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Title

Advances in Machine Learning: Theory and Applications in Time Series Prediction

Creator

London, Justin J.

Date

2021

Description

A new time series modeling framework for forecasting, prediction and regime switching for recurrent neural networks (RNNs) using machine...
Show moreA new time series modeling framework for forecasting, prediction and regime switching for recurrent neural networks (RNNs) using machine learning is introduced. In this framework, we replace the perceptron with an econometric modeling unit. This cell/unit is a functionally dedicated to processing the prediction component from the econometric model. These supervised learning methods overcome the parameter estimation and convergence problems of traditional econometric autoregression (AR) models that use MLE and expectation-maximization (EM) methods which are computationally expensive, assume linearity, Gaussian distributed errors, and suffer from the curse of dimensionality. Consequently, due to these estimation problems and lower number of lags that can be estimated, AR models are limited in their ability to capture long memory or dependencies. On the other hand, plain RNNs suffer from the vanishing and gradient problem that also limits their ability to have long-memory. We introduce a new class of RNN models, the $\alpha$-RNN and dynamic $\alpha_{t}$-RNNs that does not suffer from these problems by utilizing an exponential smoothing parameter. We also introduce MS-RNNs, MS-LSTMs, and MS-GRUs., novel models that overcome the limitations of MS-ARs but enable regime (Markov) switching and detection of structural breaks in the data. These models have long memory, can handle non-linear dynamics, do not require data stationarity or assume error distributions. Thus, they make no assumptions about the data generating process and have the ability to better capture temporal dependencies leading to better forecasting and prediction accuracy over traditional econometric models and plain RNNs. Yet, the partial autocorrelation function and econometric tools, such as the the ADF, Ljung-Box, and AIC test statistics, can be used to determine optimal sequence lag lengths to input into these RNN models and to diagnose serial correlation. The new framework has capacity to characterize the non-linear partial autocorrelation of time series and directly capture dynamic effects such as trends and seasonality. The optimal sequence lag order can greatly influence prediction performance on test data. This structure provides more interpretability to ML models since traditional econometric models are embedded into RNNs. The ability to embed econometric models into RNNs will allow firms to improve prediction accuracy compared to traditional econometric or traditional ML models by creating a hybrid utilizing a well understood traditional econometric model and a ML. In theory the traditional econometric model should focus on the portion of the estimation error that is best managed by a traditional model and the ML should focus the non-linear portion of the model. This combined structure is a step towards explainable AI and lays the framework for econometric AI.
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