
Suguru Yamane ◽  
Takeo Imoto ◽  
Masayuki Yamauchi ◽  
Yoshifumi Nishio
Keyword(s):  
Time Series ◽  
Phase Inversion ◽  
Time Series Data ◽  
Series Data ◽  
Propagation Mechanism

scholarly journals A New Strategy of Hybrid Models using ARIMA, ANN, and DWT in Time Series Modelling

2021 ◽  
Vol 25 (1) ◽  
pp. 27-50
Author(s):  
Tsung-Lin Li ◽  
◽  
Chen-An Tsai ◽  
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Arima Model ◽  
Real Data ◽  
Hybrid Models ◽  
Discrete Wavelet ◽  
Data Sets ◽  
Model Combining ◽  
Time Series Modelling ◽  
Significant Difference

Time series forecasting is a challenging task of interest in many disciplines. A variety of techniques have been developed to deal with the problem through a combination of different disciplines. Although various researches have proved successful for hybrid models, none of them carried out the comparisons with solid statistical test. This paper proposes a new stepwise model determination method for artificial neural network (ANN) and a novel hybrid model combining autoregressive integrated moving average (ARIMA) model, ANN and discrete wavelet transformation (DWT). Simulation studies are conducted to compare the performance of different models, including ARIMA, ANN, ARIMA-ANN, DWT-ARIMA-ANN and the proposed method, ARIMA-DWT-ANN. Also, two real data sets, Lynx data and cabbage data, are used to demonstrate the applications. Our proposed method, ARIMA-DWT-ANN, outperforms other methods in both simulated datasets and Lynx data, while ANN shows a better performance in the cabbage data. We conducted a two-way ANOVA test to compare the performances of methods. The results showed a significant difference between methods. As a brief conclusion, it is suggested to try on ANN and ARIMA-DWT-ANN due to their robustness and high accuracy. Since the performance of hybrid models may vary across data sets based on their ARIMA alike or ANN alike natures, they should all be considered when encountering a new data to reach an optimal performance.

scholarly journals Forecasting the daily demand for emergency medical ambulances in England and Wales: A benchmark model and external validation

2021 ◽  
Author(s):  
Thomas Monks ◽  
Michael Allen
Keyword(s):  
Time Series ◽  
Cross Validation ◽  
Prediction Interval ◽  
External Validation ◽  
Demand Forecasting ◽  
Benchmark Model ◽  
Model Combining ◽  
Emergency Ambulance ◽  
Validation Set ◽  
Interval Coverage

BackgroundWe aimed to select and externally validate a benchmark method for emergency ambulance services to use to forecast the daily number of calls that result in the dispatch of one or more ambulances. The study was conducted using standard methods known to the UK's NHS to aid implementation in practice.MethodsWe selected our benchmark model from a naive benchmark and 14 standard forecasting methods. Mean absolute scaled error and 80 and 95\% prediction interval coverage over a 84 day horizon were evaluated using time series cross validation across eight time series from the South West of England. External validation was conducted by time series cross validation across 13 time series from London, Yorkshire and Welsh Ambulance Services. ResultsA model combining a simple average of Facebook's Prophet and regression with ARIMA Errors (1, 1, 3)(1, 0, 1, 7) was selected. Benchmark MASE, 80 and 95\% prediction intervals were 0.68 (95% CI 0.67 - 0.69), 0.847 (95% CI 0.843 - 0.851), and 0.965 (95% CI 0.949 - 0.977), respectively. Performance in the validation set was within expected ranges for MASE, 0.73 (95% CI 0.72 - 0.74) 80\% coverage (0.833; 95% CI 0.828-0.838), and 95\% coverage (0.965; 95% CI 0.963-0.967).ConclusionsWe provide a robust externally validated benchmark for future ambulance demand forecasting studies to improve on. Our benchmark forecasting model is high quality and usable by ambulance services. We provide a simple python framework to aid its implementation in practice.

Learning-by-Doing as a Propagation Mechanism

2002 ◽  
Vol 92 (5) ◽  
pp. 1498-1520 ◽  
Author(s):  
Yongsung Chang ◽  
Joao F Gomes ◽  
Frank Schorfheide
Keyword(s):  
Time Series ◽  
Panel Data ◽  
Work Experience ◽  
Formal Model ◽  
Learning By Doing ◽  
Dynamic Stochastic General Equilibrium ◽  
Propagation Mechanism ◽  
Skill Accumulation ◽  
Dynamic Stochastic ◽  
Micro Level

This paper suggests that skill accumulation through past work experience, or “learning-by-doing” (LBD), can provide an important propagation mechanism in a dynamic stochastic general-equilibrium model, as the current labor supply affects future productivity. Our econometric analysis uses a Bayesian approach to combine micro-level panel data with aggregate time series. Formal model evaluation shows that the introduction of the LBD mechanism improves the model's ability to fit the dynamics of aggregate output and hours.

Assessing Frequency Domain Causality in Cardiovascular Time Series with Instantaneous Interactions

2010 ◽  
Vol 49 (05) ◽  
pp. 453-457 ◽  
Author(s):  
G. Nollo ◽  
L. Faes
Keyword(s):  
Time Series ◽  
Frequency Domain ◽  
Multivariate Time Series ◽  
Real Data ◽  
Cardiovascular Physiology ◽  
Extended Model ◽  
Partial Directed Coherence ◽  
Model Combining ◽  
Lagged Effects ◽  
Simulation Results

Summary Background: The partial directed coherence (PDC) is commonly used to assess in the frequency domain the existence of causal relations between two time series measured in conjunction with a set of other time series. Although the multivariate autoregressive (MVAR) model traditionally used for PDC computation accounts only for lagged effects, instantaneous effects cannot be neglected in the analysis of cardiovascular time series. Objectives: We propose the utilization of an extended MVAR model for PDC computation, in order to improve the evaluation of frequency domain causality in the presence of zero-lag correlations among multivariate time series. Methods: A procedure for the identification of a MVAR model combining instantaneous and lagged effects is introduced. The coefficients of the extended model are used to estimate an extended PDC (EPDC). EPDC is compared to the traditional PDC on a simulated MVAR process and on real cardiovascular variability series. Results: Simulation results evidence that the presence of zero-lag correlations may produce misleading PDC profiles, while the correct causality patterns can be recovered using EPDC. Application on real data leads to spectral causality estimates which are better interpretable in terms of the known cardiovascular physiology using EPDC than PDC. Conclusions: This study emphasizes the necessity of including instantaneous effects in the MVAR model used for the computation of PDC in the presence of significant zero-lag correlations in multivariate time series.

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